WATER RESOURCES RESEARCH, VOL. 44, W07417, doi:10.1029/2007WR006442, 2008
Physics-based continuous simulation of long-term near-surface
hydrologic response for the Coos Bay experimental catchment
Brian A. Ebel,1 Keith Loague,1 David R. Montgomery,2 and William E. Dietrich3
Received 15 August 2007; revised 20 February 2008; accepted 2 May 2008; published 29 July 2008.
[1] The study reported here employed the physics-based Integrated Hydrology Model
(InHM) to conduct continuous hydrologic-response simulation from 1990 through 1996
for the Coos Bay experimental catchment. The uniqueness of the boundary-value problem
used to simulate three sprinkling experiments was assessed, via model performance
evaluation against observed piezometric and discharge data, for 33 events extracted from
the continuous record. The InHM simulations could not adequately reproduce the
distributed observed pore water pressures, suggesting that detailed characterization of the
locations and connectivities of bedrock fractures is critical for future efforts designed to
simulate distributed hydrologic response at the field scale for locations where bedrock
fracture flow is important. The simulations presented here suggest the potential for
interaction between the deeper water table and near-surface hydrologic response. The
results reported herein suggest that while uniqueness can be reasonably achieved with
respect to the integrated response (i.e., discharge), the integrated response uniqueness is no
guarantee that the distributed response (i.e., pressure head) is either unique or well
simulated.
Citation: Ebel, B. A., K. Loague, D. R. Montgomery, and W. E. Dietrich (2008), Physics-based continuous simulation of long-term
near-surface hydrologic response for the Coos Bay experimental catchment, Water Resour. Res., 44, W07417,
doi:10.1029/2007WR006442.
1. Introduction
1.1. Motivation
[2] Hydrologic-response models based on numerical solutions to the coupled partial differential equations governing
surface and subsurface flow are commonly described as
‘‘physically-based’’ or ‘‘physics-based’’ [see Freeze and
Harlan, 1969; Loague and VanderKwaak, 2004]. One of
the purported attractions of physics-based models is that (in
theory) the governing equations, boundary conditions, and
parameter values calibrated to a brief hydrologic record
should then apply to most hydrologic conditions, even those
conditions beyond the successfully tested range [see Abbott
et al., 1986; Bathurst and O’Connell, 1992]. The question
of whether hydrologic response can be simulated as well for
a validation period outside of a calibration period addresses
the issue of uniqueness. The definition of uniqueness
[Neuman, 1973; Carrera and Neuman, 1986] requires that
only one set of parameter values can be estimated from a
given set of observations and that this parameter set must
also represent the observed behavior for other hydrologic
conditions. When employing a distributed model, the simulated hydrologic response should be compared to distrib1
Department of Geological and Environmental Sciences, Stanford
University, Stanford, California, USA.
2
Department of Earth and Space Sciences, University of Washington,
Seattle, Washington, USA.
3
Department of Earth and Planetary Science, University of California,
Berkeley, California, USA.
Copyright 2008 by the American Geophysical Union.
0043-1397/08/2007WR006442
uted observations of state variables in the watershed [see
Dunne, 1983; Beven, 1989; Grayson et al., 1992; O’Connell
and Todini, 1996]. A focus on the distributed response is of
particular importance for physics-based simulation because
of the many degrees of freedom (e.g., parameters, boundary
conditions), which can give rise to equifinality when only
the integrated response (i.e., discharge or solute concentrations in discharge) is used for evaluation [e.g., Beven,
1989, 2006; Ebel and Loague, 2006]. An additional question is whether uniqueness with regard to simulation of the
integrated response indicates if uniqueness for the distributed response will also be achieved (or if the distributed
response will be simulated correctly for any storm, much
less all storms).
[3] Despite the importance of employing both integrated
(e.g., discharge) and distributed (e.g., piezometric, soilwater content, or surface water depth) observations when
evaluating the simulated hydrologic response during a
validation period, there are relatively few studies addressing
this issue. Refsgaard [1997] reported an application of a
physically based hydrologic model where discharge and
piezometric response were shown to be nonunique for a
validation period following a calibration period. Feyen et al.
[2000] found that discharge at the catchment outlet was well
simulated during a validation period after calibration, but
internal discharges and water table levels were not well
simulated during the validation period. Anderton et al.
[2002] reported physically based simulation results in which
discharge, soil-water content, and water table levels were all
simulated worse during the validation period following a
calibration period. Bathurst et al. [2004] found that discharge, internal water table, and pressure head values were
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correctly simulated during a blind validation test. Heppner
et al. [2008], employing a characterization developed from
event-based simulations for long-term continuous simulation
with a physics-based model, found that water balance components, peak discharge, and sediment discharge were each
well simulated while distributed soil-water contents were
poorly simulated in their continuous hydrologic modeling.
[4] Clearly no consensus has been reached as to how
robust physics-based hydrologic-response models are (or
can be) with respect to uniqueness, especially with regard to
simulation of distributed hydrologic response. Yet the
question of uniqueness is of fundamental importance if
physics-based hydrologic simulations are to provide a
reliable foundation for investigations of physical processes
where the distributed hydrologic response is important, for
example, hydrogeomorphology [e.g., Loague et al., 2006;
Mirus et al., 2007]. This study examines the uniqueness of
physics-based simulation of the integrated and distributed
hydrologic response for a well characterized field site.
1.2. Objectives and Study Design
[5] The principal goal of the study presented here is to
employ continuous hydrologic-response simulation for a
nearly 7-year period to assess the uniqueness of the hydrologic parameterization and boundary conditions (BCs) used
by Ebel et al. [2007b] to simulate three sprinkling experiments at the Coos Bay 1 (CB1) catchment. Hydrologicresponse simulation of high-intensity storms at the CB1 site
is of particular interest because the field site experienced
slope failure during a storm with a high rainfall intensity (i.e.,
40 mm h1) and large rainfall depth (i.e., total accumulation
of 221 mm) in November 1996 (D. R. Montgomery et al.,
Instrumental record of debris flow initiation during natural
rainfall, manuscript in preparation, 2008). An additional
objective of this study is to further illustrate the potential
benefits and limitations of using 3-D, transient, variably
saturated hydrologic-response models to drive simulationbased hydrogeomorphology process investigations [see
Loague et al., 2006].
[6] The study reported here builds upon the three separate
week-long sprinkling experiments at the CB1 catchment
conducted in 1990 and 1992 [Anderson et al., 1997a,
1997b; Anderson and Dietrich, 2001; Montgomery et al.,
1997, 2002; Montgomery and Dietrich, 2002; Torres et al.,
1998]. Important conclusions from the CB1 field study
include the critical role of unsaturated flow in governing
the hydrologic response at CB1 [Torres et al., 1998] and the
contributions from fracture flow through the weathered
bedrock for pore water pressure development and runoff
generation [Anderson et al., 1997b; Montgomery and Dietrich,
2002; Montgomery et al., 1997, 2002]. Data from the three
sprinkler experiments and site characterization from the
long-term monitoring effort at CB1 were further analyzed
by Ebel et al. [2007a] to define the boundary-value problem
(BVP) for event-based hydrologic-response simulations
using the physics-based Integrated Hydrology Model
(InHM) [see Ebel et al., 2007b]. The CB1 simulations
reported by Ebel et al. [2007b] focus on runoff, pressure
heads, soil-water contents, and solute transport during the
sprinkler experiments and led to the conclusions that
(1) characterization of layered permeability contrasts was
important for hydrologic-response simulation, (2) neglecting fracture flow through the weathered bedrock precluded
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simulating the locations of some pore water pressure ‘‘hotspots,’’ and (3) in situ measurements of soil-water retention
provided superior parameterization, with regard to simulation of hydrologic response, than soil-texture based estimates for the CB1 soil.
[7] It should be noted that there are several important
differences between the study reported here and the sprinkling experiment simulations from Ebel et al. [2007b]. For
example, the week-long sprinkling experiments were
designed to bring the system to a hydrologic steady state,
while the variable duration storms considered in the continuous simulations reported here are transient in nature
(i.e., shorter event durations with large temporal variability
in rainfall intensities). The sprinkler experiments were conducted at relatively low intensities (i.e., 1.5– 3.0 mm h1)
while the intensities considered in this effort range up to
40 mm h1 (only 10 min in duration prior to the 1996 slope
failure). Unsaturated zone observations (e.g., pressure
heads, soil-water contents, deuterium concentrations) were
collected during the sprinkling experiments while only
piezometric and runoff data exist for the long-term effort
reported here. The event-based sprinkling experiment initial
conditions (ICs) were more closely controlled to match the
observed ICs including the deeper water table location,
while the ICs for storms during the long-term effort are
the result of months to years of previously simulated
continuous hydrologic response.
[8] The sprinkling experiment BVP [see Ebel et al.,
2007a, 2007b], referred to hereinafter as the ‘‘Base Case,’’
is used to simulate the 7 years of hydrologic response at
CB1 from 1990 through the 1996 failure. The Base Case
BVP is evaluated against runoff and piezometric data to
assess model performance and uniqueness. Alternate BVPs,
based on alternative viable parameterizations, are assessed
in the context of a sensitivity analysis to improve the
uniqueness of the CB1 BVP. It is worth pointing out that
it is not the intention of this study to meticulously calibrate
the InHM BVP to match the observed data, ‘‘declare
victory,’’ and move on. Instead, problems with the CB1
BVP uniqueness and mismatches between the observed and
simulated hydrologic response are employed to suggest
hydrologic-response observations and measurements that
would improve the uniqueness of the BVP and could be
of particular importance for simulating the hydrologic conditions preceding slope failure.
2. CB1 Field Site
[9] The CB1 study area is located 15 km northeast of the
cities of Coos Bay/North Bend (OR) near Mettman Ridge.
The 860 m2 catchment consists of a steep (43° slope)
unchanneled hollow. Clear-cut logging was completed in
1987, a broadleaf herbicide was applied in 1988, and
Douglas Fir (Pseudotsuga menziesii) seedlings were planted
in 1989 [Montgomery, 1991]. The mean annual rainfall at
the North Bend (OR) airport is 1.6 m a1 [Taylor et al.,
2005] and is distributed into a wet winter season and dry
summer season. Subsurface stormflow is the primary runoff-generation mechanism at CB1 [Montgomery et al.,
1997; Montgomery and Dietrich, 2002; Torres et al.,
1998]. The long-term monitoring effort employed detailed
site measurements of surface and geologic-interface topography, soil-hydraulic properties, and three sprinkling/tracer
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soil runoff contribution; the lower weir was installed in
October 1991, and monitored the weathered and unweathered bedrock runoff contribution that flowed underneath the
upper weir. Soil and saprolite piezometric response was
monitored from 22 automated piezometers installed in nine
nests prior to the first sprinkling experiment in 1990.
