Environmental Engineering Reference
In-Depth Information
between 305 and 381 mm, 381 and 490 mm, and
over 490 mm, respectively. Equation (
3.10
) was
derived under the assumption that recharge
was equivalent to groundwater discharge; pre-
cipitation data for Nevada were obtained from
Hardman (
1936
). Variations of this method have
been extensively used in Nevada over the years
since it was first proposed (e.g. Watson
et al
.,
1976
; Nichols,
2000
; Flint and Flint,
2007
).
Keese
et al
. (
2005
) used a power function
model to estimate annual recharge from mean
annual precipitation:
must be estimated by some technique, there
is unmeasurable uncertainty in data used to
derive Equation (
3.12
). Estimates of diffuse
recharge derived from analysis of streamflow
hydrographs (
Section 4.5
) have been used to
develop regression equations for predicting
recharge (e.g. Pérez,
1997
; Holtschlag,
1997
;
Cherkauer and Ansari,
2005
; Gebert
et al
.,
2007
;
and Lorenz and Delin,
2007
). Sophocleous (
1992
)
and Nichols and Verry (
2001
) based their regres-
sion equations on estimates of recharge obtained
from application of the water-table fluctuation
method (
Section 6.2
). Flint and Flint (
2007
) and
Tan
et al
. (
2007
) used model-generated estimates
of recharge to develop regression equations and
subsequently used the regression equations to
extrapolate model results.
R
=
aP
b
(3.11)
This equation provided better estimates of
recharge across Texas than estimates produced
by Equation (
3.9
). Flint and Flint (
2007
) used a
modified form of Equation (
3.11
), in which pre-
cipitation exceeding a threshold replaced pre-
cipitation, to extrapolate recharge estimates in
time by using historical precipitation data.
Example: Minnesota recharge map
Lorenz and Delin (
2007
) used recharge esti-
mates derived from the streamflow recession-
curve displacement method (
Section 4.5.2
) with
data obtained from 38 stream gauges across
Minnesota to generate the following equation:
3.7.2 Regression techniques
Regression techniques are commonly employed
in hydrologic studies for a multitude of purposes
(Helsel and Hirsch,
2002
). One such purpose is
the extrapolation (or upscaling) of recharge esti-
mates in space or the extension of the estimates
in time. Linear regression equations generally
take the form:
R
=
14.25
+
0.6459
P
−
0.022331
GDD
+
67.63
S
y
(3.13)
where
R
is average annual recharge in cen-
timeters (cm),
P
is annual precipitation in cm,
GDD
is growing degree days, and
S
y
is aquifer
specific yield. Growing degree days served as
a surrogate for evapotranspiration and were
calculated as the sum of average daily tempera-
ture minus 10ºC. Precipitation and growing
degree days data were obtained from National
Weather Service stations for the period 1971
to 2000. Specific yield served as a surrogate for
soil texture and was estimated as the differ-
ence between saturated soil-water content and
water content at field capacity, as calculated by
the method of Rawls
et al
. (
1982
). Percentages
of sand, silt, and clay required for estimating
water content were obtained from the STATSGO
database.
Regression equations can be conveniently
applied manually, in a spreadsheet, and with
a GIS. Equation (
3.13
) was applied with a GIS
across all of Minnesota (
Figure 3.17
). The
R
=++
aX
bX
c
(3.12)
1
2
where
a
,
b
, and
c
are coefficients determined by
regression analysis and
X
1
and
X
2
are independ-
ent parameters that reflect watershed charac-
teristics, such as soil texture, permeability,
elevation, vegetation, and geology, or climate,
such as precipitation and temperature. Equation
(
3.12
) is easy to apply; it can be applied at any
location where parameter values are known or
can be estimated. Nonlinear regression equa-
tions, some of the form of Equation (
3.11
), are
also common in recharge studies. Nolan
et al
.
(
2007
) used nonlinear regression to identify fac-
tors that influenced recharge estimates for the
eastern United States.
Derivation of a regression equation
requires a number of known recharge values.
Because recharge cannot be measured, but
