494
International Water Resources Association
Water International, Volume 32, Number 3, Pg. 494-502, September 2007
© 2007 International Water Resources Association
INTRODUCTION
Precipitation data are important to many
applications in hydrology or agriculture. However, no
matter how dense the network of measuring stations in
a region, there will always be many locations with no
available precipitation data. Therefore it is necessary
to estimate point rainfall at unrecorded locations from
values at surrounding sites (Goovaerts, �999).
A number of methods have been used in the past
for the spatial interpolation of precipitation. Spatial
interpolation methods are techniques that predict the
value at a given location by using values from sample
points. For each computation the values of measured
points are weighted depending on their locations.
There are many spatial interpolation methods including
density estimation, inverse distance weighted method,
thin-plate splines method, etc. All methods share the
underlying assumption that sample points that are closer
to the interpolated location will infuence the interpolated
value more strongly than sample points which are
further away. A key difference among these approaches
is the criterion which is used to weigh the values of
the sample points. Criteria may include simple distance
relations (e.g., inverse distance methods), minimization
of variance (e.g., kriging and co-kriging), minimization
of curvature, and enforcement of smoothness criteria
(splining) (Hartkamp et al., �999).
The interpolation methods can be classifed
in two ma�or groups depending on the nature of
the function that is used to interpolate the values. A
frst group of spatial interpolation methods uses
mathematical formulas and sample point values to
estimate unmeasured values at any point across a given
surface. The weight that is assigned to each known
value for the interpolation of unknown values depends
only on the distance between sample point and location
of the interpolated point. These methods are grouped as
deterministic and they can be global (making use of all
of the sample points) or local (using a limited number
of sample points in the vicinity of estimated value’s
location). When it comes to interpolating precipitation
data, the simplest approach consists of assigning the
record of the closest gauge to the unsampled location
(Thiessen, �9��� Goovaerts, �999). This method, also
referred to as the �nearest neighbor� method (Hartkamp
Spatial Interpolation of Annual Precipitation in South
Africa - Comparison and Evaluation of Methods
M. Coulibaly and S. Becker, University of Wisconsin Oshkosh, Department of Geography
and Urban Planning,
Abstract: Data from �4� rainfall gauges were used to interpolate the spatial distribution of annual
rainfall in South Africa. Several spatial interpolation methods (inverse distance weighting (IWD), ordinary
kriging, universal kriging, cokriging) were tested by variation analyses and cross-validation to determine the
most suitable one. The best results were achieved by ordinary kriging, whereby the setting of the parameters was
determined through sensitivity analyses. The median of the errors turned out to be 61 mm (11%). The interpolation
errors were generally small for the interior of the country and high for coastal and mountainous regions.
Keywords: Spatial interpolation, data, evaluation, South Africa