Weathered bedrock piezometric response was monitored
using 12 piezometers installed after the second sprinkling
experiment in 1990. Five of the soil/saprolite piezometers
(5 – 3, 5– 3A, 7 – 6, 9 – 5, and 9 – 5D; see Figure 1) recorded
pressure head to a precision of 0.1 m from 1 December
1993 through the landslide and therefore are only useful for
evaluating saturation during that period. Four of the weathered bedrock piezometers (B4, B4A, B5, and B5A; see
Figure 1) were outside the area simulated and two of the
weathered bedrock piezometers (B1A and B9A; see Figure 1)
had negative values because of pressure transducer problems and are consequently not used for simulated pressure
head evaluation. The deep well at the ridge crest shown in
Figure 1 was completed to a depth of 35 m (see Anderson et
al. [2002] for further information). Figure 2a shows the
monthly rainfall at North Bend airport, and Figure 2b
illustrates the continuity of the discharge and piezometer
records during the simulated period. The temporal resolution of both the discharge and piezometric records varied
between 600 s (in the winter rainy season) and 1200 s (in
the summer dry season). The weir and piezometer observations were recorded by data loggers until the 1996 landslide,
which destroyed most of the monitoring equipment.
4. The Hydrologic-Response Model
Figure 1. Locations of the Coos Bay 1 (CB1) instrumentation used in the boundary condition specification and
model performance evaluation for the long-term Integrated
Hydrology Model (InHM) hydrologic-response simulations
[after Ebel et al., 2007b] (reprinted by permission of the
American Journal of Science). Piezometer notations reference a platform number followed by an instrument number
and a letter to indicate depth (after the notation of
Montgomery et al. [2002]). MSL, mean sea level.
experiments to characterize hydrologic response at CB1 [see
Anderson et al., 1997a, 1997b; Montgomery et al., 1997,
2002; Montgomery and Dietrich, 2002; Torres et al., 1998].
3. Long-Term Hydrologic-Response Data at CB1
[10] Figure 1 shows the locations of the long-term (i.e.,
1990 – 1996) hydrologic-response observations collected at
CB1. The long-term data set consisted of discharge from
two weirs and automated piezometers installed into soil,
saprolite, and weathered bedrock [see Montgomery et al.,
1997, 2002; Montgomery and Dietrich, 2002]. The upper
weir was installed in November 1989, and monitored the
[11] The Integrated Hydrology Model (InHM) was originally developed by VanderKwaak [1999] to quantitatively
simulate fully coupled 3-D variably saturated subsurface flow
and 2-D surface/channel flow. InHM is capable of simulating
the four principal runoff generation mechanisms: Horton
overland flow (i.e., infiltration excess), Dunne overland flow
(i.e., saturation excess), subsurface stormflow, and groundwater. The flexibility of InHM has facilitated successful
simulation of hydrologic response for a variety of catchment
sizes and hydrologic environments [see VanderKwaak, 1999;
VanderKwaak and Loague, 2001; Loague and VanderKwaak,
2002; Loague et al., 2005; Mirus et al., 2007; Heppner, 2007;
Heppner et al., 2006, 2008; Jones et al., 2006; Ebel et al.,
2007b; Carr, 2006; Ran, 2006; Smerdon et al., 2007]. InHM
employs the control volume finite element method to solve
the governing equations. The subsurface and surface solute
transport [VanderKwaak, 1999; Jones et al., 2006; Ebel et al.,
2007b] and surface sediment transport capabilities [Heppner
et al., 2006, 2008; Ran et al., 2007] of InHM are not utilized
in this study.
4.1. Subsurface Flow
[12] Subsurface flow in 3-D variably saturated porous
media is estimated in InHM using
q qb qe ¼ f v
r f a~
@fSw
;
@t
ð1Þ
where ~
q is the Darcy flux [LT1], qb is a specified rate
source/sink [T1], qe is the rate of water exchange between the
subsurface and surface continua [T1], f is porosity [L3 L3],
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Figure 2. (a) Plot of the monthly rainfall depth from the continuous daily precipitation records from the
National Climatic Data Center record from the North Bend (Oregon) Municipal Airport. (b) Plot of
hydrologic data temporal coverage during the continuous simulation period. The white areas indicate
gaps in the records. Upper, middle, and lower piezometers are the soil/saprolite piezometers in the
upslope, midsection, and lower (i.e., near the upper weir) portions of CB1. The piezometers are in groups
based on which data logger recorded the observations.
Sw is water saturation [L3 L3], t is time [T], f a is the area
fraction associated with each continuum [-], and f v is the
volume fraction associated with each continuum [-]. The
Darcy flux is estimated as
~
q ¼ krw
rw g ~
krðy þ zÞ;
mw
ð2Þ
where krw is the relative permeability [-], rw is the density of
water [ML3], g is the gravitational acceleration [LT2], mw
is the dynamic viscosity of water [ML1T1], ~
k is the
intrinsic permeability vector [L2], z is the elevation head
[L], and y is the pressure head [L].
4.2. Surface Flow
[13] Surface flow is estimated using the diffusion-wave
approximation of the depth-integrated shallow water equations. The 2-D surface flow is conceptualized as a second
continuum linked with the subsurface via a thin soil layer of
thickness, as [L], with fluxes between the continua determined by dynamic pressure-head gradients [VanderKwaak,
1999]. The equation for conservation of water on the land
surface is
@ Sws hs þ ystore
s
mobile
b
e
q~s as q as q ¼
;
r ys
@t
ð3Þ
where ys [L] is the water depth with the superscripts mobile
and store denoting mobile versus stored water, ~
qs is the
surface water velocity [LT1], qb is the source/sink rate (that
is, rainfall/evapotranspiration) [T1], qe is the surfacesubsurface water exchange rate [T1], Sws is the surface
saturation [-], and hs is the average height of nondiscretized
surface microtopography [L]. A 2-D form of the Manning
water depth/friction discharge equation is used to estimate
surface water velocities as
~
qs ¼ ymobile
s
2=3
~
nF1=2
rðys þ zÞ;
ð4Þ
where ~
n is the Manning’s surface roughness tensor [TL1/3]
and F is the friction (or energy) slope [-].
5. CB1 Boundary-Value Problem: Base Case
[14] The BVP used in this study consists of equations (1)–(4),
the finite element method of numerical solution, the BCs,
the ICs, and a spatial parameterization of the surface/nearsurface hydraulic properties. The Base Case BVP [see Ebel
et al., 2007a, 2007b] for the CB1 simulations reported here
is summarized in the following sections.
5.1. Finite Element Discretization
[15] The CB1 finite element mesh consists of 264,220
prism elements (138,544 nodes) in the subsurface and 4804
triangular elements (2474 nodes) for the surface. The
vertical mesh discretization (Dz) varies from 0.04 m (near
surface) to 1.67 m (at depth) and the horizontal mesh
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element mesh. The volumetric boundary flux (Qb,l) [L3T1]
is calculated for a boundary node as
Qb;l ¼ krw
Figure 3. Fence diagram showing the hydrogeologic
characterization of the CB1 boundary-value problem [after
Ebel et al., 2007b] (reprinted by permission of the American
Journal of Science). The lettering is used to describe the
boundary conditions (see section 5.2).
discretization (Dx, Dy) varies from 0.4 m (down-gradient
areas, along the measurement platforms, and near the
hollow axis) to 2.0 m (near the up-gradient boundaries).
An adaptive time step (Dt) that ranged from several seconds
to a few hours was used.
5.2. Boundary Conditions
[16] The lettering in Figure 3 identifies the points of
interest for the BC description below. Impermeable BCs
are specified for the drainage divides at the side boundaries
for the surface (AE and BH) and subsurface (ADJE and
BCIH), the up-gradient surface drainage divide (AB) at the
ridge crest, and the basal subsurface BC (DCIJ). The depth
of the basal boundary was set deep enough so that the BC
did not impact simulated near-surface hydrologic response.
The CB1 upper weir (see Figures 1 and 3) consists of sheet
metal sealed to the bedrock using concrete and is represented using an impermeable subsurface BC (along FG
from the surface to the top of the weathered bedrock) and
a critical depth [see Chow, 1959] surface flow BC (FG). The
up-gradient (ABCD) and down-gradient (EHIJ) subsurface
BCs (except for the upper weir) use a local head BC, as
described by Heppner et al. [2008]. The local head BC
represents a known hydraulic head value (that can be time
variable) at a point outside the boundaries of the finite
rw g ~ hl hb;pm
kA
;
dl
mw
ð5Þ
where hl is the total head at the local head point [L], hb,pm is
the total head for the porous medium equation at the
boundary node [L], A is the nodal area [L2], and dl is the
(positive) distance in the x-y plane between the node and
the regional sink point [L]. It is worth noting the local head
point is treated as a vertical line of constant potential below
the specified local head point, which results from using the
two-dimensional distance (dl) in equation (5).
[17] For the Base Case long-term simulations, the upgradient local sink is parameterized using the level of the
deep well at the up-gradient ridge crest (see Figure 1). The
time variable well data are used for the period from
7 October 1992 (the start of the automated deep well record)
through failure on 19 November 1996 and the average water
level height (3.69 m) during the period of record is used for
1 January 1990 through 7 October 1992, when there are no
deep well data. It should be pointed out that the up-gradient
(ABCD) subsurface BC in the event-based simulations by
Ebel et al. [2007b] was impermeable, but the local sink BC
used in the effort reported here attempts to better represent
the long-term (i.e., multiple simulated years) deeper water
table dynamics. The down-gradient local head point is a
location of consistent observed surface saturation in the
channel downslope of CB1 just below the lower weir.
[18] A specified flux BC is employed for the surface
(ABHGFE in Figure 3) to represent precipitation fluxes.
The mean rainfall rate from three onsite automated rain
gages (see Figure 1) provides the specified precipitation flux
for the surface BC. The temporal resolution of the rain
gages is either 600 s (during the winter rainy season) or
1200 s (during the summer dry season. Evapotranspiration
is neglected during the entire simulation period; the accuracy of this assumption is evaluated in section 7.1.6.
5.3. Initial Conditions
[19] Because the long-term hydrologic-response simulations are continuous, the ICs (i.e., pressure head at every
subsurface node and the water depth at every surface node)
are specified only at 12:00 A.M., 1 January 1990. The ICs
are the outputs from a yearlong warm-up simulation driven
by the 1990 CB1 rainfall record, which had a total rainfall
depth of 2150 mm (including the two sprinkling experiments that added 463 mm of water). The total rainfall depth
at the North Bend, Oregon, Airport for 1990 was 1598 mm. It
should be noted that the mean and median annual rainfall
depths at the North Bend Airport are 1595 mm and 1596 mm,
respectively, on the basis of 104 years of record.
5.4. Parameterization of Hydraulic Properties
[20] Figure 3 shows a fence diagram of the hydrogeologic
units used to parameterize the CB1 subsurface. Table 1
contains the thicknesses and hydraulic parameter estimates
for each of the CB1 subsurface formations/layers. The soil
and saprolite depths (see Figure 3) were estimated, using
ordinary Kriging, on the basis of the 100 measurements
reported by Montgomery et al. [1997] and Schmidt [1999].
