Hydrologic Characterization and Modeling of a
Montane Peatland, Lake Tahoe Basin, California
By
Wes Christensen
B.S. (University of Utah) 1997
M.S. (University of Utah) 2002
DISSERTATION
Submitted in partial satisfaction of the requirements for the degree of
DOCTOR OF PHILOSOPHY
in
Geology
in the
OFFICE OF GRADUATE STUDIES
of the
UNIVERSITY OF CALIFORNIA
DAVIS
Approved:
________________________________________
Graham Fogg, Chair
________________________________________
James McClain
________________________________________
Tim Ginn
Committee in Charge
2013
i
ABSTRACT
Perennial wetlands in montane environments are often supported at least in part
by groundwater input. Groundwater is especially important for wetlands in areas with a
snow melt dominated precipitation regime and high summer evapotranspiration rates.
Understanding of the groundwater hydrology that supports wetlands in montane
environments is often complicated by steep topography, inadequate characterization of
the subsurface material, and sparse data. This study examines the groundwater system
supporting Grass Lake, the largest peatland in the Sierra Nevada Mountains, located
south of Lake Tahoe, California.
Field measurements are used to quantify important aspects of the hydrologic
system supporting Grass Lake. Late-season groundwater flows into the peatland are
estimated using surface water measurements and water budget. Groundwater
contributions are approximately 2 to 10 times higher than surface water contributions
after July, depending on the water year. Measurements of hydraulic gradients reveal
areas of groundwater recharge and discharge. In general, there is more groundwater
discharge along the southern portion of the peatland. Measurements of groundwater
level relative to the peat surface indicate areas that may be more susceptible to drying
and subsequent decomposition of peat.
Indirect inversion of numerical models is used to estimate the value of important
parameters governing groundwater flow in the peatland. Thermal and hydrologic
parameters of the peat are estimated using piezometer scale (~1m) models of heat
transport. Atmospheric heat exchange and inclusion of the thermal properties of a metal
piezometer improve the fit between the model and the field data. Four sets of random
parameters are used to generate synthetic data. The parameter estimation process is
tested by attempting to recover the original parameters used to generate the data.
ii
Including the entropy of the temperature time series as an observation improves the
recovery of the original parameter values.
A watershed scale hydrogeologic model is used to evaluate the potential
response of the peatland to predicted changes in climate. Watershed geology was
mapped at a scale of 1:5000 and used to define hydrogeologic units in the model. Field
data from 2010 and 2011 were used to calibrate the hydraulic conductivity of the various
geologic units in the model. Parameter estimates from the calibration process are
consistent between years for all but the most sensitive parameters. Consideration of
unsaturated properties of the subsurface material is shown to improve the fit between
the measured and simulated heads in the peatland. The predicted change from a snow
dominated to rain dominated precipitation regime results in a significant decrease in
simulated late-season pressure head and saturation over approximately half of the
peatland. The decrease in saturation is most significant on the east and west ends of
the peatland and around the edges.
iii
ACKNOWLEDGEMENTS
I would like to thank my advisor Graham Fogg for his confidence in my abilities,
the freedom to pursue this project, and his insightful guidance along the way. I would
like to thank my committee members Tim Ginn for teaching me the concepts behind
indirect inversion and to James McClain for his insightful comments on my research. I
would like to thank Michael Oskin for showing me the potential of lidar in geologic
mapping and Jeff Mount for reminding of the broader context of research. I am grateful
for the guidance and support provided by Magali Billen whose encouragement helped
me see this project through to completion. I am grateful for all the knowledge and
instruction I received at UC Davis.
I would like to thank my friends, relatives, and colleagues who helped conduct
field work over the years: Shana Gross, Sherry Devenberg, Ida Fischer, Caleb Kesling,
Sarah Howell, and David Immeker. A special thanks to Sue Norman and Mike Hamann
at the United States Forest Service for use of field equipment. I am forever grateful to
my field companion, William P. Schrumplebutt, who always remained by my side at all
times in the field. The loving support and encouragement of Shana Gross has helped
me overcome this challenge and many more. I thank my mother, Sherry Devenberg, for
her unwavering support, encouragement, and love. I thank my father, Hal Christensen,
for exposing me to the mountains and water at an early age.
I would also like to thank Bill Sluis for his help in constructing the field equipment,
Rob McLaren for his endless patience in answering my questions regarding Grid Builder
and HYDROGEOSPHERE, Mary Hill and Eileen Poeter for their help with UCODE, and
Tamir Kamai for his help with thermal modeling in COMSOL. I would also like to thank
all the great people in Geology and Land Air and Water who engaged in insightful
discussions as well as good times.
iv
TABLE OF CONTENTS
Abstract ......................................................................................................................... ii
ACKNOWLEDGEMENTS .............................................................................................. iv
LIST OF TABLES ........................................................................................................ viii
LIST OF FIGURES......................................................................................................... ix
Chapter 1: Hydrogeologic Setting of the Grass Lake Research Natural Area .......... 1
Abstract ....................................................................................................................... 1
Introduction .................................................................................................................. 2
Site Description ........................................................................................................... 5
Geology.................................................................................................................... 6
Surface Hydrology.................................................................................................... 9
Groundwater Hydrology ......................................................................................... 13
Field and Laboratory Methods ................................................................................... 15
Geology and Geomorphology................................................................................. 15
Surface Hydrology Measurements ......................................................................... 18
Groundwater and Subsurface Measurements ........................................................ 26
Specific Conductivity .............................................................................................. 29
Water budget ......................................................................................................... 30
Peat water retention experiment............................................................................. 31
Results ...................................................................................................................... 35
Surface Hydrology.................................................................................................. 35
Water budget ......................................................................................................... 39
Specific conductivity – Surface Water .................................................................... 41
Groundwater Hydrology ......................................................................................... 46
Specific conductivity – Ground Water ..................................................................... 54
Geology Results ..................................................................................................... 57
v
Peat Water Retention ............................................................................................. 58
Discussion ................................................................................................................. 60
References ................................................................................................................ 63
Chapter 2: Piezometer Scale Thermal Modeling and Parameter Estimations:
Implications of Model Structure and Thermal Boundary Conditions ...................... 65
Abstract ..................................................................................................................... 65
Introduction ................................................................................................................ 66
Background ............................................................................................................ 68
Motivation............................................................................................................... 69
Methods ..................................................................................................................... 70
Approach................................................................................................................ 70
Data Collection ....................................................................................................... 72
Analytical Model ..................................................................................................... 74
Numerical Model .................................................................................................... 75
Comparison of Analytical and Numerical Models.................................................... 78
Natural Convection of Piezometer Fluids................................................................ 79
Initial Conditions ..................................................................................................... 81
Atmospheric Heat Exchange .................................................................................. 82
Implementation of Atmospheric Heat Exchange ..................................................... 85
Entropy .................................................................................................................. 85
Observation Weights .............................................................................................. 87
Model Sensitivity .................................................................................................... 88
Parameter Estimation Approach ............................................................................. 89
Results ...................................................................................................................... 91
Comparison of Analytical and Numerical Models.................................................... 91
Comparison of Air Temperature and Atmospheric Heat Exchange ......................... 93
Sensitivity Analysis ................................................................................................. 97
vi
Parameter Estimation of Synthetic Data ............................................................... 100
Parameter Estimation of Field Data ...................................................................... 102
Discussion ............................................................................................................... 105
References .............................................................................................................. 107
Chapter 3: Watershed Scale Modeling of the Grass Lake Research Natural Area112
Abstract ................................................................................................................... 112
Introduction .............................................................................................................. 114
Background ............................................................................................................. 115
Methods ................................................................................................................... 116
Grid Construction ................................................................................................. 117
Hydraulic Conductivity .......................................................................................... 124
Anisotropy ............................................................................................................ 127
Specific Storage ................................................................................................... 127
Unsaturated Parameters ...................................................................................... 128
Initial conditions and duration ............................................................................... 130
Boundary Conditions ............................................................................................ 131
Parameter Estimation ........................................................................................... 133
Modeling Results ..................................................................................................... 134
Parameter Estimates ............................................................................................ 134
Simulation Results ............................................................................................... 136
Response to Predicted Precipitation Changes ..................................................... 141
Discussion ............................................................................................................... 145
References .............................................................................................................. 147
vii
LIST OF TABLES
Table 1.1: Estimates of seasonal surface water yield (volume of water per
contributing area) and percent of annual precipitation for GLRNA. ........................ 36
Table 1.2: Average seasonal and peak values for stream flow in the GLRNA
watershed. ................................................................................................................... 37
Table 1.3: Seasonal average flow (m3) of water into and out of Grass Lake for the
2010 and 2011 field seasons. ..................................................................................... 40
Table 1.4: Water budget calculations for available stream flow measurements in
2010 and 2011. ............................................................................................................. 42
Table 1.5: Statistics for piezometers showing the difference between piezometers
located along the north and south sides of Grass Lake........................................... 54
Table 1.6: Results of bailer tests conducted in each piezometer. ........................... 55
Table 1.7: Values of specific conductivity of groundwater recorded in Grass Lake.
All units are in µS cm-1. ............................................................................................... 55
Table 1.8: Areas of geologic units mapped in the GLRNA. ...................................... 58
Table 1.9: Physical properties and water retention characteristics of four peat
samples collected from the Grass Lake Research Natural Area, South Lake Tahoe,
CA. ................................................................................................................................ 60
Table 2.1: Parameters used in comparison between numerical and analytical
models. ........................................................................................................................ 78
Table 2.2: Parameter values influencing heat flow in numerical simulations
involving atmospheric heat exchange. ...................................................................... 88
Table 2.3: Parameter values used in the sensitivity analysis and generation of
synthetic data used in parameter estimation. ........................................................... 89
Table 2.4: Changes in modeled temperatures resulting from parameter
perturbations used in the sensitivity analysis. ......................................................... 95
Table 2.5: Parameter estimation (PE) results for synthetic data sets................... 103
Table 3.1: Storage parameter values used in all simulations and unsaturated
parameter values used in the final assessment of the Grass Lake watershed to
changes in precipitation. .......................................................................................... 130
Table 3.2: Hydraulic conductivities of geologic material used in the watershed
scale model of GLRNA. ............................................................................................. 138
Table 3.3: Differences between measured and simulated heads for select
piezometers in the “fully saturated” and unsaturated models. ............................. 139
viii
LIST OF FIGURES
Figure 1.1: Geologic map of the Grass Lake Watershed showing the location of
major hydrologic features and piezometers installed for this study. ........................ 4
Figure 1.2: A reach of Freel Meadows Creek in the upper watershed, where the
fine material has been eroded, leaving behind the oxide coated boulders
(corestones)................................................................................................................... 8
Figure 1.3: A reach of Freel Meadows Creek in the upper watershed (north side).
...................................................................................................................................... 11
Figure 1.4: Groundwater spring and mound, east of Waterhouse Creek, near
piezometer S5. ............................................................................................................. 14
Figure 1.5: Rating curve for Grass Lake Creek (outlet) for a) the 2010 field season
with stage recorded by a pressure transducer and b) 2011 field seasons with stage
recorded at the culvert. ............................................................................................... 22
Figure 1.6: Rating curve for First Creek for a) the 2010 field season with stage
recorded by a pressure transducer and b) 2011 field seasons with stage recorded
at the culvert. ............................................................................................................... 23
Figure 1.7: Rating curve for West Freel Meadows Creek for 2010 with stage
recorded by a pressure transducer. .......................................................................... 24
Figure 1.8: Rating curve for Freel Meadows Creek for 2010 with stage recorded by
a pressure transducer. ................................................................................................ 24
Figure 1.9: Rating curve for Waterhouse Creek for 2010 with stage recorded by a
pressure transducer.................................................................................................... 25
Figure 1.10: 2010 daily average streamflow based on rating relationships for all
streams into and out of Grass Lake proper............................................................... 37
Figure 1.11: 2011 manual stream flow measurements into and out of Grass Lake
proper........................................................................................................................... 39
Figure 1.12: 2010 (a) and 2011 (b) specific conductivity values recorded for
streams in the Grass Lake Watershed. ...................................................................... 44
Figure 1.13: Specific conductivity measurements of surface water near
piezometers for 2010 (a) and 2011 (b). ....................................................................... 45
Figure 1.14: Groundwater head contours in the Grass Lake peatland.
Groundwater levels measured in Fall 2010. Contours interval is 1m. .................... 47
Figure 1.15: Groundwater head contours in the Grass Lake peatland.
Groundwater levels measured in Spring 2011. Contours interval is 1m. ............... 48
Figure 1.16: Emergence of groundwater associated with preferential pathways
provided by rodent activity. ........................................................................................ 49
Figure 1.17: Vertical hydraulic gradients calculated from 2010 field data (a) and
2011 field data (b) for the north (N) and south (S) sides of Grass Lake. ................. 53
Figure 1.18: Specific conductivity measurements of groundwater in piezometers
for 2010 (a) and 2011 (b). ............................................................................................ 56
Figure 2.1: Six day temperature record for air, saturated peat 20 cm from the
piezometer (12 cm bgs), and water within the piezometer (13 cm bgs). ................. 70
ix
Figure 2.2: Geometry and mesh for the numerical models. ..................................... 77
Figure 2.3: Simulation results with sand as the substrate. ...................................... 92
Figure 2.4: Simulation results with peat as the substrate. ....................................... 93
Figure 2.5: Comparison between recorded air temperature and surface water
temperature resulting from considerations of atmospheric heat exchange. .......... 94
Figure 2.6: Components of the energy balance equation used to define
atmospheric heat exchange in the surface water layer. ........................................... 97
Figure 2.7: Change in temperature for parameter perturbations from parameter
values estimated from the literature ........................................................................ 100
Figure 2.8: Temperature time series for parameter set 1. ...................................... 104
Figure 2.9: Comparison of field observations from piezometer S4, starting
parameter values, and estimated parameter values. .............................................. 105
Figure ......................................................................................................................... 120
Figure 3.2: Cross section near Waterhouse Creek (Figure 3.1, A-A’) showing
hydrogeologic units with depth and vertical discretization. .................................. 121
Figure 3.4: Contour map showing depth to bedrock interpolated from 10 m below
the upper contact of the Tahoe age lateral moraines and 70 m below the surface
along a swath of points underlying the long axis of Grass Lake ........................... 123
Figure 3.5: Piecewise linear interpolated functions describing water retention and
relative permeability used in variably saturated watershed scale models of
GLRNA. ...................................................................................................................... 133
Figure 3.7: Measured and simulated heads for piezometers located in Grass Lake
in 2011. ....................................................................................................................... 141
Figure 3.8: Pressure head contours at the end of the water year (October) for
saturated (a and b) and unsaturated (c and d) simulations using parameter and
recharge estimates from 2010 (a and c) and 2011 (b and d)................................... 143
Figure 3.9: Simulated pressure head in Grass Lake resulting from a rain
dominated precipitation regime. Simulations are shown at the end of the wet
season (a and b) and the end of the water year (c and d). ..................................... 144
x
CHAPTER 1: HYDROGEOLOGIC SETTING OF THE GRASS LAKE RESEARCH
NATURAL AREA
ABSTRACT
Persistently wet conditions are essential to prevent the decomposition of organic
material that forms peatlands. Predicted changes in climate for the Sierra Nevada
suggest a trend towards more winter precipitation falling as rain rather than snow. High
summer evapotranspiration (ET) rates and low summer precipitation suggest this could
lead to a reduction in late-season water availability and the subsequent degradation of
peatlands. This paper uses measurements of groundwater levels, stream flow, and
specific conductivity to quantify aspects of the hydrologic system that supports Grass
Lake, the largest peatland in the Sierra Nevada. Due to large errors associated with
stream flow measurements in these steep rocky streams, groundwater contributions
could not be determined using a seasonally based water budget. However, water
budgets calculated on a daily basis show that groundwater discharge is a significant
component of the water balance in the fall. Analysis shows that late-season ET needs
are approximately balanced by groundwater inflow for near average water years (2010).
During above average water years (2011) groundwater discharge to the peatland is the
dominant component of the water budget and persists into October or later. Laboratory
experiments were performed to determine the water retention characteristics of peat
samples. Bailer tests were performed to determine the hydraulic conductivity of the
underlying sediment.
1
INTRODUCTION
The largest peatland in the Sierra Nevada is Grass Lake (96 ha), located on
Luther Pass, south of Lake Tahoe, California (Figure 1.1). The Forest Service
designated Grass Lake and the surrounding watershed as a Research Natural Area
(GLRNA) in 1987. This chapter includes field measurements, characterization, and
hydrogeologic analysis of the GLNRA.
Peatlands are wetlands with thick organic soils that have formed in place. The
formation of these organic soils requires perennial saturation to prevent decomposition
of the organic material. Peatlands provide unique habitats, covering 3% of the Earth’s
surface and making up only 0.1% of the mountain landscape (Clymo, 2004; Cooper &
Wolf, 2006b). In many areas of the Sierra Nevada, peatlands are the only source of
perennial moisture and support ecosystems with high biodiversity. High ET rates and
low summer precipitation in the Sierra Nevada Mountains suggest that most, if not all,
montane peatlands in the Sierra Nevada are sustained by substantial groundwater input.
Peatlands that are sustained by groundwater input are termed “fens” while peatlands
sustained by surface water and direct precipitation are termed “bogs” (Benedict & Major,
1982; Cooper & Wolf, 2006b).
The largest threat to peatlands is aerobic decomposition of organic material due
to desaturation and exposure to oxygen. Current climate trends and predictions suggest
warmer winter temperatures, resulting in a more rain-dominated precipitation regime
and/or earlier snow melt (Cayan, Maurer, Dettinger, Tyree, & Hayhoe, 2008).
Characterizing the hydrogeology of montane peatlands is essential in order to
understand how these systems might respond to changes in the precipitation regime. In
particular, a decrease in late-season groundwater flow due to earlier snow melt may
result in increased decomposition of the peat.
2
The water budget and physical properties of hydrogeologic systems that support
montane peatlands are not well understood. Models of montane wetlands generally
assume the surrounding terrain is comprised of low permeability bedrock and designate
the wetland-hillslope interface as a no-flow boundary. In some cases models include a
constant subsurface flux representing groundwater input based on observed changes in
meadow storage during baseflow (e.g. Loheide, 2008) or lateral inputs based on
observations such as adjacent irrigation (e.g. Hammersmark, Rains, & Mount, 2008).
However, the groundwater component of montane wetland systems remains poorly
understood and quantified.
The response of groundwater systems to changes in the precipitation regime is
determined by the topography, physical characteristics of the subsurface materials (e.g.,
hydraulic conductivity, anisotropy, storage, porosity, and spatial distribution) and the
resulting distribution of hydraulic potential. Harman and Sivapalan (2009) show that
hillslope heterogeneity can significantly affect the groundwater storage-discharge
relationship, and hence the availability of late season groundwater at the base of the
hillslope. Near surface heterogeneity has been shown to significantly influence the
storage capacity and location of recharge areas in aquifers formed by glacial moraine
deposits (Beckers & Frind, 2000).
As part of this research, field measurements were made approximately biweekly
during the 2010 and 2011 field seasons (approximately May to October). Measurements
of stream flow, temperature, and specific conductivity (SC) were made for four perennial
streams entering Grass Lake and the one outlet stream. Measurements of vertical
hydraulic gradient, temperature, and SC were made for 32 piezometers located along
the margins of Grass Lake. Bailer tests were performed in 22 of the 32 piezometers to
estimate the hydraulic conductivity of the sediments underlying the peat. Hanging water
column experiments were conducted to define the water retention characteristics of the
3
peat. Newly acquired lidar data was used to help develop detailed geologic maps of the
GLRNA, which defines the large scale heterogeneity of the system (on the order of 100’s
of meters, Figure 1.1). These
ese measurements and observations are used in later
chapters to develop hydrologic models used to constrain physical parameters that
control the storage and flow groundwater in the GLRNA watershed.
Figure 1.1:: Geologic map of the Grass Lake Watershed showing the location of major
hydrologic features and piezometers installed for this study. Geologic units were
identified using imagery from lidar data and field mapping. Piezometers along the
northern edge are denoted with the prefix N, while those along
ng the south side are
denoted with the prefix S.. Contour interval is 50 meters.
4
SITE DESCRIPTION
Grass Lake is located at Luther Pass on highway 89 just south of South Lake
Tahoe, California (UTM: 10N 764000 4298000). Geologic mapping conducted as part of
this study revealed that Luther Pass was formed in part by a spur from the glacier that
originated near Carson Pass. The glacier pushed westward from Hope Valley into the
Lake Tahoe Basin approximately 145 ka, leaving behind moraine material that forms the
outlet and sides of Grass Lake. Subsequent glaciation during the Tioga glacial period
(19 ka) left behind glacial deposits that form the east end of the Grass Lake valley.
Watershed elevations range from 2345 meters above sea level (7694 ft) in the peatland
to 2922 meters (9587 ft) along an unnamed ridge north of Freel Meadows (Figure 1.1).
The total watershed area is approximately 998 ha (2466 acres).
The Grass Lake peatland has been described as transitional between a
sphagnum bog and a fen (Burke, 1987). Three distinct peat bodies occur within the
GLRNA and cover approximately 101 ha (250 acres). The largest peat body is Grass
Lake with an area of approximately 96 ha (237 acres). The second largest is Freel
Meadows, located northeast of Grass Lake at an elevation of 2815 meter (9236 ft).
Freel Meadows covers approximately 4 ha (10 acres). The smallest documented peat
body in the GLRNA is located at the headwaters of First Creek, at an elevation of 2740
meters and covers approximately 1.4 ha (3.4 acres).
Precipitation estimates for 2010 and 2011 were acquired from the PRISM
Climate Group (2013) website. The annual precipitation at GLRNA for the 2010 water
year (October 1, 2009 to September 30, 2010) was 1.043 meters (41.05 inches). The
annual precipitation for the 2011 water year was 1.660 meters (65.34 inches). These
values represent 99.5% and 158.4% of the 1900 to 2011 estimated average annual
precipitation (1.047 meters, 41.24 inches). Approximately 90% (0.938 meters, 36.91
inches) of the 2010 precipitation fell between October 1, 2009 and May 1, 2010, and
5
approximately 88% (1.457 meters, 57.36 inches) of the 2011 precipitation fell between
October 1, 2010 and May 1, 2011, presumably as snow.
Geology
The bedrock in GLRNA is dominated by Cretaceous granodiorite (Figure 1.1).
According to Armin et al. (1983), the Bryan Meadows granodiorite makes up most of the
northern portion of the watershed and a portion of the hillslopes in the southeast corner
of the GLRNA. The Echo Lake granodiorite is exposed along the south side of the
GLRNA and forms both Waterhouse Peak and Powderhouse Peak. Much of the
contact between these two units is obscured by thin glacial deposits that were not
mapped by earlier workers, but are apparent with the new lidar dataset. The similarity
between the older Bryan Meadows granodiorite and the younger Echo Lake
granodiorite, combined with the veneer of glacial and colluvial material, makes the
location of the contact difficult to identify. The hydraulic properties of the Bryan
Meadows and Echo Lake granodiorites are assumed to be fairly similar for the purposes
of this study and the location of the contact was inferred from the existing geologic map.
Tertiary volcanic deposits unconformably overlie the Cretaceous granodiorite and are
exposed over a limited area in the northern portion of GLRNA near Freel Meadows.
The GLRNA experienced at least two major periods of glaciation. The
penultimate glacial retreat (Tahoe age) occurred approximately 145 ka (Rood, Burbank,
& Finkel, 2011). A portion of the Tahoe age glacier that originated from the Carson Pass
area and occupied Hope Valley pushed west over what is now Luther Pass and Grass
Lake and into the Lake Tahoe Basin. Tahoe age glacial deposits consist of a prominent
recessional moraine at the west end of Grass Lake and poorly preserved lateral
moraines along the north and south margins of the lake. The Last Glacial Maximum
retreat (Tioga age) occurred approximately 19 ka (Rood et al., 2011). A short spur
(approximately 550 meters, 1800 feet) of the glacier in Hope Valley entered what is now
6
the east end of Grass Lake, leaving a set of well preserved Tioga age terminal moraines.
Deposits from two Tioga age cirque glaciers are found along the south side of Grass
Lake and overlie the older Tahoe lateral moraine.
Weathered, unglaciated plutonic rocks dominate the north side of the watershed
at elevations above approximately 2600 meters (8530 ft). Rounded boulders with
significant oxide deposits on some surfaces form low tors surrounded by hillslopes of
loose sandy soil. Similar material was likely removed from the Luther Pass area during
the Tahoe glaciation, exposing a steep hillslope of freshly exposed angular corestones
and bedrock surrounded by zones of material that had been preferentially weathered by
meteoric water percolating into the subsurface. Where larger streams have eroded into
this unglaciated material, the bottom of the drainage consists almost entirely of large (up
to 4 m) rounded corestones (Figure 1.2). The adjacent hillsides consist of similarly
rounded boulders surrounded by steep, sandy soils.
Small alluvial fans occur at the mouths of the four perennial streams and one
intermittent stream that enter Grass Lake. These alluvial fans are composed of coarse
sand and gravel with some interbedded peat. First Creek and Freel Meadows Creek are
incised up to 0.6 meters (2 feet) below the upper surface of the fan, with the deepest
incision occurring just upstream of the center of the fan. Waterhouse Creek is incised up
to approximately 2 meters (6 feet) near the center of the fan. Fresh deposits of sand
overlying peat were found at the mouths of First Creek and Freel Meadows Creek after
the 2011 peak flows. West Freel Meadows Creek disperses into a broad riparian area
with several poorly defined anastomosing streams after exiting the culvert, suggesting a
depositional regime.
7
Figure 1.2: A reach of Freel Meadows Creek in the upper watershed, where the fine
material has been eroded, leaving behind the oxide coated boulders (corestones).
Access to the audibly flowing water is limited to small passages under the boulders.
Grass Lake proper is dominated by slightly humified to unhumified peat
consisting of organic material from both bryophytes and herbaceous plants. The
southern slopes of the watershed are dominated by red fir and the northern slopes are
dominated by Jeffrey pine. Aspen groves are found on alluvial fans and along the
slopes of the Tioga glacial deposits in the southern portion of the watershed. Lodgepole
pine occurs along the forest-meadow ecotone and in small (<100 m2) stands within the
meadow. A more complete description of the vegetation communities can be found in
Burke (1987) and Berg (1991).
8
Surface Hydrology
Observations of surface water flow in the Grass Lake watershed were limited to
the surface of the peatlands, streams, impervious rock surfaces, and to within
approximately 1 meter of rapidly melting snow. There are three perennial streams along
the north side of the lake (Figure 1.1): First Creek, West Freel Meadows Creek, and
Freel Meadows Creek. Waterhouse Creek is the only perennial stream along the south
side. The outlet of Grass Lake is referred to as Grass Lake Creek.
