The National Water Model (NWM) is a key tool for flood forecasting and planning and water management. Key challenges facing NWM include calibration and parameter regionalization when confronted with big data. We present two novel versions of high-resolution (~37 km2) differentiable models (a type of physics-informed machine learning): one with implicit, unit-hydrograph-style routing and another with explicit Muskingum-Cunge routing in the river network. The former predicts streamflow at basin outlets whereas the latter presents a discretized product that seamlessly covers rivers in the conterminous United States (CONUS). Both versions used neural networks to provide multiscale parameterization and process-based equations to provide structural backbone, trained them together (“end-to-end”) on 2,807 basins across CONUS, and evaluated them on 4,997 basins. Both versions show the great potential to elevate future NWMs for extensively calibrated as well as ungauged sites: the median daily Nash-Sutcliffe efficiency (NSE) of all 4,997 basins is improved to around 0.68 from 0.49 of NWM3.0. As they resolve heterogeneity, both greatly improved simulations in the western CONUS and also in the Prairie Pothole Region, a long-standing modeling challenge. The Muskingum-Cunge version further improved performance for basins >10000 km2. Overall, our results show how neural-network-based parameterizations can improve NWM performance for providing operational flood predictions while maintaining interpretability and multivariate outputs. We provide a CONUS-scale hydrologic dataset for further evaluation and use. The modeling system supports the Basic Model Interface (BMI), which allows seamless integration with the next-generation NWM.

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.

Landslide risk is traditionally predicted by process-based models with detailed assessments or point-scale, attribute-based machine learning (ML) models with first- or second-order features, e.g., slope, as inputs. One could hypothesize that terrain patterns might contain useful information that could be extracted, via computer vision ML models, to elevate prediction performance beyond that achievable with low-order features. We put this hypothesis to the test in the state of Oregon, where a large landslide dataset is available. The image-processing convolutional neural networks (CNN2D) using 2D terrain data obtained either higher Precision or higher Recall than attribute-based random forest (RF1D) models, but could not improve both simultaneously. While CNN2D can be set up to identify more real events, it would then introduce more false positives, highlighting the challenge of generalizing landslide-prone terrain patterns and the potential omission of critical factors. However, ensembling CNN2D and RF1D produced overall better Precision and Recall, and this cross-model-type ensemble was better than other ways to ensemble, leveraging information content of fine-scale topography while suppressing its noise. These models further showed robust results in cross-regional validation. Our perturbation tests showed that 10m resolution (the smallest possible) produced the best model in a range of resolutions. Rainfall, land cover, soil moisture, and elevation were the most important predictors. Based on the results of the analysis, we generated landslide susceptibility maps, providing insights into spatial patterns of landslide risk.

Net photosynthesis (AN) is a major component of the global carbon cycle, with significant feedback to decadal-scale climate change. Although plant acclimation to environmental changes can modify AN, traditional vegetation models in Earth System Models (ESMs) often rely on plant functional type (PFT)-specific parameter calibrations or simplified acclimation assumptions, both of which lacked generalizability across time, space and PFTs. In this study, we propose a differentiable photosynthesis model to learn the environmental dependencies of Vc,max25, as this genre of hybrid physics-informed machine learning can seamlessly train neural networks and process-based equations together. Compared to PFT-specific parameterization of Vc,max25, learning the environment dependencies of key photosynthetic parameters improves model spatiotemporal generalizability. Applying environmental acclimation to Vc,max25 led to substantial variation in global mean AN, calling for the attention to acclimation in ESMs. The model effectively captured multivariate observations (Vcmax25, stomatal conductance gs, and AN) simultaneously and, in fact, multivariate constraints further improved model generalization across space and PFTs. It also learned sensible acclimation relationships of Vc,max25 to different environmental conditions. The model explained more than 54%, 57% and 62% of the variance of AN, gs, and Vcmax25, respectively, presenting a first global-scale spatial test benchmark of AN and gs. These results highlight the potential of differentiable modeling to enhanced process-based modules in ESMs and effectively leverage information from large, multivariate datasets.

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.