The weathered bedrock layer thickness decreases moving
downslope from the ridge crest [Anderson, 1995] to near-
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Table 1. Hydrogeologic Properties for the CB1 Boundary-Value Problem After Ebel et al. [2007b]
Layera
Thickness
(m)
Porosity
(m3 m3)
Saturated Hydraulic
Conductivity (m s1)
Soil
Saprolite
Weathered bedrock
Unweathered bedrock
0.04 – 1.5b
0.02 – 1.1b
0.02 – 4.0c
50
0.50d
0.15e
0.15e
0.12e
3.4 104f
7.2 105g
5.0 107
5.0 107
Compressibility
(m s2 kg1)
1
1
1
1
108h
109h
109h
109h
a
See Figure 3.
Kriged from 100 data points [Schmidt, 1999], including the CB1 piezometer installation.
From Anderson [1995].
d
Estimated from the retention curves of Torres et al. [1998].
e
Estimated from Figure 3 of Anderson et al. [2002].
f
Arithmetic mean of the surface and subsurface mean estimates.
g
Arithmetic mean from 37 slug tests [see Ebel et al., 2007a].
h
From Freeze and Cherry [1979].
b
c
zero thickness near the upper weir. Soil porosity was
estimated as the mean water content at saturation from the
six retention curve experiments of Torres et al. [1998]. The
saprolite, weathered bedrock, and unweathered bedrock
porosities (see Table 1) were estimated from the CB1 drill
core data contained in the work of Anderson et al. [2002].
[21] The saturated hydraulic conductivity values in Table 1
are based on piezometer slug tests [see Ebel et al., 2007a]
and incipient-ponding sprinkling rates at the surface during
the retention-curve experiments of Torres et al. [1998]. The
uniform hydraulic conductivity values used for each of the
hydrogeologic layers (see Figure 3 and Table 1) are the
result of insufficient data for characterizing the spatial
structure for a meaningful 3-D interpolation [see Ebel et
al., 2007a]. Because of the large range in estimates of
saturated hydraulic conductivity (4 orders of magnitude)
in the weathered bedrock and no discernable spatial pattern
[Montgomery et al., 2002; Ebel et al., 2007a], the unweathered bedrock conductivity and weathered bedrock conductivity were set to the same value for the Base Case. Slug
tests were not conducted in the unweathered CB1 bedrock,
so the unweathered bedrock saturated hydraulic conductivity was estimated (via calibration) to be 5.0 107 m s1.
The range of saturated hydraulic conductivities used for this
calibration was constrained between the range of saturated
hydraulic conductivity estimates calculated from the rate
of water table decline in the deep well during the summer
dry season, which ranged between 4.0 107 m s1 and
5.0 107 m s1.
[22] Figure 4a shows the measured hysteretic soil-water
retention data [see Torres et al., 1998] and the estimated
soil-water retention curve generated using the van Genuchten
[1980] method. The hysteresis representation [Scott et al.,
1983; Kool and Parker, 1987] incorporated by Ebel et al.
[2007b] into InHM is subject to pumping effects with
repeated cycles of wetting and drying, making the method
ill-suited for long-term continuous simulation. While alternate methods of representing hysteresis that do not suffer
from pumping effects exist [e.g., Huang et al., 2005], the
large memory requirements needed to store the many
hysteretic reversals make these methods impractical for
long-term simulation [see Werner and Lockington, 2007].
Consequently, the nonhysteretic hydrologic-response simulations reported here use a ‘‘mean’’ curve between the
delimiting primary wetting and drying soil-water retention
curves. Stauffer and Kinzelbach [2001] found that the mean
curve between the primary wetting and drying soil-water
retention curves was a better approximation for nonhysteretic flow simulation than either the wetting or drying curve.
Figure 4b shows the hydraulic conductivity function estimated using the van Genuchten [1980] method. The 2 m
Figure 4. (a) Observed soil-water retention data [after
Torres et al., 1998] and the estimated nonhysteretic soilwater retention curve using the van Genuchten [1980]
method [after Ebel et al., 2007b] (reprinted by permission of
the American Journal of Science). (b) Estimated hydraulic
conductivity function using the van Genuchten [1980]
method. Note that the –2 m limit denotes the pressure head
range of the Torres et al. [1998] experimental data and is not
a pressure head limit in the simulations.
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Table 2. Rainfall Characteristics of the 33 Selected Storms at CB1
b
Rainfall Intensity
Storm
Numbera
Dates
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
5 – 9 Jan 1990
9 – 11 Jan 1990
7 – 10 Feb 1990
26 – 29 Apr 1990
8 – 14 May 1990d
23 – 27 May 1990f
19 – 23 Nov 1990
24 – 27 Nov 1990
3 – 8 Mar 1991
11 – 14 Mar 1991
7 – 9 May 1991
23 – 29 Nov 1991
5 – 8 Dec 1991
27 – 29 Jan 1992
18 – 22 Feb 1992
8 – 11 Apr 1992
27 May to 3 Jun 1992h
9 – 12 Dec 1992
19 – 23 Jan 1993
1 – 3 Dec 1993
10 – 13 Dec 1993
2 – 6 Jan 1994
31 Oct to 3 Nov 1994
4 – 6 Nov 1994
8 – 11 Nov 1994
8 – 17 Jan 1995
28 Jan to 1 Feb 1995
19 – 22 Jan 1996
26 – 28 Jan 1996
8 – 10 Feb 1996
17 – 19 Feb 1996
22 – 25 Apr 1996
15 – 18 Nov 1996j
Storm Total
Mean Maximum Depth Durationc
(mm h1) (mm h1) (mm) (hours)
2.6
2.2
3.0
3.4
0.7
1.9
1.8
2.2
2.0
2.0
4.1
2.5
3.3
2.9
2.2
2.0
0.8
3.0
2.7
1.4
0.9
1.6
2.6
3.3
2.7
1.2
1.1
2.6
1.6
3.3
2.2
2.1
2.4
12.8
16.3
10.7
13.2
2.0
16.8
12.7
8.1
16.3
13.2
21.8
17.3
13.2
13.2
21.3
10.2
2.0
23.9
22.9
8.6
5.6
7.1
20.6
15.2
19.8
10.2
5.1
17.3
10.7
7.6
9.1
14.2
39.6
111.5
21.7
134.7
76.8
47.4e
183.2g
49.0
62.8
61.7
39.4
55.5
103.5
97.8
48.2
106.0
89.3
71.9i
65.0
97.7
32.2
52.0
93.6
53.2
47.4
46.2
89.1
31.9
65.4
38.7
45.0
66.9
60.9
221.1
78.2, 42.7
11.3, 9.83
72.5, 44.5
26.2, 23.0
131.5, 65.8
97.2, 96.5
71.3, 26.8
65.7, 28.7
84.3, 31.5
41.2, 19.8
55.3, 13.5
95.7, 41.8
48.7, 29.3
27.8, 16.8
85.2, 47.2
49.0, 45.3
166.2, 88.2
18.2, 12.8
77.5, 36.5
27.3, 22.3
81.0, 54.8
91.0, 56.8
55.2, 20.3
17.8, 14.2
21.7, 17.0
194.7, 77.2
84.3, 28.5
46.5, 25.3
45.5, 24.2
16.2, 13.7
40.0, 30.0
50.8, 28.3
91.7, 55.3
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33 selected storms from 1990 through 1996. The selected
storms were chosen because the upper weir peak discharge
exceeds the upper weir peak discharge from the third
sprinkling experiment in 1992. The storm characteristics
(i.e., mean and maximum rainfall intensity, total depth, and
duration) are presented in Table 2. Figure 5a shows the
frequency histogram, which serves as an approximation of
the probability distribution function, of rainfall rates from
the automated rain gages for the nearly 7-year period of
record. Figure 5b is an enlargement of the section of Figure 5a
showing the probabilities of larger (i.e., 10 to 45 mm h1)
rainfall rates. The observed CB1 rainfall record a has a mean
rainfall rate of 1.98 mm h1, a median rate of 1.524 mm h1,
a standard deviation of 2.29 mm h1, and a skewness of
4.52. Table 2 and Figures 5a and 5b provide a framework
for analyzing model performance relative to storm characteristics. It should be noted that the model performance from
the highest-intensity sprinkling experiment (i.e., experiment 2)
a
See Figure 5.
The mean value from the three automated rain gages.
The first number is the elapsed time from the start of rainfall to the
cessation of rainfall, and the second number is the total time during the
storm when observed precipitation is greater than zero.
d
Sprinkling experiment 1.
e
The observed sprinkling depth from the manual rain gages was 196.3 mm.
f
Sprinkling experiment 2.
g
The observed sprinkling depth from the manual rain gages was 267.1 mm.
h
Sprinkling experiment 3.
i
The observed sprinkling depth from the manual rain gages was 250.0 mm.
j
The debris-flow initiating storm that destroyed the upper weir, most of
the piezometers, and much of the infrastructure (e.g., wooden platforms) at
CB1.
b
c
limit to the pressure head axes in Figures 4a and 4b solely
represent the limits of the experimental data collected by
Torres et al. [1998] and are not a ‘‘hard limit’’ to the
simulated pressure heads (i.e., the simulated pressure heads
decline beyond 2 m). The soil-water retention and hydraulic conductivity functions for the saprolite, weathered
bedrock, and unweathered bedrock layers were not measured at CB1 and are parameterized using nonhysteretic
characteristic curve values from Wu et al. [1999] and the
van Genuchten [1980] method.
6. Continuous Long-Term Simulation Results
6.1. Model Performance Evaluation
[23] The performance of InHM was quantitatively and
graphically evaluated relative to discharge and piezometric
data. The performance evaluations were conducted for
Figure 5. (a) Frequency histogram (as an approximation
of the probability distribution function) of the observed
rainfall rates from the automated rain gage record at CB1.
Rainfall rate bins of 0.5 mm h1 are used. (b) Enlarged
section of Figure 5a focusing on the rainfall rates from 10 to
45 mm h1, showing the long tail of the approximated
probability distribution.
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EBEL ET AL.: SIMULATION OF LONG-TERM HYDROLOGIC RESPONSE
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simulated by Ebel et al. [2007b] was not as good as the
model performance for the lower-intensity sprinkling
experiments (i.e., experiments 1 and 3). A more comprehensive range of storms (see Table 2) will better assess
uniqueness of the Base Case BVP [Ebel et al., 2007a,
2007b].
