Recently, rainfall-runoff simulations in small headwater basins have been improved by methodological advances such as deep neural networks (NNs) and hybrid physics-NN models — particularly, a genre called differentiable modeling that intermingles NNs with physics to learn relationships between variables. However, hydrologic routing, necessary for simulating floods in stem rivers downstream of large heterogeneous basins, had not yet benefited from these advances and it was unclear if the routing process can be improved via coupled NNs. We present a novel differentiable routing model that mimics the classical Muskingum-Cunge routing model over a river network but embeds an NN to infer parameterizations for Manning’s roughness (n) and channel geometries from raw reach-scale attributes like catchment areas and sinuosity. The NN was trained solely on downstream hydrographs. Synthetic experiments show that while the channel geometry parameter was unidentifiable, n can be identified with moderate precision. With real-world data, the trained differentiable routing model produced more accurate long-term routing results for both the training gage and untrained inner gages for larger subbasins (>2,000 km2) than either a machine learning model assuming homogeneity, or simply using the sum of runoff from subbasins. The n parameterization trained on short periods gave high performance in other periods, despite significant errors in runoff inputs. The learned n pattern was consistent with literature expectations, demonstrating the framework’s potential for knowledge discovery, but the absolute values can vary depending on training periods. The trained n parameterization can be coupled with traditional models to improve national-scale flood simulations.

Recently, runoff simulations in small, headwater basins have been improved by methodological advances such as deep learning (DL). Hydrologic routing modules are typically needed to simulate flows in stem rivers downstream of large, heterogeneous basins, but obtaining suitable parameterization for them has previously been difficult. It is unclear if downstream daily discharge contains enough information to constrain spatially-distributed parameterization. Building on recent advances in differentiable modeling principles, here we propose a differentiable, learnable physics-based routing model. It mimics the classical Muskingum-Cunge routing model but embeds a neural network (NN) to provide parameterizations for Manning’s roughness coefficient (n) and channel geometries. The embedded NN, which uses (imperfect) DL-simulated runoffs as the forcing data and reach-scale attributes as inputs, was trained solely on downstream hydrographs. Our synthetic experiments show that while channel geometries cannot be identified, we can learn a parameterization scheme for n that captures the overall spatial pattern. Training on short real-world data showed that we could obtain highly accurate routing results for both the training and inner, untrained gages. For larger basins, our results are better than a DL model assuming homogeneity or the sum of runoff from subbasins. The parameterization learned from a short training period gave high performance in other periods, despite significant bias in runoff. This is the first time an interpretable, physics-based model is learned on the river network to infer spatially-distributed parameters. The trained n parameterization can be coupled to traditional runoff models and ported to traditional programming environments.

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 region cannot normally be migrated to another. Currently in these regions, non-transferable machine learning models are habitually trained over small local datasets. Here we show that transfer learning (TL), in the sense of weights initialization and weights freezing, allows long short-term memory (LSTM) streamflow models that were trained over the Conterminous United States (CONUS, the source dataset) to be transferred to catchments on other continents (the target regions), without the need for extensive catchment attributes. We demonstrate this possibility for regions where data are dense (664 basins in the UK), moderately dense (49 basins in central Chile), and where data are scarce and only globally-available attributes are available (5 basins in China). In both China and Chile, the TL models significantly elevated model performance compared to locally-trained models. The benefits of TL increased with the amount of available data in the source dataset, but even 50-100 basins from the CONUS dataset provided significant value for TL. The benefits of TL were greater than pre-training LSTM using the outputs from an uncalibrated hydrologic model. These results suggest hydrologic data around the world have commonalities which could be leveraged by deep learning, and significant synergies can be had with a simple modification of the currently predominant workflows, greatly expanding the reach of existing big data. Finally, this work diversified existing global streamflow benchmarks.

Dissolved oxygen (DO) sustains aquatic life and is an essential water quality measure. Our capabilities of forecasting DO levels, however, remain elusive. Unlike the increasingly intensive earth surface and hydroclimatic data, water quality data often have large temporal gaps and sparse areal coverage. Here we ask the question: can a Long Short-Term Memory (LSTM) deep learning model learn the spatio-temporal dynamics of stream DO from intensive hydroclimatic and sparse DO observations at the continental scale? That is, can the model harvest the power of big hydroclimatic data and use them for water quality forecasting? Here we used data from CAMELS-chem, a new dataset that includes sparse DO concentrations from 236 minimally-disturbed watersheds. The trained model can generally learn the theory of DO solubility under specific temperature, pressure, and salinity conditions. It captures the bulk variability and seasonality of DO and exhibits the potential of forecasting water quality in ungauged basins without training data. It however often misses concentration peaks and troughs where DO level depends on complex biogeochemical processes. The model surprisingly does not perform better where data are more intensive. It performs better in basins with low streamflow variations, low DO variability, high runoff-ratio (> 0.45), and precipitation peaks in winter. This work suggests that more frequent data collection in anticipated DO peak and trough conditions are essential to help overcome the issue of sparse data, an outstanding challenge in the water quality community.