Abstract
Data assimilation techniques are widely used in hydrology and water resources management to improve model forecast uncertainty by assimilating observations. The big challenge in practical applications is how to describe model uncertainties correctly to avoid the occurrence of spurious covariance during data assimilation. In this study, the ensemble square root filter (EnSRF) is used to estimate parameters and states of a groundwater model in Guantao, China, which updates ensemble means and perturbations separately and avoids the need to perturb observations. The uncertainty in parameters and states decreased with time while assimilating observations. However, incorrect updates of parameters and states were obtained, which could not be corrected by assimilating further observations improving the representation of the hydrological system. To compensate for this effect and reduce other sampling errors introduced during assimilation, localization and two covariance-tuning methods (inflation factor and damping factor) are explored in the study. The results show that alternative scenarios with proper localization length or a large inflation factor or a small damping factor produce better model estimates and improve the filter performance. The scenario with a damping factor of 0.05 shows a distinct gain in model predictive capability. The damping factor method is superior to the inflation factor method and preferable in real field applications. The scenario combining the damping factor with localization further improved the filter performance. The performance of the EnSRF with respect to different amounts of measurement error is also analysed. Even though the increase of observation error can increase the error covariance, a corresponding filter improvement is not observed as in that case, observations are less informative.
Highlights
Hydrological modelling plays a fundamental role in understanding the response of a system such as an aquifer to natural drivers and anthropogenic impacts
The results show that alternative scenarios with proper localization length or a large inflation factor or a small damping factor produce better model estimates and improve the filter performance
The scenario EnSRF_inf(0.8) provides the best filter performance and has a Normalized error reduction index (NER) value of 0.09 indicating that the filter performance improved by 9% by introducing an inflation factor of 0.8
Summary
Hydrological modelling plays a fundamental role in understanding the response of a system such as an aquifer to natural drivers (precipitation and river infiltration) and anthropogenic impacts (irrigation, surface water diversion and pumping of groundwater). The calibrated hydrological model can only describe one realization of possible model behaviour (deterministic estimation). During the past few decades, ensemble based inverse methods are applied to quantify model uncertainty (GomezHernandez et al, 2003; Hendricks Franssen et al, 2003; Zhou et al, 2014). They are computationally intensive due to the required large ensembles (such as the Markov Chain Monte Carlo method). More details about stochastic inverse methods in model calibration can be found in (Zhou et al, 2014)
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