[24] The simulated upper weir data are quantitatively
evaluated for model performance assessment using the Nash
and Sutcliffe [1970] efficiency, calculated [James and
Burges, 1982; Loague and Green, 1991] as
"
EF ¼
n X
i¼1
n
2 X
Oi O ðPi Oi Þ2
#,
i¼1
n X
2
Oi O ; ð6Þ
i¼1
where Pi are the predicted values, Oi are the observed
values, n is the number of samples, and O is the mean of
the observed data. The EF statistic ranges from 1.0 to –1,
with 1.0 indicating a perfect match between Pi and Oi and
EF less than zero indicating that O is a better model than Pi
for simulating Oi. A second measure of model performance
used in this study is the mean absolute bias (MAB) (M.
Kirkby, personal communication, 2005), also called the
mean absolute error [Willmott, 1982], computed with the
relation
n
P
MAB ¼
jðOi Pi Þj
i¼1
n
:
ð7Þ
[25] The third measure of model performance used in this
effort is the percentage of error in the simulated variable,
calculated using
Error ¼
Oi Pi
*100%:
Oi
ð8Þ
[26] Many additional performance statistics exist [see
Willmott, 1982; Loague and Green, 1991], but EF, MAB
(or the similar root mean square error), and errors in the
timing, magnitude, and volumes of simulated and observed
discharge are the most frequently employed in hydrologicresponse simulation at the catchment scale.
6.2. Simulated Discharge Evaluation: Base Case
[27] Table 3 presents the Base Case simulated discharge
performance statistics for the 33 storms and the individual
years from 1990 through 1996. Perusal of Table 3 reveals
that most of the individual events are not well simulated.
Only five of the 33 storms have positive discharge EF
values and only one of the years (1993) has a positive
discharge EF value. It is worth noting that sprinkling
experiments 1 and 3 (storms 5 and 17 in Table 3) were
not as well simulated as in the event-based simulations
reported by Ebel et al. [2007b] for three principal reasons:
(1) the automated rain gage record used in the simulations
reported here underestimates the sprinkling rates during the
experiments because of wind-driven undercatch related to
the sprinkler heights [see Ebel et al., 2007a], (2) the eventbased simulations allow more control over the ICs at the
start of the sprinkling experiment simulation, and (3) the
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event-based simulations incorporate hysteresis in the characteristic curves for the soil.
[28] The best simulated storms (based on EF values) are
2, 7, 8, 9, 10, and 17. The mean precipitation rates observed
during these storms (approximately 2.0 mm h1; see Table 2)
are slightly higher than those observed during the sprinkling
experiments and the storm depths (with the exception of
storm 17, which is sprinkling experiment 3) have small total
rainfall depths. Examination of Figure 4a shows that the
majority of the rainfall rates observed at CB1 are approximately 2 mm h1. The storms with the smallest total
rainfall depths are also, in general, the storms with the
smallest errors in total simulated discharge (e.g., storms 2,
7, 8, 10, and 27). The smallest simulated errors in peak
discharge are also for the storms with the smaller rainfall
depths (e.g., storms 2, 7, 8, 9, 10, 14, and 23). Storms 11,
15, 18, and 19, which all have peak rainfall rates larger than
20 mm h1, are not well simulated on the basis of EF, MAB,
and errors in peak discharge. Examination of Figure 5b
shows that rainfall rates exceeding 20 mm h1 are rare at
CB1, but that observed rates range up to the 40 mm h1
value observed prior to the 1996 slope failure. Storms 20,
22, and 29 all have mean rainfall rates that are approximately equal to the mean irrigation rates applied during
sprinkling experiments 1 and 3, but these storms are not
well simulated relative to EF and total discharge. The events
simulated worst, on the basis of the EF values in Table 3,
overestimate the peak magnitude by a factor of 2 or more.
The peak simulated discharges are consistently larger than
the observed (i.e., 28 out of the 33 storms). The simulated
timing of peak discharge is also consistently larger (slower)
than the observed (i.e., 32 out of the 33 storms). The
simulated total discharge follows the same trend as the
peak magnitude and timing statistics, with 30 out of
the 33 storms having higher simulated, relative to observed,
total discharges.
[29] Figure 6 shows the observed rainfall, observed and
InHM Base Case simulated upper weir discharge, and
observed and InHM simulated cumulative discharge for
three of the seven simulated years. The three years shown
in Figure 6 were chosen to represent the worst (1991), the
median (1992), and the best (1993) simulated discharges
based on EF values for discharge (see Table 3). Gaps in the
observed discharge record shown in Figure 2b are included
in the simulated cumulative discharge shown in Figure 6
and Table 3. All of the cumulative simulated discharges are
larger than the observed cumulative discharges (i.e., 1991 is
more than twice the observed, 1992 overestimates by
approximately 40%, and 1993 overestimates by approximately 60%). The simulated hydrograph shown in Figure 6
for the worst simulated discharge year (1991) supports the
same conclusions reached from Table 3 (i.e., simulated
discharge magnitude is generally overpredicted, and peak
simulated discharge is slower than peak observed discharge). Storms 9 and 10 (see Table 3) in 1991 have
discharge EF values greater than zero, but storms 11, 12,
and 13 are poorly simulated. The year 1992 includes
sprinkling experiment 3 (storm 17) and one of the three
largest observed storms (see storm 15 in Table 3), with
respect to peak discharge, of the 7-year simulated period.
All of the simulated storms in 1992, except the third
sprinkling experiment (storm 17) have oversimulated peak
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Table 3. Model Performance for the Base Case InHM Simulated Discharges at the CB1 Upper Weira
Storm
Numberb
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
1990
1991
1992
1993
1994
1995
1996
Dates
EFc (-)
MABd
(L s1)
Peak Discharge
Errore (%)
Time to Peak
Errore (%)
Total Discharge
Errore (%)
5 – 9 Jan 1990
9 – 11 Jan 1990
7 – 10 Feb 1990
26 – 29 Apr 1990
8 – 14 May 1990f
23 – 27 May 1990g
19 – 23 Nov 1990
24 – 27 Nov 1990
3 – 8 Mar 1991
11 – 14 Mar 1991
7 – 9 May 1991
23 – 29 Nov 1991
5 – 8 Dec 1991
27 – 29 Jan 1992
18 – 22 Feb 1992
8 – 11 Apr 1992
27 May to 3 Jun 1992h
9 – 12 Dec 1992
19 – 23 Jan 1993
1 – 3 Dec 1993
10 – 13 Dec 1993
2 – 6 Jan 1994
31 Oct to 3 Nov 1994
4 – 6 Nov 1994
8 – 11 Nov 1994
8 – 17 Jan 1995
28 Jan to 1 Feb 1995
19 – 22 Jan 1996
26 – 28 Jan 1996
8 – 10 Feb 1996
17 – 19 Feb 1996
22 – 25 Apr 1996
15 – 18 Nov 1996i
1.90
0.29
2.82
2.09
0.65
1.68
0.82
0.57
0.08
0.67
25.1
0.37
2.64
0.39
4.29
2.31
0.30
16.9
10.4
11.4
1.78
9.71
1.87
2.79
1.67
6.13
4.41
30.0
9.52
24.5
8.29
1.71
2.10
0.41
1.96
0.78
0.36
0.45
0.74
14.1
0.11
0.03
0.16
0.14
0.07
0.13
0.01
0.03
0.04
0.03
0.33
0.10
0.19
0.06
0.14
0.10
0.04
0.13
0.06
0.11
0.10
0.09
0.06
0.10
0.07
0.12
0.06
0.14
0.12
0.28
0.14
0.04
0.21
0.03
0.03
0.03
0.03
0.04
0.04
0.05
79.1
2.9
107.5
108.3
56.2
101.6
7.9
5.7
1.9
9.0
465.9
75.9
124.3
34.5
75.0
142.9
41.53
184.2
122.1
137.9
21.2
156.9
37.2
67.3
89.2
92.0
84.0
155.7
102.8
202.3
134.3
69.3
86.9
74.7
69.6
88.5
5.8
8.7
3.4
22.8
62.2
1.7
71.9
10.9
5.4
7.9
81.8
4.1
13.0
18.4
39.5
27.27
75.0
42.0
30.5
53.3
70.8
33.9
304.3
5.1
28.8
20.2
15.2
10.5
9.0
0.5
69.3
22.1
79.7
98.0
60.1
60.6
2.9
4.7
29.2
7.5
266.6
68.0
88.8
54.7
119.0
88.1
32.3
110.1
22.5
160.6
73.3
83.5
91.4
112.0
114.4
52.2
22.8
100.6
79.6
136.1
83.7
32.0
94.7
109.4
130.6
43.5
61.3
17.7
26.7
160.9
a
See Figure 1 for the weir location.
See Figure 5.
c
Modeling efficiency.
d
Mean absolute bias.
e
Error is calculated as (observed minus simulated) divided by observed *100%.
f
Sprinkling experiment 1.
g
Sprinkling experiment 2.
h
Sprinkling experiment 3.
i
The debris-flow initiating storm that destroyed the upper weir, most of the piezometers, and much of the infrastructure (e.g., wooden platforms) at CB1.
b
discharges. The year 1993 is the best simulated annual
discharge because of data gaps during the larger storms
(see Figures 2b and 6), which results in the EF statistic
being weighted toward the dry season when both simulated
and observed discharges are near zero.
[30] The trends to be gleaned, relative to improving the
InHM Base Case BVP at CB1 on the basis of the simulated
versus observed discharge statistics in Table 3 and hydrographs in Figure 6, are clear in some respects and ambiguous in others. The best simulated EF values (i.e., storms 2,
7, 8, 9, 10, and 17 in Table 3) are for events with small
storm depths and peak observed discharges of the same
magnitude as the two lower-intensity sprinkling experiments simulated by Ebel et al. [2007b]. Storms with
maximum rainfall rates greater than 20 mm h1 (e.g., 11,
15, 18, and 19) are poorly simulated and storm with rainfall
rates less than or nearly equal to the irrigation rates used in
sprinkling experiments 1 and 3 are also not well simulated.
Searching for further trends employing measures of IC, such
as the antecedent precipitation index [see Kohler and
Linsley, 1951], yielded little in terms of identifiable trends.
One clear trend, based on the peak discharge timing and
magnitude errors and the total discharge error, is that the
InHM simulations consistently overestimate discharge magnitude. Another obvious trend is that the Base Case simulated peak discharge response is slow relative to the
observed. It appears that the simulated storage in the
unsaturated zone allows InHM to simulate storms with a
small rainfall depth and peak discharge approximately equal
to sprinkling experiments 1 and 3 reasonably well. Storms
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Figure 6. Observed hyetographs, observed and InHM Base Case simulated upper weir discharge, and
cumulative observed and InHM Base Case simulated upper weir discharge for the worst (1991), median
(1992), and best (1993) simulated hydrographs evaluated on the basis of EF and total discharge error. See
Tables 2 and 3 for the storm numbers, rainfall characteristics, and model performance evaluation
statistics.
with larger rainfall depths highlight an error in the Base
Case BVP related to either the way water is transmitted in
the weathered bedrock (thus bypassing the upper weir that
collects soil-water flow) or additional storage that is not
well simulated (perhaps in the fractured weathered and
unweathered bedrock).
