Environmental Engineering Reference
In-Depth Information
3.7.3 Geostatistical techniques
Kriging is an interpolation method (Journel and
Huijbregts,
1978
) that can be used to estimate
recharge at any location in a watershed if point
estimates of recharge are available at other fixed
locations within the watershed. By setting up a
grid over a watershed and determining kriged
estimates of recharge at each grid point, an
estimate of recharge integrated over the entire
watershed can be obtained. In addition, kriging
provides a measure of the uncertainty of the
interpolated values. The kriging estimate,
R
*, is
calculated as a linear combination of all avail-
able data values:
www.gis.com; accessed September 24, 2009).
These systems are widely used in hydrology and
other fields of Earth science; many of the exam-
ples cited in this topic used a GIS. Information
relevant to hydrologic studies include elevation,
soil properties, land use, population, locations
of natural features such as rivers and lakes and
human-made features such as roads and build-
ings, and depth to water table. Regression meth-
ods and geostatistics are some of the analytical
tools that are usually available in a GIS. In addi-
tion, users can create their own tools or models
and apply these models at a great many points.
For example, simple empirical models have
been created and incorporated into a GIS to look
at drainage or recharge across large areas (e.g.
Keese
et al
.,
2005
; Dripps and Bradbury,
2007
).
Detailed maps of data and of model calculations
are easily constructed. A GIS can also be used to
upscale (interpolate or extrapolate) point esti-
mates of recharge over large areas.
Keese
et al
. (
2005
) used a GIS to develop a
map of annual recharge rates over Texas for the
period 1961 to 1990. Recharge was estimated
by using Equation (
3.11
); coefficients in the
equation were determined from a series of sim-
ulations of water movement through the unsat-
urated zone with a Richards equation-based
model for 13 regions of the state. Minor
et al
.
(
2007
) used a GIS to upscale point estimates of
recharge generated by a chloride mass balance
approach to watershed-wide estimates for areas
of southwestern Nevada. Dripps and Bradbury
(
2007
) derived recharge estimates that were
integrated over an entire watershed by using a
GIS to apply a simple soil water-budget model
in many locations within the watersheds. Fayer
et al
. (
1996
) and Rogowski (
1996
) used a GIS to
look at spatial variability of recharge within
watersheds.
A GIS is also a useful tool for analyzing and
displaying remotely sensed data, climate data,
and data on soils and land use contained in
databases such as STATSGO2 and SSURGO. The
limitations of remote sensing for direct esti-
mation of recharge are discussed in
Chapter
2
. However, remotely sensed data used in con-
junction with a GIS can be quite useful in the
preparation of areally distributed parameter
=
N
obs
R
*
λ
R
(3.14)
kk
k1
=
where
N
obs
is the number of points where
recharge is known,
R
k
is the recharge value at
location k, and λ
k
is the kriging weight associated
with each data location. The kriging weights are
calculated such that the estimation is unbiased
and the variance of estimation is minimal. An
extension of this method, called cokriging, con-
siders more than one data type in the estima-
tion process (e.g. recharge rate and soil texture).
Correlation between these data types can lead
to improved estimates of recharge.
Geostatistical tools can be useful when used
in conjunction with a GIS. Szilagyi
et al
. (
2003
;
2005
) used streamflow hydrograph separation
analysis (
Section 4.5
) to estimate recharge for
selected watersheds in Nebraska; kriging and a
GIS were then used to develop recharge maps for
the entire state. Lee
et al
. (
2006
) took a similar
approach to develop a recharge map for Taiwan.
Kriging and cokriging are used in a variety of
other hydrologic applications, such as prepar-
ing gridded data for model input and displaying
model output. Hevesi
et al
. (
1992a
,
b
) cokriged
precipitation rates and elevation in the vicinity
of Yucca Mountain, NV.
3.7.4 Geographical information systems
A geographic information system (GIS) consists
of computers, software, and databases designed
to store, manage, analyze, and display informa-
tion that is spatially referenced to Earth (http://
