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The behaviors and skills of models in many geosciences (e.g., hydrology and ecosystem sciences) strongly depend on spatially-varying parameters that need calibration. A well-calibrated model can reasonably propagate information from observations to unobserved variables via model physics, but traditional calibration is highly inefficient and results in non-unique solutions. Here we propose a novel differentiable parameter learning (dPL) framework that efficiently learns a global mapping between inputs (and optionally responses) and parameters. Crucially, dPL exhibits beneficial scaling curves not previously demonstrated to geoscientists: as training data increases, dPL achieves better performance, more physical coherence, and better generalizability (across space and uncalibrated variables), all with orders-of-magnitude lower computational cost. We demonstrate examples that learned from soil moisture and streamflow, where dPL drastically outperformed existing evolutionary and regionalization methods, or required only ~12.5% of the training data to achieve similar performance. The generic scheme promotes the integration of deep learning and process-based models, without mandating reimplementation., Much effort is invested in calibrating model parameters for accurate outputs, but established methods can be inefficient and generic. By learning from big dataset, a new differentiable framework for model parameterization outperforms state-of-the-art methods, produce more physically-coherent results, using a fraction of the training data, computational power, and time. The method promotes a deep integration of machine learning with process-based geoscientific models.

Basin-centric long short-term memory (LSTM) network models have recently been shown to be an exceptionally powerful tool for simulating stream temperature (Ts, temperature measured in rivers), among other hydrological variables. However, spatial extrapolation is a well-known challenge to modeling Ts and it is uncertain how an LSTM-based daily Ts model will perform in unmonitored or dammed basins. Here we compiled a new benchmark dataset consisting of >400 basins for across the contiguous United States in different data availability groups (DAG, meaning the daily sampling frequency) with or without major dams and study how to assemble suitable training datasets for predictions in monitored or unmonitored situations. For temporal generalization, CONUS-median best root-mean-square error (RMSE) values for sites with extensive (99%), intermediate (60%), scarce (10%) and absent (0%, unmonitored) data for training were 0.75, 0.83, 0.88, and 1.59°C, representing the state of the art. For prediction in unmonitored basins (PUB), LSTM’s results surpassed those reported in the literature. Even for unmonitored basins with major reservoirs, we obtained a median RMSE of 1.492°C and an R2 of 0.966. The most suitable training set was the matching DAG that the basin could be grouped into, e.g., the 60% DAG for a basin with 61% data availability. However, for PUB, a training dataset including all basins with data is preferred. An input-selection ensemble moderately mitigated attribute overfitting. Our results suggest there are influential latent processes not sufficiently described by the inputs (e.g., geology, wetland covers), but temporal fluctuations are well predictable, and LSTM appears to be the more accurate Ts modeling tool when sufficient training data are available.

A large fraction of major waterways have dams influencing streamflow, which must be accounted for in large-scale hydrologic modeling. However, daily streamflow prediction for basins with dams is challenging for various modeling approaches, especially at large scales. Here we examined which types of dammed basins could be well represented by long short-term memory (LSTM) models using readily-available information, and delineated the remaining challenges. We analyzed data from 3557 basins (83% dammed) over the contiguous United States and noted strong impacts of reservoir purposes, degree of regulation (dor), and diversion on streamflow modeling. While a model trained on a widely-used reference-basin dataset performed poorly for non-reference basins, the model trained on the whole dataset presented a median Nash-Sutcliffe efficiency coefficient (NSE) of 0.74. The zero-dor, small-dor (with storage of approximately a month of average streamflow or less), and large-dor basins were found to have distinct behaviors, so migrating models between categories yielded catastrophic results, which means we must not treat small-dor basins as reference ones. However, training with pooled data from different sets yielded optimal median NSEs of 0.72, 0.79, and 0.64 for these respective groups, noticeably stronger than existing models. These results support a coherent modeling strategy where smaller dams (storing about a month of average streamflow or less) are modeled implicitly as part of basin rainfall-runoff processes; then, large-dor reservoirs of certain types can be represented explicitly. However, dammed basins must be present in the training dataset. Future work should examine separate modeling of large reservoirs for fire protection and irrigation, hydroelectric power generation, and flood control.

Stream water temperature (T) is a variable of critical importance and decision-making relevance to aquatic ecosystems, energy production, and human’s interaction with the river system. Here, we pro...

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 mu...

There is a drastic geographic imbalance in available global streamflow gauge and catchment property data, with additional large variations in data characteristics, so that models calibrated in one ...