4.2.2 Spatial Modeling
A lot of water resources data such as precipitation, streamflow, and water pollution
measurements are observed at point locations. A raster format of these measurements is user-friendly and allows hydrologists and engineers a quick overview of the
data. The most common method used to convert the point measurements to raster
format is spatial interpolation. This method uses the location and magnitude of the
measured data to determine estimates at the unmeasured locations. Spatial interpolation allows water resources planners and managers to analyze the spatial variability
of hydrologic processes such as precipitation [39]. Such analyses are used to
determine water budget at different spatial and temporal scales and validation of
different hydrologic models.
Spatial interpolation routines can be performed in GIS environment to save time
in exporting and importing data. The output of the interpolation can be viewed as a
grid or a vector map. Some of the commonly used interpolation methods in GIS
include inverse distance weighting, spline, and kriging. Inverse distance weighting is
based on the assumption that the nearby values contribute more to the interpolated
values than distant observations. Inverse distance weighting is by definition a
smoothing technique and that the maximum and minimum values can only occur
at the measured points. This technique will therefore never produce a value that is
higher than the maximum value in the observed data set. The spline method can be
thought of as fitting a rubber-sheeted surface through the known points using a
mathematical function. Advantages of spline functions are that they can generate
sufficiently accurate surfaces from only a few sampled points and they retain small
features. A disadvantage is that spline functions can produce estimates that are above
and below the measured minimum and maximum values. This is not always desired
as maximum and minimum values are often produced where they do not occur in
nature. Kriging is a stochastic technique similar to inverse distance weighted averaging in that it uses a linear combination of weights at known points to estimate the
value at an unknown point. Kriging depends on spatial and statistical relationships to
calculate the surface. Some advantages of this method are the incorporation of
variable interdependence and the available error surface output. A disadvantage is
that it requires substantially more computing and modeling time.
It has been shown that there is no single preferred method for data interpolation.
Aspects of the algorithm selection criteria need to be based on the actual data, the
level of accuracy required, and the time and/or computer resources available. This
assessment is important because much of geographic research includes the creation
of data for spatial analysis. The problem of interpolation is thus a problem of
choosing a plausible model to suit the data [40]. Selecting an appropriate spatial
interpolation method is key to surface analysis since different methods of interpolation can result in different surfaces and ultimately different results. The results of a
study performed on August 1990 rainfall data in Michigan are presented in Fig. 5.8.
The two interpolation techniques evaluated are inverse distance weighting and
universal kriging. The figure illustrates that depending on the accuracy required
the results could be different.
212
S. O. Darkwah et al.
A lot of water resources data such as precipitation, streamflow, and water pollution
measurements are observed at point locations. A raster format of these measurements is user-friendly and allows hydrologists and engineers a quick overview of the
data. The most common method used to convert the point measurements to raster
format is spatial interpolation. This method uses the location and magnitude of the
measured data to determine estimates at the unmeasured locations. Spatial interpolation allows water resources planners and managers to analyze the spatial variability
of hydrologic processes such as precipitation [39]. Such analyses are used to
determine water budget at different spatial and temporal scales and validation of
different hydrologic models.
Spatial interpolation routines can be performed in GIS environment to save time
in exporting and importing data. The output of the interpolation can be viewed as a
grid or a vector map. Some of the commonly used interpolation methods in GIS
include inverse distance weighting, spline, and kriging. Inverse distance weighting is
based on the assumption that the nearby values contribute more to the interpolated
values than distant observations. Inverse distance weighting is by definition a
smoothing technique and that the maximum and minimum values can only occur
at the measured points. This technique will therefore never produce a value that is
higher than the maximum value in the observed data set. The spline method can be
thought of as fitting a rubber-sheeted surface through the known points using a
mathematical function. Advantages of spline functions are that they can generate
sufficiently accurate surfaces from only a few sampled points and they retain small
features. A disadvantage is that spline functions can produce estimates that are above
and below the measured minimum and maximum values. This is not always desired
as maximum and minimum values are often produced where they do not occur in
nature. Kriging is a stochastic technique similar to inverse distance weighted averaging in that it uses a linear combination of weights at known points to estimate the
value at an unknown point. Kriging depends on spatial and statistical relationships to
calculate the surface. Some advantages of this method are the incorporation of
variable interdependence and the available error surface output. A disadvantage is
that it requires substantially more computing and modeling time.
It has been shown that there is no single preferred method for data interpolation.
Aspects of the algorithm selection criteria need to be based on the actual data, the
level of accuracy required, and the time and/or computer resources available. This
assessment is important because much of geographic research includes the creation
of data for spatial analysis. The problem of interpolation is thus a problem of
choosing a plausible model to suit the data [40]. Selecting an appropriate spatial
interpolation method is key to surface analysis since different methods of interpolation can result in different surfaces and ultimately different results. The results of a
study performed on August 1990 rainfall data in Michigan are presented in Fig. 5.8.
The two interpolation techniques evaluated are inverse distance weighting and
universal kriging. The figure illustrates that depending on the accuracy required
the results could be different.
212
S. O. Darkwah et al.