The sources of all perennial streams are located in the unglaciated, weathered
bedrock of the upper watershed. The source of First Creek is a small, unnamed
peatland located at an elevation of 2740 m (8990 ft). The source of West Freel
Meadows Creek is a small swale at an elevation of 2780 m (9120 ft), approximately 40
m (130 ft) lower than Freel Meadows (2820 m, 9250 ft) and 85 m (280 feet) lower than
the intervening ridge (2865 m, 9400 ft). The source of Freel Meadows Creek is Freel
Meadows. The source of Waterhouse Creek is not well defined. In early July, 2010, the
pass (2740 m, 8990 ft) between Waterhouse Peak and Powderhouse Peak was
saturated, resulting in surface flow north into Grass Lake and south into Big Meadow.
The surface water that was flowing from the pass into Big Meadow disappears into the
subsurface approximately 100 m (330 ft) south of the pass. In late fall the pass was dry
and the source of Waterhouse Creek was observed as low as 2650 meters (8690 ft) in
2009.
There are four sizeable (>400 m in length) intermittent streams along the south
side, three of which originate in the cirques formed by Tioga age glaciation (Figure 1.1).
The fourth originates near the upper contact of the Tahoe age moraine located along the
southwest edge of the watershed. There are three sizeable intermittent streams located
in the volcanic material approximately 400 m (1300 feet) east of Freel Meadows. These
streams flow into Freel Meadows Creek below the peatland during spring runoff. These
9
channels were observed to dry up by late-July in 2010 and 2011. Two smaller
intermittent streams, approximately 100 meters in length, are located on each side of
Grass lake, associated with springs near the upper contact of the Tahoe lateral moraines
(Figure 1.1). One intermittent stream flows out of the cirque below Powderhouse Peak,
but disappears into the Tioga age glacial deposits at elevations above 2450 m (8040 ft),
depending on flow.
Six distinct hydromorphologic zones were identified in the perennial streams in
the GLRNA. In the upper watershed on the north side of Grass Lake, the channels are
occasionally surrounded by “stringer meadows” (Ratliff, 1985) up to 30 m (100 ft) wide
and easily identified in aerial photographs (Figure 1.3). The channel bottoms in these
areas are dominated by coarse sand, gravel, and cobbles, while the channel sides and
surrounding meadow are defined by small boulders and interstitial soil. These boulders
have a faint, but notable reddish-orange mineral oxide coating. The channel banks are
deeply undercut in some areas and often heavily vegetated. The reaches between
these stringer meadows are dominated by plunge-pool sequences, with the plunges
defined by a framework of small boulders and gravel bottomed pools. In steeper
sections of Freel Meadows Creek the finer particles have been removed, leaving behind
the rounded oxide coated boulders (Figure 1.2). These boulders are interpreted as
corestones formed by preferential weathering along fractures (Twidale & Vidal Romani,
2005) and exposed as the weathered material (“grus”) was removed by erosion in
response to the steepening of the valley walls and lowering of base level resulting from
glaciation. The streams can be heard beneath the boulders throughout the summer, but
access to the water is limited to tight passages underneath the boulders. A small
riparian buffer is present along these boulder strewn reaches.
10
Figure 1.3: A reach of Freel Meadows Creek in the upper watershed (north side). Note
the wide riparian area, small rounded boulders with oxide coating, and heavily
vegetated, undercut banks.
The stream reaches located in the glaciated bedrock above the Tahoe moraines
are dominated by large, subangular boulders up to 3 meters in diameter. A well defined
channel is not observable and access to the underlying stream is limited to passages
underneath the boulders. These reaches are on the order of 20 meters wide and lack
significant riparian vegetation due to the lack of adequate substrate. Finer material is
limited to the edges of the boulder strewn gullies where it sloughs off the hillslope. The
subangular boulders are interpreted as corestones, similar to those found in the upper
11
watershed, but located closer to the base of the weathering mantle (Migon & LidmarBergstrom, 2001; Twidale & Vidal Romani, 2005).
The stream reaches located in the glacial moraine material on both sides of the
lake are surrounded by heavy riparian vegetation dominated by alder and willow, with
some aspen. The channel is not well defined and typically spreads into numerous
fingers of plunge-pool sequences formed between boulders and woody debris,
becoming more diffuse near the contact with the alluvial fans. Intermittent springs were
noted in 2010 and 2011 at the top of the glacial deposits, up to 145 m (475 ft) along
contour from First Creek and Freel Meadows Creek. These springs have temperatures
near the mean annual air temperature and SC higher than the nearby streams,
indicating significant subsurface flow and greater water-rock interaction (Pilgrim, Huff, &
Steele, 1979).
On the north side of Grass Lake, stream reaches enter the alluvial material just
before being directed into culverts that pass beneath Highway 89. First Creek and Freel
Meadows Creek are incised up to 1 m (3 ft) for approximately 150 m (490 ft) after
leaving the culvert, at which point the streams enter Grass Lake and the channel
becomes poorly defined. West Freel Meadows Creek typically exceeds channel
capacity just after leaving the culvert and occupies multiple shallow channels as it flows
through an aspen stand and heavy riparian vegetation. In 2011, during spring runoff, the
West Freel Meadows stream avulsed above the culvert, and approximately 50% of the
flow occupied a new section of channel for 20 meters before flowing under the highway.
Upon entering the alluvial fan, Waterhouse Creek is separated into a main channel and
diffuse flow through a broad riparian area to the east. The channel is incised up to 2 m
(7 ft) for approximately 150 m (490 ft) after entering the alluvial deposits.
All perennial streams discussed above, except Waterhouse Creek, were
observed to originate within small basins in the unglaciated, weathered bedrock of the
12
upper watershed. First Creek and Freel Meadows Creek originate in peatlands, which
are expected to have a significant groundwater component considering the steep
topography and sustained late-season flow. West Freel Meadows Creek originates from
a spring. Observations in the spring and fall suggest the location of the origin for West
Freel Meadows Creek varies by approximately 100 m (330 ft) horizontally and 15 m (50
ft) vertically. Flows from all sources are notably higher in the spring and reduce to a
minor trickle by the end of the fall.
Groundwater Hydrology
High ET rates and limited summer precipitation led Cooper and Wolf (2006a) to
conclude that peatlands in the Sierra Nevada Mountains require some groundwater input
in order to maintain perennial saturation. Groundwater was observed flowing from
natural seeps in the peatland at over 20 distinct locations along the southwest edge of
Grass Lake during the fall of 2009 and 2010. This area was under approximately 4cm of
water during the fall of 2011, making the seeps undetectable. Shallow soil probes
suggest that some of these seeps are associated with large woody debris buried in the
peat, providing preferential flow paths for the ground water and areas of concentrated
discharge.
A groundwater spring is located just east of the Waterhouse Creek fan (Figure
1.4a). This spring forms a small mound up to 1 meter above grade on the downhill side.
This spring was observed flowing in October 2009-2011 and is one of the first places to
melt out in the spring despite its location on the south side of the lake where it is partially
shaded by the hillslope and large conifers (Figure 1.4b). This suggests a perennial
source of groundwater with enough thermal energy to melt the accumulating snow.
13
Figure 1.4:
4: Groundwater spring and mound, east of Waterhouse Creek, near piezometer
S5. a) Photo taken June 10, 2010. The mound is surrounded by willows and rises up to
1m above the
e surrounding hillslope. b) Photo taken January 14, 2011. Lack of snow at
the spring location suggests adequate groundwater flow to melt snow.
14
Two groundwater springs surface within the Tahoe age lateral moraines (Figure
1.1). The largest spring on the north side of the lake surfaces approximately 100 meters
uphill of the Freel Meadows Creek alluvial fan and 100m east of Freel Meadows Creek.
The spring emerges at the top of the Tahoe age moraine, just below a hillslope
comprised of large rounded boulders interpreted to be exposed corestones. By late fall
flow was not measurable (<0.1 cfs) and the stream disappeared before reaching Freel
Meadows Creek. A small outcrop of rock (~3000m2) occurs between Freel Meadows
Creek and the spring. This outcrop is interpreted to be bedrock exposed through the
thin Tahoe age moraine deposits and may be responsible for diverting some water from
the stream to the spring. The spring on the south side of the lake reaches the surface
amidst subangular boulders (~2m diameter) in the Tahoe age glacial deposits,
approximately 100 meters uphill of the peat. Surface flow on the hillslope was not
detected after mid-summer. During the spring of 2011 two seeps were observed issuing
from road cuts approximately 70 meters east and 50 meters west of First Creek. These
seeps emerged from sandy material in the Tahoe moraine and stopped flowing by lateJune.
FIELD AND LABORATORY METHODS
Geology and Geomorphology
Airborne lidar data provided by Tahoe Regional Planning Agency was used to
help map the surface geology of GLRNA at a scale of 1:5000 (Figure 1.1). The vertical
accuracy of the data was estimated to be 3.5cm RMSE (TRPA, 2012). The high spatial
resolution of the lidar dataset facilitated the identification of features previously obscured
by trees and the complex, boulder strewn topography. Combination of the lidar data and
field mapping was essential for accurately mapping and identifying geologic features that
are often obscured by the steep, boulder strewn topography and large trees.
15
The contact between the peat and other deposits is not well represented in the
lidar or the field. An extendible tile probe was used to determine the depth of the peat
within 2 m (6 ft) of each piezometer as well as 10 additional locations between
piezometers. Shallow soil probes revealed occasional layers of alternating peat and
sand, presumably derived from glacial outwash or hillslope erosion, in the upper 1 m (3
ft) of soil. The horizontal extent of the sand layers parallel to the hillslope is highly
variable, while perpendicular to the hillslope there was a clear trend of decreasing sand
content towards the lake. The NRCS (1999) classifies an organic soil (Histosol) as one
in which more than 40 cm of the upper 80 cm of soil is composed of organic material.
As such, the contact between the peat and the adjacent material was mapped where
more than 40 cm of peat occurred in the upper 80 cm of the soil profile and extrapolated
between probe sites based on interpretations of vegetation and topography. The contact
between the peat and the hillslope is thought to be accurate to within 5 meters. During
this study, peat depth was probed to a maximum of 5 m (16 ft) due to probe instability or
resistance at greater depths. Soil cores collected in the western portion of the peatland
as part of an earlier study show approximately 10 meter deep peat (Clark, 2010).
Electrical resistivity imaging suggests the peat is underlain by approximately 60 to 70
meters of glacial outwash (Clark, 2010).
The break in slope apparent in the lidar hillshade maps was used to infer the
upper extent of the alluvial material. Significant subsurface channels of sand (<1 meter
wide) were encountered along the distal edge of the alluvial fans, near the contact with
the peat. These subsurface channels were not fully investigated, although their
importance to the local hydrology may be important.
Glacial deposits were divided into two groups based on the level of preservation
of their expected geomorphic form and the presence or absence of volcanic material.
The distinction between the subdued and rounded ridges of the older moraines
16
(interpreted as Tahoe age) and the younger, sharper moraines (interpreted as Tioga
age) is readily apparent in the hillshade maps generated using the lidar data (Figure
1.1). The areas identified as Tahoe age moraines tend to have rounded granodiorite
boulders (<2m) partially covered by dense crustose lichens. These deposits also
contain up to 5% volcanic material, with clasts up to 20 centimeters in diameter. The
presence of volcanic material, assumed to have been transported from Hope Valley, was
used to identify Tahoe age deposits along the south side of the lake where contacts
were not always clearly represented in the lidar data. The presence of volcanic clasts
along the north side of the watershed could not be used to definitively map the top of the
Tahoe age deposits due to the occurrence of volcanic parent material at higher
elevations. However, the combination of a subtle break in slope and the relative
abundance of volcanic material provided a reasonable approximation for the purposes of
this study. Tioga age moraines were identified by their sharp crests in the lidar
hillshades. The Tioga age cirque deposits in the southern half of the watershed contain
abundant angular boulders (<3m) with significantly less lichen cover and lack volcanic
material.
The transition between the granodiorite hillslopes influenced by glaciation in the
lower watershed and the deeply weathered granodiorites in the upper watershed is
apparent in both the lidar data and the field. Along the north side, hillslopes transition
from a steep mix of bedrock and colluvium to weathered saprolite at an elevation of
approximately 2600 meters (8500 ft) on the west end and 2800 meters (9200 ft) on the
east end. While there is no direct evidence of glaciation between these elevations and
the lateral moraines below, it is assumed these steep hillslopes are a direct result of
glaciation. The presence of steeper hillslopes along the north side of the valley is
assumed to be a result of more effective evacuation of debris from the south facing
hillslopes than the north facing hillslopes, either by meltwater (e.g. Halford & Kuniansky,
17
2002), higher glacial velocities along the outside of the bend (e.g. Valat, Jouany, &
Riviere, 1991), or higher weathering rates associated with more extreme variations in
temperature.
Surface Hydrology Measurements
Stream flow measurements were made using a combination of methods
depending on the conditions of the particular stream channel. Channel sections suitable
for cross-sectional discharge measurements were difficult to locate due to the steep,
rocky nature of the channels. Sections with greater than 1.5 m (5 ft) of relatively uniform
flow, adequate depth (>6 cm, 0.2 ft), and fairly consistent channel profile were
considered marginally adequate. Such sections were identified for Grass Lake Creek,
First Creek, West Freel Meadows Creek, and Waterhouse Creek. For these streams,
point velocities were measured using a Marsh-McBirney FLO-MATE 2000
electromagnetic current meter. Fixed-point averaging over a period of 60 seconds was
used for each velocity measurement. Velocity measurements were taken along vertical
profiles at 20%, 40%, and 80% of the total depth for depths greater than 9 cm (0.3 ft).
For depths less than 9 cm but greater than 6 cm (0.2 ft) the velocity was measured at
40% of the total depth. Velocities for water depths less than 6 centimeters could not be
measured using the available equipment. The horizontal spacing of these
measurements was dictated by the width of the channel and varied from 15 cm (0.50 ft)
for Grass Lake Creek at the outlet, to 7.6 centimeters (0.25 ft) for West Freel Meadows
Creek. Total discharge was calculated by summing the product of the velocity
measurement and the associated area for each subsection of the profile.
Shallow water depth and limited culvert height required some discharge
estimates to be made using the float method. For this method, a section of flow with the
most uniform flow and constant channel profile was used. A float was placed in the
thalwag at the upstream end of the section and the time to travel a given distance was
18
measured. The distances ranged from 1.2 to 3.0 meters (4 to 10 ft), resulting in short
travel times and hence questionable accuracy. Velocity measurements were repeated a
minimum of five times and the mean was used to calculate the average surface velocity.
The average surface velocity is multiplied by a coefficient to account for the difference
between the average water velocity and the surface velocity. When possible, estimates
using the float method were combined with cross sectional discharge measurements in
order to calculate the velocity coefficient. For natural channels in this area, the
coefficient ranged from 0.4 to 0.8. The mean of 0.6 (n=6) was used for all natural
channels.
Cross sectional discharge measurements for Grass Lake Creek were made
approximately 55 m (180 ft) below the existing culvert. Each profile was spaced 15 cm
(0.5 ft) across the width of the channel. The flow through each vertical sub-section was
typically less than 15% of the total flow, however during peak flows the subsection
containing the thalwag accounted for 32% of the total flow. Cross sectional discharge
measurements for First Creek were made approximately 10 meters below the culvert.
The float method was used in the same section when stream depth was too low to use
the flow meter. Cross sectional discharge measurements for West Freel Meadows
Creek were made approximately 10 meters above the culvert. The float method was
used just inside the culvert to compare methods, when stream depths were too low to
use the flow meter, and after the channel avulsion in the spring of 2011. Cross sectional
discharge measurements in Waterhouse Creek were made approximately 40 meters
downstream of the head of the alluvial fan. The float method was used in the same
section to compare methods and when stream depth was too shallow to use the flow
meter.
Freel Meadows Creek passes under Highway 89 through two culverts. The
majority of flow traveled through the eastern culvert (left hand culvert) during the period
19
of this study. The western culvert (right hand culvert) accommodated up to 15% of the
flow during peak flows. The only section of Freel Meadows Creek with reasonably
uniform flow was found just inside the culvert openings. As such, discharge estimates
for Freel Meadows Creek were made using the float method and measurements of
cross-section area in the appropriate portion of the culvert. Flow within the culvert was
fairly uniform during high flows and the entire length of the culvert (approximately 18 m,
60 ft) was used to determine the average velocity.
Estimates of the Manning coefficient, along with the slope of the culvert, allow
calculations of discharge from width and depth measurements alone. Freel Meadows
Creek and West Freel Meadows Creek both had culverts or sections of culverts that
were conducive to estimating a Manning’s coefficient (fairly uniform flow and constant
slope). The average velocity of water flowing over a uniform surface can be calculated
using the Manning formula:
V=
k 2 / 3 1/ 2
Rh S
n
(1)
where V is the average velocity, k is a conversion factor (k=1 m1/3 s-1 for SI units,
k=1.4859 ft1/3 s-1 for US customary units), n is the Manning coefficient, Rh is the hydraulic
radius defined as the ratio of cross-sectional (A) area to wetted perimeter (P), and S is
the slope of the water surface, which is assumed to be equal to the slope of the culvert.
Using the relationship Q=V*A, where Q is the volumetric discharge rate, V is the average
velocity, and A is the cross-sectional area, the Manning coefficient can be estimated as:
k A5 / 3 1 / 2
n=
S
Q P
(2)
20
The Manning coefficients for the Freel Meadows Creek were calculated as 0.023
(σ=0.003, n=8) for the east culvert and 0.016 ± (σ=0.002, n=4) for the west culvert.
These values of the Manning coefficient are consistent with those reported the surfaces
material of the culverts: corrugated metal and asphalt, respectively. These values were
used to calculate discharge using equation (2) when velocity measurements were not
taken. The Manning coefficient for West Freel Meadows Creek culvert was calculated to
be 0.023 ± 0.003 using independent estimates of discharge using the FLO-MATE in
2010 and concurrent measurements of water depth and width in the culvert. Peak flows
during the spring of 2011 caused West Freel Meadows Creek to avulse, bypassing the
only section suitable for cross sectional discharge measurements. All 2011 discharge
measurements for West Freel Meadows Creek are based on measurements of the
wetted width and depth in the culvert, the culvert slope, and the Manning coefficient
calculated using 2010 data.
In 2010, Levelogger Gold M5 pressure transducers were placed inside a
perforated PVC tube and secured to a piece of rebar in a still section of each stream.
Hourly stage was recorded and the average daily stage was calculated. In 2011 manual
measurements of stage, width, and/or depth were made periodically. These
measurements and the corresponding flow estimates were used to generate the rating
curves shown Figures 1.5-1.9. Stream flow measurements are assumed to be accurate
to within ± 30% due to the dynamic nature of the stream channels (First Creek, West
Freel Meadows Creek, and Waterhouse Creek), irregular culvert cross sectional areas
(Freel Meadows), heavy vegetation (Grass Lake Creek), and the limited length of
suitable sections.
21
a)
Grass Lake Creek (outlet) Rating Curve
2010 Field season
18
y = 10.854x 2.7739
R2 = 0.9992
16
14
flow (cfs)
12
10
8
6
4
2
0
0
0.2
0.4
0.6
0.8
1
1.2
2.5
3
stage (ft)
b)
Grass Lake Creek (outlet) Rating Curve
2011 Field season
90
y = 3.0869x 3.703
R2 = 0.9908
80
70
flow (cfs)
60
50
40
30
20
10
0
0
0.5
1
1.5
2
stage (ft)
Figure 1.5: Rating curve for Grass Lake Creek (outlet) for a) the 2010 field season with
stage recorded by a pressure transducer and b) 2011 field seasons with stage recorded
at the culvert.
22
a)
First Creek Rating Curve
2010 Field season
6
1.2873
y = 4.4014x
2
R = 0.9717
5
flow (cfs)
4
3
2
1
0
0
0.2
0.4
0.6
0.8
1
1.2
stage (ft)
b)
First Creek Rating Curve
2011 Field season
14
1.6958
y = 3.2696x
2
R = 0.9855
12
flow (cfs)
10
8
6
4
2
0
0
0.5
1
1.5
2
2.5
stage (ft)
Figure 1.6: Rating curve for First Creek for a) the 2010 field season with stage recorded
by a pressure transducer and b) 2011 field seasons with stage recorded at the culvert.
23
West Freel Meadows Creek Rating Curve
2010 Field season
3.50
5.1176
y = 1.7907x
2
R = 0.9571
3.00
flow (cfs)
2.50
2.00
1.50
1.00
0.50
0.00
0.0000
0.2000
0.4000
0.6000
0.8000
1.0000
1.2000
stage (ft)
Figure 1.7: Rating curve for West Freel Meadows Creek for 2010 with stage recorded by
a pressure transducer. Flows for 2011 were estimated from width and depth
measurements in the culvert and the Manning equation calculated from 2010 data.
Freel Meadows Creek Rating Curve
2010 Field season
25
2.0537
y = 14.382x
2
R = 0.9383
flow (cfs)
20
15
10
5
0
0.0000
0.2000
0.4000
0.6000
0.8000
1.0000
1.2000
stage (ft)
Figure 1.8: Rating curve for Freel Meadows Creek for 2010 with stage recorded by a
pressure transducer. Flows for 2011 were estimated from width and depth
measurements in the culvert and the Manning equation calculated from 2010 data.
24
Waterhouse Creek Rating Curve
2010 Field season
1
0.9
3.6198
y = 2273.3x
2
R = 0.9056
0.8
flow (cfs)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.0000
0.0200
0.0400
0.0600
0.0800
0.1000
0.1200
0.1400
stage (ft)
Figure 1.9: Rating curve for Waterhouse Creek for 2010 with stage recorded by a
pressure transducer.
Stream flow records for the 2010 field season cover the period from May 1, 2010
to September 20, 2010. Stream flow records for the 2011 field season cover the period
from May 13, 2011 to October 23, 2011. The stream flow averaged over each of these
periods is referred to as the “average seasonal stream flow” for the remainder of this
study and is estimated as:
N
Q=
∑ (Q
i =1
i
+ Qi −1 )(t i − t i −1 )
2t T
(3)
where N is the total number of stream flow measurements made for the stream in
question, Qi is the ith stream flow measurement made at time ti, and tT is the total time
period (142 days in 2010 and 163 days in 2011). Minimum estimates of the average
seasonal stream flow were made by assuming there was no flow prior to the first
measurement (Q1+Q0=0). Maximum estimates of the average seasonal
25
stream flow were made by extrapolating from the first measured value to a value of zero
flow at the start of the season.
Groundwater and Subsurface Measurements
A total of 33 piezometers were installed in the Grass Lake watershed (Figure
1.1): 15 along the southern edge of Grass Lake, 15 along the northern edge of Grass
Lake, 2 in the small basin east of Grass Lake proper, and 1 in Freel Meadows. The
piezometers were constructed of 1¼-inch nominal schedule 40 stainless steel pipe to
withstand the heavy snow loads and extreme temperatures. Water temperature, water
depth, and specific conductivity (SC) were measured at each piezometer, both inside
(groundwater) and outside (surface water). Temperature loggers and pressure
transducers were installed in selected piezometers to monitor short-term (hourly)
changes in head and temperature. These data are used to constrain parameters
governing heat and fluid flow through the peat (Chapter 2).
The upslope geology, vegetation characteristics, and the proximity to other
piezometers were used to determine the locations of the piezometers. Eighteen
piezometers were placed near the interface of the Tahoe age lateral moraines and the
peat. Seven of these 18 were also located down slope of the large terminal moraine
associated with the Tioga age cirque along the south side of Grass Lake. Nine
piezometers were placed near the interface of the alluvial material and the peat. Four
piezometers were placed near the Tioga age terminal moraine that forms the east side
of the Grass Lake watershed, including two in the small basin east of Grass Lake proper.
The final piezometer was placed in Freel Meadows, just upstream of an eroding headcut
in the lower half of the peatland.
Peat depth was measured near each piezometer using an extendable probe.
The depth of peat was defined as the depth at which the soil probe encountered coarse,
resistant geologic material. The piezometers were installed where peat thickness was
26
approximately 1 to 3 m (3 to 10 feet) thick. The 15cm (6 inch) screened interval of each
piezometer was placed at a depth of 1.3 to 2.8 meters (4.3 to 9.2 feet) below ground
surface and located in the sand/gravel layers that underlie the peat. Piezometers on the
alluvial fans were installed such that the screened intervals were in sand layers below
significant (>0.25m) peat deposits.
Piezometers N2 and N3 were installed in the West Freel Meadows alluvial fan to
investigate groundwater-surface water interactions at the interface between the stream
and the peatland. Piezometer N2 is screened in sand at a depth of 2.97 meters bgs
(9.75 feet). Piezometer N3 is located approximately 5 feet north and screened in sand
at a depth of 1.45 m bgs (4.75 ft). The material between the two screened intervals is
composed of interbedded peat and coarse alluvial material.
The elevation of the rim of each piezometer was determined using a total station.
The Department of Transportation established numerous survey points during a recent
project designed to improve road drainage. These survey points had elevations reported
to 0.01 ft (3mm). Three or more control points were measured at the start and end of
each survey. The estimated accuracy of each piezometer’s elevation was evaluated
using the standard deviation of the difference between the reported elevations and the
surveyed elevations. The standard deviation for most surveys is ±5cm (2 in, n>=6). The
standard deviation for the surveys that included S5, S7, S12, U1, and U2 is ±15cm (6 in,
n>=6). The elevations of the piezometer rims minus the depth to groundwater inside the
piezometers were used to construct a hand-drawn contour map of groundwater head.
The elevation of streams was used to approximate the elevation of the water table
surface in the alluvial fans.
Manual measurements of the depth to groundwater from the rim of each
piezometer were used to construct contour maps of groundwater head for the fall of
2010 and the spring of 2011, representing relatively dry conditions and relatively wet
27
conditions, respectively. Groundwater levels used to make the fall 2010 map were
measured on September 14 or September 15. Groundwater levels used to make the
spring of 2011 maps were measured on May 28 along the north side and June 26 along
the south side, due to persistent snow. When surface water was present,
measurements of the depth from the rim to water outside each piezometer were made.
These measurements were recorded with a precision of ±1/16th inch (1mm). The high
precision of these measurements allows accurate calculations of the vertical hydraulic
gradients (VHG) that exist between the bottom of the peat and the surface water at each
piezometer. Accurate VHG could not be calculated for many of the northern
piezometers due to the lack of surface water in 2010. Positive VHGs indicate a
hydraulic potential driving groundwater flow upward through the peat.
Bailer tests were conducted to estimate the hydraulic conductivity of the
underlying sediment at 22 of the 32 piezometers. The ambient groundwater level was
measured before starting each test. A Solinst Gold Levellogger set to record every 0.5
second was suspended approximately 2 meters below the rim of the piezometer. A 4
foot long section (1.2m) of sealed ¾ inch PVC pipe was pushed into each piezometer.