6.3. Simulated Piezometric Response Evaluation: Base
Case
[31] The CB1 piezometers were poorly simulated, in
terms of simulated saturation and pressure head magnitudes
and dynamics, during the continuous simulations using the
Base Case BVP. Nearly all the simulated piezometers
remained below the 0.03 m detection threshold of the
observed piezometers (owing to a 0.03 m PVC cap height)
throughout the entire 7-year simulation period, with the
exception of piezometer nest 0– 1 (see Figure 1). These
simulations support the observation-based conclusions from
Montgomery et al. [1997, 2002] that pore water pressure
generation in the CB1 soil is principally controlled by
bedrock fracture flow exfiltrating into the overlying soil,
not perched saturation at the soil-bedrock interface. The
extremely high saturated hydraulic conductivity of the soil,
the large topographic component to the hydraulic gradient
(owing to the steep slope), and the hydraulically conductive
bedrock prevent perched saturation at the soil-bedrock
interface from contributing significantly to pore water
pressure generation in the soil. This is consistent with the
simulated piezometric response from the event-based sprinkling experiment simulations from Ebel et al. [2007b],
which lead to the conclusion that capturing the pore water
pressure dynamics at the soil-bedrock interface would be
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difficult without incorporating spatially variable fracture
flow through the weathered bedrock.
7. Discussion
7.1. Why Does the Base Case BVP Poorly Simulate the
CB1 Hydrologic Response?
[32] It is clear from the simulated upper weir runoff and
piezometric response that the Base Case BVP did not
perform well over all the 33 storms evaluated. Numerous
potential reasons for this nonuniqueness exist. For example,
there is some uncertainty in the subsurface hydraulic parameterization (e.g., effective hydraulic conductivities). It is
also clear from the previous field data analysis [Anderson et
al., 1997b; Montgomery et al., 1997, 2002] that bedrock
fracture flow is critical for developing localized regions of
elevated pore water pressure and saturation in the soil.
Montgomery et al. [2002] noted that the deeper water table
position at CB1 is high and may interact with the soil to
influence runoff production and piezometric response immediately upslope of the upper weir. One possibility is that
a rise in the deeper water table, on a seasonal and stormdriven basis, may connect the soil with the saturated
subsurface via bedrock fracture flow pathways driven by the
large gradient associated with the steep slope [Montgomery et
al., 2002]. If this is the case, the poor simulation of the deeper
water table position (i.e., the simulated water table position
is commonly several meters below the observed water table
position in the bedrock piezometers) combined with not
representing fractures in the weathered and unweathered
bedrock may preclude accurate simulation of the piezometric response.
[33] A suite of hydrologic-response simulations, in the
context of a sensitivity analysis, were conducted for the year
1990 to investigate problems with the Base Case BVP and
uncertainty in the InHM simulations. These alternate BVPs
were selected to represent parameterizations that could be
deemed viable on the basis of observations and measurements at CB1, rather than arbitrarily adjusting the Base Case
parameters (e.g., ±20%). All the sensitivity analyses employ
the same ICs as the Base Case, with the exception of some
of the BC sensitivity analyses. While using the same ICs
facilitates direct comparisons with the Base Case, it is
possible that the low simulated water table position for
the IC may affect the outcome of the alternative simulations.
The sensitivity analyses are summarized in the following
sections. Selected simulations that improved aspects of
runoff generation are shown in Figure 7. EF statistics for
the selected simulations shown in Figure 7, compared to the
Base Case, are given in Table 4.
7.1.1. Saturated Hydraulic Conductivity of the
Unweathered Bedrock
[34] As neither pump nor slug tests were conducted in the
CB1 deep well, the water table decline during the dry
season was used to estimate the hydraulic conductivity of
the unweathered bedrock for the Base Case BVP. To
investigate the sensitivity of the simulated hydrologic response to the unweathered bedrock saturated hydraulic
conductivity, a simulation was conducted with the unweathered bedrock saturated hydraulic conductivity equal to twice
the value (i.e., 1.0 106 m s1) used in the Base Case
simulation. It is important to note that the weathered and
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unweathered bedrock hydraulic conductivities were set to
the same value in this simulation (as in the Base Case).
Simulated runoff generation is moderately sensitive to
doubling the unweathered bedrock hydraulic conductivity
(see Figure 7 and Table 4). The timing of the simulated
discharge response is essentially unaffected by doubling the
unweathered bedrock conductivity. Table 4 shows some
improvement in the simulated discharge EF values owing
to the reduction in simulated discharge magnitudes because
the higher unweathered bedrock conductivity facilitates
more leakage to the deeper groundwater system. The
simulated piezometric response from doubling the unweathered bedrock hydraulic conductivity is equally as poor as for
the Base Case.
[35] In addition to fractures, another parameterization
uncertainty is lithologic heterogeneity of the CB1 bedrock.
Lithologic analyses of the unweathered bedrock core from
the deep well installation described by Anderson et al.
[2002] revealed nearly flat bedded, primarily sandstone
lithology with some shale beds. The shale beds were
principally concentrated at 277 m elevation and a fault
was observed at 275 m, coinciding with the minimum water
table height observed in the deep well [Anderson et al.,
2002]. A simulation was conducted incorporating a planar
low-permeability zone located at 277 m elevation within the
unweathered bedrock layer to represent the shale beds using
a hydraulic conductivity of 1.0 1011 m s1 [Freeze and
Cherry, 1979]. The shale layer is not present in the
weathered bedrock layer in the simulations and therefore
does not intersect the soil bedrock interface. The effect of
the low-permeability zone on the simulated piezometric
response in the soil and the simulated upper weir discharge
was not significant.
7.1.2. Saturated Hydraulic Conductivity of the
Weathered Bedrock
[36] Simulations investigating the control of weathered
bedrock saturated conductivity on runoff and piezometric
responses were conducted using the geometric mean (1.7 106 m s1) and arithmetic mean (1.7 105 m s1) of the
weathered bedrock slug test estimates [see Ebel et al.,
2007a]. The timing of simulated discharge was insensitive
to the weathered bedrock hydraulic conductivity parameterization. The simulated discharge magnitude was moderately
sensitive to the hydraulic conductivity of the weathered
bedrock. As most of the Base Case simulated discharges are
overestimated, increasing the weathered bedrock conductivity results in less simulated discharge (through the soil)
captured at the upper weir. The discharge EF values are
improved considerably for the larger storms (e.g., storms 1,
3, 4, and 6 in Table 4 and Figure 7) and are slightly worse
for the smaller storms (e.g., 2, 5, 7, and 8 in Table 4 and
Figure 7) for the arithmetic mean parameterization. With
respect to storm rainfall depth, the storms with smaller
depths (e.g., 2 and 7 in Table 2) are simulated worse and
the storms with larger rainfall depths (e.g., 1 and 3 in Table 2)
are better simulated with respect to EF for the arithmetic
mean parameterization. The discharge EF for all of 1990 is
positive for the arithmetic mean parameterization. The
simulated piezometers are as poor as in the Base Case.
7.1.3. Saturated Hydraulic Conductivity of the Soil
[37] Two new simulations were conducted using the
arithmetic (i.e., 1.1 104 m s1) and geometric (i.e.,
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Figure 7. Observed and InHM simulated upper weir discharge, cumulative observed and InHM
simulated upper weir discharge, and hyetographs during 1990, including eight selected storms for the
Base Case and three alternate parameterizations: (1) doubling the unweathered bedrock hydraulic
conductivity, (2) the arithmetic mean of the weathered bedrock hydraulic conductivity estimates, and
(3) the arithmetic mean of the soil subsurface saturated hydraulic conductivity estimates.
6.2 105 m s1) mean estimates of saturated hydraulic
conductivity from the piezometer slug tests. It should be
noted that the Base Case soil saturated hydraulic conductivity value (see Table 1) included the surface saturated
hydraulic conductivity estimates from the in situ retention
curve experiments by Torres et al. [1998]. The simulated
runoff generation was extremely sensitive to variations in
saturated hydraulic conductivity for the soil, which is
consistent with previous simulation-based studies [e.g.,
Freeze, 1972a, 1972b; Rogers et al., 1985]. Not surprisingly,
the timing of simulated runoff generation was considerably
worse, relative to the Base Case, when the soil hydraulic
conductivity was decreased (see all the storms in Figure 7).
Decreasing the hydraulic conductivity of the soil did im-
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Table 4. Model Performances for InHM Simulated Discharges at the CB1 Upper Weira
EFc (-)
Storm Numberb
1
2
3
4
5
6
7
8
1990
Dates
5 – 9 Jan 1990
9 – 11 Jan 1990
7 – 10 Feb 1990
26 – 29 Apr 1990
8 – 14 May 1990h
23 – 27 May 1990i
19 – 23 Nov 1990
24 – 27 Nov 1990
Base Cased
Kunweathered
e
bedrock 2
Kweathered bedrock
Arithmetic Meanf
Ksoil Arithmetic
Meang
1.90
0.29
2.82
2.09
0.65
1.68
0.82
0.57
0.41
1.45
0.46
2.31
1.70
0.76
1.33
0.83
0.61
0.26
0.45
0.03
0.05
0.18
1.65
0.08
1.46
0.21
0.29
1.28
0.05
2.27
0.88
1.01
1.76
0.46
0.20
0.12
a
See Figure 1 for the weir locations.
See Figure 6.
c
Modeling efficiency.
d
The Base Case refers to the BVP from the sprinkling experiments [see Ebel et al., 2007b].
e
This BVP is the same as the Base Case, except the hydraulic conductivity for the unweathered bedrock (see Figure 3) is twice as high.
f
This BVP is the same as the Base Case, except the hydraulic conductivity for the weathered bedrock (see Figure 3) is set to the arithmetic mean of the
slug tests [see Ebel et al., 2007a].
g
This BVP is the same as the Base Case, except the hydraulic conductivity for the soil (see Figure 3) is set to the arithmetic mean of the slug tests, not
including the surface hydraulic conductivity estimates [see Ebel et al., 2007a].
h
Sprinkling experiment 1.
i
Sprinkling experiment 2.
b
prove the EF values for the larger storms (e.g., storms 1, 3,
and 4 in Table 4 and Figure 7) as well as for the entire year
of 1990 owing to the reduction in simulated discharge
magnitude. The simulated piezometer response remained
as poor as for the Base Case.
7.1.4. Role of Bedrock Fractures
[38] Montgomery et al. [1997, 2002] determined that
piezometric response in the soil and saprolite at CB1 was
largely controlled by fracture discharge from the weathered
bedrock. Unfortunately, insufficient data are available to
characterize the locations, connectivities, and hydraulic
properties of the fractures in the CB1 weathered and
unweathered bedrock. However, estimates of saturated
hydraulic conductivity from the piezometer slug tests at
the interface of the soil/saprolite with the bedrock may serve
as a proxy for the locations of hydraulically active fractures.
