A geostatistical spatially varying coefficient model for mean annual runoff that incorporates process-based simulations and short records

Abstract. We present a Bayesian geostatistical model for mean annual runoff that incorporates simulations from a process-based hydrological model by treating the simulations as a covariate in the statistical model. The regression coefficient of the covariate is modeled as a spatial field such that the relationship between the covariate (simulations from a hydrological model) and the response variable (observed mean annual runoff) is allowed to vary within the study area. Hence, it is a spatially varying coefficient. A preprocessing step for including short records in the modeling is also suggested and we obtain a model that can exploit several data sources by using state of the art statistical methods.

The geostatistical model is evaluated by predicting mean annual runoff for 1981–2010 for 127 catchments in Norway based on observations from 411 catchments. Simulations from the process-based HBV model on a 1 km × 1 km grid are used as input. We found that on average the proposed approach outperformed a purely process-based approach (HBV) when predicting runoff for ungauged and partially gauged catchments: The reduction in RMSE compared to the HBV model was 20 % for ungauged catchments and 58 % for partially gauged catchments, where the latter is due to the preprocessing step. For ungauged catchments the proposed framework also outperformed a purely geostatistical method with a 10 % reduction in RMSE compared to the geostatistical method. For partially gauged catchments however, purely geostatistical methods performed equally well or slightly better than the proposed combination approach. It is not surprising that purely geostatistical methods perform well in areas where we have data. In general, we expect the proposed approach to outperform geostatistics in areas where the data availability is low to moderate.