Estimating mean annual runoff by using a geostatistical spatially varying coefficient model that incorporates process-based simulations and short records

In this work, we suggest a new framework for estimating mean annual runoff, which is a key water balance component.  The framework consists of two steps: 1) A process-based hydrological model is used to simulate mean annual runoff on a grid covering the whole study area. 2) Since the parameters of the process-based model are calibrated globally, there are local biases in the runoff estimates relative to the observed runoff. We therefore correct the gridded simulations based on runoff data. Here, step 2 is done by using a Bayesian geostatistical model that treats the process-based simulations as a covariate. The regression coefficient of the covariate is modelled as a spatial field such that the relationship between the covariate (simulations from the process-based model) and the response variable (the observed mean annual runoff) is allowed to vary within the study area. Hence, it is a spatially varying coefficient model. A preprocessing step for including short records in the modelling is also suggested such that we can exploit as much data as possible in the correction procedure. We use state of the art statistical methods such as SPDE and INLA to ensure fast Bayesian inference.

 

The framework for estimating mean annual runoff is evaluated by predicting mean annual runoff for 1981-2010 for 127 catchments in Norway based on streamflow observations from 411 catchments. Simulations from the process-based HBV model on a 1 km x 1 km grid for the whole country 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. 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 two step procedure. In general, we expect the proposed approach to outperform purely geostatistical models in areas where the data availability is low to moderate.