460 
element in the catchment. Grid elements are then coupled to each other by using global mass bal 
ance considerations. The catchment average hydrologic response is simply the average of the local 
grid element responses. 
2.2.1 Topographic-Soil Index. Assuming that saturated subsurface flow from grid elements is con 
trolled by topographic and soil properties, Sivapalan et al. (1987) have derived a simple expression 
relating the local water table depth, z x , with the local topographic-soil index, ln(aT e ) / (Ttan(3 ): 
Zl = f -7{'"(r^) _A } (9 > 
where / is a parameter which describes the exponential decay of saturated hydraulic conductivity 
with depth, a is the area drained through the local unit contour, T e is the catchment average value of 
the saturated transmissivity, T is the local value of the transmissivity, (3 is the local slope angle, A is 
the catchment average value of the topographic variable ln(a/tan[3 ), and a is the catchment average 
water table depth which is defined as 
= H 
r.dA 
( 10 ) 
in which A is the catchment area. It can be seen from Eq.(9) that knowledge of the spatial distribution 
of the topographic- soil index allows for prediction of the spatial distribution of water table depth. 
2.2.2 Water Table Dynamics. The temporal changes in the spatial distribution of hydrologic variables 
are achieved through modelling the catchment average water table dynamics. According to Eq.(9), 
the rate of change of the local water table depth is equal to the rate of change of the catchment 
average water table depth, which is given by catchment mass balance considerations as 
Af _ [Exg 1 + Qb/A + Ex/ e x ] / n x 
Ai { Ex(0* - 0>z) x + /,[ 9s - 9 tz (z) ] x dz } 1 1 
where the grid index, x, represents a local grid element, Qb = Qoexp(-fz) is the contribution 
from the base flow (Sivapalan et al., 1987) and 9 S is the saturated soil moisture content. The terms 
in the denominator represent the catchment storage deficit in the surface and transmission zones, 
respectively. The moisture profile in the transmission zone, 0 tz (z), is given by Salvucci (1993) as a 
function of g' = g/K„: 
*«•<«) = »' + (*. - Or) { [o + «') j] (12) 
3 APPLICATION TO MAC-HYDRO’90 
3.1 Data Description 
MAC-HYDRO’90 was conducted over a portion of the Mahantango Creek which is a lA-km 2 
research watershed operated by the Northeast Watershed Research Center of the USDA, ARS in 
central Pennsylvania. The average annual precipitation and évapotranspiration for this watershed 
were 1128 mm and 479 mm per year, respectively. The soils within this watershed were primarily silt 
loams and loams. The intensive study area included a subwatershed (WD38) of approximately 60 ha 
on the eastern portion of Mahantango Creek. The WD38 subwatershed contained a mixture of land 
uses (corn, wheat, oat, pasture, and hay) and was bounded on the south by forest. Topography of 
the watershed was depicted by the 30 m x 30 m digital elevation model (DEM) data. The weather 
conditions during the experiment were dry initially. No rain was recorded during the preceding 5 
days, resulting in uniformly dry soil conditions. After the first flight (July 10, 1990), there was an 
approximately 52 mm of precipitation over a four-day period, followed by a strong dry down.