This usually resulted in significant overflow. Excess water was siphoned off to bring the
groundwater level back to within 1/8th inch (2mm) of the ambient level. The water level
was monitored occasionally for 5 to 10 minutes to ensure the system had re-established
equilibrium. After a sufficient equilibration time, the PVC pipe was quickly removed and
the water level was allowed to recover. The volume of water displaced was calculated
from the length of the submerged PVC pipe. The data were fit using the Bower-Rice
method (e.g. Halford & Kuniansky, 2002).
Solinst Gold Levelloggers ® (model M5) were installed near the bottom of 20
piezometers. Ten additional Levelloggers were installed in other piezometers to monitor
temperature and pressure fluctuations associated with the recession of the snowmelt
28
signal in the hillslope aquifers. The Gold Levelloggers record pressure with a stated
accuracy of 2.5 mm (resolution < 0.1 mm) and temperature with a stated accuracy of
±0.05°C (resolution 0.03°C). The TidBit v2 tempera ture sensor records temperature with
a stated accuracy of ±0.2°C (resolution of 0.02°C). Atmospheric pressure and air
temperature were recorded using Solinst Barologgers at two locations along the north
edge of Grass Lake. The pressure from each Levellogger was corrected for fluctuations
in atmospheric pressure using the Barologger data. Twenty Onset TidBit v2 data
loggers were placed at various depths inside and outside of ten piezometers. Data was
logged at hourly or shorter intervals. These data are define boundary conditions in the
models of heat transport used to constrain the hydraulic conductivity of the peat
(Chapter 2).
Specific Conductivity
Specific conductivity (SC) is a measure of the ability of a fluid to conduct
electricity and is directly related to the concentration of dissolved ions in solution.
Measurements of SC and temperature were made using an Oakton multi-parameter
PCTestr 35 at each piezometer during field visits. A 6-foot (1.8m) hose was used to
siphon water from the piezometer. The instrument and sampling vessel were rinsed
three times or until the temperature reading stabilized before a final reading was made.
Surface water was measured using the same technique when present. The instrument
was calibrated at the beginning, middle, and end of each field season using an 84 µS
cm-1 solution. The instrument was within ±3.0 µS cm-1 and 1.0°C at the time of each
calibration. The reported accuracy of the instrument is ±2.0µS/cm (resolution 0.1
µS/cm) for SC and 0.5°C (resolution 0.1°C) for temp erature.
Hydrograph separation based on the assumption of a conservative tracer with a
known and constant concentration for each component has been used to estimate the
contribution of old and new water to the total flow. Pilgrim et al. (1979) showed that the
29
SC of water increases with time as the water is exposed to weathering geologic material
and/or accumulated ions. The change in SC with time is specific to the material through
which the water flows and depends on the concentration of accumulated ions and/or the
rate of weathering. Neglecting the increase in SC with exposure time is likely to result in
overestimates of the contributions of old water to the total flow.
The SC of one spring, two seeps, and three streams identified on the north side
of Grass Lake were used to constrain estimates of subsurface water input into the
streams during peak snowmelt. During peak flow the SC of the stream water is
determined by the relative contributions of direct surface runoff from snowmelt, shallow
subsurface flow (“interflow”), and deeper groundwater flow. The fraction of total flow
coming from the groundwater in a two component mixing model is given by:
fg =
SCT − SC s
SC g − SC s
(4)
where the subscript T refers to total flow, the subscript s refers to the component of flow
coming from snowmelt or surface water, and the subscript g refers to the component of
flow coming from groundwater. The relatively constant SC values recorded for a
perennial spring near Freel Meadows are used to infer the equilibrium SC value for
subsurface flow. Shallow seeps issuing from road cuts near First Creek during the
spring of 2011 have intermediate values of SC and are expected to be typical of shallow
subsurface flow. The SC values of the streams during baseflow provide the lowest
reasonable estimate of SC for the subsurface component.
Water budget
The contribution of groundwater can be estimated using a simple water budget
give by
‫ܩ‬௜௡ = ܵ௢௨௧ + ‫ ܶܧ‬− ܵ௜௡ − ܵ௦௡௢௪
(5)
30
where G is the net volume (or flux) of groundwater entering Grass Lake, Sin is the
volume (or flux) of surface water inflow, Sout is the volume (or flux) of surface water
outflow, Ssnow is the volume (or flux) of water resulting from direct snow melt, and ET is
the volume (or flux) of water leaving due to ET. The water budget is evaluated on a
seasonal volume basis, as well as a daily flux basis. Maximum and minimum estimates
of the ET rate are determined from the literature and included in the water budget
analysis. For easier comparison to stream flow values, ET rates are converted from
units of mm day-1 to the equivalent average daily cubic feet per second (cfs). For the
daily flux estimates, the average rate of spring snow-melt is estimated and applied to
dates before June 21, 2011. Snow melt ceased around June 7, 2010 and stream flow
records did not being until June 17, 2010. As such, no snow melt contributions are
added to the 2010 water budget calculations.
Peat water retention experiment
Four peat samples were collected from Grass Lake to measure the water
retention characteristics. The transition between the low density living peat (acrotelm)
and the higher density non-living peat (catotelm) is better defined in low lying hollows
than in the elevated hummocks. To avoid complications associated with defining this
boundary and potential complications with hydrophobicity in dried woody and
herbaceous peat (e.g. Valat et al., 1991), samples were taken from fully saturated
hollows. Two samples separated by approximately 30 meters were collected at each
location. The first peat sample (PC1) was collected approximately 40 meters south of
the toe of the Freel Meadows Creek alluvial fan. The second sample (PC2) was
collected approximately 30 meters northeast of PC1, perpendicular to the long axis of
the Freel Meadows Creek fan. The third sample (PC3) was collected near the outlet of
Grass Lake, approximately 20m from the northeast boundary of Grass Lake. The fourth
sample (PC4) was collected 30m southwest of PC3.
31
Soil tins with a diameter of 9.6 cm and a height of 6.4 cm were used to collect the
samples. Surface vegetation was clipped to expose the peat surface and prevent
interference with the sampling. The soil tin was gently pressed into the peat (~0.5 cm)
with a twisting motion. A serrated knife was used to cut around the edge of the soil tin to
a depth of ~2 cm. The soil tin was pushed deeper into the peat along the cut. The
procedure was repeated until the bottom of the soil tin was level with the peat surface.
In order to gain access to the bottom of the soil, a cuboid of peat approximately 10 x 30
x 10 cm was cut along one side of the soil tin. With the sample still secure inside the soil
tin, the knife was used to cut the base of sample from the main peat body. The water
level in the sampling pits rose to approximately 6cm below the surface of the peat within
two minutes, suggesting the samples were near saturation, but may not have been fully
saturated. Excess material was carefully cut from the top of the soil tin (bottom of the
sample) and the samples were weighed. The soil tin lids were secured with electrical
tape. The samples were stored at approximately 3ºC until the hanging water column
experiments were performed.
Pyrex Buchner funnels with a diameter of 9.5 cm and reported pore size of 4.5 to
5 µm were saturated with a hydraulic gradient imposed across the porous plate for 12
hours to ensure no air was trapped in the porous plate. The bottoms of the funnels were
connected to water-filled, air-free tubing with a 3-way valve in the middle of the line. The
3-way valve was connected to a water reservoir and a constant head apparatus. The
top of the reservoir was positioned approximately 1cm above the porous plate to
maintain saturation. The peat samples were transferred into the Buchner funnels with
little disturbance. The slight difference between the soil tin diameter (9.6 cm) and the
funnel diameter (9.5 cm) required minor compression of the peat. The peat was
positioned firmly against the ceramic plate on the bottom of the funnel and left to
equilibrate under the imposed constant head conditions for 12 hours. The constant head
32
apparatus was then moved up to the middle of the sample and allowed to equilibrate for
12 hours. Finally, the constant head apparatus was moved up to top of the sample and
allowed to equilibrate for 12 hours. This progressive saturation of the sample from the
bottom to the top was intended to minimize the amount of air trapped in the pores.
The samples were disconnected from the reservoir, connected to a constant
head apparatus positioned at the interface between the peat and the ceramic plate, and
the excess water pooled in the depressions was decanted from the samples. Water
discharged from the constant head apparatus was collected in graduated cylinders and
recorded periodically. The graduated cylinder and peat samples were covered to
minimize evaporation. The constant head apparatus was moved down in progressively
larger increments ranging from 3 cm to 50 cm. The suction is defined by the difference
in elevation between the center of the sample and the constant head apparatus. The
final constant head level was 1.79 m below the bottom of the sample, resulting in an
average suction of approximately 17.2 kPa, depending on the thickness of the sample.
The final volumetric water content (Vf) was determined by subtracting the weight
of the dried sample from the weight of the sample recorded at the end of the hanging
water column experiment. The samples were removed from the funnels, weighed, and
spread in oven pans to allow water to escape. The samples were dried at 103ºC for 15
hours and then reweighed. The final volumetric water content of the peat samples was
calculated gravimetrically as:
θf =
(W f − Wd )
ρwVT
=
Vf
VT
(6)
where Wf is the weight of the sample after equilibration at the final suction step, Wd is
the dry weight of the sample, ρw is the density of water (1000.0 kg m-3), Vf is the volume
of water remaining in the sample after the last suction step, and VT is the total volume at
33
saturation. The total volume of each sample was calculated using the area of a cylinder
with the height measured once the sample was fully saturated in the funnel. The bulk
densities and water content are reported on a saturated volumetric basis and changes in
the volume of the samples were not considered.
The volume of water at saturation (Vs) is calculated by adding the final water
content (Vf) to the water released from the sample during the experiment (Vr):
N
Vr = ∑ Vi
i =1
(7)
Vs = V f + Vr
(8)
where Vi is the volume of water released during suction step i and N is the total number
of suction steps. The saturated water content (θs) is the ratio of (Vs) to total volume (VT).
Similarly, the volume of water contained in the sample for a given value of suction (Vcn)
is calculated by subtracting the volume of water released in all subsequent suction steps
(Vn) from the volume of water at saturation (Vs), where (Vn) is given by:
n
Vn = ∑ Vi
i =1
(9)
where n is the suction step of interest. The water content at suction step n is given by:
θψ =
n
V f + Vr − Vn
VT
=
Vcn
VT
(10)
The degree of saturation (Sw) is the ratio of (θψn)/(θs), and equal to 1 when n=0 and the
sample is at full saturation. The pressure intervals and resulting degree of saturation
34
data are used in the numerical models to define the pressure-saturation relationships for
unsaturated subsurface flow through the peat (Chapter 2).
Bulk density (ρb) was calculated as the ratio of dry weight (Wd) to total saturated
volume (VT) of each sample. To calculate solid density (ρs), each sample was portioned
into three roughly equal subsamples, lightly ground with a mortar and pestle, and
weighed. Each subsample was added to a known volume of water and vigorously
stirred. The difference between the initial volume of water and the final volume of the
peat-water mixture was taken as the volume of the solids (Vs). The solid density was
calculated as the ratio of the weight of the solids to the volume of the solids as
determined by the displacement of the water. The total porosity (θT) of the peat was
calculated from the bulk density (ρb) and solid density (ρs) as:
θT = 1 −
ρb
ρs
(11)
RESULTS
Surface Hydrology
The dominant source of surface water entering Grass Lake is Freel Meadows
Creek. First Creek is the second most abundant source of surface water, followed by
West Freel Meadows and Waterhouse Creeks. These results are consistent with
expectations based on the relative contributing area of each subwatershed (Table 1.1).
Surface water yield calculations from each watershed ranged from 6% to 23% of the
annual precipitation in 2010 and 10 to 43% of the annual precipitation in 2011.
Estimates of average seasonal stream flow (ASSF) and peak flow for 2010 (May 1 to
September 20) and 2011 (May 13 to October 23) are shown in Table 1.2. The ASSF
values for 2011 are 1.9 (First Creek) to 2.7 times (West Freel Meadows Creek, Freel
Meadows Creek, Waterhouse Creek) higher the 2010 values. The ASSF out of Grass
35
Lake in 2011 was 2.2 times higher than the 2010 value. In 2010 stream flow for the four
streams entering Grass Lake proper fell below 1.0 cfs between late June (Waterhouse
Creek) and late July (Freel Meadows Creek). In 2011 stream flow for the four streams
entering Grass Lake fell below 1.0 cfs between late July (West Freel Meadows Creek
and Waterhouse Creek) and mid-August (Freel Meadows Creek). Despite the similarity
in late-season stream flow into Grass Lake between the two years, late-season stream
flow out of Grass Lake dropped to 0.6 cfs by September 10 in 2010 and maintained
flows as high as 8.0 cfs into October in 2011.
Contrib. area
(ha)
Table 1.1: Estimates of seasonal surface water yield (volume of water per contributing
area) and percent of annual precipitation for GLRNA.
2010
2011
Seasonal
Percent
Seasonal
Percent of
surface
annual
surface
annual
water yield precip. (1.04 water yield
precip.
(m3/m2)
m)
(m3/m2)
(1.66 m)
Watershed
min
max
min
max
min
max
min max
First Creek
108 0.07 0.23
6% 22% 0.21 0.51 13% 31%
W. Freel
Meadows Ck
65 0.08 0.15
8% 14% 0.24 0.45 15% 27%
Freel Meadows
Ck
210 0.13 0.24 13% 23% 0.39 0.72 23% 43%
Waterhouse
Creek
66 0.04 0.13
3% 13% 0.17 0.39 10% 23%
Grass Lake
8% 16% 0.22 0.41 13% 24%
Creek
998 0.09 0.16
The average daily stream flow for each stream in the GLRNA was estimated from
the rating curves and pressure transducer data in 2010 (Figure 1.10). Peak discharge
for Grass Lake Creek, First Creek, and Waterhouse Creek were not captured due to
complications with the field equipment. Peak flows for Grass Lake Creek occurred
sometime between May 7 and June 13 in 2010. Stream flow data collected on May 20
indicates that peak flow in Grass Lake Creek was at least 23.0 cfs (±30%). The data
suggests that peak discharge in First Creek occurred on or before June 7th but is not well
36
Table 1.2: Average seasonal and peak values for stream flow in the GLRNA watershed.
An assumed measurement error of ±30% has been included in the minimum and
maximum estimates of average seasonal values. * indicates best estimate and date of
peak stream flow due to missing data.
2010
2011
Seasonal
Seasonal
Average
Average
(cfs)
Peak (cfs)
(cfs)
Peak (cfs)
Source
min
max
flow
date
min
max
flow
date
First Creek
0.2
0.7
4.7*
7-Jun*
0.6
1.4
11.4 26-Jun
W. Freel
Meadows Ck
0.1
0.3
3.3
7-Jun
0.4
0.7
4.8 26-Jun
Freel Meadows
1.5
14.8
8-Jun
2.0
3.8
33.1 26-Jun
Ck
0.8
Waterhouse
Creek
0.1
0.2
1.2*
17-Jun*
0.3
0.6
4.0*
7-Jul*
Grass Lake
4.7 23.0* 20-May*
5.5 10.2
70.6 29-Jun
Creek
2.5
30
2010 Daily Stream Flow Estimates
Stream discharge (cfs)
25
First Creek
West Freel Meadows
20
Freel Meadows Creek
Waterhouse Creek
15
Grass Lake Creek
10
5
0
4/30/2010
5/31/2010
7/1/2010
8/1/2010
Date
9/1/2010
10/2/2010
Figure 1.10: 2010 daily average streamflow based on rating relationships for all streams
into and out of Grass Lake proper.
37
represented in the data. The highest stream flow recorded for First Creek was 4.7 cfs on
June 7th. Peak discharge in Freel Meadows Creek (14.8 cfs) and West Freel Meadows
Creek (3.3 cfs) occurred on June 7 and June 8, 2010, respectively.
Four storms in the summer of 2010 produced slight increases in stage at Grass
Lake Creek, and to a lesser extent Freel Meadows Creek. These storms occurred on
June 26, July 7-8, July 24-26, and August 7-9, 2010 with total accumulations of 0.6mm
(0.02 inches), 4.6mm (0.18 inches), 2.3mm (0.9 inches), and 14.2mm (0.56 inches),
respectively. The change in discharge resulting from the first three storms was not
significant given the measurement accuracy of ± 30%. However, the last storm in 2010
produced a notable increase in discharge (0.6 cfs) at Freel Meadows Creek on August
8th. A similar increase in outflow (0.5cfs) was observed in Grass Lake Creek two days
later on August 10th. The distance from Freel Meadows Creek to the outlet is
approximately 2000 m. Assuming the storm water travels an average distance of 2000
m over two days, the average velocity of the water would be 12 mm s-1. This estimated
velocity is consistent with surface flow over a gentle slope with heavy vegetation.
The results of manual steam measurements made in 2011 are shown in Figure
1.11. The highest values of discharge for Freel Meadows Creek (33.1 cfs), First Creek
(11.4 cfs), and West Freel Meadows Creek (4.8 cfs) were recorded on June 26, 2011.
The highest value of discharge for Grass Lake Creek (70.6 cfs) was recorded three days
later on June 29, 011. The highest value of discharge for Waterhouse Creek (4.0 cfs)
was recorded on July 7, 2011. The apparent delay in peak stream flow for Waterhouse
Creek may be explained by the predominantly northern aspect of the Waterhouse Creek
watershed. There were no significant storms recorded in the data in 2011.
38
100
2011 Stream Flow Measurements
90
First Creek
80
Stream discharge (cfs)
W Freel Meadows
70
Freel Meadows Ck
60
Waterhouse Creek
Grass Lake Creek
50
40
30
20
10
0
4/30/2011
5/31/2011
7/1/2011
8/1/2011
Date
9/1/2011
10/2/2011
Figure 1.11: 2011 manual stream flow measurements into and out of Grass Lake proper.
Water budget
Seasonal stream flow out of Grass Lake contains a significant amount of water
from the snow accumulated on the surface of the peat, in addition to the water from
inflowing streams. It is assumed here that all of the winter precipitation (October 1
through May 1) accumulated on the peat surface contributes to the average seasonal
stream flow in Grass Lake Creek. Using the area of peat mapped in the field (96 ha, 237
acres), the contribution of flow from the accumulation of winter precipitation was
approximately 0.9x106 m3 in 2010 and 1.4x106 m3 in 2011. Snow melt on the surface of
Grass Lake is estimated to have begun in mid-April both years. The peat was mostly
snow-free by June 7, 2010 and June 21, 2011. The contribution of snowmelt to the
outflow at Grass Lake Creek averaged over this period is 6.8 cfs in 2010 and 8.4 cfs in
2011.
39
The rate of water outflow due to ET is another important component of the
surface water budget. The ET rate at Pope Marsh, located approximately 10 miles
north-northwest of Grass Lake, was estimated to be 4.2 mm day-1 (Green, 1998). This
value is comparable to the value of 4.0 mm day-1 reported by Kelliher et al. (1993) for
canopy-scale ET rates of dry conifer forests. ET rates ranging from 5.0 to 6.5 mm day-1
have been estimated for riparian meadow sites in the Sierra (Loheide & Gorelick, 2005).
Comer et al. (2000) reported values of latent heat flux from seven peatlands in Canada
and the northern United States ranging from 69 to 142 W m-2 for fens and 105 to 199 W
m-2 for bogs. These values of latent heat flux are equivalent to ET rates of 2.6 to 5.4 mm
day-1 for fens and 4.0 to 7.6 mm day-1 for bogs. The average rate of ET for the
peatlands mentioned above is 5.0 mm day-1.
A seasonally based surface water budget shows no measurable difference
between the total seasonal stream flow into and out of Grass Lake in 2010 or 2011
(Table 1.3). This is attributed to the large errors (30%) associated with measuring
stream flow in these steep, dynamic mountain streams and the uncertainty in the range
of ET flux. Groundwater contributions cannot be estimated using a seasonally based
water budget.
Table 1.3: Seasonal average flow (m3) of water into and out of Grass Lake for the 2010
and 2011 field seasons.
Seasonal water budget
2010
2011
Source
min
max
min
max
Stream flow (Sin)
423425
946394 1307446 2614892
IN
direct snowmelt (Ssnow)
900480
900480 1398720 1398720
(m3)
TOTAL IN 1323905
1846874 2706166 4013612
stream flow (Sout)
878737
1631940 2184664 4057233
OUT
Evapotranspiration (ET)
369200
1079200
423800 1238800
(m3)
TOTAL OUT 1247937
2711140 2608464 5296033
OUTFLOW-INFLOW (Gin)
-75969
864266
-97702 1282421
40
A water budget conducted on the basis of available stream flow measurements
and estimates of daily average ET is shown in Table 1.4. The maximum groundwater
contribution is estimated using the maximum values for Sout and ET along with the
minimum values for Sin. Based on the available storm flow and peak flow data
discussed above, the direct snow melt on the surface of Grass Lake is expected to move
through the system quickly (2-3 days). As such, snow melt contributions to outflow are
not considered in the water budget after June 7 in 2010 and June 21 in 2011 and errors
in the contribution of direct snow melt are expected to be minimal. Maximum and
minimum estimates of groundwater flux into Grass Lake include consideration of 30%
error in all stream flow measurements and ± 1.0 cfs (over 24 hours) in ET.
The results of the water budget based on measured stream flow values and
estimated rates of ET show a positive groundwater contribution after August 13, 2010.
The magnitude of groundwater inflow is estimated to be 0.8 to 2.6 cfs after August 13,
2010 and exceeds total stream inflow (0.4 cfs) by September 10, 2010. Groundwater
contributions are not detectable before August 13, 2010 due to errors in estimated flow
rates.
The groundwater contribution in 2011 is estimated to be between 0.8 and 9.3 cfs
after July 26, 2011. Groundwater inflow exceeds total stream inflow (2.1 cfs) by August
16, 2011 and remains above 4.4 cfs through at least the end of October 2011.
Specific conductivity – Surface Water
Waterhouse Creek had the lowest SC in both 2010 and 2011, with values
consistently less than 17.0 µS cm-1 (Figure 1.12). West Freel Meadows Creek, Freel
Meadows Creek, and First Creek had similar values of SC during both years. In the
spring of 2010 the SC values dropped from approximately 34 (σ=4, n=12) to 20 (σ=2,
n=9) µS cm-1 between late April and mid-June. Similarly, in 2011 the SC values dropped
from approximately 33 (σ=6, n=8) to 18 (σ=1, n=11) µS cm-1 between mid-May and midJuly. The SC of snow samples was 5.2 µS cm-1 (σ=2, n=9). The declining trend in SC
41
during the spring and early summer can be explained by low conductivity snow melt
mixing with higher conductivity subsurface flow in the streams. The SC values for these
three streams climbed from approximately 20 to 33 (σ=13, n=14) µS cm-1 between midJune and the end of the 2010 field season. In 2011 the SC for these streams climbed
from 18 to 31 (σ=3, n=5) µS cm-1 between mid-July and the end of the season.
Table 1.4: Water budget calculations for available stream flow measurements in 2010
and 2011. Calculations of Gmax and Gmin include consideration of ±30% error in stream
flow measurements and ± 1.0 cfs uncertainty in the estimate of ET.
Sout
Ssnow
Gmax
Gmin
Gave
Date
ET (cfs) Sin (cfs)
(cfs)
(cfs)
(cfs)
(cfs)
(cfs)
6/17/2010
17.1
2.0
18.4
0.0
12.4
-10.9
0.8
6/25/2010
14.2
2.0
12.8
0.0
12.6
-5.7
3.4
6/29/2010
12.2
2.0
10.0
0.0
11.9
-3.4
4.3
7/27/2010
3.0
2.0
3.5
0.0
4.5
-1.5
4.3
8/13/2010
1.6
2.0
1.0
0.0
4.4
0.8
2.6
9/10/2010
0.6
2.0
0.4
0.0
3.5
0.9
2.2
6/13/2011
19.1
2.0
18.6
8.4
6.5
-18.1
-5.8
6/20/2011
37.4
2.0
37.8
8.4
16.8
-30.4
-6.8
6/26/2011
46.8
2.0
51.9
0.0
27.5
-33.6
-3.0
6/29/2011
70.6
2.0
40.9
0.0
66.2
-2.8
31.7
7/7/2011
43.7
2.0
32.5
0.0
37.0
-10.7
13.2
7/26/2011
10.1
2.0
5.6
0.0
12.3
0.8
6.5
8/16/2011
8.7
2.0
2.1
0.0
12.8
4.4
8.6
9/3/2011
7.4
2.0
1.1
0.0
12.0
4.9
8.4
10/15/2011
8.0
2.0
0.8
0.0
12.9
5.6
9.3
10/23/2011
7.2
2.0
0.8
0.0
11.8
5.0
8.4
The SC values of the springs and seeps originating in the Tahoe age moraines
along the north side of Grass Lake were higher than the SC values recorded for the
streams. The average SC value of the spring east of Freel Meadows Creek was 78
(σ=2, n=11) µS cm-1 2010. The same spring had SC values of 69 (σ=1.5, n=5) µS cm-1 in
early July, 2011. In 2011 two seeps manifested in road cuts located near First Creek
along highway 89. The average SC value for these seeps was 52 (σ=6, n=19) µS cm-1
between late April and late June, after which they dried up. Melting snow banks with SC
values of 8.5 µS cm-1 were identified approximately 20 meters upslope of each seep,
42
suggesting an increase of approximately 2.18 µS cm-1 per meter of subsurface flow
through the forest soils.
A two component mixing model was used to estimate the contributions of
subsurface flow to peak stream flow. The value for the groundwater component may
vary between the values of stream baseflow (33 µS cm-1) and the values of the perennial
spring (78 µS cm-1). The maximum contribution of groundwater to peak flows is
estimated by using the SC value of baseflow to represent (SCg) in equation (3). The
maximum contribution of groundwater to peak flow ranges from 40 to 60%. The
minimum contribution of groundwater to peak flows is estimated by using the SC values
of the perennial springs. The minimum estimate of groundwater contributions to peak
flows ranges from 18% to 20%.
Grass Lake Creek had higher SC values than the other streams. In 2010 SC
values of Grass Lake Creek dropped from a high of 235 to a low of 28 µS cm-1 between
late March and mid June, and climbed to 40.0 µS cm-1 by mid September. In 2011 SC
values of Grass Lake Creek dropped from approximately 125 to a low of 23 µS cm-1
between late April and early July and climbed to 49 µS cm-1 by late October.
The SC of surface water near each piezometer was measured during field visits.
The SC of surface water near each piezometer was significantly higher on the north side
of Grass Lake than that on the south side (Figure 1.13). The higher values of SC on the
north side maybe attributable to salts used for highway deicing that are carried over the
pass by vehicles or by increased weathering rates associated with southern exposure.
