Geoscience Reference
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the estimated values of
k
0
and
n
e
. Among the other parameters, the hydraulic conduc-
tivity was found to be only weakly (if at all) scale correlated in that range of scales of
L
(
2 km). The hydraulic diffusivity
D
h
, the hydraulic desorptivity
De
h
, and the drain-
able porosity or specific yield
n
e
showed no evidence of any scale dependency in the
same range of scales.
>
The effect of mean aquifer slope
From the analyses developed in this chapter it is clear that the slope of the riparian aquifers
can be expected to exert a strong influence on the magnitude and evolution of the base flow
from a basin. Cursory inspection of the unit response function of a hill slope (10.146) with the
accompanying Figures 10.27 and 10.28 indicates that Hi can indeed play a major role. This
was also brought out in the investigation of measured drought flow data from 19 watersheds
in a mountainous section of the Appalachian Plateau by Zecharias and Brutsaert (1985;
1988a); the results of a factor analysis indicated that, among the geomorphic parameters
that are related to groundwater outflow, total length of perennial streams, drainage density
and average basin slope are most closely related to the process. Moreover, the influences
of these three parameters on groundwater outflow behavior are independent of each other;
thus, the inclusion of additional parameters would not necessarily yield a better relationship,
and may result in redundancy. This empirical result is consistent with the linear basin-scale
formulation of the phenomenon in Equations (10.166) and (10.157) with (10.167), which
indicates that
L
,
L
/
A
and Hi are the only three geomorphic parameters which control the
flow. For the present purpose, geomorphic parameters may be considered the ones that can
be derived from topographic maps.
Unfortunately, in contrast to stream length and drainage density, until now attempts to
include slope in basin-scale parameterizations have been less than successful. The problem
was addressed in Zecharias and Brutsaert (1988b) in the context of the applicability of
Equation (10.157) in hilly terrain. The same 19 representative catchments in the Allegheny
Mountain section of the Appalachian Plateau, mentioned above, were analyzed on the basis
of (10.157) with
b
=
1. The results showed that
a
, taken as the slope of the lower envelope of
(linearly) plotted
dQ
/
dt
vs
Q
data, is dependent on drainage density (
L
/
A
) and on (
k
0
/
n
e
),
in agreement with Equation (10.167), but surprisingly not on land surface slope. However,
the results also showed, that in these same plots both the slope of the upper envelope and the
mean slope through all the data points, decrease with time. For instance, in one watershed
in the region, with flow values that occurred 2, 4, 6, and 7 days following a rainfall event,
the slopes of the upper envelopes were observed to evolve as
a
=
0.33, 0.23, 019, and
0.15 d
−
1
, respectively, whereas the lower envelopes remained at around 0.063 d
−
1
.As
illustrated in Figure 10.38, a similar evolution of
a
of the upper envelopes was observed in
the Washita River Basin.
The value of the rate of flow
Q
of a receding hydrograph depends mainly on the storage
of water in the watershed. But the upper envelope in graphical representations like Figure
10.38 provides information on the groundwater outflow regime in the early stages of a dry
period when the rates of recession, i.e.
−
dQ
/
dt
, are high. The successive values of
a
show
that there are aquifers in the basin whose recession rates are initially large, but decrease
sensibly as the rainless period continues. Advanced states of the outflow process, which
are accompanied by small recession rates, are represented by the lower envelopes, whose
a
values in the successive scatter diagrams remain essentially the same. It is likely that
the variation of the parameter
a
of the upper envelopes with time is largely the result of
