PE EIE[R-Rg RESEARCH ON - HJ Andrews Experimental Forest

Proceedings-Research on Coniferous Forest Ecosystems-A symposium .
Bellingham, Washington-March 23-24, 197 2
Modeling water movement within
the upper rooting zone of a
Cedar River soil
W. H . Hathewa y
P. Machn o
an d
E . Hamerl y
University of Washingto n
Seattle, Washington 9819 5
Abstract
The Richards equation for unsaturated soil water flow is used to represent flow in a natural forest soil . Th e
differential equation and the corresponding finite difference technique used to obtain an approximate solutio n
are discussed. Independent estimates of soil moisture conductivity and of initial soil water content at severa l
depths are used as inputs to the finite difference equation. Conductivity was estimated by laboratory techniques,
and initial conditions in the field were measured by tensiometer. A tension lysimeter system provided
estimates of soil water flow. Predicted values were compared with values measured in the field . Results sugges t
that the model gives a satisfactory representation of actual soil water flow despite considerable variability in
forest soil properties.
Introduction
In the Coniferous Forest Biome, we hav e
been interested in models which represent th e
movement of water through unsaturated soil s
for use as possible components of a larger
computer model which describes water relations
within a local soil-plant-atmospher e
system. Other components of the larger
model include uptake of water by the roots of
trees, conduction of water through the vascular
system to the leaves, and transpiratio n
from the leaves to the surrounding atmosphere
. When we find that existing submodel s
can be used-possibly with slight modifications-in
our larger soil-plant-atmospher e
model, we prefer to use them rather than t o
invent them anew . Where existing models ar e
not well suited to our objectives, we prefer t o
develop new ones . For example, we are currently
constructing a model which represent s
the flow of water through the vascular syste m
of a tree. We evaluate existing or new sub -
models on the basis of (1) their behavior in
isolation and (2) their compatibility with
other components of the system . In the
present paper we report our experiences with
the Richards equation, a model which de -
scribes the flow of water in an unsaturate d
soil .
The Model
The Richards equation (Richards 1931) is
essentially a modification of the well-known
Darcy relationship for saturated flow i n
porous media. Because the Richards model
allows for variation in hydraulic conductivity
with changes in soil water content, it is wel l
suited for the description of water flow in
unsaturated media . Darcy 's law with variabl e
conductivity and negative hydraulic head can
be written (Rose 1966 )
v=K aia 6 ae aZ
K (1)
95