Spatial evaluation of pedotransfer functions using wavelet analysis

If predictions of pedotransfer functions (PTFs) are distributed in space, then they require a spatial evaluation. Three aspects of performance can be considered in the evaluation of a spatially distributed PTF: (i) the correlation of observed and predicted quantities across different spatial scales; (ii) the reproduction of observed variance across different spatial scales; and (iii) the spatial pattern of the model error. Further, when there is more than one PTF available, we must be able to choose which is the most appropriate for a particular spatial scale. In this study, we observed soil hydraulic properties (water retention and saturated hydraulic conductivity) at 100 regularly spaced locations on a 5000-m transect in southern Italy. Four PTFs (referred to as Model V, Model S, Model W, and Model L) were then used to predict the hydraulic properties at the sampled locations. We used wavelet analysis to examine how the variances and correlations of the observed and predicted properties varied with spatial scale and location in the landscape. This spatial analysis revealed aspects of variability that could not be investigated under assumptions of stationarity (e.g. by geostatistics). These results included: the underestimation of observed variances at particular spatial scales; the failure of the predictions to correlate adequately with the observed variables at particular spatial scales; and, also, evidence of scale- and location-dependent correlations, which imply that non-spatial correlation coefficients do not suffice to describe the joint spatial variation of the observations and predictions. We also found significant correlations between model errors and auxiliary variables, which indicated how the site-specific predictions of the PTFs might be improved. Finally, we proposed a wavelet concordance correlation to rank the performance of each PTF, thereby enabling the choice of the best PTF at a particular spatial scale. In general terms, we found that a locally calibrated PTF (Model L) yielded the best results.