Values on both the north and south side of Grass Lake were lower in 2011 than they
were in 2010, which is likely due to the higher snowpack in 2011.
43
a)
Stream Specific
Conductivity (uS cm-1)
250.0
1st Creek
WFM Creek
FM Creek
WH Creek
GL outlet
FMC seep
200.0
150.0
100.0
50.0
0.0
3/30/2010 4/30/2010 5/31/2010 7/1/2010 8/1/2010 9/1/2010 10/2/2010
Date
b)
Stream Specific
Conductivity (uS cm-1)
250.0
1st Creek
WFM Creek
FM Creek
WH Creek
GL Creek
FMC seep
1st Creek roadcut (E)
1st Creek roadcut (W)
200.0
150.0
100.0
50.0
0.0
3/30/2011 4/30/2011 5/31/2011 7/1/2011 8/1/2011 9/1/2011 10/2/2011
Date
Figure 1.12: 2010 (a) and 2011 (b) specific conductivity values recorded for streams in
the Grass Lake Watershed.
44
a)
600.0
400.0
200.0
0.0
4/1/2010
6/1/2010
N1
N5
N9
N13
N2
N6
N10
N14
8/1/2010
Date
N3
N7
N11
N15
10/1/2010
Surface water Specific
Conductivity (uS cm-1)
Surface water Specific
Conductivity (uS cm-1)
800.0
200.0
150.0
100.0
50.0
0.0
4/1/2010
6/1/2010
S1
S5
S9
S13
N4
N8
N12
U1
8/1/2010
Date
S2
S6
S10
S14
S3
S7
S11
S15
10/1/2010
S4
S8
S12
U2
600
500
400
300
200
100
0
4/1/2011
N1
N5
N9
6/1/2011
N2
N6
N10
8/1/2011
Date
N3
N7
N11
10/1/2011
N4
N8
N12
Surface Water Specific
Conductivity (uS cm-1)
45
Surface Water Specific
Conductivity (uS cm-1)
b)
120
100
80
60
40
20
0
4/1/2011
6/1/2011
S1
S5
S9
S13
S2
S6
S10
S14
8/1/2011
Date
S3
S7
S11
S15
10/1/2011
S4
S8
S12
Figure 1.13: Specific conductivity measurements of surface water near piezometers for 2010 (a) and 2011 (b). Note the difference in
scale between the north and south (right and left, respectively).
Groundwater Hydrology
Groundwater levels were recorded in 32 piezometers around the Grass Lake
field site. Contour maps of groundwater levels for fall 2010 and spring 2011,
representing the driest and wettest periods of the study, were drawn by visual
interpolation and consideration of surface water elevations in the unconfined hillslope
aquifers (Figures 1.14 and 1.15). Groundwater levels were on average 0.32 m (σ=0.21
m) higher in the spring of 2011 than the fall of 2010. The largest recorded groundwater
level difference occurred in piezometer N7, which increased by 0.86 m. Piezometer S12
showed a decrease of 0.06 m between fall of 2010 and spring of 2011. This unexpected
drop in water level may be explained by changes in permeability and/or changes in
groundwater flow paths. Groundwater seepage associated with recent rodent activity
was observed approximately 50 meters north (down slope) of piezometer S12 (Figure
1.16).
The head data and contour maps of piezometric head (Figures 1.14 and 1.15)
show deflections where streams enter Grass Lake and where bedrock outcrops are
located immediately above the piezometers. Inflowing streams deflect head contours
into the lake, creating a groundwater mound. These deflections are more pronounced
along the north side of Grass Lake. This may be explained by higher stream flows
associated with the larger subwatersheds. The deflections associated with Waterhouse
Creek appear to be offset slightly to the east, suggesting preferential flow towards S5.
This is consistent with field observations of persistent saturation along the east side of
the Waterhouse Creek fan and drier conditions to the west. Bedrock outcrops on the
hillslopes near the margin of Grass Lake appear to deflect head contours away from the
lake, creating a “shadowing” effect (piezometers N1 and N9). This may be explained by
hillslope groundwater being diverted around the edges of the impermeable bedrock,
46
Figure 1.14: Groundwater head contours in the Grass Lake peatland. Groundwater
levels measured in Fall 2010. Contours interval is 1m.
47
Figure 1.15: Groundwater head contours in the Grass Lake peatland. Groundwater
levels measured in Spring 2011. Contours interval is 1m.
48
Figure 1.16: Emergence of groundwater associated with preferential pathways provided
by rodent activity. Four of these seeps noted along the south side of Grass Lake
between S12 and S8. The piezometer in the picture is 1.7 meters (68 inches) long.
creating a low pressure zone below the outcrop. No other significant deflections of the
head contours are apparent in the data.
The highest horizontal hydraulic gradients (HHGs) occur near the interface of the
hillslope and the peatland. The head contour maps suggest maximum HHGs on the
order of 5% near piezometers S1, S2, and S3. Water level data near piezometers S5,
S12, and S11 suggest HHGs around 3% along the hillslope. Similar HHGs were
inferred along other hillslopes. The HHG along the length of Grass Lake is on the order
of 0.25%. The dominant driving force for groundwater flow is from the hillslopes into the
peatland.
49
Trends in vertical hydraulic gradients (VHGs) for each piezometer are shown in
Figure 1.17. Positive VHGs indicate upward flow of groundwater through the peat
(groundwater discharge), whereas negative VHGs indicated downward flow
(groundwater recharge). The VHGs were typically higher along the southern edge of
Grass Lake than the northern edge and higher in 2011 than in 2010. The persistence of
positive VHGs along the interface between the hillslope materials and the peat suggests
substantial groundwater discharge from the hillslope aquifer to the peatland. The HHGs
are small compared to the VHGs, indicating the horizontal hydraulic conductivity in the
peat is higher than the vertical hydraulic conductivity.
The highest VHGs recorded in 2010 were approximately 20% for piezometers S5
and S9 (i.e. the groundwater level in the piezometer was 20 cm per meter of submerged
piezometer higher than the elevation of the surface water). Positive VHGs were
maintained until late-September 2010 in piezometers S1, S5, S8, S9, and S12. This
indicates late-season groundwater discharge through the peat near these piezometers.
All measurements of VHG were negative (downward flow) in piezometer S6, indicating
groundwater recharge at that location. The convex contours of the broad hillslope above
S6 could lead to divergent groundwater flow and lower groundwater head at S6. The
highest VHGs recorded in 2010 along the northern edge were approximately 8% for N1,
N8, and N14. Most of the northern piezometers had no surface water present and/or
maintained a nearly neutral VHG during the 2010 field season.
The highest vertical gradients recorded in 2011 were approximately 30% in S9,
S15, and N5. Piezometers S5, S7, S11, N7, and N14 had VHGs of approximately 20%
in the spring. Piezometer S7 maintained a VHG of over 15% until mid-October or later.
All the southern piezometers had positive vertical gradients in the early summer of 2011,
except S13 which is located on the Waterhouse Creek alluvial fan. The VHG in
piezometers S6 and S12 went from positive to negative near the end of July, indicating a
50
change from groundwater discharge to groundwater recharge in these locations. This
contrasts with the 2010 observations which indicate groundwater discharge at S12 until
late-September. All other piezometers along the southern edge had positive gradients
until mid-October or later. These persistently high VHGs indicate substantial pressure
available to drive late-season groundwater flow up through the peat. The VHG in
piezometer N7 went from positive to negative in late July, with a slight but notable
increase by mid-October. This increase may be due to decreased ET needs in the fall,
allowing groundwater levels to be replenished. The VHG in N9 went from positive in
mid-May 2011 to negative by late-July 2011, indicating a change from groundwater
discharge to groundwater recharge in that area.
The West Freel Meadows Creek alluvial fan is a site dominated by groundwater
recharge. Piezometer N2, located in the West Freel Meadows Creek alluvial fan, had a
negative VHG throughout the 2010 field season. The VHG in the nearby piezometer N3
went from slightly positive in mid-May to negative by late-July. This indicates discharge
from the shallow groundwater system (1.45m bgs) to the surface during the spring and
early summer, switching to groundwater recharge by mid-summer. The SC of water
from small seeps scattered throughout the aspen grove is indistinguishable from that of
stream water, suggesting a shallow groundwater system connected to the stream. The
nearby deeper piezometer N2 remained negative and fairly constant for the duration of
2011, indicating groundwater recharge. The VHG between the screened interval of N2
and N3 was -5.3% on July 26, 2011 and dropped to -15.4% by September 3, 2011. The
consistently negative VHG between the screened intervals of piezometers N2 and N3
indicates downward flow from the shallow aquifer into the deeper groundwater system
(2.97 m bgs).
The presence of surface water at most piezometers into October allowed
calculation of late season gradients.Unsaturated conditions lead to increased rates of
51
peat decomposition by aerobic microbes and may result in significant ecosystem
changes. The water level in many piezometers did not fall below the level of the peat in
2010, indicating persistent groundwater discharge and persistently saturated conditions
at these locations (N1, S1, S3, S4, S5, S7, S8, S9, S11, S12, U1). However, the
average groundwater level was 0.123 m below the surface of the peat in mid-September
2010, indicating significant dewatering of the peat. For the piezometers that did
experience unsaturated conditions, the average rate of decrease in groundwater head
was 2.77 mm day-1 (σ=1.9) in 2010. For comparison, the water level in the center of
Grass Lake dropped 0.130 m between July 7 and September 20, 2010, a rate of 1.73
mm day-1. In 2010, the late-season groundwater levels were lower along the north side
(average -0.21m) than along the south side (average 0.03m) (Table 1.5). The lowest
groundwater levels along the north side were recorded in piezometers N7 (-0.64m) and
N15 (-0.55m). Along the south side the lowest groundwater levels were recorded in
piezometers S13 (-0.28m) and S6 (-0.11m). The earliest unsaturated conditions were
observed in piezometer N9 and N5, which dropped below the level of the peat in early
May and early July, 2010, respectively. This suggests that the surrounding area may be
more susceptible to aerobic decomposition in dry years. In the remainder of the
piezometers, the groundwater level dropped below the peat surface between mid-July to
mid-August. In 2011, the average late-season groundwater levels did not drop below
the peat on either the north side (average 0.0 m) or south side (average 0.19m). The
lowest water levels in 2011 along the north side were recorded in N13 (-0.30m) and N9
(-0.18m). The lowest water levels in 2011 along the south side were recorded in S13 (0.23m) and S11 (-0.20m).
52
0.300
0.200
0.100
0.000
-0.100
-0.200
4/1/2010 6/1/2010 8/1/2010 10/1/2010 12/1/2010
N1
N6
N11
N2
N7
N12
Date
N3
N8
N13
N4
N9
N14
Vertical hydraulic gradient
(m/m)
Vertical hydraulic gradient
(m/m)
a)
N5
N10
N15
0.300
0.200
0.100
0.000
-0.100
-0.200
4/1/2010 6/1/2010 8/1/2010 10/1/2010 12/1/2010
Date
S1
S6
S11
S2
S7
S12
S3
S8
S13
S4
S9
S14
S5
S10
S15
0.300
0.200
0.100
0.000
-0.100
-0.200
4/1/2011 6/1/2011 8/1/2011 10/1/2011 12/1/2011
N1
N6
N11
N2
N7
N12
Date
N3
N8
N13
N4
N9
N14
N5
N10
N15
Vertical hydraulic gradient
(m/m)
53
Vertical hydraulic gradient
(m/m)
b)
0.300
0.200
0.100
0.000
-0.100
-0.200
4/1/2011 6/1/2011 8/1/2011 10/1/2011 12/1/2011
S1
S6
S11
S2
S7
S12
Date
S3
S8
S13
S4
S9
S14
S5
S10
S15
Figure 1.17: Vertical hydraulic gradients calculated from 2010 field data (a) and 2011 field data (b) for the north (N) and south (S)
sides of Grass Lake.
Table 1.5: Statistics for piezometers showing the difference between piezometers
located along the north and south sides of Grass Lake.
2010
2011
Ave
max
min
max
min
piez
piez
Sept
piez
piez
(m)
(m)
(m)
(m)
(m)
North 0.27
U1
-0.64
N7
-0.21
0.6
N13
-0.3
N7
South 0.57
S5
-0.28
S13
0.03
0.7
S5
-0.23
S13
Ave
Sept
(m)
0
0.19
The drawdown curves generated during the bailer tests were fit using the BowerRice model to estimate hydraulic conductivity (Table 1.6). These values represent
estimates of hydraulic conductivity of the coarse sediment directly beneath the peat.
The fit was deemed “good” for 16 of the 25 of the tests, “moderate” for 5 of the tests, and
“poor” for the remaining 4 tests. The average value of saturated hydraulic conductivity
estimated from the bailer tests is 4.7x10-5 m s-1 (σ=8.8x10-5). The geometric mean of the
hydraulic conductivity estimates is 1.1x10-5 m s-1. The minimum value of hydraulic
conductivity (4.9x10-8 m s-1) occurred in piezometer S11 and the maximum value
occurred in piezometer S4 (3.3x10-4 m s-1).
Specific conductivity – Ground Water
Specific conductivity (SC) measurements indicate a distinct difference between
groundwater along the north side of Grass Lake (road side) and the south side of Grass
Lake during both years (Figure 1.18, Table 1.7). The higher values of SC along the
north side may be attributable to salt from the adjacent highway or increased weathering
rates due to the southern exposure. The lower values of SC were recorded in the spring
and are likely due to the influence of low SC snowmelt (5.2 µS cm-1) and/or stream water
(16.5 µS cm-1). The high value of SC recorded in U2 during the fall of 2010 may be due
to the increased concentration of dissolved ions resulting from ET from stagnant water.
The lower SC values of groundwater in 2011 compared to 2010 are believed to be a
54
result of a larger contribution of low SC snowmelt associated with the larger, persistent
snowpack.
Table 1.6: Results of bailer tests conducted in each piezometer. Data was fit using the
Bower-Rice model.
Piez K (m/s) date
fit
Piez
K (m/s)
date
fit
N1
1.7E-04
8/3/2010 good
S1
2.6E-06 8/18/2010 good
N2a 2.4E-06 7/30/2010 moderate
S3a
3.0E-06 8/18/2010 good
N2b 7.8E-06
8/2/2010 poor
S3b
1.1E-05 8/18/2010 poor
N3
3.0E-07 7/30/2010 good
S4
3.3E-04 8/18/2010 moderate
N4a 9.2E-06 7/29/2010 good
S5
2.7E-05
8/4/2010 moderate
N4b 8.8E-06 7/29/2010 good
S6
2.2E-05 8/18/2010 good
N5
1.7E-05 7/29/2010 good
S7
5.6E-06 8/18/2010 good
N7
2.3E-05 7/30/2010 good
S8
1.2E-05
8/4/2010 poor
N8
2.9E-06 7/30/2010 good
S9
1.4E-05
8/4/2010 good
N9
2.4E-04 7/29/2010 poor
S10
2.4E-06
8/4/2010 good
N10 1.1E-05 7/30/2010 good
S11
4.9E-08
8/4/2010 good
N12 2.0E-04
8/3/2010 good
S12
1.3E-05
8/4/2010 moderate
N13 3.4E-05
8/3/2010 moderate
Table 1.7: Values of specific conductivity of groundwater recorded in Grass Lake. All
units are in µS cm-1.
2010
2011
-1
[µS cm ] mean max piez min
piez mean
max
piez min piez
north
159.7
524 N8
45.9 N3
113.6
275 N7
27 U1
south
42.9 97.6 U2
23 S2
38.6
116.3 S14 6.7 U2
55
600
500
400
300
200
100
0
4/1/2010
6/1/2010
N1
N5
N9
N13
N2
N6
N10
N14
8/1/2010
Date
N3
N7
N11
N15
10/1/2010
Groundwater Specific
Conductivity (uS cm-1)
Groundwater Specific
Conductivity (uS cm-1)
a)
120
100
80
60
40
20
0
4/1/2010
6/1/2010
S1
S5
S9
S13
N4
N8
N12
U1
8/1/2010
Date
S2
S6
S10
S14
10/1/2010
S3
S7
S11
S15
S4
S8
S12
U2
b)
500
400
300
200
100
0
4/1/2011
6/1/2011
N1
N5
N9
N13
N2
N6
N10
N14
8/1/2011
Date
N3
N7
N11
N15
10/1/2011
N4
N8
N12
Groundwater Specific
Conductivity (uS cm-1)
Groundwater Specific
Conductivity (uS cm-1)
56
120
600
100
80
60
40
20
0
4/1/2011
S1
S5
S9
S13
6/1/2011
S2
S6
S10
S14
8/1/2011
Date
S3
S7
S11
S15
10/1/2011
S4
S8
S12
Figure 1.18: Specific conductivity measurements of groundwater in piezometers for 2010 (a) and 2011 (b). Note the difference in
scale of the y-axis.
Geology Results
Lidar data was used to help identify geologic contacts that were otherwise
obscured by the boulder strewn hillslopes and large trees. The dominant geologic unit
was the Bryan Meadows Granodiorite (Table 1.8). Tahoe age glacial deposits make up
the dominant hillslope material immediately upslope from the peatland. These deposits
contain a significant amount (>5%) of volcanic clasts up to 15 centimeters in diameter.
The Tahoe moraines along the south side of Grass Lake occur below approximately
2650 meters (8694 ft), while Tahoe moraines along the north side of Grass Lake occur
below approximately 2430 meters (7970 ft). Tioga age glacial deposits are distinguished
by their sharp crests and form the terminal moraines near the east end of Grass Lake
and down slope of the cirques located in the southern portion of the watershed. The
majority of peat (95%) occurs in the lower portion of the watershed where groundwater
from the hillslopes is discharged. Two other peat deposits are located in the GLRNA,
forming the headwaters of Freel Meadows Creek and First Creek. The Echo Lake
Granodiorite is limited to the southwest portion of the watershed. The undivided
andesitic volcanic rocks are limited to the northern portion of the watershed, near Freel
Meadows. Alluvial fan deposits occur at the mouths of all perennial streams, as well as
the intermittent stream east of Waterhouse Creek. Open water was delineated using the
lidar imagery and covers less than 2 ha (5 acres).
Shallow soil probes were used to identify the interface between the peat and
underlying coarse sediment. Peat depths increase at a rate of approximately 10% (0.1
m/m) from the shore for the first 10 to 30 meters in most locations, beyond which the
peat depth increased rapidly. Resistant layers and/or probe instability in the deep, soft,
and/or floating peat limited soil probe data to less than 5 meters below ground surface.
Coarse sand and gravel deposits ranging from 0.1 to over 0.5 meter (0.3 to 1.6 feet)
thick were encountered below the peat. Probing was limited to approximately the upper
57
1 meter (3 ft) on alluvial fans and revealed the presence of alternating peat and coarse
sandy deposits along the edges. The fans are dominated by coarse sand, gravel, and
cobbles. On the edges of the alluvial fans, peat thickness was more variable and
contained interbedded layers of coarse sediment and peat on the order of 1.0 and 0.1
meter (0.3 to 3.0 ft) thick, respectively.
Table 1.8: Areas of geologic units mapped in the GLRNA.
Area
Area
Geologic Unit
(ha)
(acres)
Water
1.8
4.5
Peat
101.1
249.8
Alluvium
20.1
49.6
Tioga
89.5
221.1
Tahoe
149.7
369.8
Undivided Andesitic Volcanic
24.0
59.2
Bryan Meadows Granodiorite
558.2
1379.3
Echo Lake Granodiorite
53.8
133.1
Total map area
998.1
2466.4
Percent of
GLRNA
0%
10%
2%
9%
15%
2%
56%
5%
100%
Peat Water Retention
The peat samples were dominated by moss and vascular plant material that had
experienced various levels of decomposition and some sediment. Sample PC1
contained notable sand and gravel (~10% volume), but was dominated by slightly
decomposed to undecomposed vascular plant material. Sample PC2 contained
moderately decomposed moss with some slightly decomposed vascular plant material
near the top of the sample (<5% volume). Sample PC3 contained roughly equal parts
vascular plant material and moss, both slightly decomposed. Sample PC4 contained
undecomposed to slightly decomposed moss with minor amounts of undecomposed
vascular plant material (<5%).
The results of the water retention experiment are shown in Table 1.9. Samples
PC1, PC2, and PC3 have similar saturated water content and water retention
characteristics. Sample PC3 shows slightly less water retention than PC1 and PC2, but
58
the difference is not discernible when measurement errors are taken into account.
Sample PC4 shows significantly less water retention than the other samples at suctions
above approximately 0.17m. Samples PC3 and PC4 have lower bulk densities (0.16
and 0.12 g cm-3, respectively) than PC1 and PC2 (0.25 and 0.21 g cm-3, respectively).
Sample PC4 has significantly lower saturated water content (76%) than the other
samples (83%). The average saturated water content for all four samples is 81.5%.
These results are consistent with the work of Boelter (1964).
The average solid density of the nine subsamples is 1.15 g cm-3 (σ=0.35). The
solid density for subsamples of PC1 had higher solid density (1.58 g cm-3) and a higher
standard deviation (σ=0.31) than other samples. The higher solid density is attributed to
the presence of approximately 10% sand and gravel by volume in the sample, and the
higher standard deviation is attributed to unequal partitioning of the soil constituents
during sample separation in the lab. Subsamples from PC4 had the lowest solid density
(0.88 g cm-3) and lowest standard deviation (±0.09). Subsamples from PC2 and PC3
had intermediate solid densities and standard deviations of 0.97 (±0.11) and 0.98
(±0.17) g cm-3, respectively.
The results of the peat retention experiments show that the water retention
curves from a montane peatland that experiences heavy winter snowpack are consistent
with earlier studies of peat from significantly different climatic regimes (Boelter, 1964;
Dasberg & Neuman, 1977; Silins & Rothwell, 1998). The water retention in PC4 shows
approximately 10% lower water retention than similar samples (“undecomposed
mosses”) studied by Boelter (1964). This may be due to compression from the heavy
snowpack, a higher level decomposition, or higher vascular plant content. All other
samples fall within the range of samples reported as “partially decomposed mosses” and
“herbaceous peat”.
59
Table 1.9: Physical properties and water retention characteristics of four peat samples
collected from the Grass Lake Research Natural Area, South Lake Tahoe, CA.
Thickness is the saturated thickness of the peat sample at the beginning of the
experiment. Bulk densities (Db) were measured on a saturated volume basis. ρs is the
density of the solids. θ(field) and θ(sat) are the field and saturated water content,
respectively. θ(ψ) is the volumetric water content at suction ψ.
PC1
PC2
PC3
PC4
thickness
thickness
thickness
thickness
(cm)
6.3 (cm)
7.1 (cm)
6.9 (cm)
8.0
Db (g/cc)
0.25 Db (g/cc)
0.21 Db (g/cc)
0.16 Db (g/cc)
0.12
ρs (g/cc)
1.58 ρs (g/cc)
0.99 ρs (g/cc)
1.14 ρs (g/cc)
0.88
θ(field)
0.77 θ(field)
0.82 θ(field)
0.78 θ(field)
0.73
θ(sat)
0.84 θ(sat)
0.83 θ(sat)
0.83 θ(sat)
0.76
ψ (m)
θ (ψ)
ψ (m)
θ (ψ)
ψ (m)
θ (ψ)
ψ (m)
θ (ψ)
0.00 0.84
0.00 0.83
0.00
0.83
0.00
0.76
0.03 0.81
0.03 0.79
0.03
0.79
0.03
0.71
0.06 0.76
0.06 0.77
0.06
0.78
0.06
0.68
0.09 0.74
0.09 0.72
0.09
0.75
0.09
0.65
0.12 0.71
0.12 0.70
0.12
0.73
0.12
0.62
0.17 0.69
0.17 0.69
0.17
0.70
0.17
0.57
0.22 0.68
0.22 0.67
0.22
0.68
0.22
0.55
0.27 0.65
0.27 0.65
0.27
0.65
0.27
0.51
0.32 0.63
0.32 0.63
0.32
0.63
0.32
0.49
0.42 0.60
0.42 0.61
0.42
0.60
0.42
0.46
0.52 0.58
0.52 0.59
0.52
0.57
0.52
0.44
0.82 0.52
0.82 0.54
0.82
0.52
0.82
0.39
1.32 0.47
1.32 0.49
1.32
0.46
1.32
0.35
1.82 0.43
1.82 0.45
1.82
0.42
1.82
0.33
DISCUSSION
Surface water outflows from the peatland exceed surface water inflows by midAugust in 2010 and late-July by 2011. Persistently positive VHGs in many of the
piezometers suggest groundwater discharge from the coarse sediment beneath the peat
for much of the season. Estimates of late-season groundwater flow into Grass Lake
during the 2010 field season are similar to the expected ET requirements of the
peatland. The rate of ET taken from applicable studies ranges from 2.6 to 7.6 mm day-1
(1.0 to 3.0 cfs over 24 hours) with an average value of 5.0 mm day-1 (2.0 cfs over 24
hours). The estimated average values of groundwater flow into the peatland range from
3.8 to 6.6 mm day-1 (1.5 to 2.6 cfs over 24 hours) after August 18, 2010. This suggests
60
that during years with a near average snowpack, late-season groundwater inflows may
be adequate to meet the ET needs of the peatland. Groundwater flow into the peatland
after August 16, 2011 was over 8.4 cfs and was the dominant component contributing to
the water budget of the peatland.
The contribution of water from the dewatering of the peat and lowering of the lake
level may also contribute to stream outflow. This contribution can be estimated using
the average rate of water table drop between mid-July and late-September, 2010 (2.77
mm day -1). Appling the average rate over the 75 day period results in a calculated
water level approximately 0.208 m below the peat surface. This is significantly deeper
than the average water level depth recorded in mid-September (0.123 meters) and
hence represents a maximum estimate. Based on the water retention experiments, a
suction pressure of 0.235 meters would result in a reduction of volumetric water content
of approximately 18%. Assuming a constant rate of water table drop applied over the
entire peat body with an average porosity of 81.5%, the dewatering of peat over a 75
day period could yield 33,100 m3 of water and account for a flow of approximately 0.5
mm day-1 (0.2 cfs over 24 hours). This suggests that dewatering of the peat alone is not
capable of supplying the amount of water necessary to satisfy the late-season water
budget calculations or the expected ET needs of approximately 3.0 to 5.0 mm day-1 (1.2
to 2.0 cfs over 24 hours).
Based on the results of the water retention experiments, peat dominated by
undecomposed moss is expected to release more water than peat dominated by
herbaceous plant material or partially decomposed moss when the water table is
lowered more than 0.17m. A decrease in the water table of this magnitude in an area
where the peat is dominated by moss would result in a reduction of volumetric water
content of approximately 19%. In contrast, the same decrease in the water table for a
peat dominated by partially decomposed moss and/or herbaceous material would result
61
in a reduction of water content of only 14%. As such, areas with peat dominated by
undecomposed and/or living moss are expected to experience a wider range of
volumetric water content due to fluctuations in the water table than areas with peat
dominated by partially decomposed moss and/or herbaceous plants.
