Itza Mendoza-Sanchez

A geometric approach to joint inversion with applications to contaminant source zone characterization

This paper presents a new joint inversion approach to shape-based inverse problems. Given two sets of data from distinct physical models, the main objective is to obtain a unified characterization of inclusions within the spatial domain of the physical properties to be reconstructed. Although our proposed method generally applies to many types of inverse problems, the main motivation here is to characterize subsurface contaminant source zones by processing down-gradient hydrological data and cross-gradient electrical resistance tomography observations. Inspired by Newtons method for multi-objective optimization, we present an iterative inversion scheme in which descent steps are chosen to simultaneously reduce both data-model misfit terms. Such an approach, however, requires solving a non-smooth convex problem at every iteration, which is computationally expensive for a pixel-based inversion over the whole domain. Instead, we employ a parametric level set technique that substantially reduces the number of underlying parameters, making the inversion computationally tractable. The performance of the technique is examined and discussed through the reconstruction of source zone architectures that are representative of dense non-aqueous phase liquid (DNAPL) contaminant release in a statistically homogenous sandy aquifer. In these examples, the geometric configuration of the DNAPL mass is considered along with additional information about its spatial variability within the contaminated zone, such as the identification of low and high saturation regions. Comparison of the reconstructions with the true DNAPL architectures highlights the superior performance of the model-based technique and joint inversion scheme.

Manifold Regression Framework for Characterizing Source Zone Architecture

In this paper, we develop machine learning approaches for estimating quantitative features (or metrics) characterizing subsurface zones of chemical contamination, focusing on problems involving dense nonaqueous-phase liquid (DNAPL). Source zone characterization, a necessary first step in the development of a remediation strategy, is challenging due to practical constraints associated with the data available for processing. Our methods focus on the use of manifold regression techniques for estimating source zone metrics related to the distribution of contaminant mass in highly saturated pool regions, as well as more diffuse ganglia regions, based on downgradient measurements of dissolved contaminant concentration at a defined time. We use manifold methods for jointly representing labeled training data composed of known source zone metrics, as well as features derived from the corresponding dissolved concentration data sets. We then propose a new integrated approach to the problems of 1) robustly embedding test data (downgradient dissolved concentration) into the manifold when the source zone metrics are not available and 2) constructing a regression function operating directly in the manifold space for source zone metric estimation. The utility of the approach is enhanced by the explicit incorporation of physical constraints associated with the metrics into the problem formulation. Results based upon simulated data demonstrate the potential effectiveness of the manifold regression approaches, as well as significant improvement in performance relative to the case where the algorithmic components are designed serially.

Manifold regression for subsurface contaminant characterization

Characterization of sites contaminated by chemicals such as trichloroethylene, perchloroethylene, and other dense non-aqueous phase liquids (DNAPLs) is a necessary first step in the design and implementation of successful remediation strategies. In this paper, we develop a machine learning-based approach for estimating characteristics of a source zone related to the distribution of contaminant mass in highly saturated pool regions and more diffuse ganglia based on observations of down-gradient concentration images. After extracting a set of morphological features from training images, Laplacian Eigenmaps is employed to embed these features with the known source zone metric in a low dimensional manifold. A spectral regression scheme is used to embed the test data into the same manifold after which a Bayesian approach is employed to estimate the associated metric as well as a confidence interval. Results based upon simulated data demonstrate the potential effectiveness of the overall approach.

Efficient Algorithms for Modeling the Transport and Biodegradation of Chlorinated Ethenes in Groundwater

Predicting the fate of chlorinated ethenes in groundwater requires the solution of equations that describe both the transport and the biodegradation of the contaminants. Here, we present a model that accounts for (1) transport of chlorinated ethenes in flowing groundwater, (2) mass transfer of contaminants between mobile groundwater and stationary biofilms, and (3) diffusion and biodegradation within the biofilms. Equations for biodegradation kinetics account for biomass growth within the biofilms, the effect of hydrogen on dechlorination, and competitive inhibition between vinyl chloride and cis–dichloroethene. The overall model consists of coupled, non-linear, partial differential equations; solution of such a model is challenging and requires innovative numerical algorithms. We developed and tested two new numerical algorithms to solve the equations in the model; these are called system splitting with operator splitting (SSOS) and system splitting with Picard iteration (SSPI). We discuss the conditions under which one of these algorithms is superior to the other. The contributions of this paper are as follows: first, we believe that the mathematical model presented here is the first transport model that also accounts for diffusion and non-linear biodegradation of chlorinated ethenes in biofilms; second, the SSOS and SSPI are new computational algorithms developed specifically for problems of transport, mass transfer, and non-linear reaction; third, we have identified which of the two new algorithms is computationally more efficient for the case of chlorinated ethenes; and finally, we applied the model to compare the biodegradation behavior under diffusion-limited, metabolism-limited, and hydrogen-limited (donor-limited) conditions.