Figure 8 shows a Kriged map of the base-10 logarithm of
estimates of the saturated hydraulic conductivity from slug
tests in the deepest piezometers (i.e., those at the colluvium/
saprolite and bedrock interface). Obviously, collapsing the
3-D saturated hydraulic conductivity data set into 2-D (plan
view) poses serious limitations on the accuracy of any
spatial estimation method, and therefore Figure 8 is best
considered in a qualitative sense. Figure 8 reveals that the
saturated hydraulic conductivities in the soil are generally
high [also see Montgomery et al., 2002; Ebel et al., 2007a].
In Figure 8, the areas of lower conductivity are labeled with
the piezometer numbers (also see Figure 1). Table 5 lists all
the piezometers in the soil layer that exhibited a large
pressure head response during sprinkling experiment 3 as
well as the saturated hydraulic conductivity estimates for the
soil/saprolite and weathered bedrock at the same locations.
It should be noted that what was considered a large pressure
head response is greater than 0.1 m, which is still relatively
small owing to the high hydraulic conductivity of the soil
and large topographic component of the hydraulic gradient.
Inspection of Figure 8 and Table 5 shows a correlation
between higher piezometric responses and low saturated
hydraulic conductivity estimates in the soil, saprolite, and
weathered bedrock. Notable exceptions to the correlation
between piezometric response and saturated hydraulic conductivity estimates shown in Table 5 include some piez-
Figure 8. Kriged map of the base-10 logarithm of the soil
and saprolite saturated hydraulic conductivity estimates
closest to the weathered bedrock contact (i.e., the deepest
measurement) with selected piezometers labeled (see Table 5).
Piezometer notations reference a platform number followed
by an instrument number and a letter to indicate depth (after
the notation of Montgomery et al. [2002]).
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Table 5. Piezometers Exhibiting Greater Than 0.1 m of Pressure
Head During Experiment 3 and Slug Test Estimates of Saturated
Hydraulic Conductivity in Those Piezometersa
Piezometerb
Ksat Soil/
Saprolite
(m s1)
Rank
(Low K to
High K)c
0–1
0 – 1A
0–3
0–4
1–3
2–2
2 – 2A
4 – 5A
5 – 3D
5–4
7–6
7 – 6C
7 – 6D
9–3
9–4
9–5
10 – 2B
11 – 4
8.0 105
5.2 105
2.1 105
Ne
7.6 105
1.6 104
2.8 106
4.8 108
1.8 105
9.5 105
5.5 107
8.0 108
1.0 106
1.0 107
4.0 108
3.1 108
1.7 106
5.2 107
74
54
34
Ne
71
118
15
3
31
83
9
4
12
5
2
1
14
8
Ksat Weathered
Bedrockd
(m s1)
5.4 107
4.9 107
3.7 107
1.2 107
6.4 108
a
From Ebel et al. [2006a]. Piezometer notations reference a platform
number [see Ebel et al., 2007a] followed by an instrument number and a
letter indicating depth (see the notation of Montgomery et al. [2002].
b
See Figures 1 and 7 for the piezometer locations.
c
The ranking out of the 156 slug test measurements (lowest K is 1).
d
The weathered bedrock saturated hydraulic conductivity estimate
beneath the selected piezometer (if a nearby measurement is available).
e
N means that the slug test data was insufficient to estimate saturated
hydraulic conductivity.
ometers at the down-gradient end of CB1 (0– 1, 0– 1A, 0 – 3,
and 1– 3), where convergent flow and saturation backing up
behind the impermeable wing walls of the upper weir and
exfiltration owing to the steep slope may cause high pore
water pressures. The correlation between piezometric response and saturated hydraulic conductivity estimates suggests that the areas of low estimated saturated conductivity
may serve as a proxy for fracture locations, which is
supported by partial field mapping of exposed weathered
bedrock fracture locations (D. R. Montgomery et al.,
manuscript in preparation, 2008), after the 1996 landslide
removed portions the overlying soil, showing fractures near
piezometer nests 7 – 6, 6 – 3, 5 – 3, and 2 – 2 (see Figure 1).
[39] It is unclear whether the low saturated hydraulic
conductivity values presented in Table 5 are representative
of the porous media or are a byproduct of hydrologic
conditions during the slug tests. The slug tests were conducted during the third sprinkling experiment, and exfiltrating gradients from the weathered bedrock fractures into the
soil (see the analysis of Montgomery et al. [2002]) could
have prevented the entry of the water ‘‘slug’’ into the soil
through the piezometer screen, thereby lowering the estimate of saturated hydraulic conductivity. There is, however,
no independent evidence that exfiltrating gradients significantly impacted the slug testing at CB1. Exfiltrating gradients from the weathered bedrock into soil are present at
some of the piezometers exhibiting low values of saturated
hydraulic conductivity (for example, piezometer nest 5 – 3)
whereas infiltrating gradients from the soil into the weathered bedrock are present at other piezometers exhibiting low
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values of saturated hydraulic conductivity (for example,
piezometer nest 7– 6). It is also possible that the weathered
bedrock fractures are hydraulically active because of emplacement in a low saturated hydraulic conductivity matrix.
[40] Two new simulations were conducted to investigate
whether the low-conductivity areas in Figure 8 represent
actual low-conductivity zones or areas of high conductivity
that inhibit slug testing owing to exfiltrating weathered
bedrock fracture flow. Localized hydraulic conductivity
zones (either high or low saturated hydraulic conductivity
values) determined from Figure 8 were embedded into the
Base Case parameterization. The low- or high-conductivity
zones fully penetrate the saprolite and weathered bedrock
and extend 10 m into the unweathered bedrock. For the lowconductivity case, a saturated hydraulic conductivity of
5.4 108 m s1 was used, which corresponds to the
minimum slug test estimate in the weathered bedrock [see
Ebel et al., 2007a]. For the high-conductivity case, the
estimated saturated hydraulic conductivity of the weathered
bedrock fractures, based on the bromide tracer tests of
Anderson et al. [1997b], was 2.0 103 m s1. Neither
the high- nor low-conductivity simulation produced major
differences in either simulated discharge magnitude or timing
relative to the Base Case. Not surprisingly, the simulated
piezometric response for both the high- and low-conductivity
zone simulations was different than the Base Case only for
the localized regions near the specified conductivity anomalies. The high-conductivity zone simulation better represents
the dynamics (both timing and magnitude) of observed
piezometric response than either the Base Case or the lowconductivity zone simulation. However, the high-conductivity
zone simulation still does not capture the magnitudes of
piezometric response to an acceptable degree of accuracy,
consistently underestimating the observed magnitude of
piezometric response. While using the spatial patterns of
saturated hydraulic conductivity estimates shown in Figure
8 as a proxy for weathered bedrock fracture locations shows
some promise, it is likely that the poor simulated water table
position combined with the isolated nature of the specified
conductivity variations (i.e., the connectivity is unknown
and unrepresented) are overwhelming limiting factors.
While other research efforts have had success simulating
fracture flow in deterministically defined fracture networks
[e.g., Lapcevic, 1997], there is seldom sufficient data to
employ such an approach at the field scale [see Novakowski
et al., 2007], as is the case at CB1.
7.1.5. Role of Subsurface Boundary Conditions
[41] BCs can significantly influence simulated hydrologic
response, and there is some uncertainty regarding the
specification of the subsurface BCs at CB1. As noted
previously, using a no-flow up-gradient subsurface BC (as
in the work of Ebel et al. [2007b]) causes the water table at
the ridge crest to drop too low in the long-term simulations
conducted here, which is why a local head BC was used to
attempt to better replicate the deeper water table position.
However, the local head (i.e., specified head) BC used as
the up-gradient BC (ABCD in Figure 3) changes the water
balance by adding water into the subsurface. A water
balance for the 1990 simulated hydrologic response shows
that 1.7 times the volume of total rainfall is added into the
subsurface by the up-gradient local head BC. However, this
addition of water does not contribute to the upper weir
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discharge, based on the water balance, as the up-gradient
local head BC increases the 1990 cumulative simulated
discharge by only 0.2 m3 or approximately 0.2 mm of runoff
depth, relative to a simulation conducted using the Base Case
parameterization with an impermeable up-gradient subsurface
BC rather than a local head BC. The water added by the upgradient local head BC flows out of the down-gradient local
head BC (EHIJ in Figure 3) rather than contributing to
runoff. The largest difference, other than the increase in the
down-gradient BC flux, between having the up-gradient BC
being parameterized as a local head rather than a no flow
BC is the change in the unweathered bedrock storage (i.e.,
the deeper water table height). The simulation with the no
flow up-gradient BC loses nearly 12 times as much volume
in storage from the unweathered bedrock as the simulation
with the up-gradient local head BC does.
[42] To test whether other down-gradient BCs would
produce simulated deep water table positions that are more
similar to observed values (at the ridge crest), two simulations were conducted for 1990 employing a no flow upgradient BC combined with (1) a ‘‘radiation’’ downgradient BC that employs an explicit boundary flux based
on the upstream hydraulic gradient of the boundary node
and (2) a no-flow down-gradient BC. All of the simulations
run for the BC sensitivity analyses in this section use the
1990 record to maintain consistency with the other sensitivity analyses in this effort. Both the radiation and no-flow
downstream BCs produce a higher water table near the
downstream BC, but the upstream deeper water table is
poorly simulated on the basis of comparison with the
observations from the ridge crest well in other years (both
simulations underestimate the water table height, note that
there is no deep well data in 1990). Changing the IC to set
the initial water table above the level typically observed in
the ridge crest well at the beginning of January does not
maintain a high water table in the up-gradient portion of
CB1 through the spring months. It should be noted that
there are few physically realistic choices of a subsurface BC
for the down-gradient boundary. This is because the catchment boundaries at CB1 were chosen for the original
observational study on the basis of surface features, such
as the surface topography and a seepage face (where the
upper weir was constructed). Essentially all of the subsurface instrumentation and subsurface characterization is
located within these specified boundaries.
7.1.6. Consideration of Evapotranspiration
[43] Two new simulations were conducted to examine the
affect of considering evapotranspiration, which was not
considered in the Base Case, for the simulated hydrologic
response during 1990. Potential evapotranspiration for one
of the simulations was estimated using the Thornthwaite
method [Thornthwaite and Mather, 1955] corrected for
latitude (see Table 5 – 2 from Dunne and Leopold [1978])
using daily temperature data from the North Bend Municipal Airport (from National Climatic Data Center, where
daily weather data for the North Bend Municipal Airport are
available at http://cdo.ncdc.noaa.gov/ulcd/ULCD) located
15 km away and 300 m lower in elevation relative to
CB1. While the Thornthwaite method is not a robust
estimation technique for potential evapotranspiration, it is
consistent with the temporal discretization and type of
meteorological data available for CB1 during the simulation
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period. The second simulation estimated potential evapotranspiration using the method of Hargreaves and Allen
[2003]; also see the work of Hargreaves and Samani [1985]
and Hargreaves et al. [1985]. The same meteorological data
were used for the Hargreaves and Allen estimates as for the
Thornthwaite estimates. Potential evapotranspiration is converted to actual evapotranspiration by scaling the potential
estimate by the InHM-simulated soil saturation. The actual
evapotranspiration is removed from the subsurface (during
the simulation) distributed linearly over an average vegetation rooting depth of 0.5 m, based on the rooting depth
measurements of Schmidt [1999] at CB1. Evapotranspiration is set to zero during rainfall events.