The significant differences in water retention characteristics may have important
implications for plant communities, the distribution and movement of water within
peatlands, and the response of the peat surface elevation to changing hydrologic
conditions. The greater loss in volumetric water content may result in exposure to
oxygen, leading to the decomposition of the organic material. This in turn is expected to
result in higher water retention. The expected increase in water retention resulting from
the partial decomposition of the moss may help to slow subsequent decomposition.
62
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Beckers, J., & Frind, E. O. (2000). Simulating groundwater flow and runoff for the Oro
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Journal of Hydrology, 229(3–4), 265-280.
Benedict, N.B., & Major, J. (1982). A physiographic classification of subalpine meadows
of the Sierra Nevada, California. Madrono, 29, 1-12.
Berg, K.S. (1991). Establishment record for Grass Lake Research Natural Area within
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Boelter, D. H. (1964). Water Storage Characteristics of Several Peats in situ. Soil Sci.
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Burke, M.T. (1987). Biological survey of Grass Lake candidate Research Natural Area.
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Clark, D. (2010). [Personal communication regarding unpublished research at Grass
Lake Research Natural Area].
Clymo, R. S. (2004). Hydraulic conductivity of peat at Ellergower Moss, Scotland.
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Comer, N.T., Lafleur, P.M., Roulet, N.T., Letts, M.G., Skarupa, M., & Verseghy, D.L.
(2000). A test of the Canadian land surface scheme (class) for a variety of
wetland types. Atmosphere-Ocean, 38(1), 161-179.
Cooper, D.J., & Wolf, E.C. (2006a). Fens of the Sierra Nevada, California (pp. 47).
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Rangeland and Watershed Stewardship.
Cooper, D.J., & Wolf, E.C. (2006b). The influence of groundwater pumping on wetlands
in Crane Flat, Yosemite National Park, California Report to Yosemite National
Park, Yosemite, CA (pp. 52).
Dasberg, S., & Neuman, S. P. (1977). Peat hydrology in the Hula Basin, Israel: I.
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Green, C.T. (1998). Integrated studies of hydrogeology and ecology of Pope Marsh,
Lake Tahoe. (Master of Science), University of California, Davis.
Halford, K.J., & Kuniansky, E.L. (2002). Documentation of spreadsheets for the analysis
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59-66.
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Berkeley, CA: Pacific Southwest Forest and Range Experiment Station.
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glaciations in the Sierra Nevada, California, from 10Be surface exposure dating.
Quaternary Science Reviews, 30(5–6), 646-661.
Silins, U., & Rothwell, Richard L. (1998). Forest Peatland Drainage and Subsidence
Affect Soil Water Retention and Transport Properties in an Alberta Peatland. Soil
Sci. Soc. Am. J., 62, 1048-1056.
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http://dx.doi.org/10.5069/G9PN93H2
Twidale, C.R., & Vidal Romani, J.R. (2005). Landforms and Geology of Granite Terrains.
London, UK: Taylor & Francis Group.
Valat, Beatrice, Jouany, Claire, & Riviere, Louis M. (1991). Characterization of the
Wetting Properties of Air-Dried Peats and Composts. Soil Science, 152(2), 100107.
64
CHAPTER 2: PIEZOMETER SCALE THERMAL MODELING AND PARAMETER
ESTIMATIONS: IMPLICATIONS OF MODEL STRUCTURE AND THERMAL
BOUNDARY CONDITIONS
ABSTRACT
Accurate measurements of subsurface temperatures can be used to constrain
groundwater flux, as well as hydraulic conductivity when simultaneous measurements of
hydraulic gradient are available. It is shown using analytical and numerical models that
significant differences in subsurface temperatures (1°C) can be expected when the
thermal properties of the piezometer material differ significantly from those of the
surrounding substrate. To demonstrate this, indirect inversion schemes using synthetic
data are used to estimate the original parameters used to generate the data. The
parameter estimation runs with numerical models that specifically model the thermal
effects of the metal piezometer perform significantly better than those that neglect the
influence of the piezometer. In the parameter estimation runs that model the effects of
the piezometer, the inclusion of signal entropy as an observation improves the accuracy
of the parameter estimates. The parameter estimation scheme is applied to field data
collected in Grass Lake, a montane peatland located near South Lake Tahoe, CA.
65
INTRODUCTION
Propagation of heat flux and surface temperature variations into the subsurface
is controlled by both conductive and convective heat transport. Heat transport by
conduction is described by Fourier’s Law and depends only on the effective thermal
properties of the materials present and the temperature gradient. Convection is the
transfer of heat by the movement of fluids. Convection of heat by fluids can cause
subsurface temperatures to deviate significantly from those expected in a purely
conductive regime. The deviation depends on the temperature of the fluids, the fluid
flux, and the direction of fluid flow. The relative role of conduction and convection in a
one-dimensional homogeneous system can be described using the Péclet number.
However, the Péclet number is not applicable to two-dimensional heterogeneous
systems.
In areas of infiltration, surface temperature fluctuations can be carried deeper
into the subsurface than they would be by conduction alone. In areas of groundwater
discharge, surface temperature fluctuations are attenuated quickly with depth and the
temperature signal is influenced by the temperature of the upwelling groundwater.
These trends have led to the use of vertically distributed temperature measurements to
constrain estimates of vertical groundwater flow (Becker, Georgian, Ambrose,
Siniscalchi, & Fredrick, 2004; Bravo, Jiang, & Hunt, 2002; Stallman, 1965). A review of
heat as a groundwater tracer can found in Anderson (2005).
Surface temperature perturbations attenuate with depth as heat energy is stored
in the subsurface material. The temperature signal associated with diurnal changes in
surface temperature are typically limited to the upper 1.5 meters, while larger seasonal
changes can be detected at depths of up to 15 meters (Anderson, 2005). The
appropriate sampling depth for temperature depends on the magnitude and duration of
surface energy inputs, the thermal conductivity of the substrate, and the groundwater
66
flux. For example, Silliman et al. (1995) used temperature measurements in the upper
0.15 meter to constrain downward groundwater flow in a losing stream with diurnal
surface water temperature variations on the order of 5ºC. Similarly, Becker et al. (2004)
used temperature measurements in the upper 0.1 meter of a streambed to estimate
groundwater discharge to sections of a gaining stream with similar temperature
fluctuations. Bravo et al. (2002) used temperature measurements in the upper 5.5 feet
(1.67 meters) to constrain annual groundwater flow to a wetland with annual air
temperature variations on the order of 30ºC. Constantz et al (2001) suggest that a depth
of approximately 0.15 meter is optimal for detecting temperature disturbances
associated with recharge events on the order of 20 mm/hr (0.79 in/hr) in ephemeral
streams of the American southwest.
The installation of monitoring equipment with thermal properties that differ
significantly from those of the surrounding substrate has the potential to disrupt the heat
flow regime in the vicinity of the instruments, especially at the shallow depths affected by
diurnal temperature fluctuations. Alexander and MacQuarrie (2005) used laboratory
tests, field experiments, and numerical models to investigate the influence of different
piezometer materials on subsurface temperatures. The piezometers in their study were
constructed of PVC, which has low thermal conductivity (κ=0.2 W m-1 K-1) and low
volumetric heat capacity (Cv=1950 kJ m-3 K-1), and or stainless steel, which has high
thermal conductivity (κ=16.0 W m-1 K-1) and high volumetric heat capacity (Cv=3935 kJ
m-3 K-1). All of their tests involved piezometer installations in saturated sand or gravel
with a moderately high bulk thermal conductivity (2.2 W m-1 K-1) and moderate volumetric
heat capacity (Cv=2120 kJ m-1 K-1). They concluded that the installation of piezometers,
regardless of the material, did not significantly affect subsurface temperatures.
In this investigation of the groundwater system supporting a montane peatland,
durable stainless steel piezometers were installed due to the heavy winter snow pack
67
and harsh weather conditions. The high organic content of peat results in a significantly
lower bulk thermal conductivity, with values as low as 0.2 W m-1 K-1 (Farouki, 1986;
Kettridge & Baird, 2007). Installation of stainless steel piezometers in peat results in a
much higher contrast in thermal conductivity than that explored by Alexander and
MacQuarrie (2005).
This study uses synthetic data generated from a heterogeneous numerical model
that explicitly models the effects of a metal piezometer. Four sets of randomly
generated parameters are used to explore the ability of the parameter estimation
scheme to recover the original parameter values. The implementation of an ordinary
differential equation describing heat flux and heat storage in the surface water layer is
compared to a specified temperature boundary condition along the top boundary. The
parameter estimation scheme is applied to field data collected in a piezometer located
along the edge of Grass Lake, the largest peatland in the Sierra Nevada Mountains of
California. Consideration of the thermal properties of the piezometer and the heat flux
boundary condition was motivated by the need to investigate the discrepancy between
the model results and field data.
Background
Peatlands are wetlands with thick organic soils that have formed in place.
Peatlands provide unique habitats, covering 3% of the Earth’s surface and making up
only 0.1% of the mountain landscape (Clymo, 2004; Cooper & Wolf, 2006b). In many
areas of the Sierra Nevada Mountains peatlands are the only source of perennial
moisture and support ecosystems with high biodiversity. The largest peatland in the
Sierra Nevada is Grass Lake (~82 ha), located on Luther Pass, south of Lake Tahoe,
California. High evapotranspiration rates and low summer precipitation in the Sierra
Nevada Mountains suggest that most, if not all, montane peatlands in the Sierra Nevada
68
are sustained by substantial groundwater input. Peatlands that are sustained by
groundwater input are termed “fens” (Benedict & Major, 1982; Cooper & Wolf, 2006b).
Models of topographically driven groundwater flow through homogeneous media,
in which the water table is represented as a subdued replica of surface topography,
indicate significant vertical discharge in areas located at the base of hillslopes (Toth,
1963). In models of heterogeneous systems, a discontinuous lens of higher permeability
substrate overlain by low permeability substrate results in the focusing of significant
vertical discharge towards the down gradient end of the high permeability lens (Freeze &
Witherspoon, 1967). Lowry et al. (2009) presented evidence that suggests groundwater
springs in the Allequash Wetland, a peatland in Northern Wisconsin, are associated with
the thinning of the sand/gravel aquifer. The thinning is associated with the steepening of
the peat-aquifer contact and increased peat thickness with distance from the peatland
margin. Flow models from their study show dominantly vertical flow through the
relatively impermeable peat layers near this transition. At Grass Lake the peat is
typically underlain by coarse sand and gravel deposits. The thickness of the peat
increases with increasing distance from the edge of the peat. We assume that the
topography and geometry of the peat underlying sediment results in dominantly vertical
flow through the less permeable peat. This assumption is thought to produce negligible
errors in temperature based estimates of flow when horizontal heat and fluid flows are
<10% of the vertical (Lu & Ge, 1996).
Motivation
Diurnal fluctuations in air temperature at Grass Lake during the 2010 and 2011
field seasons ranged from 10 to 20 degrees Celsius, with a maximum temperature of
35°C and a minimum temperature of -5°C during the s tudy period. Figure 2.1 shows a
6-day period of recorded air temperature, temperature inside the piezometer at 13 cm
below the peat surface (bgs), and temperature in the peat 20 cm away from the
69
piezometer and 12 cm bgs. The maximum air temperature (~30°C) occurred within a
couple hours of noon, depending on the day. The maximum temperature in the
piezometer (~16°C) and the peat (~19°C) occurred ap proximately 9 hours later (21:00).
The minimum air temperature (~3°C) was recorded aro und dawn (6:00) and the
minimum temperature inside the piezometer (~11°C) w as recorded within an hour of the
minimum air temperature. However, the minimum temperature recorded in the
surrounding peat (~14°C) occurred approximately 4 h ours later (10:00). The difference
in maximum and minimum temperatures, and the difference in timing between the
minimum temperature in the piezometer and peat, prompted consideration of the
influence of the piezometer material on heat transport and the resulting temperature
record.
Recorded Temperatures at Piezometer S4
30
Temperature (C)
25
20
15
10
5
air
peat, 12 cm bgs
piezometer, 13 cm bgs
0
-5
7/16/2010
7/17/2010
7/18/2010
7/19/2010
7/20/2010
7/21/2010
7/22/2010
Date
Figure 2.1: Six day temperature record for air, saturated peat 20 cm from the piezometer
(12 cm bgs), and water within the piezometer (13 cm bgs).
METHODS
Approach
An analytical model of subsurface heat transport with homogeneous thermal
properties is compared to a numerical model with heterogeneous thermal properties
70
representing various piezometer materials installed in various substrates. Piezometers
of various lengths were installed within Grass Lake. The length of the piezometers and
measured depth to sand were used to define the model domains. Temperature data
was extracted from the models at depths corresponding to the average depth of
pressure transducers and temperature loggers installed in the field. Impacts of including
the heterogeneity associated with the metal piezometer material (numerical model) are
evaluated by comparing the results of the heterogeneous numerical model to those of
the numerical and analytical models with homogeneous properties. The homogeneous
numerical model (without the metal piezometer) produces the same results (±<0.01°C)
as the analytical model.
The analytical solution uses a specified temperature boundary condition along
the upper surface, usually approximated by air temperature. A boundary condition that
includes consideration of atmospheric and ground heat fluxes is more applicable to real
world situations. Numerical simulation results using the specified temperature boundary
condition equal to air temperature are compared to numerical simulation results using
the atmospheric heat flux boundary condition. Natural convection due to uneven heating
of water inside the piezometer is addressed through consideration of the Nusselt
number, which is the ratio of heat transferred by natural convection to the heat
transferred by conduction alone (see Numerical Model section below).
Indirect inversion of the numerical models using UCODE ((Poeter, Hill, Banta,
Mehl, & Christensen, 2005) is used to estimate the values of important thermal and
hydrologic parameters. Synthetic observations are generated using random parameter
values in the heterogeneous model. The parameter estimation process is tested by
attempting to recover the original parameter values used to generate the synthetic data.
The results of the parameter estimation process using the heterogeneous model is
compared to the results using a homogeneous numerical. The effect of adding the
71
entropy of the temperature time series as an observation in the parameter recovery
process is explored. The parameter estimation process is applied to data collected in
Grass Lake.
Data Collection
Peat depth was measured near each piezometer using an extendable probe up
to a depth of 5 meters. Peat depths increase at a rate of approximately 10% (0.1 m/m)
from the shore for the first 10 to 30 meters in most locations, beyond which the depth to
the coarse sediment increased rapidly. Resistant layers and/or probe instability in the
deep, soft peat prevented deeper exploration. Coarse sand and gravel deposits were
easily identified based on the feel of the probe moving through the material and
confirmed by inspection of the sediment removed during piezometer installation. Coarse
sediment deposits from 0.1 to 0.5 meter thick were measured below the peat. On the
alluvial fans, peat thickness was more variable and often contained interbedded layers of
coarse sediment and peat on the order of 0.1 and 1.0 meter (0.3 to 3.0 ft) thick,
respectively.
Piezometers constructed of 1.25-inch nominal schedule 40 pipe were installed
along the edge of Grass Lake. The position chosen for each piezometer was based on
the presence of surface water features (streams, springs, seeps, pools),the upslope
geology, vegetation density, and peat depth. The piezometers were installed
approximately 1 to 3 meters (3 to 10 feet) shoreward of where the depth to the
sand/gravel deposits, and hence peat thickness, began increasing rapidly. The 6”
(~15cm) screened interval of each piezometer was placed at a depth of 4.2 to 9.2 feet
(1.3 to 2.8 meters), located in the sand and gravel layers that underlie the peat. Water
temperature was measured both inside and outside (surface water) at each piezometer
during field visits.
72
Piezometers were instrumented with Solinst Gold Levelloggers near the bottom
of the piezometer and Onset TidBit v2 data loggers at various depths. The Gold
Levelloggers record pressure with a stated accuracy of 2.5 mm (resolution < 0.1 mm)
and temperature with a stated accuracy of ±0.05°C ( resolution 0.03°C). The TidBit v2
temperature sensor records temperature with a stated accuracy of ±0.2°C (resolution of
0.02°C). Atmospheric pressure and air temperature were recorded using Solinst
Barologgers at two locations along the north edge of Grass Lake. The pressure from
each Levellogger was corrected for fluctuations in atmospheric pressure using the
Barologger data. Temperature and head were logged at hourly or shorter intervals.
Data from piezometer S4 is used in the parameter estimation procedure discussed
below.
The uneven peat surface resulted in measurement uncertainties in the depth of
the surface water present. The surface water depth was measured from the interface
between the low density, living portion of the peat (acrotelm) and the higher density,
nonliving portion of the peat (catotelm). The maximum depth of surface water within
one meter of each piezometer was measured. A correction factor is considered in the
parameter estimation procedure to address the difference between the measured water
depth and the effective water depth influencing heat exchange with the atmosphere (see
Numerical Model section below). The depths of the instruments were measured from
the piezometer rim and estimated to accurate to within 2cm, less than the diameter of
the instrument. The distance to the phreatic surface inside and outside of the piezometer
was measured to +/- 1.6mm (0.0625-inch), allowing calculation of the vertical hydraulic
gradient to better than 0.1%.
73
Analytical Model
Heat transport influenced by fluid flow is described by coupling the governing
equations for heat diffusion and fluid flow. The one-dimensional (1D) heat transport
equation can be written as (Domenico & Schwartz, 1998):
∂Ti
∂ 2 T nρ c
∂T
= α 2i − w w v z i (1)
∂t
∂z
ρ ' c'
∂z
where Ti is the temperature, vz is the steady-state average linear velocity of the water, n
is the porosity, ρ’ is the bulk density of the saturated substrate, c’ is the specific heat
capacity of the saturated substrate, and α is the thermal diffusivity of the saturated
material, calculated as the ratio of the effective bulk thermal conductivity (κe) and the
bulk volumetric heat capacity of the saturated material (C’=ρ’c’). The bulk volumetric
heat capacity of the saturated material is calculated as:
C ' = nCw + (1 − n)Cs
(2)
where Cs is the volumetric heat capacity of the solids (ρscs) and Cw is the volumetric heat
capacity of water (ρwcw).
Given the following initial and boundary conditions:
Ti ( z,0) = 0,
Ti (0, t ) = ∆Ti ,
(3)
Ti ( z → ∞, t ) = 0,
the analytical solution to equation (1) given (3) is:
Ti ( z, t ) =
∆Ti
2

 z − βt 
 z + βt 
 βz 
 + exp erfc

erfc
α 
 2 αt 
 2 αt 

74
(4)
where ∆Ti is the magnitude of temperature perturbation at the boundary, erfc is the
complimentary error function, and β=( ρwcw/ρ΄c΄)nvz. Equation (4) describes the
propagation of a single temperature perturbation (∆Tw) into the subsurface. By the
principle of superposition, and given an initial homogeneous temperature To equal to the
temperature at z=∞, the temperature resulting from a series of temperature perturbations
can be written as:
T ( z , τ ) = To + ∑ Ti ( z, ti )
(5)
where τ is the time since the beginning of the simulation and ti is the time elapsed since
temperature perturbation i. The sum indicates the cumulative effects of all prior
temperature perturbations (Ti).
The analytical model described above has been used to estimate groundwater
recharge (Silliman et al., 1995) and discharge (Becker et al., 2004) in streams. This
formulation assumes a homogeneous medium, steady-state fluid flow, and a uniform
initial temperature equal to the temperature at z=∞. The specified temperature along the
upper boundary is allowed to vary with time.
Numerical models that include material heterogeneity, transient fluid flow, and
specified flux boundary conditions are more computationally expensive, but may be
more applicable to real world field applications. The simulated temperatures and
parameter estimation using the analytical model above are compared to those from
numerical models that explicitly model the effects of the pipe and account for
atmospheric heat fluxes.
Numerical Model
Numerical models that include heterogeneity and transient boundary conditions
were constructed using the COMSOL numerical modeling package. The model domain
75
was designed to explore the effects of a metal pipe with high thermal conductivity (16 W
m-1 K-1) installed in organic soils with low bulk thermal conductivity (0.5 W m-1 K-1). A
two-dimensional axisymmetric model was constructed with the center of the piezometer
located at the origin. The model domain (Figure 2.2) represents four different materials:
1) saturated substrate, 2) a 1¼-inch nominal, schedule 40 stainless steel pipe, 3) the
water column inside the pipe, and 4) the underlying sediment. The bulk thermal and
hydrogeologic parameters of each material were taken from the available literature and
are listed in Table 2.1.
The model domain is 1.5 m in the vertical direction with a radius of 1.0 m,
representing a 4.7 m3 volume. The center of the pipe is located at r=0, the inner radius
of the pipe is 17.5 mm, the outer radius is 21.0 mm, and the thickness of the metal is 3.5
mm. The domain is discretized using 9099 triangular mesh elements. The 4801 nodes
are spaced 5mm along the edge of the domain (r=0) and the top of the peat surface
(z=0). Node spacing is allowed to increase to approximately 10cm along the other
edges of the domain.
The constant vertical flux required for the solution of the analytical model was
implemented in the numerical model by assigning constant specified head boundary
conditions along the top and bottom of the domain. The head along the upper boundary
(hu)is specified as zero and the head along the bottom boundary (hb) is specified as 0.15
meters. This imposes a steady-state vertical hydraulic gradient of 10%, a typical value
observed in the spring and summer at Grass Lake (Chapter 1). Although the hydraulic
conductivity of the peat (Kh) and sand are likely different, they are assigned the same
hydraulic conductivity in these simulations in order to compare results with the same
vertical flux. The assumption of steady-state fluid flow is relaxed in the simulations using
field data. The sides of the domain (r=0 and r=1.0) are no flow boundaries.
76
Figure 2.2: Geometry and mesh for the numerical models.
77
Table 2.1: Parameters used in comparison between numerical and analytical models.
(Domenico & Schwartz, 1998; Farouki, 1986; Ivanov, 1981)
Thermal
Heat
Density
of
Hydraulic
Conductivity,
Capacity of
bulk saturated
Solids
Material Porosity Conductivity
Material
(W m-1 C-1)
(J kg-1 C-1) (kg m-3)
(%)
(m s-1)
sand
2.2
800
2650
30
5.0E-06
peat
0.5
1900
400
80
5.0E-06
metal
16.0
490
8030
0
1.0E-20
PVC
0.2
1500
1300
0
1.0E-20
water
0.6
4174
1000
100
1.0E-20
The thermal boundary conditions required for the analytical solution are
implemented in the numerical model by assigning a specified temperature boundary
condition along the top and bottom of the domain. The analytical solution assumes a
constant temperature equal to the initial temperature at z=∞. This is approximated by
assigning a specified temperature, equal to the initial temperature, along the lower
boundary (z=-1.5m). A sinusoidal function of temperature ranging from 25ºC to 5ºC with
a period of 24 hours is used to represent diurnal fluctuations in temperature along the
upper boundary. This assumes thermal equilibrium between the air and the surfaces of
the piezometer and peat, a requirement for comparison with the analytical solution. The
assumption of thermal equilibrium between the air and the peat surface is relaxed in the
parameter estimation runs, where energy exchange with the atmosphere and heat
storage in the surface water is considered.
Comparison of Analytical and Numerical Models
The solution to the analytical model is called simulation “A.” The numerical
model (versions B,C, and D) are compared with the results of the analytical model,
referred to as simulation “A”. Simulation “B” mimics the analytical solution by assigning
the same thermal and hydrologic properties of the substrate to the pipe and enclosed
water, effectively creating a homogeneous domain. The upper portion of the pipe (z>0)
is retained in the homogeneous numerical simulations. For numerical simulations that
78
include a pipe, convective heat transport is eliminated in the pipe and enclosed water.
The effects of explicitly modeling the thermal properties of a PVC, and of a metal
piezometer, along with the enclosed water, are addressed in simulations “C” and “D”,
respectively. Equivalent boundary and initial conditions were used for all simulations (A,
B, C, and D). The same mesh was used for simulations B, C, and D.
Natural Convection of Piezometer Fluids
Heat flow due to natural convection inside the piezometer is approximated by
consideration of the Nusselt number (NuL). The Nusselt number is the ratio of convective
heat transfer to conductive heat transfer:
N uL = qL
α∆E
(6)
where q is the heat flux, α is the thermal diffusivity, and ∆E is the difference in energy
density over the characteristic length (L). The difference in energy density is the
product of the volumetric heat capacity (C=ρc) and the change in temperature (∆T).
Using the definition for the thermal diffusivity of water (α=κ/cp ), equation (6) can be
rewritten as:
q = N uLκ
∆T
L
(7)
Exploiting the similarity between equation (7) and Fourier’s Law used to describe heat
conduction in the numerical models, heat transport by natural convection inside the
piezometer is modeled using an effective thermal conductivity (κpw) equal to:
κ eff = N uLκ w
(8)
where κw is the thermal conductivity of water.
79
Correlation equations are often used to describe the Nusselt number for systems
in which the geometry influences heat flow (Churchill & Chu, 1975). For natural
convection, the Nusselt number is often expressed as a function of the Rayleigh number
and the Prandtl number. The Rayleigh number is a dimensionless number that
expresses the ratio of buoyancy forces to viscous forces (Churchill & Chu, 1975):
Ra =
L3 gβ w ∆T
(9)
ν wα w
where g is the acceleration due to gravity, βw is the thermal expansion coefficient of
water, and νw is the dynamic viscosity of water. The Prandtl number is a dimensionless
number that expresses the ratio of momentum diffusion through viscosity to thermal
diffusion (Churchill & Chu, 1975):
Pr =
νw
αw
(10)
The correlation equation for flow around a vertical pipe can be calculated as (Churchill &
Chu, 1975):
N uL = 0.68 +
0.670Ra L
1/ 4
[1 + (0.492 / Pr ) ]
9 / 16 4 / 9
(11)
The correlation equation (11) is valid when the curvature of the pipe does not
interfere with flow, specifically when D/L>35(Pr/RaL)1/4 where D is the diameter of the
pipe and L is the length of the interface between the pipe surface and the fluid. This
condition is not satisfied for the piezometers and temperature ranges in this study.
However, in the absence of any applicable correlation equations in the literature, and
assuming the curvature effects would tend to inhibit flow, equation (11) is assumed to
80
provide a reasonable maximum estimate of the ratio between conductive and convective
heat transport due natural convection.
The Rayleigh number was calculated to be 2.4x108 for the approximate
temperature range recorded in the field (3 to 20 °C ) and a characteristic length equal to
the approximate length of pipe above ground (0.1 m). This reasonably high value
suggests heat transport due to natural convection may be important. The Prandtl
number is approximately 7.0 for water under ambient conditions. Equation (11) gives a
value of approximately 61 for the Nusselt number. This suggests the maximum heat
transfer due to natural convection is on the order of 61 times higher than the thermal
conductivity of still water. Increased thermal transport by natural convection inside the
piezometer is approximated by considering an effective bulk thermal conductivity of the
enclosed water (κpw) ranging from 0.58 to 36.0 W m-1 °C -1.
