HR: 09:15h
AN: SF11A-06    [Abstracts]
TI: A Data-Driven Approach for Upscaling Solute Transport Models
AU: * Hill, D J
EM: djhill1@uiuc.edu
AF: Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 2516 Hydrosystems Laboratory, MC 250 205 N. Mathews Ave, Urbana, IL 61801
AB: The goal of this study is to use a machine learning tool, genetic programming (GP), a domain independent model generator, to search for an upscaled hydrologic model. The development of upscaled models of hydrologic processes has long been a concern of researchers, because computational limitations prevent the use of high-resolution models capable of resolving all of the spatial variability of model domains. In particular, researchers have struggled for decades to develop upscaled numerical models for solute transport in porous media, where the scale of variability can range from the order of a few meters in the horizontal direction but only ten to twenty centimeters in the vertical direction. A wide variety of methods have been employed to develop upscaled solute transport models, including stochastic analysis, spatial filtering, and homogenization. However, these methods all rely upon various simplifying assumptions (e.g. small conductivity variance, a grid-scale significantly larger than the largest scale of heterogeneity). Moreover, these methods usually make additional assumptions about the physics of the sub-grid processes. This study examines the use of GP to search for an upscaled model of transport of a solute pulse by horizontal flow in a perfectly stratified aquifer. GP was chosen because it creates mathematical models of input data from which information about the underlying physical processes can be extracted. This type of transport system was selected as the first application of the proposed upscaling method, because it has been extensively studied in the literature, and thus will allow for a direct comparison that will demonstrate the efficacy of the data-driven upscaling method. It has been suggested that if the upscaled model domain of this type of system is a depth averaged representation of the aquifer, the plume evolution can be modeled in a Lagrangian coordinate system as a Fickian dispersive process with a time dependent dispersion coefficient. GP was provided with depth-averaged solute flux data as well as other depth-averaged plume characteristics (e.g. local and non-local concentration gradients) calculated from a high-resolution numerical model of the system. GP performed a symbolic regression of this data, and the resulting models were analyzed for quality of fit, as well as physical meaning. This analysis resulted in an upscaled model that expressed the transport of solute by unresolved sub-grid velocity variations, which can be expressed entirely in terms of vertically-averaged parameters. The strong evidence of a sub-grid advective component of the upscaled solute transport found by GP was surprising, and this result has led to the creation of new upscaled models that incorporate a sub-grid advection term for modeling the solute transport. For the perfectly stratified aquifer, these new upscaled transport models are able to capture features of the solute plume that are relevant to environmental and hydrological problems that the Fickian model alone cannot predict. This result has far-reaching implications for management models as the new upscaled solute transport models can make higher quality predictions of the solute distribution, without any significant additional computational expense. It is suspected that with further work, the methodology presented here may be applicable to other upscaling problems, such as those encountered in turbulent flow or atmospheric modeling.
DE: 1829 Groundwater hydrology
DE: 1831 Groundwater quality
DE: 1832 Groundwater transport
SC: Special Focus: Advances in Data Acquisition, Management, Analysis and Display [SF]
MN: 2004 AGU Fall Meeting