Environmental Engineering Reference
In-Depth Information
Combining Equations (
2.7
) and (
2.8
) results
in a new water-budget equation for the control
volume consisting of the watershed and the
underlying unsaturated zone:
out differences between daily precipitation
and evapotranspiration. If data permit, daily
time steps are recommended for water-budget
tabulations.
2.2.1 Uncertainty in water budgets
Uncertainty in recharge estimates generated by
water-budget methods can arise from inaccur-
acy in the underlying conceptual model, inad-
equate accounting of spatial and temporal
variability of water-budget components, and
uncertainty in measuring or estimating values
for those components. Incorrect conceptual
models of the hydrologic system introduce the
most serious errors in using a water-budget
method, or any other approach, to estimate
recharge. An incorrect conceptual model
can result in an incorrect water-budget equa-
tion, one with missing or superfluous terms.
Conceptual models are addressed in
Chapters
1
and
9
. The effects of other sources of error on
recharge estimates are discussed herein.
A simple example can be used to illustrate
the effects of water-budget uncertainties on
recharge estimates. Consider a soil column
with no surface storage and no surface-water
flow onto it, as described in Equation (
2.1
).
Precipitation falling on the soil column runs
off, is evapotranspired, remains in storage in
the column, or drains out of the bottom of the
column. Considering only measurement error,
classical statistics can be applied to define the
variance of the drainage estimate (σ
2
D
) as:
P
+ =+ + +
+
Q
sw
R
∆
∆∆
ET
sw
ET
uz
S
sw
on
(2.9)
S
snow
+
SR
uz
+
off
Watershed models (
Section 3.4
) are usually
based on some form of Equation (
2.7
) or (
2.9
).
For residual water-budget methods, all
terms in a water-budget equation, except
recharge, are independently measured or esti-
mated and recharge is set equal to the residual
value. Equations (
2.1
), (
2.8
), or (
2.9
), or some
variation of them, serve as the basis for most
water-budget methods for estimating recharge.
However, other equations can also be used. The
residual water-budget approach is also used to
estimate other water-budget components, such
as evapotranspiration (e.g. Allen
et al
.,
1998
;
Wilson
et al
.,
2001
).
Water-budget components can display
markedly different trends. Precipitation can
be highly episodic, and rates can range from 0
upward toward 100 mm/h; evapotranspiration,
on the other hand, usually follows a distinct
seasonal trend with rates ranging between 0
and 1 mm/h. Rates of water movement through
the unsaturated zone vary considerably, being
affected by soil properties, climate, land use,
and depth to water table. Depending on condi-
tions, rainfall that infiltrates might move to the
water table (and thus become recharge) over the
course of 1 day. In another system, infiltrating
water may take several months to reach the
water table. Because of these different temporal
trends, recharge calculations are sensitive to
the time step over which water budgets are tab-
ulated. Recharge generally is predicted to occur
only over a time interval in which precipitation
exceeds evapotranspiration. This condition can
occur on any day in virtually any environment.
On a monthly basis, however, evapotranspir-
ation exceeds precipitation for summer months
in most environments. Hence, monthly time
steps are likely to produce recharge estimates
that are less than those produced by using daily
time steps; longer time steps tend to dampen
(2.10)
σσσ σ σ
∆
2
=++ +
2
2
2
2
D
P
ET
S
Roff
where σ
2
j
is the variance of component j (Lerner
et al
.,
1990
). This analysis requires assumptions
that the water-budget components are inde-
pendent of each other and that the measure-
ment errors for all methods are unbiased and
normally distributed with a mean of 0. If these
assumptions are valid and the variances were
known, confidence intervals could be calcu-
lated for drainage estimates. However, this
approach cannot account for any spatial or tem-
poral trends in water-budget components.
Dages
et al
. (
2009
) analyzed the water
budget for a small Mediterranean watershed,
