On the spatial scaling of soil moisture

Abstract The spatial scale of soil moisture measurements is often inconsistent with the scale at which soil moisture predictions are needed. Consequently a change of scale (upscaling or downscaling) from the measurements to the predictions or model values is needed. The measurement or model scale can be defined as a scale triplet, consisting of spacing, extent and support. ‘Spacing’ refers to the distance between samples; ‘extent’ refers to the overall coverage; and ‘support’ refers to the area integrated by each sample. The statistical properties that appear in the data, the apparent variance and the apparent correlation length, are as a rule different from their true values because of bias introduced by the measurement scale. In this paper, high-resolution soil moisture data from the 10.5 ha Tarrawarra catchment in south-eastern Australia are analysed to assess this bias quantitatively. For each survey up to 1536 data points in space are used. This allows a change of scale of two orders of magnitude. Apparent variances and apparent correlation lengths are calculated in a resampling analysis. Apparent correlation lengths always increase with increasing spacing, extent or support. The apparent variance increases with increasing extent, decreases with increasing support, and does not change with spacing. All of these sources of bias are a function of the ratio of measurement scale (in terms of spacing, extent and support) and the scale of the natural variability (i.e. the true correlation length or process scale of soil moisture). In a second step this paper examines whether the bias due to spacing, extent and support can be predicted by standard geostatistical techniques of regularisation and variogram analysis. This is done because soil moisture patterns have properties, such as connectivity, that violate the standard assumptions underlying these geostatistical techniques. Therefore, it is necessary to test the robustness of these techniques by application to observed data. The comparison indicates that these techniques are indeed applicable to organised soil moisture fields and that the bias is predicted equally well for organised and random soil moisture patterns. A number of examples are given to demonstrate the implications of these results for hydrologic modelling and sampling design.