A geostatistical two field model that combines point observations and nested areal observations, and quantifies long-term spatial variability -- A case study of annual runoff predictions in the Voss area

Abstract

In this study, annual runoff is estimated by using a Bayesian geostatistical model for interpolation of hydrological data of different spatial support. That is, streamflow observations from catchments (areal data), and precipitation and evaporation data (point data). The model contains one climatic spatial effect that is common for all years under study, and one year specific spatial effect. Hence, the framework enables a quantification of the spatial variability that is due to long-term weather patterns and processes. This can contribute to a better understanding of biases and uncertainties in environmental modeling. By using integrated nested Laplace approximations (INLA) and the stochastic partial differential equation approach (SPDE) to spatial modeling, the two field model is computationally feasible and fast. The suggested model is tested by predicting 10 years of annual runoff around Voss in Norway and through a simulation study. We find that on average we benefit from combining point and areal data compared to using only one of the data types, and that the interaction between nested areal data and point data gives a spatial model that takes us beyond smoothing. Another finding is that when climatic effects dominate over annual effects, systematic under- and overestimation of runoff over time can be expected. On the other hand, a dominating climatic spatial effect implies that short records of runoff from an otherwise ungauged catchment can lead to large improvements in the predictability of runoff.