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Incorporating Soil Variability into a
Spatially Distributed Model of
Percolate Accounting
Andrew S. ~ o ~ o w s k i '
Abstract.-The Soil-Plant-Atmosphere-Water simulation model ( S P A ~ ) ~
was used to compute percolate flux below the root zone from profile water
balance. The water balance was based on the prevailing conditions in the
atmosphere, physical variables describing water status of soil, and
physiological variables related to a stage of growth and water use by
plants. Although measured, or estimated at a point, most of the above
variables are likely to vary in space and in time. The study addresses this
variability and describes how to simulate spatial and temporal
distributions of hydrologic variables which are conditioned by a set of
field observations. We use sequential indicator simulation to convert water
flow evaluated at a point in relatively few locations, into spatial flow
estimates. The study describes distribution of vertical and horizontal
percolate flux in time. It is cast in a GIs format at a catchment scale.
INTRODUCTION
To describe behavior of natural systems we often rely on field observations and
numerical models. Observations are generally made at a point, while models
attempt to integrate the response spatially and temporally. The field observations
considered representative of an area, or volume of soil, serve as input to a model.
At other times when field data are not available, modelers use published soil
surveys to extract pertinent input variables needed to run a model. Such variables
are assumed to apply uniformly to an entire area mapped as the same soil polygon.
In truth however, the variables represent observations made at a site, which
although typical for a given soil, may be far removed from the study
area. Moreover soil polygons themselves are far from pure and contain inclusions
of associated materials (Rogowski and Wolf, 1994). The objective of this study
was to incorporate spatial soil variability expressed as different descriptions of the
same soil into a simulation model of percolate accounting.
Soil Physicist, USDA-ARS-PSWMRL, University Park, PA
h he SPAW model was developed by Dr.Keith Saxton USDA-ARS Pullman, W k
METHODS AND MATERIALS
Soil-Plant-Atmosphere-Water(SPAW) Model
The SPAW simulation model (Saxton et al., 1992) provides estimates of
evapotranspiration (ET), plant water stress and layer-by-layer changes in soil water
content and percolate flux from below the root zone. The model is designed to
provide a daily, one dimensional (vertical) water budget at a point. Actual
measurements of ET, soil water content and other input variables may be
substituted for default values, or periodically used to validate, or recalibrate the
model. The model requires climatic and plant data and a detailed in situ horizon by
horizon description of the soil profile, including pertinent soil water characteristics,
or textural classification information for each soil layer.
Potential evapotranspiration (PET) is determined from measured values of pan
evaporation. The PET values are used to compute actual ET which is then
subtracted from the available soil water in storage. Daily precipitation, corrected
for interception and runoff, infiltrates and is distributed among soil layers by
cascading down from the surface. The amount of water which reaches the bottom
boundary layer becomes a deep vertical percolation flux (q,). Adjustments among
layers due to unsaturated water flow by redistribution are made using a Darcy
subroutine.
The output consists of daily summaries of soil water for each layer, in addition
to a digital and graphical output of precipitation, ET, and percolation flux q,. The
major feature of the model is that it addresses the soil-plant-air continuum at a
point, and estimates are made conditional to the profile hydrologic properties,
subject to the local climatic and biotic factors.
Study Area and Soils
The study area described in this application is on the Mahantango Creek watershed
in Pennsylvania, USA, (Rogowski and Wolf, 1994). The watershed is situated in
the Valley and Ridge physiographic province of the Appalachian Mountains,
characterized by varying relief: upland hills, valleys, and forested mountain ridges
dissected by streams. The climate is humid with well-distributed rainfall (about
1000 d y r . ) . Elevation ranges from less then 100 m in the valleys to over 500 m
on the ridge tops. The ridges, valleys and streams are oriented northeastsouthwest, corresponding to the regional strike of major rock formations, while
beds dip to the northwest and southeast along the centrally located anticline. The
land use is predominately cropland in a rotation management system of corn, small
grains, and meadow, intermingled with numerous tracts of woodland, areas of
permanent pasture and orchards.
Elevation (m)
Slope (%)
N
Aspect
Soils
Ab (Albrights)
Bk (Berks)
Ca (Calvin)
Ht (Hartleton)
Ln(LeckKil1)
Mk (Mecksville)
We(Weikert)
Wt (Watson)
-
=
=
=
Figure 1. Overlay maps of elevations, aspect, slope, and soils based on the detailed 5m
DEM of the study area; locations of conditioning pedons are shown on the soils' map.
The experimental area is 1.2 km on the side with the individual cell size of 5x 5 m
corresponding to a detailed DEM. Figure 1 shows distributions of georeferenced
(GPS) elevations, slopes, aspects, and soils at the experimental site. Points on the
soils map indicate assigned locations of the soil pedons used as input to the SPAW
model. The displays and calculations were carried out within the framework of
GIs IDRISI~(Eastman, 1993).
