Integration of evolutionary based assimilation into Kalman-type methods for streamflow simulations in ungauged watersheds

Data assimilation (DA) has emerged as a valuable tool for the design and application of streamflow forecasting systems. But DA applications for streamflow simulations in ungauged basins are still very limited primarily because most updated ensemble members are not usually associated with converged state and model parameterizations. Other limitations include the evaluation of massive number of ensemble members, weak/unknown relationships between parameter values and predictors, and the transfer of several members from gauged watersheds to ungauged ones is computationally expensive. But the inherent dynamics of DA to account for uncertainties in model, forcing data, and imperfect observation provide an appealing approach to simulate watershed response in ungauged basins. This study proposes a DA method namely the Pareto-Particle-Ensemble Kalman Filter (ParetoParticleEnKF) to generate and archive a small number of continuously evolved members using multi-objective evolutionary strategy where these members are updated using particle and ensemble Kalman filtering methods. The archived members for gauged watersheds are combined using inverse distance weighting where they are applied to simulate watershed response in ungauged basins.The proposed method is demonstrated by assimilating daily streamflow into the Sacramento Soil Moisture Accounting (SAC-SMA) model for 10 watersheds in southern Ontario, Canada. After successfully transferring ensemble members from gauged watersheds to ungauged ones, the updated ensembles were applied to simulate streamflow for up to 10-days ahead to determine how long into the future would the quality/accuracy of simulations persist before they begin to deteriorate in the ungauged basin. The results show that the designed method can facilitate simulation of accurate streamflows for any time step, and generate accurate simulations for up to 10days ahead in the ungauged basins. A unique evaluation procedure is the transfer of updated members in the form of forcing data uncertainties, and state and model parameterizations from gauged to ungauged watersheds and their subsequent assessment for multiple time step ahead simulations. The overall decline in accuracy from gauged to ungauged watersheds for the entire 10-day lead time across all 10 watersheds is 20% for Nash–Sutcliffe efficiency and 12% for percent bias.