Data assimilation in integrated hydrological modelling in the presence of observation bias

Jørn Rasmussen,Jens Christian Refsgaard,Henrik Madsen,Karsten Høgh Jensen

doi:10.5194/hess-20-2103-2016

Abstract

Abstract. The use of bias-aware Kalman filters for estimating and correcting observation bias in groundwater head observations is evaluated using both synthetic and real observations. In the synthetic test, groundwater head observations with a constant bias and unbiased stream discharge observations are assimilated in a catchment-scale integrated hydrological model with the aim of updating stream discharge and groundwater head, as well as several model parameters relating to both streamflow and groundwater modelling. The coloured noise Kalman filter (ColKF) and the separate-bias Kalman filter (SepKF) are tested and evaluated for correcting the observation biases. The study found that both methods were able to estimate most of the biases and that using any of the two bias estimation methods resulted in significant improvements over using a bias-unaware Kalman filter. While the convergence of the ColKF was significantly faster than the convergence of the SepKF, a much larger ensemble size was required as the estimation of biases would otherwise fail. Real observations of groundwater head and stream discharge were also assimilated, resulting in improved streamflow modelling in terms of an increased Nash–Sutcliffe coefficient while no clear improvement in groundwater head modelling was observed. Both the ColKF and the SepKF tended to underestimate the biases, which resulted in drifting model behaviour and sub-optimal parameter estimation, but both methods provided better state updating and parameter estimation than using a bias-unaware filter.

Highlights

Sequential assimilation of observations in models is a widely used method in several fields, including meteorology and hydrology
Observation bias is a notable challenge in integrated hydrological modelling and needs to be addressed when applying data assimilation to the models
Both methods improved the groundwater head and stream discharge of the model, and with varying degrees of success estimated the observation bias when using synthetic observations. Both bias estimation methods resulted in improved streamflow modelling, but little improvement was seen in groundwater heads

Summary

Introduction

Sequential assimilation of observations in models is a widely used method in several fields, including meteorology and hydrology. Camporese et al, 2009; Shi et al, 2014; Rasmussen et al, 2015) The latter presents a number of challenges that have yet to be comprehensively addressed; relating to the differences in process timescales, e.g. between groundwater flow and surface runoff, and the coupling between these processes. In Camporese et al (2009), the ensemble Kalman filter (EnKF) was applied to an integrated model of a synthetic tilted v-catchment and both stream discharge and groundwater hydraulic head observations were assimilated to update both groundwater and stream states. Shi et al (2014) applied the EnKF to an integrated land surface hydrological model of a small catchment and, using seven different observation types, successfully es- In Camporese et al (2009), the ensemble Kalman filter (EnKF) was applied to an integrated model of a synthetic tilted v-catchment and both stream discharge and groundwater hydraulic head observations were assimilated to update both groundwater and stream states. Shi et al (2014) applied the EnKF to an integrated land surface hydrological model of a small catchment and, using seven different observation types, successfully es-

Methods

Results

Conclusion