Spatial interpolation - Spatial Data Analysis: An Introduction for GIS Users - page 154

it suggests over-prediction. Ideally, therefore, the mean error would be 0. h e RMSE
represents the magnitude of errors and a small RMSE value corresponds to accurate
predictions. With IDW, the mean cross-validation error was -0.520 and the RMSE
was 47.82. h e i gures for TPS were mean error -0.418 and RMSE 53.87. For OK the
i gures were mean error -0.189 and RMSE 47.81. In this case, the least biased predic-
tions (mean error closest to 0) are provided by OK. h e smallest errors overall (as
measured by the RMSE) are also for OK, although the dif erence between the OK and
IDW RMSE values is very small. Note that TPS predictions are the least accurate in
this case, but that more accurate predictions are obtained when other variants of TPS
(e.g. TPS with tension, which can be conducted in ArcGIS™, and is dei ned by Lloyd
(2006)) are used.
Summary
This chapter provided an introduction to some of the most widely used approaches to the
generation of surfaces from point data. In addition, a short outline of areal interpolation
was given. In terms of selection of methods, it was noted that differences in prediction
results are a function of sampling density and spatial variation. Approaches like cross-
validation offer a way of assessing the performance of different approaches. However,
such approaches should not be used blindly and other approaches, such as jackknifi ng
(predicting to one set of locations (at which there are observed values) using a second
data set and computing the errors of the predictions), are likely to be more robust.
Further reading
More information on spatial interpolation is provided by Burrough and McDonnell (1998) ,
Lloyd (2006) , and Chang (2008) , for example. There are many introductions to geosta-
tistics (e.g. Goovaerts, 1997 ; Armstrong, 1998 ; Webster and Oliver, 2007 ; Atkinson and
Lloyd, 2009 ). Many different applications of interpolation procedures can be found in the
literature. Interpolation has been used to map elevation ( Lloyd and Atkinson, 2002 ), pre-
cipitation amount ( Goovaerts 2000 ; Lloyd 2002 , 2005 , 2009 , 2010 ), and airborne pollutants
( Lloyd and Atkinson, 2004 ), amongst many other variables.
The next chapter is concerned with the analysis of gridded data and the latter part
of the chapter has a particular focus on the analysis of DEMs.