[44] Simulated actual evapotranspiration amounts for
both the Thornthwaite and Hargreaves methods are small,
totaling only 24 mm for the Thornthwaite method and
76 mm for the Hargreaves method for the entire year of
1990. These small ET amounts are 1% (for the
Thornthwaite method) or 3% (for the Hargreaves method)
of the 2150 mm of rainfall and sprinkling that fell on CB1 in
1990. Analysis of the effects of inclusion of ET will focus
on comparing the simulation using the larger Hargreaves
potential evapotranspiration estimates with the Base Case.
Comparison of the peak simulated discharge for the eight
storms in 1990 yields a difference between the Base Case
with and without evapotranspiration of 0.008 L s1 on
average, with a maximum of 0.03 L s1 for storm 4. The
percent differences in timing of peak discharge are indistinguishable, at the 600 s observed discharge resolution,
between the Base Case with and without evapotranspiration.
Incorporation of evapotranspiration improved the EF values
relative to the Base Case, but only by 0.06 [-] on average
with a maximum improvement of 0.21 [-] for storm 4
(improving from 2.08 [-] for the Base Case to 1.87 [-].
Inclusion of evapotranspiration had a minimal effect on
simulated piezometric response during the eight storms
evaluated in 1990, which is a result of the Base Case
simulated piezometric response undersimulating the observed piezometric response. Incorporating evapotranspiration causes drier simulated ICs in the soil leading to further
undersimulated piezometric response when evapotranspiration is included.
[45] While the 76 mm actual evapotranspiration estimate
for the Hargreaves method for the entire year of 1990 may
seem small, these estimates are consistent with the values
reported by other researchers for young saplings in clear-cut
areas. For example, Livingston and Black [1987] measured
transpiration rates from 1- to 3-year-old Douglas Fir seedlings on a south facing clear-cut slope and found that
transpiration rates varied from 0.1– 1.1 mm d1, with a
cluster of values in the 0.3 –0.4 mm d1 range. It should be
noted that the CB1 seedlings were 1 year old in 1990 and
that broadleaf vegetation, primarily consisting of alder
(Alnus) and blackberry (Rubus), was periodically trimmed
from 1990 to 1992. The north facing Coos Bay aspect
(shown in Figure 1) combined with the 43° slope also
reduces evapotranspiration. Additional water inputs, such
as fog drip from coastal fog, are not considered in this study
and may supply water to plants at CB1 in the summer
months. The water balance analyses by Montgomery et al.
[1997] at the catchment adjacent to CB1 found that total
runoff accounted for 87– 93% of the rainfall, leaving 7 –
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Table 6. Model Performance for the Improved Case InHM Simulated Discharges at the CB1 Upper Weira
Storm Numberb
Dates
EF c (-)
MABd (L s1)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
1990
1991
1992
1993
5 – 9 Jan 1990
9 – 11 Jan 1990
7 – 10 Feb 1990
26 – 29 Apr 1990
8 – 14 May 1990f
23 – 27 May 1990g
19 – 23 Nov 1990
24 – 27 Nov 1990
3 – 8 Mar 1991
11 – 14 Mar 1991
7 – 9 May 1991
23 – 29 Nov 1991
5 – 8 Dec 1991
27 – 29 Jan 1992
18 – 22 Feb 1992
8 – 11 Apr 1992
27 May to 3 Jun 1992h
9 – 12 Dec 1992
19 – 23 Jan 1993
1 – 3 Dec 1993
10 – 13 Dec 1993
0.75
0.72
0.62
0.70
1.89
0.26
3.39
0.37
0.73
0.79
4.85
0.76
0.50
0.24
0.32
0.66
0.97
1.15
6.57
0.32
0.37
0.38
0.31
0.09
0.05
0.03
0.04
0.04
0.04
0.09
0.07
0.07
0.08
0.05
0.06
0.09
0.03
0.05
0.03
0.03
0.03
0.06
0.04
0.06
0.03
0.04
0.03
0.01
0.03
0.03
Peak Discharge
Errore (%)
Time to Peak
Errore (%)
Total Discharge
Errore (%)
9.5
54.0
35.9
10.7
92.3
31.5
61.6
52.7
54.5
65.8
214.0
0.9
36.5
41.6
1.1
41.1
85.8
55.3
3.8
16.5
33.5
75.3
53.6
88.5
9.4
23.3
3.4
8.9
73.0
1.7
74.0
14.6
7.0
7.9
130.0
5.8
14.5
12.9
44.7
32.6
87.5
50.4
1.0
43.0
11.8
11.5
95.8
5.8
64.4
51.3
47.8
62.1
109.0
19.2
6.4
36.2
20.1
1.9
89.2
15.5
41.5
21.3
8.4
10.8
28.6
48.8
49.1
a
See Figure 1 for the weir locations.
See Figure 5.
Modeling efficiency.
d
Mean absolute bias.
e
Error is calculated as (observed minus simulated) divided by observed *100%.
f
Sprinkling experiment 1.
g
Sprinkling experiment 2.
h
Sprinkling experiment 3.
b
c
13% of the water balance partitioned between leakage to a
deep groundwater system and evapotranspiration, which
provides observational evidence that evapotranspiration is
a minimal component of the water balance. On the basis of
the simulations reported here, neglecting evapotranspiration
during long-term hydrologic-response simulation at CB1 is
a reasonable hydrologic assumption for investigations focused on storm-scale hydrologic response.
7.2. BVP Improvements Based on Sensitivity Analyses
[46] The objective of this section is to incorporate some
of the BVP aspects from the sensitivity analyses that
positively affect simulated discharge and piezometric response in an attempt to improve the uniqueness of the Base
Case BVP. The differences between the Base Case BVP and
the Improved Case BVP are summarized below. The BCs
are the same as the Base Case except that, owing to the lack
of continuous deep well data for the period from 1990
through 1993 (see Figure 2b), the 1995 well data are used to
parameterize the up-gradient local head BC. The 1995 well
data are chosen because of the three complete years of well
records (i.e., 1994 – 1996); the 1995 data are higher in
magnitude than the 1994 data but lower in magnitude than
the 1996 data. The unweathered bedrock was changed to
incorporate the low saturated hydraulic conductivity shale
layer, as described in section 7.1.1. The weathered bedrock
saturated hydraulic conductivity is parameterized using the
arithmetic mean of the piezometer slug test estimates. The
saprolite saturated hydraulic conductivity was not specifically analyzed in the sensitivity analysis in this effort;
however, the event-based simulations of Ebel et al.
[2007b] suggested that the saturated hydraulic conductivity
value used for the saprolite in the Base Case was too high.
Consequently, the geometric mean of the piezometer slug
test estimates in the saprolite [see Ebel et al., 2007a] was
used to parameterize the saturated hydraulic conductivity of
the saprolite layer, which is now 2.0 105 m s1. The ICs
used for the 1990 Improved Case simulations are the same
as those employed for the 1990 Base Case simulations.
[47] Table 6 presents the performance statistics for the
Improved Case simulation results for the 4-year period from
the start of 1990 through 1993. Figure 9 shows observed
and simulated Base Case and Improved Case hydrographs
from eight selected storms from Table 6. Figure 10 presents
observed and simulated cumulative discharges for 1990
through 1993. The Improved Case results are only shown
for 1990 through 1993 because CB1 was more carefully
monitored and maintained during this period, which
includes the sprinkling experiments. The observed discharge and piezometer records are also more complete
between 1990 and 1993 (see Figure 2b). Because the period
from 1990 through 1993 includes more than half the
simulated Base Case storms (i.e., 21 out of 33) and an
adequate range of storm magnitudes, generalized conclusions can be made about the Improved Case BVP. Examination of Table 6 and Figure 9 reveals that the Improved
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Figure 9. Observed and InHM simulated upper weir discharge and hyetographs for eight selected
storms from 1990 to 1993 for the Base Case and Improved Case boundary-value problems (BVPs) (see
also Table 6).
Case simulated discharges are generally better than the Base
Case simulated discharges, especially for storms with larger
rainfall depths (i.e., storms 1, 3, 4, 6, 12, 13, 15, 16, 21).
The EF and total discharge error values are worse for the
smaller rainfall depth events for the Improved Case. Examination of the initial discharges for storms 4, 12, 14, 20, and
21 in Figure 9 suggests that the Improved Case is better than
the Base Case for simulating hydrologic processes between
storms. Figure 10 and Table 6 show that the cumulative
simulated discharge is better for the Improved Case for
1990 and 1991. The cumulative simulated discharge for the
Improved Case oversimulates cumulative discharge in 1990
because of the gap in the observed discharge from midOctober through mid-November (see Figures 2b and 7). The
Improved Case appears to undersimulate the cumulative
discharge in 1992 and 1993. However, in 1992 there is a
period from 4 March through 8 April where the observed
discharge record holds steadily at 0.1 L s1 when there is
little rainfall (see Figure 6), which adds 227 m3 to the
observed cumulative discharge record. There is another
similar period from 12 December 1992 through 19 January
1993 (see Figure 6), which adds 133 m3 in 1992 and 162 m3
in 1993. Another period of sustained discharge data near
0.1 L s1 exists from 23 April to 11 May 1993, which adds
271 m3. The steep slope and highly hydraulically conductive soil at CB1 prevent significant (i.e., near 0.1 L s1)
sustained discharges for weeks at a time and draw the
observed discharge data during the aforementioned periods
into question and could make the observed cumulative
discharges during 1992 and 1993 closer to the Improved
Case simulated values. Another interesting observation
from the Improved Case hydrographs shown in Figure 9
is the asymmetry in time of the observed hydrographs
relative to the more symmetrical simulated hydrographs. It
is possible that rapid fracture flow through the unweathered
bedrock contributes to the rapid rise in discharge while the
hydrograph recession is slower, reflecting drainage from the
unsaturated zone (in agreement with the CB1 data analysis
by Montgomery and Dietrich [2002]).
[48] While the Improved Case appears to represent the
bulk behavior of weathered bedrock, with respect to better
simulation of runoff for large storms, this equivalent porous
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Figure 10. Cumulative observed and InHM simulated upper weir discharge and hyetographs for 1990–
1993 for the Base Case and Improved Case BVPs (see also Table 6).
