How well do indicator variograms capture the spatial connectivity of soil moisture?

Abstract

Indicators are binary transforms of a variable and are 1 or 0, depending on whether the variable is above or below a threshold. Indicator variograms can be used for a similar range of geostatistical estimation techniques as standard variograms. However, they are more flexible as they allow different ranges for small and large values of a hydrological variable. Indicator geostatistics are also sometimes used to represent the connectivity of high values in spatial fields. Examples of connectivity are connected high values of hydraulic conductivity in aquifers, leading to preferential flow, and connected band-shaped saturation zones in catchments. However, to the authors' knowledge the ability of the indicator approach to capture connectivity has never been shown conclusively. Here we analyse indicator variograms of soil moisture in a small south-east Australian catchment and examine how well they can represent connectivity. The indicator variograms are derived from 13 soil moisture patterns, each consisting of 500–2000 point TDR (time domain reflectometry) measurements. Winter patterns are topographically organized with long, thin, highly connected lines of high soil moisture in the drainage lines. In summer the patterns are more random and there is no connectivity of high soil moisture values. The ranges of the 50th and 90th percentile indicator semivariograms are approximately 110 and 75 m, respectively, during winter, and 100 and 50 m, respectively, during summer. These ranges indicate that, compared with standard semivariograms, the indicator semivariograms provide additional information about the spatial pattern. However, since the ranges are similar in winter and in summer, the indicator semivariograms were not able to distinguish between connected and unconnected patterns. It is suggested that new statistical measures are needed for capturing connectivity explicitly. © 1998 John Wiley & Sons, Ltd.