Environmental Engineering Reference
In-Depth Information
methods such as streamflow hydrograph ana-
lysis (
Section 4.5
); thus, maps or other products
derived from those estimates pertain only to
diffuse recharge. Any focused recharge would
go unaccounted for. Some models and water-
budget methods can account for both diffuse
and focused recharge; if recharge estimates
generated by these methods are used as the
basis for upscaling, then resulting products
would represent total recharge.
3.7 Upscaling of recharge
estimates
The focus of this section is on upscaling of
recharge estimates from one space or time scale
to a larger scale, for example, by using point
estimates of recharge at a few locations within
a watershed to determine average recharge for
the entire watershed. Upscaling techniques are
also used for developing parameter values for
input to hydrologic models. Upscaling is a com-
plex operation that has applications in many
areas of science and continues to be a topic of
active research. Formal statistical approaches
take into account data values, sampling loca-
tions, probability distributions, and data uncer-
tainty (e.g. Nœtinger
et al
.,
2005
). Such formal
approaches are not commonly taken in hydro-
logic studies, and the level of detail required to
apply such approaches is beyond the scope of
this text. What will be reviewed are the upscal-
ing approaches that have been used in hydro-
logic studies, concentrating specifically on
recharge.
The simplest procedure for upscaling point
measurements is to average all data values.
This approach does not account for the spatial
distribution of data points. Weighted averaging
approaches may be used, with weights calcu-
lated on areal distribution of sites or by delin-
eation of subregions of uniform properties.
Additional upscaling techniques addressed in
this section include regression, geostatistics,
and geographical information systems (GIS).
Simple empirical equations are frequently
used to obtain initial estimates of recharge.
They are included in this section because some
of the same tools (such as regression analysis)
that are used for upscaling can be used to
develop those equations and because empirical
models are embedded in other techniques for
upscaling (e.g. they are often used in conjunc-
tion with a GIS).
The nature of the recharge estimates that
are extrapolated in space or time is import-
ant, regardless of the upscaling approach that
is used. Most upscaling procedures are based
on estimates of diffuse recharge derived by
3.7.1 Simple empirical models
One of the most widely used and easiest
approaches for estimating recharge (
R
) is to
assume that it is equal to some fraction,
a
, of
annual precipitation (
P
):
R
=
aP
(3.9)
This is a simple yet useful approach. The ratio of
annual recharge to precipitation is reported in
countless studies and serves as a parameter that
allows comparison of recharge rates from dif-
ferent regions and time spans. Reported ratios
for studies cited in this text range from about
0.02 to more than 0.5. There are many factors
that influence this ratio, but depth to the water
table may be the most influential. Shallow water
tables usually receive more recharge (relative to
precipitation) than deep water tables. Many vari-
ations of Equation (
3.9
) exist. Sometimes annual
precipitation is replaced with precipitation dur-
ing the nongrowing season (fall through early
spring).
Maxey and Eakin (
1949
) proposed a modi-
fied form of Equation (
3.9
) for estimating
total recharge volume to valleys in Nevada
where there is a large variation in precipita-
tion between mountains and valley floors. Five
zones were delineated on the basis of annual
precipitation rates, and a separate coefficient
was determined for each zone:
R
=
0.03 1
P
+
0.07 2
P
+
0.15 3
P
+
0.25 4
P
(3.10)
where
R
is now the volume of annual recharge
for the watershed;
P
1 is volume of precipita-
tion that fell in zones where precipitation was
between 203 and 305 mm; and
P
2,
P
3, and
P
4
are volumes for zones where precipitation was
