458
Int. runoff
Sat. runoff
S*1
S*1 ep
fi A fe
7^1
1
~l
1
: 0sz
surface zone
\
Zsz
1
1
\
1
1
etz(z) \
9
1
Ztz
Vc
transmission zone
2
\
1 1
Figure 1: Schematic representation of the local water balance model.
flow is assumed to be of negligible importance in this version of the model.
2.1 Local Water Balance Model
Figure 1 depicts a schematic representation of the various soil moisture fluxes at a grid element. To
allow for dynamic simulation of critical state variables such as surface soil moisture, the unsaturated
zone is divided into two regions—the surface zone and the transmission zone. The surface zone is
subjected to high-frequency atmospheric forcings which result in rapid change of moisture content.
Consequently, a continuous water accounting is maintained in this zone whose depth is related to
the penetration depth of the remote sensor used in soil moisture monitoring. For the transmission
zone, the effects of the rapidly varying boundary conditions are usually damped out by the overlying
medium. We will assume that the moisture state in the transmission zone has achieved a steady flow
condition. The computation of various vertical soil moisture fluxes and runoff are described below.
2.1.1 Infiltration. The infiltration rate, /,, is taken as the minimum of the infiltration capacity,
/*, and the precipitation rate p:
fi = min [f*,p] (1)
To estimate the infiltration capacity, we employ the time condensation approximation (Ibrahim
and Brutsaert, 1968; Milly, 1986) on the Philip’s solution (1957) to an initially uniform moisture
profile subjected to a step change in soil moisture at the soil surface. As a result, f* depend only
on cumulative infiltration in the surface zone, Fi, and the initial condition at the start of a rainfall
event:
f: = a 0
4a 0 f;\
% )
1/2
( 2 )
where Si is the sorptivity and Aq is a constant term which accounts for the effect of gravity. Employing
the results of Eagleson’s (1978) synthesis of work on nonlinear diffusion by Crank (1975), Milly (1986)
has evaluated Si and Aq from the case of infiltration into a soil that is i-nit.ia.11y dry, and obtained the
following expressions:
Aq
(3)
where 9 U re]
minus entra]
moisture diff
2.1.2 Percoli
ing the inter
characterise
estimated us
where g is tl
for percolati
is the tensic
distribution
2.1.3 Exfiltr
f e , by takini
Neglect
tration capa
at the start
where S e is
2.1.4 Runoj
Saturation <
jacent to tl
Infiltration
is carried o
summing tl
the subsurf
2.2 Water
Given t
scheme sim
scale hydro
spatially-di
resented b]
