A Physics-Informed, Machine Learning Emulator of a 2D Surface Water Model: What Temporal Networks and Simulation-Based Inference Can Help Us Learn about Hydrologic Processes

Abstract

While machine learning approaches are rapidly being applied to hydrologic problems, physics-informed approaches are still relatively rare. Many successful deep-learning applications have focused on point estimates of streamflow trained on stream gauge observations over time. While these approaches show promise for some applications, there is a need for distributed approaches that can produce accurate two-dimensional results of model states, such as ponded water depth. Here, we demonstrate a 2D emulator of the Tilted V catchment benchmark problem with solutions provided by the integrated hydrology model ParFlow. This emulator model can use 2D Convolution Neural Network (CNN), 3D CNN, and U-Net machine learning architectures and produces time-dependent spatial maps of ponded water depth from which hydrographs and other hydrologic quantities of interest may be derived. A comparison of different deep learning architectures and hyperparameters is presented with particular focus on approaches such as 3D CNN (that have a time-dependent learning component) and 2D CNN and U-Net approaches (that use only the current model state to predict the next state in time). In addition to testing model performance, we also use a simplified simulation based inference approach to evaluate the ability to calibrate the emulator to randomly selected simulations and the match between ML calibrated input parameters and underlying physics-based simulation.

Training machine learning with physics-based simulations to predict 2D soil moisture fields in a changing climate

“…Where CNN is really outperforming is on the scenarios, which are much drier than the "average year". These conclusions are consistent with the out-of-sample testing results in Maxwell et al (2021). When developing a framework such as the one presented here, it is important not only to ensure that enough training data are generated with the physics-based model, but also that those are tailored to the specific application of interest and intended use.…”

“…The benefits of the combination of physics based modeling and machine learning have been shown here in the context of a changing climate but they extend to other potential applications which require a large number of simulations such as improving physics based models parametrisation (refer to e.g., Maxwell et al, 2021). , used for all the results reported here is marked blue.…”

“…Building upon the model exploration carried out in Maxwell et al (2021), we select two CNNs: a 2D CNN consisting of 2 Convolution+ReLu layers, each followed by a Max Pooling layer, and two fully connected linear layers (refer to Table A3 in Maxwell et al, 2021), and a 3D CNN which has the same architecture as the 2D model, but an additional Convolution+ReLu first layer (refer to Table A1 in Maxwell et al, 2021).…”

“…The most widespread application of machine learning in hydrology is for the prediction of streamflow with Long-Short Term memory (LSTM) models (e.g., Kratzert et al, 2019;Chen et al, 2020). However, few recent studies have shown the potential of machine learning approaches also in the prediction of distributed hydrological variables (ElSaadani et al, 2021;Maxwell et al, 2021;Tran et al, 2021), and advanced techniques have also been explored in the field of the weather forecast (e.g., Weyn et al, 2019) and in particular precipitation nowcasting (e.g., Shi et al, 2008;Chen et al, 2020;Su et al, 2020).…”

Geospatial Artificial Intelligence (GeoAI) in the Integrated Hydrological and Fluvial Systems Modeling: Review of Current Applications and Trends

“…ML application in hydrological predictions dates to the 1990s [16], but the development of the new GeoAI and ML algorithms, particularly the deep learning techniques, alongside new data collection technologies, has substantially increased in recent years [17,18]. Moreover, there are new studies on developing hybrid models (ML and physical-based models) [14,19,20] and physical process-guided ML methods [21][22][23][24]. Therefore, a review of the potential of the new GeoAI and ML methods for integrated hydrological and fluvial systems modeling is needed to guide scientists and practitioners to select the proper tools and to be aware of current and potential future methodologies.…”