Ra1

Distance (Km)

Fig. 9.10 Experimental and fitted spherical variograms for 36 monthly December rainfall observation stations in a 5000 km2 area in southern Portugal (after Goovaerts, 2000, with kind permission of Elsevier).

Distance (Km)

Fig. 9.10 Experimental and fitted spherical variograms for 36 monthly December rainfall observation stations in a 5000 km2 area in southern Portugal (after Goovaerts, 2000, with kind permission of Elsevier).

is called the range of the variogram (about 25 km in the case of Fig. 9.10). Some functions allow a non-zero intercept at a distance of zero (this can be seen in Fig. 9.10, though in this case it is small). This is called the nugget variance (it gets this name because a mining engineer call Krige first made the method popular in estimating gold concentrations from point assays in mining operations in South Africa). A large nugget variance is an indication of small-scale variability relative to the spacing of the observation points.

The kriging method has been used for the interpolation of rainfalls at larger scales, e.g. by Goovaerts (2000) in Portugal (Fig. 9.11), and Clark and Slater (2006) in Colorado. The simplest kriging method has one important requirement to be a good interpolation technique: that the variable to be interpolated should be statistically stationary in space. This means that the rainfalls should not be subject to strong trends in the mean values (or in the variance, or other statistical moments). For precipitation variables, of course, this is often the case, particularly where precipitation is strongly related to the topography. In this case, techniques such as kriging with an external drift or co-kriging can take account of other variables, such as elevation, in defining the pattern of rainfalls and integrating it to get the areal average over an area.

Fig. 9.11 Predicted map of December monthly rainfall amounts in southern Portugal interpolated using ordinary Kriging (after Goovaerts, 2000, with kind permission of Elsevier).

Goovaerts (2000) suggests that this can be a much more reliable estimator than simpler univariate interpolation methods based on distance alone, such as Thiessen polygons or multi-quadric interpolation.

One advantage of kriging as an interpolation technique is that it can provide estimates of uncertainty in the interpolated rainfall at both point and areal average scales. The general use of kriging, however, is limited by the fact that the shape of the variogram is likely to change for every storm or time period (e.g. Bigg, 1991), and requires a large number of gauges to define it well (Fig. 9.10 also illustrates that the observed variogram may not be smooth when derived from only a small number of gauges).

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