CSDMS 2014 annual meeting poster Francis Rengers
Parameter Optimization for a Headcut Erosion Model
Monte Lunacek, University of Colorado Boulder Colorado, United States. Monte.Lunacek@Colorado.EDU
Greg Tucker, University of Colorado Boulder Colorado, United States. gtucker@colorado.edu
Abstract:
In order to understand the geomorphic legacy of headcut retreat, we have developed a numerical model that simulates headcut erosion over time. One of the difficulties with this type of modeling is the uncertainty in the model parameters. For example, there is limited data for estimates of the resistive shear stress of a grassy channel. Moreover, some parameters, such as soil infiltration capacity, vary in space, and in-situ field measurements can overestimate the actual infiltration that occurs during rainfall events at the watershed-scale. Traditional optimization techniques are not an option because our model is non-differentiable. Consequently, we estimate the best-fit parameters for the model by using a parallel evolutionary algorithm on a cluster supercomputer.
Our model uses conservation of mass for both water and sediment to predict how overland flow erosion and deposition, combined with headcut retreat, will shape the longitudinal profile of a channel over time. We simulate channels that are mostly grass-lined, and thus take into consideration the roughness changes in grassy areas and the changes in erodibility. Within the model we optimize ten independent variables, including the critical shear stress for erosion, channel roughness, and effective site infiltration.
The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is an iterative process where samples are created based on a distribution of parameter values that evolves over time to better fit the features of the objective function. We use this algorithm to optimize the parameters of our model. Initially the distribution will explore more of the parameter space. As the CMA-ES iterates, the distribution changes in size and shape to focus the samples in a region of the parameter space that is more likely to have effective solutions. CMA-ES is able to efficiently find effective parameters, even with high dimensional objective functions that are non-convex, multimodal, and non-separable. We ran model instances in parallel on a high-performance cluster supercomputer, and from hundreds of model runs we obtained the best parameter choice.
Initial results of best-fit model parameters were obtained by CMA-ES without requiring a time-intensive, brute force combinatorial approach to explore a 10 dimensional parameter space. This effort revealed a convergence of certain parameters toward a single value, such as the critical basal shear stress. However, some pairs of parameter values diverged (for example, precipitation and infiltration rates) show up to four values that produced similar results. The non-convergence of some parameter values is useful in showing that some physical processes are non-unique, but can still produce a similar morphology. CMA-ES pinpoints these non-unique areas, which allows for further investigation of the physical reality and sensitivity of parameter choices. This offers increased efficiency compared to the testing of every single parameter choice.
In summary, this study is a proof of concept for employing advances in computer science optimization to a numerical model simulating geomorphic processes. We are thus able to solve the problem of parameter choice for variables that are difficult or impossible to measure by using an objective methodology. It is likely that many models in the earth science community would benefit from this type of analysis.
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