Catchments as space-time filters – a joint spatio-temporal geostatistical analysis of runoff and precipitation

摘要

In this paper catchments are conceptualised as linear space-time filters.Catchment area A is interpreted as the spatial support and the catchmentresponse time T is interpreted as the temporal support of the runoffmeasurements. These two supports are related by T~Aκ whichembodies the space-time connections of the rainfall-runoff process from ageostatistical perspective. To test the framework, spatio-temporalvariograms are estimated from about 30 years of quarter hourly precipitationand runoff data from about 500 catchments in Austria. In a first step,spatio-temporal variogram models are fitted to the sample variograms forthree catchment size classes independently. In a second step, variograms arefitted to all three catchment size classes jointly by estimating theparameters of a point/instantaneous spatio-temporal variogram model andaggregating (regularising) it to the spatial and temporal scales of thecatchments. The exponential, Cressie-Huang and product-sum variogram modelsgive good fits to the sample variograms of runoff with dimensionless errorsranging from 0.02 to 0.03, and the model parameters are plausible. Thisindicates that the first order effects of the spatio-temporal variability ofrunoff are indeed captured by conceptualising catchments as linearspace-time filters. The scaling exponent κ is found to vary between 0.3 and0.4 for different variogram models.