Achieving Robust and Transferable Performance for Conservation-Based Models of Dynamical Physical Systems

Because physics-based models of dynamical systems are constrained to obey conservation laws, they must typically be fed long sequences of temporally consecutive (TC) data during model calibration and evaluation. When memory time scales are long (as in many physical systems), this requirement makes it difficult to ensure distributional similarity when partitioning the data into independent, TC, calibration and evaluation subsets. The consequence can be poor and/or uncertain model performance when applied to new situations. To address this issue, we propose a novel strategy for achieving robust and transferable model performance. Instead of partitioning the data into TC calibration and evaluation periods, the model is run in continuous simulation mode for the entire period, and specific time steps are assigned (via a deterministic data-allocation approach) for use in computing the calibration and evaluation metrics. Generative adversarial testing shows that this approach results in consistent calibration and evaluation data subset distributions. When tested using three conceptual rainfall-runoff models applied to 163 catchments representing a wide range of hydro-climatic conditions, the proposed “distributionally consistent (DC)” strategy consistently resulted in better overall performance than achieved using the traditional “TC” strategy. Testing on independent data periods confirmed superior robustness and transferability of the DC-calibrated models, particularly under conditions of larger runoff skewness. Because the approach is generally applicable to physics-based models of dynamical systems, it has the potential to significantly improve the confidence associated with prediction and uncertainty estimates generated using such models.