Initial Conditions
The initial temperature of the entire domain for all models used to explore the
influence of the piezometer material is 5.0 ºC. The initial head is defined as a linear
function of depth, with head along the top of the model equal to zero and head along the
bottom equal to 0.15 meters. The simulation period used to explore the effects of the
piezometer materials represents 6 days.
In the numerical models used for the parameter estimation, the initial
temperature profile was calculated assuming a semi-infinite solid with a uniform initial
temperature equal to the temperature at depth (T∞) with constant surface heating (Ts).
The solution to this problem is given by Carslaw and Jaeger (1959):
 −z 

T (z, t ) = T∞ + (Ts − T∞ ) * erfc
 2 α pt 


(12)
81
where erfc is the complimentary error function. The temperature recorded by the lowest
sensor at the start of the field season was taken as the temperature at depth (T∞). The
position and average daily temperature of the sensor in the peat was used for z1 and
T(z=z1,t=0) in equation (12), respectively. Equation (12) is solved for t0, the time since
surface heating began, during each parameter estimation iteration and used to calculate
T(z,0) for all depths.
Atmospheric Heat Exchange
Heat flux from various atmospheric components plays an important part in driving
shallow subsurface temperatures. According to Brookfield (2009), neglecting
atmospheric thermal components in simulations can result in simulated temperature
differences of up to 10°C in the shallow subsurface (<10cm depth), with the relative
importance of the components varying depending on site conditions. We consider long
wave and short wave radiation fluxes, latent heat flux, and sensible heat flux to
determine the thermal boundary condition along the upper boundary of the models
based on the literature and data discussed below.
Researchers from the Tahoe Environmental Research Center have been
collecting incoming shortwave and longwave radiation data at Lake Tahoe since 1998.
Data from the summers of 2010 and 2011 show daily incoming shortwave radiation with
an average maximum value of approximately1050 W m-2 between 12:00 and 15:00, and
an average minimum value of approximately zero from 22:00 to 6:00. The energy flux
across a surface due to shortwave radiation is described by:
Q net
= (1 − rs ) K ↓
K
(13)
where rs is the albedo or reflection coefficient and K↓ is the incoming shortwave radiation.
Shortwave radiation input is assumed to be negligible along the vertical surface of the
82
piezometer due to the vertical orientation and high reflectivity of the material. The
albedo for meadows ranges from 0.03 for meadows inundated with water to 0.17 for
meadows dominated by vascular plants (Chen et al., 2011; Gao & Merrick, 1996;
Kellner, 2001; Peltoniemi et al., 2010).
Data from the summers of 2010 and 2011 show incoming longwave radiation
typically varied between 250 and 350 W m-2, with values typically above 300 W m-2 and
a diurnal amplitude of approximately 60 W m-2. Outgoing longwave radiation can be
approximated using the relationship:
QLout = σTg
4
(14)
where σ is the Steffan-Boltzman constant [W m-2 K-4] and Tg is the temperature of the
ground [K] (Fassnacht, Snelgrove, & Soulis, 2001). Net longwave radiation (QLnet) is the
difference between the incoming and outgoing longwave radiation.
The latent heat flux is the heat removed from the system due to the conversion of
liquid water to water vapor during evaporation and transpiration (“evapotranspiration”).
The prevalence of clear skies and relatively low humidity in the Lake Tahoe region
suggest that the latent heat flux is an important component of the energy balance.
Priestly and Taylor (1972) show that the heat flux due to evapotranspiration in the
absence of advective effects (i.e. wind) can be approximated using a modified form of
the Penman equation:
Qr =
δ (NR − G )
, for NR >0
(δ + γ )
Qa = K crop Qr
(15)
(16)
83
where Qr is the reference latent heat flux, δ is the slope of the vapor pressure vs. air
temperature curve [kPa C-1], γ is the psychrometric constant [kPa C-1], NR is the net
radiation [W m-2], and G is the ground heat flux. The actual latent heat flux is given by
Qa and Kcrop is defined as the ratio of actual latent heat flux to the latent heat flux from a
reference crop. The reference crop is typically a well watered lawn with ample moisture.
Kellner (2001) found that the mean value of Kcrop ranged from 0.61 to 0.77 for a
sphagnum peatland in Sweden. The value δ was calculated using the relationship
presented by Hidalgo et al. (2005):
es = 0.6108e (17.27Ta / (Ta + 237.3))
(17)
δ = 4099es / (Ta + 237.3)2
(18)
where es is the saturation vapor pressure and Ta is the air temperature. The
psychrometric constant appearing in equation (15) is defined as:
γ = ca Pa /(0.622 ∗ λw )
(19)
where ca is the heat capacity of air [J kg-1 K-1], Pa is the atmospheric pressure [kPa].
Sensible heat is the amount of heat energy exchanged between a surface and
the air due to differences in temperature only. The sensible heat flux was calculated
using the CLASS scheme described by Verseghy (1991):
Qh = ρ a ca va C D (Ta − Ts )
(20)
where ρa is the density of air (1.2 kg m-3), va is the wind speed (1.8 m s-1 estimated), CD
is the drag coefficient (0.002), Ta is the air temperature, and Ts is the surface
temperature. In this formulation a positive Qh indicates heat flow from the air into the
84
model domain. The thermal boundary condition along the surface of the piezometer is
defined as the sensible heat flux.
Implementation of Atmospheric Heat Exchange
Atmospheric heat exchange was implemented by solving the following ordinary
differential equation (ODE) describing heat flux and thermal storage in a shallow surface
water layer:
dT
= (QKnet + QLnet − Qa + Qh + G ) ( ρ wCwd sw )
dt
(21)
where dsw is the depth of surface water. The ground heat flux (G) is calculated as the
sum of the nodal heat flux along the peat surface divided by the length of the peat
surface. A positive value for G indicates heat flow from the ground (numerical domain)
into the surface water boundary layer. Equation (21) is solved for T for each time step
and the resulting temperature is applied as a Dirichlet boundary condition along the
upper boundary.
Field measurements of the depth of surface water vary significantly due to the
uneven nature of the peat surface. It is assumed the effective surface water depth is ½
the maximum water depth measured within 1m of the piezometer. However, the effects
of this assumption are explored by calculating an effective depth (dsw) based on the
maximum depth recorded in the field (dm) using a multiplication factor (fsw) such that :
d sw = f swd m
(22)
Entropy
Nonlinear regression of complex models with multiple parameters are often illposed in the sense that multiple non-unique parameter sets may exist that produce local
minima in the objective function (Poeter et al., 2005). Initial parameter estimation
85
attempts using only hourly temperature data failed to recover the original parameter
values and produced a poor fit to the synthetic observations. This failure was attributed
to the presence of local minima in the objective function. Inspection of the temperature
time series of the synthetic observations and that resulting from the parameter
estimation process revealed significant differences in the complexity of the signal.
Entropy, in the context of Information Theory, is used to quantify the amount of
information contained in a signal. The entropy of a signal is defined as:
H ( X ) = − ∑ pi ( x ) log pi ( x )
(23)
where p(x) is the probability mass function of X. The entropy of a system increases as
the number of potential states increases. Conversely, repetition of states leads to a
reduction in entropy. A system with only one potential state (x’) and probability density
p(x)=δ(x-x’), where δ is the Dirac delta function, will have zero entropy. When the base
of the logarithm is 10, the units of H(X) are “dits.”
Following Shannon’s (1948) interpretation of entropy as a measure of information
contained in a signal, a model that fails to reproduce the entropy of a signal fails to
accurately simulate the information contained in the forcing data and/or the conveyance
of information through the system. Following this line of reasoning, the entropy of each
temperature time series is treated as an observation in the sensitivity analysis and
parameter estimation runs. The probability density function used to calculate the
entropy for each signal is defined as:
pi ( x ) =
ni
N
(24)
86
where ni is the number of hourly temperatures (rounded to the nearest 0.1°C) equal to Ti
and N is the total number of unique hourly temperature values contained in the overall
signal.
Observation Weights
The weights assigned to observations need to produce weighted residuals that
all have the same units and reflect the errors associated with the observations (Hill &
Tiedeman, 2007). In these simulations, the weight is calculated as:
wi = 1
σi2
(25)
where σi is the standard deviation of the observation. The instrument resolution of 0.2°C
was used as the standard deviation for all hourly temperature measurements. The
standard deviation of daily mean temperatures was also assumed to be 0.2°C. The
standard deviation of the entropy was estimated to be 0.02 dits based on the
reproducibility of entropy calculations from simulations with the same parameters. This
represents a change in pi of 1/72 or 1.4%.
A weight multiplier is used to adjust the contribution of each group of
observations to the overall objective function. The observations in this study are
grouped into: hourly temperature, daily mean temperature, and entropy. A weight
multiplier of 1.0 was assigned to the hourly temperature measurements and a weighting
factor of 24 is assigned to the daily mean temperature group. This achieves similar
overall contributions to the objective function for the 720 hourly temperature
measurements and the 30 daily mean temperature measurements. Weighted residuals
from the sensitivity analysis suggest a weight multiplier of 24.0 applied to the group of
entropy observations (n=3) would result in a contribution to the objective function similar
to that for the other groups of observations.
87
Model Sensitivity
The process model described above, with atmospheric heat flux components,
contains eight unknown parameters: αp, Kcrop, Kh, rs, κpw, fsw, Ts, and T∞. Reasonable
parameter values were determined from the available literature (Table 2.2) and used to
generate a synthetic temperature time series representing observations. The response
of the model to a change (perturbation) in each parameter value (Table 2.3) is
evaluated. These perturbations produce a significant change in the model output and/or
represent the maximum range of parameter values expected. The perturbation amounts
used to determine sensitivities in each parameter estimation run are 1/5th the
perturbations used in the original sensitivity analysis. For convenience, the log
transformed values of Kh and αp are reported.
Table 2.2: Parameter values influencing heat flow in numerical simulations involving
atmospheric heat exchange. Values are based on data reported in the cited literature.
Parameter
High
Low
Sources
Campbell and Williamson (1997); Kellner
(2001); Priestley and Taylor (1972);
Kcrop
1.10
0.60
Thompson, Campbell, and Spronken-Smith
(1999)
Ivanov (1981); Letts, Roulet, Comer, Skarupa,
log(Kh)
-3.66
-8.00
and Verseghy (2000); Lowry et al. (2009);
(log[ms-1])
Price (2003)
Farouki (1986); Kettridge and Baird (2007);
log(αp)
-6.76
-7.88
Letts et al. (2000); Peters-Lidard, Blackburn,
(log[Wm-1K-1])
Liang, and Wood (1998)
Chen et al. (2011); Gao and Merrick (1996);
rs
0.17
0.03
Kellner (2001); Peltoniemi et al. (2010)
κpw
36.0
0.58
Welty, Wicks, Wilson, and Rorrer (2008)
(Wm-1K-1)
Field observation assuming the effective
fsw
1.10
0.10
surface water depth ranges from 110% to 10%
of the maximum measured depth (dm)
Average daily air temperature recorded in the
Ts
15.0
7.0
field
T∞
5.0
3.0
Temperature recorded in bottom of piezometer
88
Table 2.3: Parameter values used in the sensitivity analysis and generation of synthetic
data used in parameter estimation. Perturbation amounts used in the parameter
estimation procedure were 1/5th of the values listed here.
Initial
Perturbation Perturbed
Parameter
Value
Amount
Value
Set 1
Set 2
Set 3
Set 4
Kcrop
0.80
0.2
0.96
0.79
0.92
0.66
0.75
log(Kh)
-5.00
-0.2
-4.00
5.72
5.04
7.45
4.57
log(αp)
-7.06
-0.1
-6.35
7.13
6.90
6.60
6.80
rs
0.13
0.5
0.20
0.09
0.19
0.15
0.14
fsw
0.50
1.5
1.25
0.45
1.08
0.81
0.76
Κpw
14.00
1.5
35.00
9.38
18.87
23.47
49.05
Ts
10.00
0.5
15.00
7.90
11.74
10.64
7.72
T∞
3.0
0.5
4.00
3.38
4.25
3.48
3.71
Parameter Estimation Approach
The inverse modeling package UCODE facilitates parameter estimation for a
given process model or set of models. The estimation process uses a modified GaussNewton method for nonlinear regression to minimize the sum of squared weighted
residuals (SSWR) between the output from the process model with a given set of
parameters and the values of the observations the model is intended to simulate (Poeter
et al., 2005). Sensitivities for simulations in this study were derived by perturbing the
parameter values, running the process model, and comparing the resulting SSWR to
that of the results of the model with the unperturbed parameter values.
To test the ability of the parameter estimation approach, we used the numerical
model with a metal piezometer and heat flux boundary condition to generate four sets
synthetic data representing 10 days of hourly temperature observations. The parameter
values were taken from a uniform distribution with upper and lower limits defined by the
literature values (Table 2.3). The synthetic observations were extracted from the model
domain at three sampling locations: shallow peat (r1=100mm, z1=150mm), shallow
piezometer (r2=0mm, z2=150mm), and mid-piezometer (r3=0mm, z3=500mm). The daily
89
mean temperatures and hourly temperatures at each sampling location were used as
observations for PE1. The signal entropy was added as additional observations to PE2.
Indirect inversion with UCODE is used to estimate the parameter values that best
reproduce the synthetic observations generated using four sets of parameters.
Parameter estimates using the homogeneous numerical model with air temperature
defining the upper boundary condition (PE1A and PE2A) are compared to those
estimated using the heterogeneous numerical model that include a metal piezometer
and atmospheric heat exchange (PE1B and PE2B). The homogeneous numerical
model has been shown to closely approximate the analytical solution. The three most
sensitive parameters (Kcrop, log(Kh), and log(αp)) determined from the sensitivity analysis
(below) are used in the PE1B and PE2B parameter estimation. Atmospheric heat
exchange is not considered in PE1A and PE2A. As such, only log(Kh), and log(αp) are
estimated. The approach used in PE2B is applied to field data collected at piezometer
S4 (Chapter 1).
Instrument uncertainty and environmental noise in the temperature signal were
considered in the indirect inversions using the synthetic data as observations.
Uncertainty in air temperature was addressed by adding uniformly distributed noise
between ±2.5°C to the air temperature data. This s hift in air temperature was used to
generate the synthetic data but not used in the parameter estimation iterations.
Instrument uncertainty was addressed by shifting the synthetically generated
temperature records for each location by a random number taken from a uniform
distribution between ±0.1°C.
90
RESULTS
Comparison of Analytical and Numerical Models
Results for the analytical and numerical simulations with sand as the substrate
are presented in Figure 2.3. The close match between the analytical model (As),
homogeneous (Bs), PVC piezometer (Cs), and metal piezometer (Ds) numerical models
support the conclusion of Alexander and MacQuarrie (2005). That is, the piezometer
material does not significantly affect the temperature in the subsurface when the
substrate has a sufficiently high thermal conductivity, such as sand. The difference
between all numerical models and the analytical solution is always less than 0.2ºC. The
discrepancy is greater at shallow depths and more pronounced in the simulations that
include a PVC pipe, which results in the highest contrast of thermal properties.
Results for the simulations with peat as the substrate are presented in Figure 2.4.
Simulations with the explicitly modeled metal piezometer in peat (Dp) show a significant
deviation from the analytical solution, while the other simulations (Bp and Cp) match the
analytical solution relatively well. The high thermal conductivity of the metal piezometer
in the low thermal conductivity peat results in the extrema being shifted approximately 3
hours earlier at a depth of 10cm, and approximately 6 hours earlier at a depth of 20cm.
The diurnal temperature fluctuations in simulation Dp are approximately 4.9 ºC at a depth
of 10cm, while those in the other simulations are 3.2ºC. The maximum daily
temperature at a depth of 10 cm after 6 days is approximately 1.4ºC higher in simulation
Dp than the other simulations, while the minimum temperature is 0.2ºC lower. The
diurnal fluctuation at 20cm is less than 0.5ºC in simulations Ap, Bp, and Cp, but increases
to approximately 0.9ºC for simulation Dp. The close fit between simulations Ap, Bp, and
Cp suggests that the low thermal conductivity of the PVC has a negligible impact on
subsurface temperatures.
91
Figure 2.3: Simulation results with sand as the substrate. The analytical solution (As)
closely matches the numerical solutions (Bs, Cs, and Ds), regardless of the piezometer
material or lack thereof.
92
Figure 2.4: Simulation results with peat as the substrate. The analytical solution (Ap)
closely matches the numerical simulation with homogeneous thermal properties (Bp) and
the numerical solution that explicitly models the effects of the PVC pipe (Cp). However,
the analytical solution does not match the numerical solution that explicitly models the
effects of the metal pipe (Dp).
Comparison of Air Temperature and Atmospheric Heat Exchange
Surface temperatures calculated in models with the atmospheric heat flux
contributions are higher than the recorded air temperature. The daily extrema in surface
water temperatures for simulations using the “initial parameter” values (Table 2.4), a
maximum surface water depth of 0.1 meter, and field data for a 10 day period are
approximately 5 to 6°C higher than the correspondin g measured extrema in daily air
temperatures (Figure 2.5). The maximum temperatures simulated in the surface water
boundary layer occur approximately 2.5 hours after the maximum air temperatures
93
recorded in the field, while the minimum temperatures occur within 30 minutes of each
other.
Figure 2.5: Comparison between recorded air temperature and surface water
temperature resulting from considerations of atmospheric heat exchange.
Heat flux into the surface water layer is positive when heat is being added to the
boundary layer, either from the atmosphere or the ground, and negative when heat is
removed from the surface water. The dominant component of heat flux described by
equation (21) is the net shortwave radiation (red pentagrams, Figure 2.6), providing a
daily maximum input of up to 900 W m-2, with a daily mean of 254 W m-2. The latent
heat flux (blue crosses) has the second highest magnitude and is of opposite sign,
94
Table 2.4: Changes in modeled temperatures resulting from parameter perturbations used in the sensitivity analysis.
CSS is the composite scaled sensitivity calculated by UCODE and H is entropy of the signal. The minimum, maximum, and average
changes in temperature (∆T) are calculated using days 2 through 10, with values using all 10 days in parenthesis.
shallow peat
pert
val
CSS
∆H
(dits)
0.2
0.96
0.42
-0.13
-5.00
-0.2
-4.00
0.90
-0.43
log(αp)
-7.06
-0.1
-6.35
1.00
0.17
rs
0.13
0.5
0.20
0.03
-0.02
fsw
0.50
1.5
1.25
0.02
-0.03
κpw
14.00
1.5
35.00
0.01
0.01
Ts
10.00
0.5
15.00
0.02
0.03
T∞
3.00
0.5
4.00
0.07
0.02
param
initial
value
pert
Kcrop
0.80
log(Kh)
95
ave
∆T
-2.2
(-2.0)
-5.0
(-5.4)
2.0
(2.0)
-0.3
(-0.3)
-0.7
(-0.6)
0.2
(0.2)
0.1
(0.2)
0.5
(0.5)
max
∆T
-0.7
(0.0)
-1.9
(-0.1)
5.8
(6.4)
-0.1
(0.0)
-0.1
(0.2)
0.3
(0.3 )
0.7
(0.8)
0.6
(0.6)
shallow piezometer
min
∆T
-3.3
(-3.3)
-7.5
(-7.5)
-1.0
(-1.0)
-0.5
(-0.5)
-1.2
(-1.2)
0.0
(-0.0)
0.0
(0.0)
0.4
(0.0)
∆H
(dits)
-0.14
-0.23
0.11
-0.01
-0.10
0.06
-0.02
0.01
ave ∆T
-2.4
(-2.2)
-4.1
( -4.4)
1.7
(1.6)
-0.4
(-0.3)
-0.7
(-0.6)
0.4
(0.4)
0.1
(0.2)
0.5
(0.5)
max
∆T
-0.8
(0.0)
-1.8
(-0.7)
4.4
(4.6)
-0.1
(0.0)
0.2
(0.4)
1.7
(1.8)
0.6
(0.8)
0.6
(0.6)
mid-piezometer
min
∆T
-3.5
(-3.5)
-6.2
(-6.2)
-0.6
(-0.8)
-0.5
(-0.5)
-1.7
(-1.7)
-0.4
(-0.4)
0.0
(0.0)
0.4
(0.1)
∆H
(dits)
-0.13
-0.75
0.21
-0.02
-0.03
0.04
0.01
-0.08
ave ∆T
-0.3
(-0.3)
-1.3
(-1.4)
2.6
(2.4)
0.0
(0.0)
-0.1
(-0.1)
0.4
(0.3)
0.0
(0.0)
1.2
(1.2)
max
∆T
0.0
(0.0)
-0.1
(0.0)
3.4
(3.4)
0.0
(0.0)
0.0
(0.0)
0.5
(0.5)
0.0
(0.0)
1.4
(1.5)
min
∆T
-0.8
(-0.8)
-3.1
(-3.1)
0.7
(0.0)
-0.1
(-0.1)
-0.2
(-0.2)
0.2
(0.0)
-0.0
(-0.0)
1.1
(1.1)
removing a maximum of approximately 530 W m-2. The daily mean heat flux out of the
surface water layer (129 W m-2) is comparable to values reported by Comer et al. (2000)
for 8 wetlands throughout Canada and the northern United States (69 to 142 W m-2 for
fens and 105 to 199 W m-2 for bogs). The maximum sensible heat flux during the day
ranges from 32 to 91 W m-2. The minimum sensible heat flux drops to as low as -165 W
m-2 and occurs at approximately 9:00pm, when the warm surface water is losing heat to
the cooler air. The daily mean sensible heat flux is -11 W m-2. The minimum ground
heat flux (green diamonds) during the day is -147 W m-2, when the warm water is losing
heat to the subsurface. The maximum ground heat flux during the night is 57 W m-2,
when the warm peat is losing heat to the surface water. The daily mean ground heat
flux is 17 W m-2. The net long-wave radiation (black boxes) is always negative and
ranges from -170 W m-2 during the night to -4 W m-2 during the day, with a daily mean of
-104 W m-2. The net heat flux out of the boundary layer (pink stars) is the highest (-270
W m-2) during the evening, when heat loss due to long wave radiation, sensible heat flux,
and ground heat flux are the highest. The net heat flux into the boundary layer is the
highest (197 W m-2) during mid-day. The daily mean heat flux out of the surface water
layer is 50 W m-2.
96
Figure 2.6: Components of the energy balance equation used to define atmospheric heat
exchange in the surface water layer. Positive values indicate heat flow into the surface
water boundary layer described by Equation (21).
Sensitivity Analysis
The temperature time series resulting from simulations using the initial parameter
set and perturbed values are listed in Table 2.3 are shown Figure 2.7. Results for
parameter perturbations that produced a maximum change in the absolute value of
temperature less than 1.0°C are not shown for clari ty. Differences in entropy, minimum,
maximum, and average temperature are shown in Table 2.4. Heat associated with initial
conditions affects the average, minimum, and maximum temperatures within the first 24
hours of the simulation. As such, the average, minimum, and maximum differences in
temperature are calculated using the last 9 days of the simulation, with calculations
using all 10 days reported in parenthesis.
97
The increase in log(Kh) (Figure 2.7, light blue diamonds) used in the sensitivity
analysis represents an order of magnitude increase in hydraulic conductivity. This
perturbation of Kh produced a decline in temperature over the 10 day simulation and the
largest decrease in entropy at all depths. The maximum difference in temperature ( 7.5°C) occurred in the shallow peat near the end of the simulation. This decrease in
temperature is due to an increase in cold water flowing up through the peat. The
decrease in entropy is associated with a damping of the surface temperature fluctuations
by the upward flow of cooler groundwater, leading to a loss in the information content of
the signal.
The increase in log(αp) (Figure 2.7, red squares) represents an increase in
thermal conductivity of the peat from an initial value of 0.3 to 1.6 W m-2, assuming a
volumetric heat capacity of 3.5x106 J m-3 °C -1. This change could theoretically represent
an increase in the sediment content of the peat (e.g. Farouki, 1986). The increase in
thermal diffusivity results in more extreme diurnal temperature fluctuations in the shallow
peat and shallow piezometer, but a continuous increase in temperature in the midpiezometer. The greatest increase in amplitude occurs in the shallow peat with
temperature increases up to 6.4°C. The average dai ly temperatures are higher for all
sampling locations, with the greatest overall increase occurring in the mid-piezometer.
The higher diurnal fluctuations and increase in average daily temperature are due to
more effective conduction of the surface temperature fluctuations into the peat. The
entropy of the temperature signal increases at all sampling locations, with the greatest
increase occurring in the mid-piezometer. The increase in entropy is due to the increase
in the range of distinct temperature values contained in each signal.
The perturbation of Kcrop represents a 20% increase in evapotranspiration. This
perturbation produced the second largest decrease in entropy at all locations and a
continuous decrease in temperature at the shallow sampling locations. The maximum
98
decrease in temperature (-3.6°C) occurs in the shal low piezometer. The biggest
difference in minimum temperature occurs in the mid-piezometer (-0.8°C). The
decrease in temperature is due to the increased latent heat flux associated with an
increase in Kcrop, representing an increase in evapotranspiration.
The increase in the surface water depth factor (fsw, Figure 2.7, dark blue
triangles) represents a change in effective surface water depth from 0.05 to 0.125 m.
This change results in a decrease in average temperature, with a greater decrease
experienced at shallower depths in the model. The minimum temperature also
decreases in all sampling locations, with the greatest decreases occurring at shallower
depths. The decrease in temperature is due to increased heat storage in the deeper
surface water layer, and hence less heat available to affect subsurface temperatures.
The entropy decreases for all sampling locations, with the largest decrease occurring in
the shallow piezometer. The decrease in entropy is attributed to the damping of the heat
flux signal resulting from increased heat storage in the surface water layer.
The effective thermal conductivity of the piezometer water (κpw) used in the
sensitivity analysis is approximately equal to the maximum expected value resulting from
consideration of the Nusselt number. This change produces higher average and
maximum temperatures and lower minimum temperatures in the shallow piezometer. A
small increase in average, minimum, and maximum temperatures occurs in the other
sampling locations. The entropy increases are greatest for sampling locations in the
piezometer. These temperature changes and increase in entropy is attributed to
enhanced heat transport into the subsurface within the piezometer.
99
Figure 2.7: Change in temperature for parameter perturbations from parameter values
estimated from the literature: thermal diffusivity (red squares), crop coefficient (green
upward triangles), hydraulic conductivity (light blue diamonds), surface water depth (dark
blue downward triangles), piezometer water effective bulk thermal conductivity (blue
circles), initial surface temperature (pink plus signs). Parameter values and perturbation
amounts are found in Table 2.3.
