Ensembling Differentiable Process-based and Data-driven Models with Diverse Meteorological Forcing Datasets to Advance Streamflow Simulation

Abstract. Streamflow simulations via different hydrological models have different features and can provide valuable information after being ensembled. While few studies have focused on ensembling simulations via models with significant structural differences and evaluating them under both temporal and spatial tests. Here we systematically evaluated and utilized the simulations from two highly different models with great performances: a purely data-driven long short-term memory (LSTM) network and a physics-informed machine learning (“differentiable”) HBV (Hydrologiska Byråns Vattenavdelning) model (δHBV). To effectively display the features of the two models, multiple forcing datasets are employed and utilized in two ways. The results show that the simulations of LSTM and δHBV have distinct features and complement each other well, leading to better Nash-Sutcliffe model efficiency coefficients (NSE) and improved high-flow and low-flow metrics across all spatiotemporal tests, compared to within-class ensembles. Ensembling models trained on a single forcing outperformed a single model using fused forcings, challenging the paradigm of feeding all available data into a single data-driven model. Most notably, δHBV significantly enhanced spatial interpolation when incorporated into LSTM, and even more prominent benefits for spatial extrapolation where the LSTM-only ensembles degraded significantly, attesting to the value of the structural constraints in δHBV. These advances set new benchmark records on the well-known CAMELS (Catchment Attributes and Meteorology for Large-sample Studies) hydrological dataset, reaching median NSE values of ~0.83 for the temporal test (densely trained scenario), ~0.79 for the ungauged basin test (PUB, Prediction in Ungauged Basins), and ~0.70 for the ungauged region test (PUR, Prediction in Ungauged Regions). This study advances our understanding of how various model types, each with distinct mechanisms, can be effectively leveraged alongside multi-source datasets across diverse scenarios.