Joint model state-parameter retrieval through the evolutionary data assimilation approach

Data assimilation (DA) methods have been widely used to improve model state estimation by merging model outputs with observations. Traditionally, studies have focused on updating model state variables but recent studies have augmented model parameters alongside model state variables to improve the estimation procedure. The updated model ensemble members represent a compromised estimation between prediction and observation. The compromise, which is usually in objective space subject to agreement between observation and model predictions, is important. However, few studies have actually employed DA procedures to investigate the updated members in decision space, through examination of the temporal changes of model states and parameters. Usually, the model states and parameters evolve/change: (i) subject to changes in observation, (ii) to account for the varied uncertainties in different land surface conditions, and (iii) due to their intricate connection with hydrologic conditions which evolve across assimilation time periods. Moreover, the update procedure in most DA methods is controlled predominantly by matchings between observation and model predictions with limited impact from decision space through model state variables and parameters. As a result, DA procedures are needed to tightly link the compromise in objective space to decision space, with the capability to examine the temporal changes of model states and parameters. To address these challenges, this study has employed the Evolutionary Data Assimilation (EDA) method in a joint state-parameter estimation to assimilate: (i) synthetic daily soil moisture into the Joint UK Land Environment Simulator (JULES), and (ii) hourly streamflow into the Hydrologiska Byråns Vattenbalansavdelning (HBV) model. The EDA is a relatively new formulation of the multi-objective evolutionary strategy for the purpose of data assimilation. The EDA was applied to illustrate its capability to both retrieve model parameter values and to improve estimation of soil moisture and streamflow in a two-step procedure. In the soil moisture assimilation, the first step involved the generation of initialization model state and parameter values as the original ‘truth’ where they were applied into the JULES model to simulate surface soil moisture, representing the synthetic soil moisture. The second step assimilated the synthetic soil moisture into a perturbed version of the JULES model to retrieve the original model state and parameter values. The updated model states and parameter values were compared to the original ‘truth’ to show that the EDA can both retrieve the original ‘truth’ parameter values and the soil moisture states. The soil moisture assimilation was illustrated for the Yanco region in New South Wales, Australia from January to December 2010. In the streamflow assimilation, the original ‘truth’ values of the HBV model were obtained from two independent studies generated using: (i) the Multistart weight-adaptive recursive parameter estimation, and (ii) the Shuffled Complex Evolution. The EDA was applied to assimilate hourly streamflow into the HBV model to retrieve the calibrated model state and parameter values. The streamflow assimilation was illustrated for the Bellebeek catchment in Belgium from August 2006 to July 2007. The input data for the HBV model and data sets in the Bellebeek catchment were provided by the authors of the two independent studies. The synthetic soil moisture were compared to the EDA updated soil moisture in the soil moisture assimilation, whereas the observation streamflow were compared to the EDA updated streamflow. The findings show a high estimation accuracy of the EDA for soil moisture and streamflow based on the evaluation measures and the two independent studies. Moreover, the updated ensemble of model states and parameter values were evaluated across the assimilation time steps showing the level of convergence for model state variables and parameters. The evaluation of the temporal evolution of updated ensemble members in decision space demonstrates the capability of the EDA to retrieve model state variables and parameters. Thus, the key potential of the EDA lies in the evaluation of updated members for model state and parameter linkages in decision space.