Parameter Estimation of Synthetic Data
The fit of the temperature time series from each parameter estimation run to the
original data is illustrated for parameter set 1 (Figure 2.8). The resulting temperatures
from PE2A produce a very poor fit to the synthetic observations. The fit is significantly
improved by using the numerical model (PE1B and PE2B). These discrepancies
support the use of the more complex heterogeneous models that explicitly model the
thermal properties of a metal piezometer in substrate with low thermal conductivity.
100
The values of Kh estimated in PE1A, using the homogeneous model and air
temperature boundary condition, differed by up to 4.3 orders of magnitude from the
original values used to generate the synthetic observations. In all but parameter set 2
the estimate of Kh reached the minimum constraint of 1x10-10 m s-1. Estimates of αp
were off by -0.6 to 1.0 orders of magnitude. Inclusion of the signal entropy (PE2A) did
not improve the accuracy of the parameter estimates (Table 2.5).
The estimates of Kh from PE1B, using the heterogeneous model and heat flux
boundary condition, were not consistently improved compared to the starting values.
The value of hydraulic conductivity (Kh) was estimated to within 2.26 orders of magnitude
of the original value (Table 2.5). The starting values of Kh were closer to the original
values than those resulting from PE1B for all but one parameter sets (set 3). The value
of thermal diffusivity (αp) was recovered to within 0.45 orders of magnitude of the original
value. The crop coefficient (Kcrop) was recovered to within 0.18 of the original value. All
starting parameter values were closer to the original values than those estimated in
PE1B, except those in set 3 and αp in set 4. However, the temperatures generated
using the values estimated in PE1B are much closer to the synthetic data than those
generated using the starting parameters (Figure 2.8).
The recovery of Kh was improved by addition of the signal entropies to the
observations (PE2B) for all but set 3. Hydraulic conductivities were estimated to within
0.94 order of magnitude of the original value (Table 2.5). This is attributed to the
sensitivity of the modeled signal entropy to values of Kh (Table 2.4). Thermal diffusivity
was estimated to within 0.50 order of magnitude and the crop coefficient was recovered
to within 0.18 of the original value, values similar to those estimated in PE1B (Table 2.5).
The estimates of Kh, αp, and Kcrop were closer to the original values for sets 3 and 4,
while the starting values were closer to the original values in sets 1 and 2. The
101
temperatures generated using the parameter values estimated in PE2B are similar to
those generated using values from PE1B (Figure 2.8).
Parameter Estimation of Field Data
Temperature data recorded in piezometer S4 is used to estimate parameter
values using the same scheme as PE2B discussed above. The maximum temperature
discrepancy between the field observations and the simulation with the estimated
parameter values is 2.7°C and occur in the mid-piez ometer (Figure 2.9). Based on the
sensitivity analysis, these discrepancies may be reduced by considering the effects of
natural convection within the piezometer (through Κpw) and the depth of surface water
(fsw).
The estimates of Kh (6.1x10-6 m s-1) and αp (2.0x10-8 m s-1) fall within the range of
values reported in the literature. The estimate of Kcrop is 0.1 lower than the value
reported by Kellner (2001). However, this difference is comparable to the differences
associated with recovering the original parameters used to generate the synthetic data.
102
103
Table 2.5: Parameter estimation (PE) results for synthetic data sets. Original values were taken from a uniform distribution
constrained by literature values (Table 2.1). Parameter estimation runs PE1A (without entropy) and PE2A (with entropy) use the
analytical model with the upper boundary condition defined by the air temperature. Parameter estimation runs PE1B (without
entropy) and PE2B (with entropy) use the numerical model with the upper boundary condition defined by atmospheric heat exchange
(equation 21).
Parameter
Paramete Origin
Starting
PE1A
PE2A
PE1B
PE2B
(range)
r Set
al
Start
PE1A PE2A
PE1B
PE2B
Diff.
Diff.
Diff.
Diff.
Diff.
0.80 NA
NA
0.68
0.66
-0.01 NA
NA
0.10
0.12
set 1
0.79
set 2
0.92
0.80 NA
NA
1.10
1.10
0.12 NA
NA
-0.18
-0.18
Kcrop
(1.1 to 0.6) set 3
0.66
0.80 NA
NA
0.56
0.55
-0.14 NA
NA
0.11
0.11
set 4
0.75
0.80 NA
NA
0.82
0.75
-0.05 NA
NA
-0.07
-0.01
Average (Kcrop)
0.78
0.80 NA
NA
0.79
0.77
-0.02 NA
NA
-0.01
0.01
set 1
5.72
5.00 10.00
10.00
7.98
6.65
0.72
-4.28
-4.28
-2.26
-0.94
set 2
5.04
5.00
4.37
4.82
6.23
5.74
0.04
0.67
0.22
-1.19
-0.71
-log(Kh)
(-3.7 to -8.0) set 3
7.45
5.00 10.00
10.00
7.37
6.73
2.45
-2.55
-2.55
0.08
0.72
set 4
4.57
5.00
7.44
10.00
5.92
4.87
-0.43
-2.87
-5.43
-1.34
-0.30
Average (-log(Kh))
5.69
5.00
7.95
8.71
6.87
6.00
0.69
-2.26
-3.01
-1.18
-0.30
set 1
7.13
7.06
6.17
6.18
6.78
6.86
0.08
0.96
0.95
0.35
0.27
set 2
6.90
7.06
7.44
7.50
7.34
7.40
-0.16
-0.54
-0.60
-0.45
-0.50
-log(αp)
(-6.8 to -7.9) set 3
6.60
7.06
5.85
5.93
6.62
6.59
-0.46
0.75
0.67
-0.02
0.00
set 4
6.80
7.06
6.48
6.42
6.71
6.68
-0.25
0.32
0.39
0.09
0.13
Average (-log(αp))
6.86
7.06
6.49
6.51
6.86
6.88
-0.20
0.37
0.35
-0.01
-0.02
Figure 2.8: Temperature time series for parameter set 1. See text for description of the
parameter estimation schemes.
104
Figure 2.9: Comparison of field observations from piezometer S4, starting parameter
values, and estimated parameter values.
DISCUSSION
Metal piezometers with high thermal conductivity (16.0 W m-1 K-1) installed in
peat with low thermal conductivity (0.5 W m-1 K-1), results in significantly higher water
temperatures (3°C) recorded inside the piezometer c ompared to water temperatures
recorded outside the piezometer. Numerical models that explicitly account for the
thermal effects of the metal piezometer show temperature differences similar to those
seen in the field (2°C). Field data shows synchron icity in maximum temperatures inside
and outside the piezometer, while minimum temperatures occur earlier inside the
piezometer than outside the piezometer. This discrepancy is thought to be a result of
natural convection inside the piezometer. Numerical models show maximum and
105
minimum temperatures occurring earlier inside the piezometer. Numerical modeling
results suggest the thermal effects of the piezometer are negligible when installed in
substrate with high thermal conductivity, such as sand (2.2 W m-1 K-1).
Previous studies have used air temperature to define the upper thermal boundary
condition (Becker et al., 2004; Bravo et al., 2002; Stallman, 1965). However,
considerations of atmospheric heat exchange produce surface temperatures that are
significantly higher (5°C) than the air temperature . This difference is expected to
produce significant differences in parameter estimates based on subsurface temperature
measurements.
Parameter estimation by indirect inversion was accomplished using the UCODE
modeling software. The parameter estimation scheme was tested using synthetic data
generated by the numerical model using four sets of eight parameter values derived
from uniform distributions and constrained by values reported in the literature. However,
only the three most sensitive were considered in the parameter estimation process.
Parameter estimates, and the resulting temperature time series, were significantly closer
to the original values when the effects of the piezometer and atmospheric heat exchange
were considered. Incorporating the signal entropy, a measure of information contained
in the signal, improved the parameter estimates. The temperatures generated using the
original parameters differ from those generated using the estimated parameter values by
up to 3°C. This discrepancy is believed to be the cumulative result of differences in the
values of the five parameters (rs, fsw, κpw, Ts, T∞) not considered in the parameter
estimation process.
106
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natural and modified raised peat bogs in New Zealand. Agricultural and Forest
Meteorology, 95, 85-98.
Toth, J. (1963). A theoretical analysis of groundwater flow in small drainage basins. J.
Geophys. Res., 68, 4795-4812.
TRPA. (2012). Lake Tahoe Basin LiDAR. Retrieved 8/15, 2012, from
http://dx.doi.org/10.5069/G9PN93H2
Twidale, C.R., & Vidal Romani, J.R. (2005). Landforms and Geology of Granite Terrains.
London, UK: Taylor & Francis Group.
Valat, Beatrice, Jouany, Claire, & Riviere, Louis M. (1991). Characterization of the
Wetting Properties of Air-Dried Peats and Composts. Soil Science, 152(2), 100107.
van Genuchten, M. Th. (1980). A Closed-form Equation for Predicting the Hydraulic
Conductivity of Unsaturated Soils1. Soil Sci. Soc. Am. J., 44(5), 892-898. doi:
10.2136/sssaj1980.03615995004400050002x
Verseghy, D.L. (1991). A Canadian land surface scheme for GCMS. I. Soil Model.
Climatology, 11, 111-133.
Welty, J.R., Wicks, C.E., Wilson, R.E., & Rorrer, G.L. (2008). Fundamentals of
momentum, heat, and mass transfer: John Wiley and Sons.
Wetzel, Karl-Friedrich. (2003). Runoff production processes in small alpine catchments
within the unconsolidated Pleistocene sediments of the Lainbach area (Upper
Bavaria). Hydrological Processes, 17(12), 2463-2483. doi: 10.1002/hyp.1254
111
CHAPTER 3: WATERSHED SCALE MODELING OF THE GRASS LAKE RESEARCH
NATURAL AREA
ABSTRACT
Groundwater may be an important component of the hydrologic system that
supports montane wetlands in areas with a snow dominated precipitation regime.
However, groundwater systems that support montane wetlands are often poorly
understood. This study uses geologic observations to develop a three dimensional,
spatially explicit hydrogeologic model of the Grass Lake Research Natural Area
(GLRNA) located south of Lake Tahoe, California. The GLRNA incorporates the entire
watershed that supports Grass Lake, the largest peatland in the Sierra Nevada
Mountains. The hydraulic conductivities of different geologic units are calibrated using
head observations from an average water year (2010) and an above average water year
(2011). Parameter estimates from both years are comparable for all but the least
sensitive geologic units. Van Genuchten relationships used to describe the water
retention and relative permeability of the variably-saturated materials increase the
computation time from minutes to hours. As such, the initial model calibration neglects
the effects of variably saturation. The Van Genuchten relationships are included in the
final assessment of the model to explore the effects of simulating the unsaturated
properties of the subsurface material. Consideration of the unsaturated properties of the
subsurface material is shown to improve the model fit. The potential effects of predicted
changes from a snow melt dominated precipitation regime to a rain dominated
precipitation regime are addressed using the unsaturated parameters along with
estimates of hydraulic conductivity from the calibration process. The change from a
snow melt dominated precipitation regime to a rain dominated precipitation regime
results in lower pressure heads and saturation levels in the peatland. Simulations show
112
approximately half of the peatland is expected to reach saturation levels less than 70%
of total saturation by the end of the water year.
113
INTRODUCTION
High evapotranspiration rates and low summer precipitation suggest that late
season groundwater contributions may be required to maintain the health and proper
functioning of perennial wetlands in the Sierra Nevada Mountains. However, little is
known about the specifics of groundwater systems that support montane wetlands.
Predicted changes in climate suggest a trend towards precipitation falling as rain rather
than snow (Cayan et al., 2008). This will likely result in a shift from spring snowmelt
dominated recharge to winter rain dominated recharge. In steep, rocky watersheds with
limited subsurface storage capacity, this may significantly reduce the availability of lateseason water for wetland vegetation.
The water table in topographically driven groundwater systems is often
represented as a subdued replica of surface topography. In these systems, groundwater
is recharged at high elevation and discharged at topographic lows (Toth, 1963).
Watersheds with steep terrain have the potential to produce high hydraulic gradients that
drive groundwater flow from the hillslopes to the lower lying valleys. The rate and
duration of groundwater discharge is related to the hydraulic gradients driving flow, the
hydraulic conductivity and storage properties of the subsurface material, and the timing
and amount of recharge. Watersheds with relatively impermeable subsurface material
will allow rapid infiltration and groundwater recharge. However, in steep terrain with high
hydraulic gradients, this highly permeable subsurface material may also drain quickly,
limiting late-season groundwater availability. Watersheds with low permeability
subsurface material may experience little infiltration, resulting in a surface water
dominated hydrologic regime with little or no groundwater component.
This study explores the groundwater system of the Grass Lake Research Natural
Area (GLRNA), the largest peatland in the Sierra Nevada Mountains. Observations of
watershed geology are used to build a 3D, spatially explicit model of groundwater flow
114
using the software modeling package HYDROGEOSPHERE (Therrien, McLaren,
Sudicky, & Panday, 2008). Measurements of hydraulic heads discussed in Chapter 1
are used to calibrate the hydraulic conductivities of the geologic units in the watershed
model. The sensitivity of the model to differences in the hydraulic conductivity of each
unit is explored. The influence of simulating the unsaturated properties of the
subsurface material is explored and shown to improve the fit between the model results
and the field measurements. The calibrated model is used to explore the potential
response of the groundwater system to changes in the precipitation regime.
BACKGROUND
Peatlands are wetlands with thick organic soils that have formed in place.
Peatlands provide unique habitats, covering 3% of the Earth’s surface and making up
only 0.1% of the mountain landscape (Clymo, 2004; Cooper & Wolf, 2006b). In many
areas of the Sierra Nevada Mountains peatlands are the only source of perennial
moisture and support ecosystems with high biodiversity. The largest peatland in the
Sierra Nevada is Grass Lake (~82 ha), located on Luther Pass, south of Lake Tahoe,
California. Water budget calculations and measurements of hydraulic gradients
(Chapter 1) confirm that groundwater is an important component of the Grass Lake
system. Peatlands that are sustained by groundwater input are termed “fens”(Cooper &
Wolf, 2006b).
Peatland soils are classified as Histosols, having at least 40 centimeters of
organic material in the upper 80 centimeters of the soil profile (NRCS, 1999). Peat
accumulates over thousands of years and requires perennially saturated soil to prevent
the decomposition of the organic matter (Benedict & Major, 1982). As such, the
presence of peatlands in the Sierra Nevada Mountains suggests the presence of long
lived groundwater systems capable of maintaining dominantly saturated conditions,
115
despite high evapotranspiration rates and low summer precipitation (Benedict & Major,
1982).
The geology in the GLRNA is dominated by granitic bedrock, overlain by glacial
deposits from the Tahoe and Tioga glacial periods. The upper watershed is composed
of weathered granitic saprolite (grus) and a minor amount of andesitic volcanic rocks.
Steep, glacially eroded hillslopes of shallow colluvium and bedrock dominate the midelevations to the north of Grass Lake. Two small cirques occur at mid-elevations along
the south side of the lake. The cirque below Powderhouse Peak (west) is larger and has
more developed moraine deposits than the cirque below Waterhouse Peak (east).
Tahoe-age lateral moraines form the majority of hillslope material along the edges of the
valley. A Tahoe-age moraine forms the western edge and outlet of Grass Lake. A
Tioga-age moraine from a glacier in Hope Valley forms the east end of the lake and
isolates a small upper peatland east of Grass Lake proper. Alluvial fans are formed by
the four perennial streams and one intermittent stream that empty into the lake. See
Chapter 1 for a more complete description of the geologic observations and hydrologic
measurements.
METHODS
The hydrologic modeling software HYDROGEOSPHERE (Therrien et al., 2008)
was used to simulate watershed scale processes in the GLRNA. HYDROGEOSPHERE
is a finite element numerical model capable of simulating fully coupled, threedimensional variably-saturated groundwater and surface water flow. The nonlinear
nature of the surface flow equations combined with the steep topography causes
numerical instabilities that could only be resolved with small time steps, resulting in
excessively long simulation times. Reasonable computation times are necessary to
efficiently estimate parameter values via indirect inversion of the numerical model. To
decrease computation time, the combined effects of shallow subsurface flow and surface
116
flow were approximated using a recharge spreading layer with high hydraulic
conductivity (Therrien et al., 2008). Field observations revealed that surface flow is
limited to the surface of the peatland, streams, impervious rock surfaces, and within 1
meter of rapidly melting snow. Errors associated with this assumption are expected to
be most significant near channels where surface flow is not accurately simulated.
Grid Construction
The GLRNA watershed was delineated using the Spatial Analyst extension (SA)
in ArcGIS (version 9.3.1) and lidar data provided by Tahoe Regional Planning Agency
(TRPA, 2012). A custom digital elevation model (DEM) with 5 meter cells was
generated using the minimum elevation recorded within a 5 meter radius of each cell
center. Depressions were filled, flow direction and accumulations were calculated, and
the watershed boundary determined using the procedures outlined in the Hydrologic
Analysis section of the ArcGIS SA help manual (Environmental Systems Research
Institute, 2009).
The elevations of the piezometers and a reference point on solid bedrock were
determined to within ± 15cm (6 in) using a total station survey (Chapter 1). These
elevations were a minimum of 1.11 meters lower than the elevations determined from
the lidar data. It is assumed this discrepancy represents a systematic error associated
with different datums used during data collection. To achieve consistency with the lidar
data, 1.11 meters is added to the elevations determined by the total station survey.
Inspection of the data suggests larger discrepancies between the total station survey
and lidar data may be associated with thicker riparian vegetation, which would result in
false ground returns during lidar data collection and processing. An area of thick, tall
riparian vegetation was delineated around the edge of the peatland using field
observations and consideration of textures present in the lidar data. Elevations used to
define the model surface were interpolated between the piezometer elevations from the
117
total station survey (after datum correction) and the lidar elevations outside this riparian
area. This method allows for direct comparison of groundwater elevations calculated
from the field data and simulation results.
The geologic contacts and watershed boundary (Figure 1.1) were simplified to
accommodate efficient grid generation and solution of the equations governing fluid flow
in the hydrologic models (Figure 3.1). Grid Builder (McLaren, 1995) was used to build a
2D unstructured finite-element mesh consisting of triangular prismatic elements.
Maximum node spacing along the watershed boundary was limited to 50 meters (164 ft).
Maximum node spacing along all geologic contacts was limited to 25 meters (82 ft).
Node spacing was allowed to grow to 50 meters in the lower watershed and 100 meters
in the upper watershed, with a node spacing stretch factor of 1.5 throughout the model.
The geologic material overlying the bedrock is assigned properties based on the
geologic mapping discussed in Chapter 1. In the upper watershed, the bedrock is
overlain by saprolite (“grus”). The depth of the contact between the bedrock and the
overlying grus in the upper watershed is inferred from a borehole drilled in unglaciated
granitic bedrock near the top of the Heavenly Gondola (~9170 ft), approximately 10
miles north of Grass Lake. The Well Completion Report (No. 714169 filed at DWR)
indicates “DG” and “pretty solid DG” in the upper 28 feet (~8.5 m) of the well. It is
assumed “DG” refers to decomposed granite, also known as “grus,” a name often used
to describe granitic saprolite. The depth to bedrock in the upper watershed is modeled
as 10 meters.
In the lower watershed surface deposits consist of glacial deposits, alluvial
material, and peat. According to Clark (2010), the depth to bedrock under Grass Lake is
approximately 70 to 100 meters based on electrical resistivity studies conducted as part
of another study. The glacial deposits near the peatland interface are expected to
influence the flow of groundwater into Grass Lake. However, there is little data available
118
to define the thickness of these deposits. The depth to bedrock under the glacial
deposits is modeled using an interpolated surface extending from 10 meters below the
surface along the upper contact of the glacial deposits to 70 meters below the surface
along a swath of points through the center of Grass Lake. In the locations where the
interpolated surface intersects the ground surface, a minimum depth of one meter is
used. Elements below this surface are assigned the properties of bedrock. Elements
above this surface are assigned properties based on the geologic units mapped in the
field. Elements between the peat of Grass Lake proper and the bedrock are assigned
properties of Tahoe deposits. Elements between the peatland to the east and the
bedrock, as well as the glacial cirques on the south side of the watershed, are assigned
properties of Tioga deposits. Alluvial deposits are limited to the upper two layers of
elements. Three significant bedrock outcrops occur along the north side of Grass Lake
and are assigned properties of bedrock (Figure 3.1).
The surface DEM described above is used to define the upper surface of the
model and is used as a starting point for the other two surfaces used to define the
vertical discretization (Figure 3.2). The second surface is defined by subtracting the
depth of peat estimated from soil probes (Figure 3.3), or 1.0 meter where peat is not
present, from the surface DEM. The model contains two layers of elements between the
upper surface and the second surface. The minimum element thickness is 0.5 meters in
the upper watershed and the maximum element thickness is 5 meters under the deepest
sections of the peatland. The third surface represents the contact between the bedrock
and the various overlying geologic materials, discussed above (Figure 3.4). The model
contains four layers of elements between the second and third surfaces, with layer
thickness increasing by a factor of 1.2 with increasing depth. There are 11 layers
between the third surface and the bottom of the model at an elevation of 2000 m above
sea level.
119
Figure 3.1: Simplified geology and numerical mesh used in watershed scale models of
the Grass Lake Research Natural. Cross section A-A’ is shown in Figure 3.2.
120
Figure 3.2: Cross section near Waterhouse Creek (Figure 3.1, A-A’) showing
hydrogeologic units with depth and vertical discretization. Surface shading is used to
highlight the slope and aspect of each cell.
121
Figure 3.3: Contour map showing the depth of peat estimated from soil probes and
previous work (Clark, 2010). Depths less than 5 m are visually interpolated from soil
probes. Depths greater than 5 m are inferred from limited soil cores collected by Clark.
122
Figure 3.4: Contour map showing depth to bedrock interpolated from 10 m below the
upper contact of the Tahoe age lateral moraines and 70 m below the surface along a
swath of points underlying the long axis of Grass Lake.
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Hydraulic Conductivity
The dominant bedrock unit in the GLRNA is the Bryan Meadows granodiorite.
The hydraulic conductivity of the bedrock (Kbd) in the GLRNA is based on the results of
pumping tests conducted in 2005 as part of South Tahoe Public Utilities study
(Bergsohn, Fogg, Trask, Roll, & Labolle, 2007). The hydraulic conductivity of the Bryan
Meadows granodiorite was estimated to be 2.8x10-7 m s-1 for a well located on Ralph
Drive, approximately 14.3 kilometers (8.9 miles) due north of Grass Lake. The hydraulic
conductivity for a bedrock well located at the Big Meadow trailhead, approximately 2.2
kilometers (1.4 miles) west of the outlet of Grass Lake, was estimated to be 4.6x10-8
m s-1. The Big Meadow trailhead well is thought to be screened in the Quartz Diorite of
Grass Lake, which intrudes the Bryan Meadows granodiorite. The slower
cooling rate of the intruding magma is expected to result in lower fracture density and
hence lower permeability. The hydraulic conductivity of the bedrock associated with the
Heavenly Gondola well was estimated to be between 2.5x10-6 and 1.7x10-5 m s-1. This
well is located at the top of the Heavenly Gondola and is screened in the East Peak
granodiorite, which is older than the Bryan Meadows granodiorite found in the Grass
Lake watershed. The older East Peak granodiorite is expect to have higher hydraulic
conductivity due to the accumulation of fractures and damage associated with the
intrusion of younger igneous bodies and tectonic forces. The well log descriptions,
mapped geology, high value of hydraulic conductivity, and heat flow measurements
suggest a portion of the Heavenly Gondola well intersects a high conductivity fault or
fracture zone (Bergsohn et al., 2007). As such, this likely represents a maximum value
for hydraulic conductivity for the bedrock in the GLRNA. The initial value for the
hydraulic conductivity of bedrock is 5.0x10-7 m s-1 and constrained to values between
1.0x10-9 and 1.0x10-4 m s-1 during parameter estimation process.
124
The hydraulic conductivity of glacial deposits varies greatly depending on the
composition of the parent material, the extent of glaciation, and the extent of weathering.
Literature values for the hydraulic conductivity of glacial deposits range from as low as
1x10-9 m s-1 for moraines dominated by limestone material (Wetzel, 2003) to as high as
2x10-3 m s-1 for moraines dominated by gravel (Beckers & Frind, 2001; Mace, Rudolph,
& Kachanoski, 1998). The glacial deposits in the GLRNA are expected to have high
hydraulic conductivity based on the dominance of coarse sand and gravel. Silica
cemented horizons and evidence of more extensive weathering are found in Tahoe age
glacial deposits but not Tioga age deposits, suggesting a lower hydraulic conductivity of
the older deposits (Birkland, 1964). Glaciated volcanic rocks located south of Luther
Pass likely contributed to the valley fill material. The occurrence of readily weathered
volcanic material is expected to reduce hydraulic conductivity. Bailer tests conducted in
piezometers screened in the material below the peat gave values of hydraulic
conductivity ranging from 4.9x10-8 m s-1 to 3.3x10-4 m s-1 (Chapter 1). The geometric
mean (1.1x10-5 m s-1) is similar to the value reported by Loheide (2007) for coarse
montane meadow sediments in the Last Chance watershed (2x10-5) and typical values
for medium to coarse sand (Domenico & Schwartz, 1998). The hydraulic conductivity of
the grus (Kgrus) and alluvium (Kalluv) are expected to have hydraulic conductivities similar
to those of the glacial material (Ktioga and Ktahoe) based on the similarity of soil properties
(NRCS, 2010). In the parameter estimation process a value of 1.0x10-5 m s-1 is used as
the initial hydraulic conductivity of all units other than the bedrock and peat. The
hydraulic conductivity of these units are constrained to values between 1.0x10-8 and
1.0x10-2 m s-1 during the parameter estimation process.
Peat is typically divided into the upper acrotelm (living portion) and the lower
catotelm (nonliving portion). The low density acrotelm typically has values of hydraulic
conductivity on the order of 0.01 m s-1 (Hoag & Price, 1997; Ivanov, 1981). Literature
125
values for the hydraulic conductivity of the deeper catotelm (Kpeat) range from 1x10-8 to
4x10-4 m s-1 and depend on composition, compaction, climate, and the level of
decomposition (Chason & Siegel, 1986; Drexler, Bedford, Scognamiglio, & Siegel, 1999;
Ivanov, 1981; Reeve, Siegel, & Glaser, 2000; Silins & Rothwell, 1998). Based on the
undecomposed nature of the peat, a value of 5x10-5 m s-1 is used as the initial hydraulic
conductivity in the parameter estimation process. The hydraulic conductivity of peat is
constrained to values between 1.0x10-9 and 1.0 m s-1 during the parameter estimation
process.
