Inferring the location of catchment characteristic soil moisture monitoring sites. Covariance structures in the temporal domain

Information shortage is a fundamental constraint in catchment hydrology that severely affects the possibilities for secure inference of the generic hydrologic landscape, as well as for secure validation of physically deduced distributed models. The introduction of databases with high enough spatiotemporal resolution to properly reflect generic hydrological catchment characteristics may therefore be considered as an inferential breakthrough. The work presented here is part of a project where observations from such an Australian catchment (the Tarrawarra) are utilised to estimate the discrepancy for individual soil moisture monitoring sites in reflecting generic catchment characteristics. With low enough discrepancy, observation sites may be considered as catchment characteristic soil moisture monitoring (CASMM) sites, thus capturing unbiased catchment characteristics and being well suited to represent the catchment in a monitoring effort. In this particular study, covariance structures in the temporal domain are inferred in order to enable subsequent enquiries regarding CASMM discrepancies. This is accomplished with ARMAX filters applied to the conditional auto- and cross-covariance structures that connect observations of soil moisture to the temporal variation of meteorology. The results suggest that weekly observations of Tarrawarra soil moisture are quite consistent realisations of first order auto-regressive processes, which means that the present state of soil moisture is generally acquired through the past week. With auto-correlative effects filtered out, cross-correlative meteorological effects on Tarrawarra soil moisture are identified and generally represented by the present week's accumulation of rainfall, the present week's accumulation of global radiation, and the previous week's maximum wind speed. After successive filtering of conditional cross-correlative effects, residual time-series observations may be considered as temporally independent, and therefore are well suited for subsequent inferences regarding covariance structures in the spatial domain. Since the exclusion of auto-correlative effects is necessary for unambiguous model interpretation, the estimated cross-correlative parameters should reflect the true nature of underlying physical processes.