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Who’s afraid of the Saint Venant Equations? (Everyone, so I replaced it with Machine Learning)

  • Author(s): Crompton, Octavia V
  • Advisor(s): Thompson, Sally
  • Fung, Inez
  • et al.

This thesis addresses the development of a coupled 2D Saint Venant Equation - 1D Richards equation (SVE-R) model, emulation of its output using a machine learning algo- rithm, and the application of the resulting emulations to predict storm-driven overland flow and infiltration in patchily vegetated dryland systems. The motivation for this work lies in the critical importance of runoff-runon processes in the function of dryland ecosystems: evaluating how these processes work in real or designed settings is crucial for assessing the vulnerability to desertification or the probability of success of management or restoration plans. The SVE-R equations describe the physics of runoff-runon processes, and are solved here by coupling a finite element SVE solver developed by Bradford and Katopodes [1999] to the Richards equation solver developed by Celia et al. [1990]. The coupled SVE-R model is validated against analytical solutions to the kinematic wave equations [Giraldez and Wool- hiser, 1996]. I firstly show that the hydrological outcomes of interest in dryland systems (i.e. the distribution of infiltration, the runoff ratio and peak flow velocities) were insensi- tive to the choice of a roughness closure scheme. I then develop a machine learning (ML) approach to emulate its predictions. This approach involves training random forest (RF) regressors on collections of pre-computed SVE-R model runs to predict the spatial patterns of infiltration and maximum flow velocity. The RF emulator is very accurate and is several orders of magnitude faster than the SVE-R model. To demonstrate the utility of the ML emulation approach for simulating and managing dryland ecosystems, I present two case studies. Firstly, I apply RF regression to represent within-storm processes in an ecohydro- logical model of spatial patterning of vegetation on the landscape. For the first time, I show that the modeled spatial patterns of vegetation are sensitive to storm characteristics such as duration and intensity. Secondly, I develop a web-based tool to assess plant water availabil- ity and erosion risk at hillslope scales for user-supplied vegetation patterns, which embeds random forest regressors trained on a representative library of storm and hillslope conditions. This case study demonstrates how the combination of machine learning and a web tool can make otherwise challenging predictive insights available to a broad set of potential users.

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