Forest soils with abundant organic material (“duff”) facilitate shallow subsurface
flow and rapid redistribution of surface water. All shallow subsurface and surface flow is
approximated using a recharge spreading layer (RSL) reflecting the properties of the
forest soils. Preliminary simulations that excluded the RSL produce heads tens of
meters higher than those observed in the field. Including the RSL allows subsurface
water to discharge quickly, reducing head in discharge zones and providing a better fit to
the field observations.
The recharge spreading layer is divided into two zones, representing the peat
surface (Krslpeat) and the rest of the watershed (Krslforest) , based on the obvious
differences in material. The saturated hydraulic conductivity of mapped soils in the area
(excluding exposed rock) ranges from approximately 1.4x10-4 m s-1 to 1x10-5 m s-1
(NRCS, 2010). Flow through the organic rich surface material (O horizon) is likely to
experience less resistance, requiring a higher hydraulic conductivity to approximate fluid
flow in the models. The initial value for the hydraulic conductivity of both recharge
spreading layers is 1.0 m s-1 and constrained to values between 1.0x10-5 m s-1 and 5.0 m
s-1 during the parameter estimation process. The thickness of both recharge spreading
layers is held constant at 0.1 meter based on the approximate depth of the acrotelm
126
observed in the field and the depth to a restrictive layer reported in the NRCS soil survey
(2010).
Anisotropy
The horizontal and vertical hydraulic gradients observed in the field differed by as
much as two orders of magnitude. The horizontal hydraulic conductivity of stratified
sedimentary deposits can be as high as two to three orders of magnitude greater than
the vertical hydraulic conductivity. An anisotropy factor for the peat is defined by:
௛
௩
݉௣௘௔௧ = ‫ܭ‬௣௘௔௧
ൗ‫ܭ‬௣௘௔௧
(1)
௛
௩
is the horizontal hydraulic conductivity of the peat and ‫ܭ‬௣௘௔௧
is the vertical
where ‫ܭ‬௣௘௔௧
௛
hydraulic conductivity of the peat. Lab experiments have shown ‫ܭ‬௣௘௔௧
to be as much as
௩
, although most samples had anisotropy
two orders of magnitude higher than ‫ܭ‬௣௘௔௧
factors closer to one order of magnitude (Beckwith, Baird, & Heathwaite, 2003). The
initial value of mpeat is 10.0 and constrained to values between 0.1 and 1000.0 during the
parameter estimation process.
Fractured bedrock may also show significant anisotropy due to preferentially
oriented fracture networks. However, the limited bedrock outcrops that occur in the
GLRNA show closely spaced (typically less than 1 m), irregular fractures with limited
extent. Based on the high fracture density (several per meter) and lack of preferred
fracture orientation, the bedrock is modeled as an isotropic equivalent porous medium.
Specific Storage
The specific storage of bedrock is estimated to be between 1x10-4 to 7x10-5 m-1
based on applicable literature, with a mean value of 3.73x10-5 m-1 (Illman & Tartakovsky,
2006; Kahle, 1987; Lee & Lee, 2000). The porosity of the bedrock is assumed to be 1%.
Dasberg and Neuman (1977) report a value of 0.12 m-1 for the specific storage of peat.
127
The porosity of the peat was calculated to be 83% from field samples (Chapter 1). The
specific storage of the alluvium, glacial material, and grus are calculated using
ܵ௦ = ߛ௪ (ߚ௠ + ݊ߚ௪ )
(2)
where γw is the specific weight of water (9.8 kN m-3), βm is the compressibility of the
material (1x10-8 m2 N-1), βw is the compressibility of water (4.6x10-10 m2 N-1), and n is the
porosity. The porosity for these materials is estimated as 0.25 based on typical values
for sand and gravel (Domenico & Schwartz, 1998) and data reported in the NRCS soil
survey (NRCS, 2010), resulting in a value for specific storage of approximately 1.0x10-4
m-1.
Unsaturated Parameters
A modified form of the Richard’s equation is used to describe flow and storage in
the model (Therrien et al., 2008):
డ
ሺߠ௦ ܵ௪ ሻ
డ௧
= ∇ሺ‫݇ ∙ ܭ‬௥ ∇ℎሻ ± ܳ
(3)
where θs is the saturated water content, Sw is the degree of saturation defined as the
ratio of the water content to saturated water content, K is the hydraulic conductivity, kr is
the relative permeability of the porous medium as a function of water content, h is the
head, and Q is the source/sink term. The storage term on the left-hand side of equation
(3) is approximated assuming negligible compressibility under unsaturated conditions
and constant compressibility for saturated to near saturated conditions, giving:
డ
ሺߠ௦ ܵ௪ ሻ
డ௧
≈ ܵ௪ ܵ௦
డఝ
డ௧
+ ߠ௦
డௌೢ
డ௧
(4)
128
where Ss is the specific storage and φ is the pressure head. Water content (Sw) and
relative hydraulic conductivity (Kr) as a function of pressure head (φ) can be computed
using van Genuchten relationships (van Genuchten, 1980):
ܵ௪ = ܵ௪௥ + ሺ1 − ܵ௪௥ ሻൣ1 + |ߙ߮|ఉ ൧
‫ܭ‬௥ = ܵ௘
(௟௣)
(5)
ଶ
ቂ1 − (1 − ܵ௘ )௩ ቃ
ଵ/௩
ି௩
(6)
where
ଵ
‫= ݒ‬1−ఉ
(7)
and Swr is the residual water content, Se is the effective saturation given by Se=(SwSwr)/(1-Swr), φ is the pressure head, and lp is a pore-connectivity factor. Parameters α
and β are generally determined by fitting equation (5) and (6) to experimental data. In
this study, α and β are taken from applicable literature.
Based on the similarity of materials, the Van Genuchten parameters describing
variably saturated flow in coarse sand and gravel are used for all units other than the
bedrock and peat (Table 3.1). The Van Genuchten parameters describing variably
saturated flow in the bedrock are based on experiments conducted in fractured bedrock
in Yucca Valley (Mukhopadhyay, Tsang, & Finsterle, 2009). Water retention data from
peat samples discussed in Chapter 1 was fit to the Van Genuchten equations using
values consistent with those reported by Silins and Rothwell (1998).
Hydrogeosphere can be run in “fully saturated” mode, in which Sw and Kr take on
the value of zero for cells above the water table (P>0) and values of one below the water
table.
Experience has shown that the nonlinear nature of the unsaturated equations (3-
5) increases computation time by up to four orders of magnitude. Computation time can
be reduced in HGS by linear interpolation between tabulated values of φ, Se, and kr.
129
However, simulations of unsaturated conditions are still slow (hours) compared to
simulations of fully saturated conditions (minutes). As such, a “fully saturated” model is
used during the model calibration process in which hydraulic conductivity of each unit is
estimated. The effects of unsaturated flow are explored using values of hydraulic
conductivities from the calibrated model and tabulated relationships generated using the
parameters listed in Table 3.1 (Figure 3.5). The absolute value of global mass balance
errors associated with the nonlinear calculations remain less than 1.0x10-9 m s-1 for the
duration of the simulation. Since the “fully saturated” model does not include information
on saturation, pressure head is used to compare the results of calibrated model to those
of the unsaturated model.
Table 3.1: Storage parameter values used in all simulations and unsaturated parameter
values used in the final assessment of the Grass Lake watershed to changes in
precipitation.
Van Genuchten
Parameters
Material
α
Peat
Alluvium
Tioga
Tahoe
Grus
Bedrock
8.50
3.52
3.52
3.52
3.52
10.00
β
Swr
30%
5%
5%
5%
5%
1%
1.50
3.18
3.18
3.18
3.18
2.70
θs (%)
83%
25%
25%
25%
25%
2%
Ss (m-2)
1.5E-01
1.0E-04
1.0E-04
1.0E-04
1.0E-04
5.0E-05
Initial conditions and duration
The initial head for all nodes in all models is given by a linear function increasing
from 2348 meters at the furthest west edge of the peatland to 2357 meters at the
furthest west edge of the peatland, representing the approximate surface water
elevations at the beginning of the snow melt period. The 2010 simulation is run for 6.5
months, representing the estimated time between initial snow melt (early-March) and the
last observations made in 2010 (late-September). The duration of the 2011 simulation is
130
the same, although represents calendar dates approximately 3 weeks later due to the
heavy snowpack and delayed snowmelt.
Boundary Conditions
Areas within Grass Lake mapped as open water are initially assigned a specified
head equal to the elevation recorded in the lidar data. A pressure transducer positioned
in the open water recorded a water level drop of 0.13 meters from July 7 to September
20, 2010. This change is approximated by decreasing the value of the specified head
boundary condition by 0.15 meters over duration of each simulation. The lowest nodes
on the west end of Grass Lake are assigned a specified head boundary condition equal
to their elevation to approximate surface flow out of Grass Lake. Various specified flux
boundary conditions are applied to portions of the upper surface based on precipitation
estimates, observed snow melt patterns, evapotranspiration estimates, and expected
changes in precipitation associated with climate change (see below). All other
boundaries are no-flow.
During the field study approximately 90% of the annual precipitation fell between
October and May, presumably as snow (PRISM, 2013). This represents a potential of
0.938 meters of water available for spring recharge in 2010. In 2011 the potential water
available for spring recharge was 1.457 meters. A linearly increasing rate of recharge is
applied to the upper surface of the watershed for 30 days, followed by a linearly
decreasing rate of recharge for the following 30 days. The maximum rates of recharge
are 3.62x10-7 and 5.76x10-7 m s-1 for 2010 and 2011, respectively. Field observations
suggest the majority of snowmelt occurred along the north side of the watershed over
approximately 60 days between the first week of March and the first week of May in
2010. The majority of snowmelt along the south side of the watershed occurred
approximately 50 days later, between late-April and late-June. The duration of snowmelt
was similar in 2011, but delayed 2-3 weeks due to the heavy snowpack and cooler
131
weather. As such, recharge along the south side begins 50 days after recharge on the
north side to approximate the effects of aspect on snow melt timing.
Evapotranspiration (ET) is simulated by applying a constant negative flux equal
to 5.79x10-8 m s-1 (5 mm day-1) for 100 days. The peatland was snow free by June 7,
2010 and June 27, 2011. As such, the ET flux starts 90 days into the simulation, the
approximate time the peat surface was snow free. A constant negative flux of 1.16x10-8
m s-1 (1 mm day-1) is applied to the surrounding watershed for the duration of the
simulation to approximate ET from the surrounding forest.
The potential response of the Grass Lake watershed to predictions of more rain
and less snow is explored by changing the recharge rate. The monthly average
precipitation for 1900-2011 is 41.24 inches (1.047 m) (PRISM, 2013). Approximately
94% of the annual precipitation falls between October and May, with average monthly
totals greater than 2 inches during that period. The change from a snow melt dominated
to a rain dominated precipitation regime is approximated by applying a constant
recharge rate equivalent to 38.76 inches (0.984 m) distributed over 240 days. Although
the total annual recharge remains approximately the same, the recharge rate is
decreased by an order of magnitude (4.75x10-8 m s-1).
132
Figure 3.5: Piecewise linear interpolated functions describing water retention and relative
permeability used in variably saturated watershed scale models of GLRNA.
Parameter Estimation
The inverse modeling package UCODE (Poeter et al., 2005) is used to estimate
the set of hydraulic conductivities that produce the best fit to the observed groundwater
heads in 2010 and 2011 (see Chapter 1 for discussion of measurements). The
sensitivity of the model is determined by perturbing each parameter individually and
comparing the resulting change in the sum of squared weighted residuals (SSWR)
between the observations and the simulation results. A modified Gauss-Newton search
criterion is used to estimate the parameter values expected to minimize the SSWR
based on the calculated sensitivities. The model is run with the updated parameter
133
estimates, a new SSWR is calculated, and the process is repeated. Sensitivities are
determined using a perturbation of 5%. Each observation (field measurement) is
weighted by the inverse of the squared standard deviation of the elevation determined
from the piezometer surveys (see Chapter 1).
Parameters with composite scaled sensitivities (Poeter et al., 2005) within an
order of magnitude of the most sensitive parameter are used in the first two parameter
estimation runs. Insensitive parameters are added to the final two parameter estimation
runs. Highly correlated parameters are removed from the parameter estimation runs.
Parameter values are constrained using the values presented in Table 3.2. The
maximum change for any parameter is limited to 20% per iteration in the first two PE
runs and 10% per iteration in final two PE runs. Convergence is accepted when
parameter estimates do not change by more than 10% between iterations.
MODELING RESULTS
Parameter Estimates
The initial sensitivity analysis shows the watershed model is most sensitive to
Kzpeat, Ktahoe, and mpeat. Due to the high correlation between Kpeat and mpeat, Kzpeat is held
constant at the initial values for the first three runs. The first parameter estimation run
(PE1) converges within six iterations for both years. The results of PE1 show in a slight
decrease in the value of Ktahoe for the 2010 simulations and a slight increase for the 2011
simulations (Table 3.2). The value of mpeat increases by a factor of 3 for both years,
indicating that a higher value of horizontal hydraulic conductivity results in a better fit to
the data.
A sensitivity analysis shows that Ktioga becomes sensitive when the new values of
Ktahoe and mpeat from PE1 are used. The second parameter estimation run (PE2)
includes Ktioga, Ktahoe and mpeat. PE2 converges within three iterations for both years.
The value of Ktioga increases by a factor of 1.9 in the 2010 simulations and a factor of 3.5
134
in the 2011 simulations (Table 3.2). The value of Ktahoe and mpeat stay approximately the
same for both years.
The third parameter estimation run (PE3) includes all parameters except Kzpeat,
which is excluded due to high correlation with mpeat. Parameter estimation runs do not
converge for either year after 20 iterations. The final values are taken from the
parameter set with the lowest sum of squared, weighted residual (Table 3.2). The value
of Krsl increases by a factor of 12 in the 2010 simulations and a factor of 2 in the 2011
simulations. The value of Kalluv increases by a factor of 420 in the 2010 simulations and
a factor of 13,000 in the 2011 simulations. The value of Kgrus increases by a factor of
approximately 40 for both years. The value of Kbd decreases by a factor of 500,
reaching the lower constraint in simulations of both years. The value of Ktioga is reduced
by a factor of 0.5 for both years. The value of mpeat increases by a factor of 1.8 for the
2010 simulations and 1.3 for the 2011 simulations. The value for Ktahoe increases by a
factor of 1.3 for both years.
The final parameter estimation run (PE4) includes Kzpeat, which is the only
parameter not yet considered in the parameter estimations runs. All other parameters
are included except mpeat which is excluded due to high parameter correlation with Kzpeat.
Parameter estimation runs for both years converge within eight iterations. The value of
Krsl decreased by a factor of 7.8 in the 2010 simulations and increased by a factor of 2.4
in the 2011 simulations. The value of Kgrus increased by a factor of 1.4 in the 2010
simulations and decreased by a factor of 0.8 in the 2011 simulations. All other
parameters change by less than a factor of 0.2 between PE3 and PE4.
The largest discrepancy between the final parameter estimates from the 2010
and 2011 simulations occurs for Kalluv, the least sensitive parameter, which differs by a
factor of 3.2. The 2010 and 2011 estimates for Krsl and Ktioga differ by slightly more than
a factor of two. The 2010 and 2011 estimates for Ktahoe and Kgrus differ by less than a
135
factor of two. The estimates from the 2010 and 2011 simulations are approximately the
same for Kzpeat, Kbd, and mpeat. The final sensitivity analysis shows Ktahoe and Kzpeat to be
the most sensitive, followed by Kgrus, Ktioga, and Kalluv. The model is relatively insensitive
to Krsl and Kzbd.
Simulation Results
The average difference between the measured heads and the simulated heads
from the calibrated model is 0.67 (σ=1.13, n=247) m and 0.58 (σ=1.05, n=186) m in
2010 and 2011, respectively. The average weighted residual is 9.46 (σ=18.1, n=247) m
for 2010 and 8.58 (σ=18.0, n=186) for 2011. Measured heads in piezometers near the
perennial spring (S5 an S12) and near the mouths of West Freel Meadows Creek (N2,
N3) and Waterhouse Creek (S8, S11, S13) are higher than the simulated heads for both
years and account for the majority of the discrepancy between the field measurements
and the simulation results (Figures 3.6 and 3.7, Table 3.3). Measured heads in
piezometer N9, located below a bedrock outcrop, are lower than simulated heads for
both years. Due to the weighting factors associated with survey accuracy,
measurements made in piezometers N9, S5, S6, S8, S11, and S13 contribute to the
majority of sum of squared, weighted residuals that drives the parameter estimation
process.
The fit of the calibrated model (PE4) is improved by consideration of the
unsaturated properties of the material (Figures 3.6 and 3.7). The average difference
between the measured heads and the simulated heads in the unsaturated simulations is
0.27 meters (σ=0.84, n=247) and 0.25 meters (σ=0.77, n=186) for 2010 and 2011,
respectively. The average weighted residual from the unsaturated model is 3.63
(σ=19.2, n=247) m for 2010 and 4.44 (σ=18.5, n=186) m for 2011. The sum of squared,
weighted residuals is reduced by approximately 9% for each year when unsaturated
properties are simulated.
136
The average difference between measured and simulated heads in S5 and S12
and the associated average weighted residuals are reduced significantly for both years
when unsaturated properties are considered (Table 3.3). The average difference
between measured and simulated heads in N2 and N3 and the associated average
weighted residuals are also reduced when unsaturated properties are considered.
However, the difference between measured and simulated heads and the associated
average weighted residuals in N7 and N8 increase significantly for both years when
unsaturated properties are considered. The differences between measured and
simulated heads in N9, S6, S8, S11, and S13 do not change significantly when
unsaturated properties are considered. These changes in model fit suggest simulations
that include unsaturated properties may produce a better calibrated model than
simulations that neglect unsaturated properties. However, this was not pursued due to
excessive simulation time.
Simulations that consider the unsaturated properties of the subsurface materials
produce higher pressure heads in the peatland (Figure 3.8). The most significant
differences occur on the east end of Grass Lake and the upper peatland to the east of
Grass Lake proper. Differences in pressure head between the “fully saturated” and
unsaturated models exceed 0.4 m for 2010 and 0.8 for 2011 in Grass Lake proper, and
over 1.0 m in the upper peatland. Areas of excess pressure head (P>0), expected to be
associated with groundwater discharge, occur in the western and eastern portions of the
peatland. An area of excess pressure also occurs near the convergence of Freel
Meadows Creek and Waterhouse Creek. A small swath of negative pressure head
occurs just east of this convergence and coincides with a relatively dry section frequently
used by humans and wildlife to cross the peatland. A wider swath of negative pressure
head occurs along the Tioga-age moraine that separates the upper peatland and Grass
Lake proper.
137
Table 3.2: Hydraulic conductivities of geologic material used in the watershed scale model of GLRNA. Upper and lower bounds are
based on extreme values reported in the literature. Initial values are estimates from the available literature as discussed in the text.
Parameter estimates (PE) were determined by indirect inversion of the model.
Hydraulic Conductivity (m s-1)
Material
Lower
bound
Upper
bound
Initial
RSL
1.0E-5
1.0
Peat
1.0E-8
Alluvium
2010
2011
138
PE1
PE2
PE3
PE4
PE1
PE2
PE3
PE4
1.0E-4
-
-
1.2E-3
9.4E-4
-
-
1.7E-4
4.1E-4
1.0E-2
5.0E-5
-
-
-
5.0E-5
-
-
-
4.9E-5
5.0E-8
1.0E-2
1.0E-5
-
-
4.2E-3
4.0E-3
-
-
0.13
0.13
Tioga
5.0E-8
1.0E-2
1.0E-5
-
1.9E-5
1.1E-5
1.1E-5
-
3.5E-5
2.4E-5
2.4E-5
Tahoe
5.0E-8
1.0E-2
1.0E-5
8.2E-6
7.7E-6
1.4E-5
1.4E-5
1.3E-5
1.3E-5
2.3E-5
2.2E-5
Grus
5.0E-8
1.0E-2
1.0E-5
-
-
4.0E-4
5.4E-4
-
-
3.9E-4
3.2E-4
Bedrock
1.0E-9
1.0E-2
5.0E-7
-
-
1.0E-9
1.0E-9
-
-
1.0E-9
1.0E-9
mpeat
0.001
1000
100
322.3
357.8
626.3
-
439.8
518.0
650.4
-
139
Table 3.3: Differences between measured and simulated heads for select piezometers in the “fully saturated” and unsaturated
models.
2010
2011
Fully Saturated
Unsaturated
Fully Saturated
Unsaturated
ave head
ave head
ave head
ave head
difference ave wt difference ave wt
difference ave wt difference ave wt
Piezometer
(m)
residual
(m)
residual n
(m)
residual
(m)
residual
n
N2
9
1.31
8.74
0.20
1.31
4
1.40
9.33
0.76
5.06
N3
12
1.51
10.09
0.35
2.33
5
1.56
10.43
0.92
6.12
N7
11
0.00
0.04
-0.72
-16.41
7
-0.09
-2.06
-0.96
-21.82
N8
8
-0.18
-4.14
-0.89
-20.11
4
-0.13
-2.80
-1.05
-23.96
N9
8
-0.91
-56.99
-0.94
-58.50
9
-0.67
-41.93
1.05
-41.43
S5
10
4.75
24.32
2.58
18.72
6
4.73
24.24
2.02
14.60
S6
11
0.47
29.40
0.39
24.62
4
0.45
28.02
0.42
26.25
S8
8
1.16
30.58
1.07
28.18
6
1.10
29.00
1.07
28.13
S11
7
1.59
41.97
1.48
39.09
4
1.51
39.87
1.36
35.86
S12
8
3.24
16.59
2.11
15.26
5
3.03
15.53
1.83
13.23
S13
8
0.90
24.41
0.89
24.08
7
0.84
22.74
0.88
23.80
Figure 3.6: Measured and simulated heads for piezometers located in Grass Lake in
2010. Piezometers that show major differences between the fully saturated simulations
(blue circles) and simulations that include unsaturated properties (red plus) are labeled.
140
Figure 3.7: Measured and simulated heads for piezometers located in Grass Lake in
2011. Piezometers that show major differences between the fully saturated simulations
(blue circles) and simulations that include unsaturated properties (red plus) are labeled.
Response to Predicted Precipitation Changes
Simulations with a rain dominated precipitation regime show lower pressure
heads and unsaturated conditions throughout the peatland (Figure 3.9). The maximum
pressure heads simulated in the peatland for the rain dominated regime occur at the end
of the wet season (end of May). These maximum pressure heads are comparable to
those occurring at the end of the water year (Oct) in the “fully saturated” snow melt
dominated simulations. The maximum pressure heads and area with pressure heads
greater than zero are larger in the “fully saturated” snow melt dominated simulations,
141
and larger still in the unsaturated snow melt dominated simulations. In simulations using
the model calibrated to 2010 heads, most of the peatland experiences maximum
pressure heads greater than -0.2 m while the upper peatland to the east experiences
maximum pressure heads less than -1.0 m. In simulations using the model calibrated to
2011 heads, a large portion of the western peatland experiences maximum pressure
heads less than -0.4 m and the upper peatland to the east experiences maximum
pressure heads less than -2.0 m. A swath along the hillslope east of Feel Meadows
Creek shows pressure heads above 5.0 meters at the end of the wet season, suggesting
this may be a site of significant seasonal groundwater discharge in a rain dominated
system.
The pressure heads and degree of saturation decrease through the dry season
(June-Oct) as ET fluxes remove water and the surrounding watershed continues to
drain. In simulations using the model calibrated to 2010 heads, pressure heads less
than -0.4 m occur to the west of First Creek and to the east of Freel Meadows Creek by
the end of the water year. In simulations using the model calibrated to 2011 heads, this
same area experiences pressure heads less than -0.7 m. This suggests a large portion
of the peatland may be susceptible to desaturation under a rain dominated regime. The
upper peatland experiences pressure heads as low as -1.5 m using the 2010 calibrated
parameters and -2.7 m using the 2011 calibrated parameters. In all cases, the pressure
head in the peatland is less than zero by the end of the water year, indicating
unsaturated conditions and the potential for peat decomposition.
142
143
Figure 3.8: Pressure head contours at the end of the water year (October) for saturated (a and b) and unsaturated (c and d)
simulations using parameter and recharge estimates from 2010 (a and c) and 2011 (b and d).
144
Figure 3.9: Simulated pressure head in Grass Lake resulting from a rain dominated precipitation regime. Simulations are shown at
the end of the wet season (a and b) and the end of the water year (c and d). Parameter values are based on estimates from 2010 (a
and c) and 2011 (b and d) model calibrations.
DISCUSSION
A watershed scale model that includes spatially explicit geology was calibrated to
head observations made during the summer following an average water year (2010) and
an above average water year (2011). Parameter estimates from both calibrations were
comparable for all parameters except the hydraulic conductivity of the alluvial deposits
(Kalluv). Consideration of unsaturated properties of the subsurface material reduced the
discrepancy between the measured head and simulated head, as well as the average
weighted residual and overall sum of squared, weighted residuals used to drive the
calibration process. However, due to long computation times the unsaturated model
was not calibrated. The largest discrepancies between heads measured in the field and
simulation results occur at piezometers located near West Freel Meadows Creek and
Waterhouse Creek. Model fit might be improved by better characterization of the
geometry and hydrologic properties of the alluvial fan deposits.
The calibrated models were used to explore the potential response of the
peatland to the predicted change from a snow melt dominated precipitation regime to a
rain dominated precipitation regime. For both sets of parameters the pressure head in
the peatland is significantly reduced in the simulations of a rain dominated regime. The
magnitude and spatial distribution of pressure heads are significantly different in the rain
dominated system compared to the snow melt dominated system. Pressure heads at
the end of the wet season (May) in the rain dominated system are lower than pressure
heads at the end of the water year in the snow melt dominated system. Summer ET and
watershed drainage further dry the peatland, resulting in much lower pressure heads by
the end of the water year. The east and west ends of the peatland experience the
lowest degree of saturation, reaching levels less than 70% by the end of the water year.
The central portion of Grass Lake proper maintains high levels of saturation, which may
145
be partially attributed to the specified head boundary condition imposed on the open
water.
This study suggests a rain dominated precipitation regime may lead to
desaturation of the Grass Lake peatland. The most significant drying is expected to
occur in the eastern and western portions of the peatland, resulting in approximately half
of the peatland experiencing saturation levels 70% or less of total saturation by the end
of the water year. This is expected to lead to increased aerobic decomposition near the
edges of the peatland (Clymo, 1984). The predicted increase in temperature is expected
to further increase the rate of peat decomposition (Ise, Dunn, Wofsy, & Moorcroft, 2008).
The center of the peatland maintains saturation levels above 80% of total saturation in
all simulations, suggesting this area is least susceptible to aerobic decomposition and
may contain the longest history of peat accumulation despite changes in the precipitation
regime.
146
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