Soil Profiles
Soil profile locations (pedons) were assigned at random, using as input the
information from PSU Soils Database (Ciolkosz and Thurman, 1992). This
database is a compilation of 800 pedons representing 170 different soil series
which have been collected and analyzed by the soil characterization laboratory. It
contains detailed profile and site descriptions, as well as layer-by-layer physical,
chemical and mineralogical data. There are generally several descriptions of the
same series sampled at different locations. For the eight soils found in the
experimental area 60 pedons were described in the database, these were
augmented with pedons of a different series considered as inclusions, for a total of
100 pedons. The pedons, assigned at random to soil polygons of the same series
(figure1), constituted the conditioning data sites.
Conditioning Data
At each of the conditioning sites we extracted from the soils database the
textural information, as well as percent sand, silt, and clay, and depth to each layer.
We used daily precipitation and PET data from the 1990 season, and assumed a
uniform crop cover (corn) over the entire area. The SPAW model was run on each
profile from Spring to Fall. The model was started with a uniform water content
(8,) of 0.20 cm3/cm3and recalibrated to volumetric field capacity for each layer.
Soil Anisotropy
Field saturated hydraulic conductivity Kfs of each layer was estimated from the
ten textural classes in the SPAW supplied tables. The Kv (vertical) for the soil was
computed as a harmonic mean of component layers weighted by a layer thickness.
The Kh (horizontal) for the soil was taken as the conductivity of top layer, if
followed by a layer with lower K. If K in the following layer(s) was higher, Kh was
taken as an arithmetic average of component layers weighted by the layer
thickness. The ratio, n = Kh / Kv was assumed to represent profile anisotropy
(Zaslawsky and Rogowski, 1969). Given percolation flux qv computed from the
SPAW, horizontal flow component qh was approximated as,
qh = qvx n x tan a
[ 1I
where a represents land slope in % (figure 1) derived from a detailed 5 m DEM,
and tan a is equivalent to (slope gradient)'1 definition in IDRISI~
3 ~ hmention
e
of trade names does not constitute an endorsement of the product by the US Department of Agriculture.
Sequential Indicator Simulation
Results in literature (Journel and Alabert, 1989), suggest that a geostatistical
conditional simulation approach known as sequential indicator simulation (SISIM)
can be used to reproduce spatial patterns of continuity and to introduce a measure
of uncertainty into soil survey data. The purpose of the simulation is to construct
from the conditioning data (100 profiles), numerous, equiprobable spatial
"realizations", or outcomes, of an attribute qv, that would reproduce spatial
patterns associated with the occurrence of extreme values.
To model different portions of an irregular distribution, the sequential indicator
simulation partitions observed population into several classes each separated by a
threshold. For each observed value it then defines the indicator transformation
with respect to that threshold. Thus for a random variable Z(u) at a location u and
a threshold value z, the corresponding indicator transformation I(u;z) would be,
[21
I(u;z) = 1, if Z(u) 5 z
= 0, otherwise
Given a set of qv values, the SISIM procedure converts them into indicator
distributions for each threshold. It then attempts to define an algorithm for adding
an indicator value at an unsampled location which is consistent with a spatial
structure (variogram or covariance) of observed population for a particular
threshold (Deutsch and Journel, 1992).The first step involves estimation of the
conditional probability that a new value is less then a given threshold. This is done
by kriging each unsampled location using the surrounding indicator values. The
resulting estimate of the conditional cumulative distribution fbnction (ccdf) is
between 0 and 1. The actual simulation of a corresponding indicator value at an
unsampled grid location is accomplished by drawing a random number between 0
and 1 from a uniform distribution (Monte Carlo). If this number is less than, or
equal to a kriged value, a simulated indicator value of 1 is assigned to that
location. If it is more, a value of 0 is assigned. The new value becomes a part of
the conditioning data set and the procedure is repeated at another location until all
unsampled locations in a catchment grid are filled.
RESULTS
Distributed Flow
After generating 25 equiprobable realizations of cumulative percolate flux qv,
expected values and quantiles of the average of 25 distributions were analyzed for
three dates: March 30", August 15', and November 15", 1990. We show these in
figure 2. We also generated 25 realizations of n = K,,/KV.Subsequently, expected
values of n and qv at each pixel, and slope from the overlay of slope in figure 1
were used in Eq. 3 to compute distributions of the horizontal flux component qh
qr March 30
1
2
3
4
sl.18l.lSl.U 1.U1.80wl.M
qr November 15
qr August 15
1
2
Q O l ZRZ-244
3
z u z m wZ03
5
qh August 15
Figure 2. Simulated (SISIM) quantiles of expected values of q, (cm) on Mar 3oth,Aug IS",
and Nov 15' and of qh (em) on Aug 1 5 based
~ ~ on 100 conditioning d a t a
Figure 3 Distribution of q, (em) for three quantiles (Q) of 25 SISIM simulations on ~ ~ ~ 1 5 ~ ' ' ;
and probability (Prob) of values lower than Q5 (1.52 cm), or higher than Q95 (3.72 cm).