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Figure 11. Observed pressure heads in the deep well and selected weathered bedrock piezometers (see
Figure 1) from 1993 through 1996. See Figure 2 for gaps in the record.
medium approach does not capture the localized piezometric response well. The simulated piezometric response is
slightly better for the Improved Case, relative to the Base
Case, but still not of acceptable accuracy to drive processbased hydrogeomorphology investigations. Novakowski et
al. [2007] points out that the equivalent porous media
approach will not work well when the study domain is
small enough that individual fractures influence the flow
system, which seems to be the case as CB1. A simulation
combining the Improved Case parameterization with the
high saturated conductivity zones used to represent bedrock
fractures (see section 7.1.4) improves the simulated piezometric response, relative to both the simulated piezometric
response from the Base Case with high conductivity zones
to represent fractures and the Improved Case with no highconductivity fracture zones, but still consistently underestimates piezometric response relative to the observed
values.
7.3. Insights and Future Directions
[49] While the Improved Case simulations represent a
clear improvement over the Base Case simulations relative
to simulated discharge and piezometric response, the Improved Case simulation results are far from perfect. Relative
to the simulated piezometric response, better representation
of the weathered and unweathered fracture flow in the CB1
hydrologic-response simulations is needed to accurately
simulate pore water pressure development in the soil. This
is not surprising, given that previous studies have demonstrated that spatial variations in hydraulic conductivity can
control pore water pressure hot spots [e.g., Pierson, 1977;
Wilson and Dietrich, 1987; Wilson et al., 1989; Johnson and
Sitar, 1990; Reid and Iverson, 1992; Montgomery et al.,
1997, 2002]. It would likely be beneficial to complete a
‘‘post-mortem’’ at CB1 by removing all the soil and
saprolite and inspecting the locations of exposed fractures.
As noted by Novakowski et al. [2007], characterization of
the spatial distribution and correlation of fractures at the
field scale is prohibitively expensive using traditional techniques. However, recent advances in near surface geophysical techniques have shown promising results in detecting
the locations [e.g., Holden et al., 2002] and connectivities
[e.g., Holden, 2004] of subsurface preferential flow paths
and may prove useful for future studies at locations similar
to CB1. Hydraulic tomography [see Gottlieb and Dietrich,
1995; Yeh and Liu, 2000] has also shown to prove instructive for detailed characterization of the unsaturated zone
[Yeh and Šimůnek, 2002] and fractures in rock [McDermott
et al., 2003; Renshaw, 1996]. Techniques such as hydraulic
tomography may prove useful for future studies that employ
hydrologic-response models similar to InHM in locations
where accurate representation of fracture locations and
connectivities are important.
[50] The CB1 results presented here suggest that the
deeper water table plays a larger role in pore water pressure
development than would be expected. Figure 11 shows time
series of observed pressure head in selected weathered
bedrock piezometers and the deep well (see Figure 1 for
locations) from 1993 through the slope failure. Figure 11
illustrates the impact of the water table decline during the
dry season (i.e., July through October) on observed weathered bedrock piezometric response in piezometers B1, B9,
and B13 in 1995; note that the summer period data is
missing for 1993, 1994, and 1996 (see also Figure 2).
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Correlation coefficients between deep well pressure head
and weathered bedrock piezometers are 0.002 for piezometer B1, 0.27 for piezometer B12, 0.64 for piezometer B13,
0.53 for piezometer B9, and 0.52 for piezometer B1. The
correlation coefficients suggest that, for the down-gradient
weathered bedrock piezometers (i.e., B13, B9, and B1), that
a higher water table position (i.e., larger pressure head in the
deep well) produces larger magnitude piezometric response.
The up-gradient weathered bedrock piezometers (i.e., B16
and B12) seem to have pressure head dynamics that appear
independent of the water table position. It should be noted,
however, that a high water table position is common in the
winter months when large precipitation events occur at CB1
that increase the magnitude of observed piezometric response, suggesting that the correlations are not without
uncertainty. The conclusions drawn from Figure 11 echo
those of Montgomery et al. [2002], who found that for the
sprinkling experiments and natural storms, piezometric
response in the soil and weathered bedrock was dependent
on both position in the CB1 catchment and seasonal water
table position. For example, Montgomery et al. [2002] noted
that for soil piezometers in nest 5 – 3 and the nearby
weathered bedrock piezometer B13, which occur in the
midslope section of CB1, that early season storms exhibited
infiltrating gradients from the soil into the bedrock while
midwinter storms when the water table was several meters
higher exhibited exfiltrating gradients with water flowing
from the weathered bedrock into the overlying soil.
Montgomery et al. [2002] also found that piezometers up
gradient (further toward the ridge crest) of soil piezometer
5 – 3 and bedrock piezometer B13 illustrated consistently
infiltrating gradients regardless of water table position. On
the basis of the data-based and simulation-based conclusions of previous CB1 efforts and this research, it seems that
bedrock fracture flow, heterogeneity in the unweathered
bedrock, and wetting front propagation through the unsaturated zone all complicate simulation of pore water pressure
at CB1 and may all need to be well characterized (and
correctly represented in the BVP) to accurately simulate the
distributed hydrologic response.
[51] Anderson et al. [1997b], Montgomery et al. [1997],
and Montgomery and Dietrich [2002] concluded that the
runoff generation at the CB1 upper weir during the sprinkling experiments was controlled by a ‘‘subsurface variable
source area’’ at the soil-bedrock interface. The work by
Montgomery et al. [1997, 2002] demonstrated that the
patchy subsurface saturation occurring at the soil-bedrock
interface (i.e., the subsurface variable source area that feeds
runoff generation) is produced by flow exfiltrating from
weathered bedrock fractures. If, as suggested in the work by
Montgomery et al. [2002] and this effort, exfiltrating fracture flow from the weathered bedrock into the overlying soil
depends on the seasonal dynamics of the deeper water table
and these factors then control the extent of the subsurface
variable source area then correct simulation of both the
deeper water table and the fracture flow would be critical for
correctly simulating runoff generation at CB1. If this is the
case at CB1, then simulations that reproduce the observed
runoff without reproducing the fracture-flow-dominated
piezometric response or the deeper water table position
may be ‘‘right for the wrong reasons.’’
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[52] The issue then becomes what information is needed
to get the simulated hydrologic response ‘‘right for the right
reasons’’? It is clear that despite the immense effort invested
into characterizing the CB1 hydrologic BVP with fieldwork
and observations, information on the unweathered bedrock
layer is insufficient. No information exists regarding the
water-retention curves and hydraulic conductivity functions
of the unweathered bedrock, other than lithology. Pump
tests at various depths within the deep well would have been
useful for parameterizing the magnitude and variability with
depth of the saturated hydraulic conductivity of the unweathered bedrock to account for heterogeneity and anisotropy
as well as storage parameter estimates. The aforementioned
hydraulic information for the unweathered bedrock would
likely improve the simulated deeper water table and pore
water pressures at CB1. Spatial lithologic characterization,
including the presence of permeability contrasts at bedding
planes such as the shale interbeds at CB1, may be critical
for slope failure simulation at locations similar to CB1. For
example, Iverson and Major [1986] noted that horizontal
seepage at a permeability contrast increases the probability
of slope failure. Long-term monitoring in the unsaturated
zone (i.e., soil-water content or tensiometric response)
would also have helped to evaluate the simulated state
variables in the unsaturated zone. There is also little
information on the distributed position of the deeper water
table throughout CB1. Such information could assist in
finding the correct BCs, unweathered bedrock saturated
conductivities, and unweathered bedrock storage parameters
needed to correctly simulate the dynamics of the deeper
water table. On the basis of the findings of this study, it
appears that the characterization of the deeper subsurface
may be needed for accurate simulation of near-surface
hydrologic response for field sites like CB1 with steep
slopes and hydrologically active deeper water tables.
8. Summary and Conclusions
[53] Ebel et al. [2007b] had reasonable success simulating the hydrologic response to three sprinkling experiments
using the physics-based InHM. The study reported here
assessed the uniqueness of the BVP used by Ebel et al.
[2007b], called the Base Case herein, for continuous InHM
hydrologic-response simulation from 1990 through 1996.
The Base Case BVP poorly reproduced the piezometric
response (i.e., undersimulated pore water pressure magnitudes) and only the discharges from small magnitude storms
(i.e., of similar peak discharge magnitude as the three
sprinkling experiments) were well simulated. Sensitivity
analyses of the BVP parameterization indicated that during
the long-term CB1 hydrologic-response simulations,
(1) soil-saturated hydraulic conductivity strongly impacts
simulated discharge, (2) representation of layered permeability contrasts can moderately affect simulated discharge,
(3) inclusion of evapotranspiration had a minimal effect on
simulated integrated hydrologic response, and (4) simple
representations of heterogeneity in saturated hydraulic conductivity attempting to mimic bedrock fractures improved
simulated pore water pressures but still underestimated pore
water pressure magnitudes.
[54] Improvements to the Base Case employing insights
from the sensitivity analyses conducted in this study did
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improve the uniqueness of simulated discharge but did not
improve the simulated piezometric response to an acceptable level. The inability of any of the simulations presented
in this effort to reproduce the observed pore water pressure
magnitudes and dynamics suggest that more information is
needed to characterize the locations and connectivities of
bedrock fractures for models like InHM to accurately
simulate of hydrologic effects of fracture flow at locations
like CB1. The results shown here also indicate the potential
role of the deeper water table position in influencing the
CB1 hydrologic response. It needs to be pointed out that
care should be exercised when generalizing the simulationbased conclusions from this study to other locations. Relative to using models like InHM for simulation of hydrologically driven landslide initiation, this study shows that
uniqueness can be a problem relative to employing a BVP
used successfully for smaller magnitude storms to simulate
a failure-causing storm. This study further supports the
conclusion of Ebel and Loague [2006] that simulating an
integrated hydrologic response (i.e., discharge) reasonably
well in no way guarantees that distributed hydrologic
responses (e.g., pore water pressure) will be correctly
simulated. Integrated hydrologic responses are potentially
the least useful performance evaluation data relative to
simulating hydrologically driven slope failure owing to
the importance of the distributed pore water pressures.
The results reported here indicate that further studies conducting detailed comparisons between observed and simulated hydrologic responses are needed before physics-based
hydrologic-response models, similar to InHM, can be used
reliably for operational purposes (e.g., landslide hazard
assessment).
[55] Acknowledgments. The work reported here was supported by
National Science Foundation grant EAR-0409133. The data collection
efforts of people from UC Berkeley, including Ray Torres and Suzanne
Anderson, as well as the Weyerhaeuser Company facilitated this study.
Kevin Schmidt supplied additional data on the soil and saprolite depths.
The presentation benefited from the thoughtful comments of Ben Mirus on
an earlier manuscript.
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B. A. Ebel and K. Loague, Department of Geological and Environmental
Sciences, Stanford University, Stanford, CA 94305-2115, USA. (bebel32@
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D. R. Montgomery, Department of Earth and Space Sciences, University
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W. E. Dietrich, Department of Earth and Planetary Science, University of
California, Berkeley, CA 94720-4767, USA.
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