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

Reed M Maxwell,Peter Melchior,Laura E Condon

doi:10.3390/w13243633

Reed M Maxwell, Peter Melchior + Show 1 more

Open Access

https://doi.org/10.3390/w13243633

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Journal: Water	Publication Date: Dec 17, 2021
Citations: 13	License type: CC BY 4.0

Affiliation: Princeton University, University of Arizona

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.

Highlights

Hydrologic models are powerful tools that can represent processes and connections within the hydrologic cycle, facilitating both simulation and discovery [1]
One of the two test datasets was constructed to have same parameter ranges as the training dataset (In Range), while the other was constructed to have parameters outside the range used for training (Full Range). The solution for both ParFlow and the Machine learning (ML)-emulator models results in a 2D timedependent map of pressure-head over the domain, which represents the height of ponded water above the ground surface
Only the surface pressure was used in the loss function during training, not the outflow hydrograph from the ParFlow simulations. This is in contrast to prior ML approaches that might focus on learning the hydrograph directly [3,5]. This approach is more general and allows for the ML model to produce other hydrologic quantities that could be of interest for, e.g., flooding or water management; the hydrographs produced are very sensitive to the convergence of the surface pressure

Summary

Introduction

Hydrologic models are powerful tools that can represent processes and connections within the hydrologic cycle, facilitating both simulation and discovery [1]. ML approaches were first introduced to solve groundwater problems decades ago [2] While discussion of these approaches in hydrology rapidly expanded [3,4], and adoption of these approaches has been increasing [5], there has been a strong focus on time-series prediction of streamflow at a gage. There has been an increasing push for methods that can incorporate established theory subsurface, and a lack of representative training samples [9,10]. Reproduce the simulation results at a fraction of the comStill, studies that develop ML-emulator models are rare in hydroHloegrye,anwdehdyedvroegloeoploagys.uRiteeceonft eMxaLm-epmlesuilnactolurdme uosdeeolfsmfoordealstwtooa-udgimmeenntstiiomneal, time poebnsedrveanttiosniaml dualtaatsieotns foorf satrebaemnflcohwmparrekdiscutiorfna[c1e8-]w, leaatrenrincgatscuhbmsuerfnatcepcroonbstlietumti.vWe reelau-se a ph ctiaolnlyshbipassiendvahriyadblryo-lsoatguyratmedosdyesltetmos p[1r9o,2v0i]d, eflotordaifnoriencgasdtinagta[2f1o],ranthdirsecMenLt eemmuulaltaotros r, whic torfa3inDehdydursoilnoggicgrmidoddeelds [2p2r]e. This test problem is solved with the surface water equations. The integrated hydrologic model ParFlow [26,28,29] was used to solve these equations

Numerical Solution of the Tilted V and General Training Approach

ML Model Architectures

ML Model Training

Parameter Evaluation

Results and Discussion

Model Sensitivity to Training Data

Conclusions