62
for each location and date. Since there was not much difference among the three
dates, figure 2 shows qh for August 15' only. We represent the q, and q h as
quartiles (Q) of the average (25 SIS) distribution: (1)yellow < Q1, (2) green Q1 to
Qz, (3) blue Q2 to Q3, and (4) red >Q3. Results suggest that areas with high qv
(red) may be the sites of preferential recharge. Similarly locations with above
average qh may indicate preferential interflow, or runoff producing zones. The
values of qh are very dependent on interaction among the distributions of slope
(from 5 m DEM), and distributions of n and q, (from two separate 25 SISIM runs).
The overall distribution of qv does not differ much from season to season. In the
Spring a very prominent red zone occurs the middle of the catchment. As time
goes on, this zone becomes more diffuse in the Summer, and brakes into several
patches in the Fall. When results for q, in figure 2 are compared with
corresponding terrain properties in figure 1, the primary recharge area seems to be
in the center of the catchment. This is also zone of terrain depression and a natural
flow-pathway which connects part of the catchment to the main drainage.
Ironically, the farm buildings are located in this same general area.
Quantile Maps
To derive a quantile map, 25 simulated values for each pixel were ranked and the
quantiles (Q), were selected as simulated pixel values corresponding to the 25",
5 0 t and 75* percentile in the ranking. These pixels were subsequently combined
into a single quantile overlay.The three quantiles (figure 3) were Qz5 , median
(Q50), and 4 7 5 . The Q25 realization focuses on highlighting the potential outliers,
since the probability of a lower value than shown is only 25%. The median (Qso)
quantile map tends to minimize the mean of absolute deviations for each pixel
location, that is, individual pixel values are close to what they appear to be. In the
Q75 map the focus shifts to the reliable low zones, because in this case the
probability of exceedance would be only 25%. This map and the Qsomap are the
closest in appearance to that in figure 2. The results suggest that the red zone is
real and its occurrence persists in the quantile maps. Equally persistent are the low
flow (yellow) areas in the east and south east corner and along the lower portion
of western boundary.
Probability Maps
Probability maps (figure 3) provide additional detail about the existence and
continuity patterns associated with either the low, or high zones of qv. The maps
are expressed as percent probability that an area is either higher, or lower than a
given cutoff. The choice of a cutoff is arbitrary. Our maps were constructed for
two cutoffs: Prob 5 Q5and Prob 2 Q95. The P5Q5 map delineates potential low
flow zones, while the P2Qs5map shows high flow areas in terms of the probability
of occurrence. Both maps confirm the existence of centrally located, connected,
high q, area , and corresponding low flow zones in the eastern and western
portions of the catchment.
CONCLUSIONS
To introduce a measure of spatial variability into soil survey data, we extracted
detailed pedon information from a soils7 data base and assigned it at random to
locations within a mapped polygon representing that soil. The assigned pedon
locations became the sites of conditioning data. We run a model (SPAW) to
compute daily water balance for each pedon, extracting the percolate flux
component q,. The values of q, were then used as conditioning data in the
sequential indicator simulation model to distribute q, over the catchment. Results
suggested the existence of high an low flow zones reflecting terrain properties.
Their continuity was confirmed by the quantile and probability of exceedance
maps. An added benefit was the identification of horizontal flux component qh,
related to soil anisotropy. Distributions of q h were strongly slope dependent and
reflected contributions by the percolate flux q, and local anisotropy n.
ACKNOWLEDGMENTS
Contributions by D. Simmons to data visualization and processing are appreciated.
Ciolkosz, E.J. and Thurman, N.C. 1992. Soil Char. Lab. Database System. Agron.
Ser. No. 124. Agron. Dept., Pen State Univ., University Park, PA 16802. 59p.
Deutsch, C.V. and Journel, A.G. 1992. GSLIB, Geostatistical software library and
users guide. Oxford Univ.Press, New York, NY.
Eastman, J.R. 1992. IDRISI a grid based geographic analysis system. Version 4.1.
Clark University Graduate School of Geography, Worcester, MA 0 1610. 178p.
Journel, A.G and Alabert, F. 1989. Non-Gaussian data expansion in earth sciences.
TerraNova 1: 123-134.
Rogowski, A.S. and Wolf, J.K. 1994. Incorporating variability into soil map unit
delineations. Soil Sci.Soc.Am.J.,58:163-174.
Saxton, K.E., Porter, M.A., and McMahon 1992.Climatic impacts on dryland
winter wheat by daily soil water and crop stress simulations. Agric. and Forest
Meteorology, 58:177- 192.
Zaslavsky, D. and Rogowski, AS. 1969. Hydrologic and morphologic implications
of anisotropy and infiltration in soil profile development. Soil Sci.Soc.Am.J.,
33(4): 594-599.
BIOGRAPHICAL SKETCH
Andy Rogowski is a Soil Scientist at the USDA-ARS Pasture Systems and
Watershed Management Research Laboratory, he graduated from the Iowa State
University at Ames with a Ph.D. degree in Soil Physics.