Some machine learning (ML) methods such as classification trees are useful tools to generate hypotheses about how hydrologic systems function. However, data limitations dictate that ML alone often cannot differentiate between causal and associative relationships. For example, previous ML analysis suggested that soil thickness is the key physiographic factor determining the storage-streamflow correlations in the eastern US. This conclusion is not robust, especially if data are perturbed, and there were alternative, competing explanations including soil texture and terrain slope. However, typical causal analysis based on process-based models (PBMs) is inefficient and susceptible to human bias. Here we demonstrate a more efficient and objective analysis procedure where ML is first applied to generate data-consistent hypotheses, and then a PBM is invoked to verify these hypotheses. We employed a surface-subsurface processes model and conducted perturbation experiments to implement these competing hypotheses and assess the impacts of the changes. The experimental results strongly support the soil thickness hypothesis as opposed to the terrain slope and soil texture ones, which are co-varying and coincidental factors. Thicker soil permits larger saturation excess and longer system memory that carries wet season water storage to influence dry season baseflows. We further suggest this analysis could be formalized into a novel, data-centric Bayesian framework. This study demonstrates that PBM present indispensable value for problems that ML cannot solve alone, and is meant to encourage more synergies between ML and PBM in the future.

Recently, recurrent deep networks have shown promise to harness newly available satellite-sensed data for long-term soil moisture projections. However, to be useful in forecasting, deep networks must also provide uncertainty estimates. Here we evaluated Monte Carlo dropout with an input-dependent data noise term (MCD+N), an efficient uncertainty estimation framework originally developed in computer vision, for hydrologic time series predictions. MCD+N simultaneously estimates a heteroscedastic input-dependent data noise term (a trained error model attributable to observational noise) and a network weight uncertainty term (attributable to insufficiently-constrained model parameters). Although MCD+N has appealing features, many heuristic approximations were employed during its derivation, and rigorous evaluations and evidence of its asserted capability to detect dissimilarity were lacking. To address this, we provided an in-depth evaluation of the scheme’s potential and limitations. We showed that for reproducing soil moisture dynamics recorded by the Soil Moisture Active Passive (SMAP) mission, MCD+N indeed gave a good estimate of predictive error, provided that we tuned a hyperparameter and used a representative training dataset. The input-dependent term responded strongly to observational noise, while the model term clearly acted as a detector for physiographic dissimilarity from the training data, behaving as intended. However, when the training and test data were characteristically different, the input-dependent term could be misled, undermining its reliability. Additionally, due to the data-driven nature of the model, the two uncertainty terms are correlated. This approach has promise, but care is needed to interpret the results.