Flooding hazard assessment at Tulancingo (Hidalgo, Mexico): Flooding hazard assessment at Tulancingo (Hidalgo, Mexico)

In recent decades, the Tulancingo municipality (Mexico), has been affected by numerous extreme weather phenomena that caused heavy flooding events with severe damage to property and people. Most of the weather phenomena placed several dams under hydrologic risk. The hurricane “ Dean”, in 2007, led to the overflow of the dam “ La Esperanza”, generating inundations that reached levels of 1 m in Tulancingo. Mexico does not have a specific regulation that establishes critical thresholds for the construction of flooding hazard maps. With the aim to provide a tool for the flooding hazard assessment, we performed a numerical study of inundation waterdepths by means of the IBER software. The study is based on the construction of different inundation scenarios that are based on the hydrologic study of “ La Esperanza” dams basin, associated to regional precipitation and different return periods. Inundation waterdepths, flow velocity and land use were used to construct flooding hazard maps. We calculated the occurrence probability of the considered inundation events. The hazard maps presented here and the evaluation of the flooding likelihood can support long-term planning that would help minimize the impact of such events in Tulancingo.

Numerical Simulations of a Dam Overflowing. Case Study: “La Esperanza” Dam in Hidalgo, Mexico. Implications for Risk Evaluation

Dam safety is an issue that affects directly or indirectly all society sectors. Up to now, Mexico does not have a proper federal or state legislation to evaluate dam safety, thus it is difficult to assign liability when total or partial dam failure occurs or to prevent failure by programming cost-effective dam supervision. Dam safety risk analysis by means of numerical simulations has the objective of evaluating the occurrence probability of a phenomenon, or group of phenomena, that affects dam safety. This work is focused on obtaining the overflow probability of the dam “La Esperanza” located in Hidalgo, Mexico. With this purpose, first, a statistical hydrologic analysis using daily maximum rains was conducted to obtain dam inflow as a function of rainfall duration and return periods. Second, different inflow scenarios were simulated to obtain their associated maximum hydraulic head values using the Smoothed Particle Hydrodynamics (SPH) numerical method. Finally, simulation results of maximum hydraulic head reached by water particles were used to calculate the overflow probability. We have obtained a high overflow probability for the “La Esperanza” dam warranting more studies, for this and other dams with similar conditions, given that the hazard potential to populated downstream areas is high.

A discriminative-generative approach to the characterization of subsurface contaminant source zones

Large-scale contamination of ground water due to improper disposal of hazardous chemicals poses a global threat to drinking water supplies. Effective restoration and remediation of such sites relies upon a knowledge of the contaminants distribution within the subsurface. Obtaining a detailed map of the existing distribution is usually not feasible; rather partial knowledge in terms of certain metrics that characterize the distribution has recently been shown to be sufficient for planning and monitoring remediation strategies. In this work we explore the prediction of a representative metric based upon down-gradient concentration profiles using a classification framework where each class represents a particular sub-range of the metric. Initial experiments show that our proposed model can be used effectively for predicting the metric.

A mixture of experts based discretization approach for characterizing subsurface contaminant source zones

Accidental releases and improper disposal of hazardous chemicals has led to widespread chemical contamination of subsurface soils and water-bearing formations. Effective remediation and restoration of such contaminated sites is dependent upon knowledge of the contaminants mass and distribution within the aquifer. Recent research has shown that the estimation of certain metrics which summarize the distribution of the contaminant in the source-zone is sufficient for designing effective remediation strategies. In this work we explore the task of predicting such a metric based upon down-gradient concentration profiles. Motivated by the underlying physics of this problem we model this as a classification task where each class represents a particular sub-range of the metric. The solution to this problem is obtained by adapting the mixture of experts (MoE) scheme to learn a suitable quantization of the metric. Experimental evidence shows that this scheme outperforms baseline methods.

Modeling the influence of coupled mass transfer processes on mass flux downgradient of heterogeneous DNAPL source zones

Sequestered mass in low permeability zones has been increasingly recognized as an important source of organic chemical contamination that acts to sustain downgradient plume concentrations above regulated levels. However, few modeling studies have investigated the influence of this sequestered mass and associated (coupled) mass transfer processes on plume persistence in complex dense nonaqueous phase liquid (DNAPL) source zones. This paper employs a multiphase flow and transport simulator (a modified version of the modular transport simulator MT3DMS) to explore the two- and three-dimensional evolution of source zone mass distribution and near-source plume persistence for two ensembles of highly heterogeneous DNAPL source zone realizations. Simulations reveal the strong influence of subsurface heterogeneity on the complexity of DNAPL and sequestered (immobile/sorbed) mass distribution. Small zones of entrapped DNAPL are shown to serve as a persistent source of low concentration plumes, difficult to distinguish from other (sorbed and immobile dissolved) sequestered mass sources. Results suggest that the presence of DNAPL tends to control plume longevity in the near-source area; for the examined scenarios, a substantial fraction (43.3-99.2%) of plume life was sustained by DNAPL dissolution processes. The presence of sorptive media and the extent of sorption non-ideality are shown to greatly affect predictions of near-source plume persistence following DNAPL depletion, with plume persistence varying one to two orders of magnitude with the selected sorption model. Results demonstrate the importance of sorption-controlled back diffusion from low permeability zones and reveal the importance of selecting the appropriate sorption model for accurate prediction of plume longevity. Large discrepancies for both DNAPL depletion time and plume longevity were observed between 2-D and 3-D model simulations. Differences between 2- and 3-D predictions increased in the presence of sorption, especially for the case of non-ideal sorption, demonstrating the limitations of employing 2-D predictions for field-scale modeling.

Joint electrical and hydrological inversion for reconstruction of subsurface contaminant source zones

Remediation of sites polluted by hazardous chemicals such as dense non-aqueous phase liquids (DNAPLs) represents an important environmental problem due to the large scale threat these releases pose to water supplies throughout the world. Successful cleanup and restoration relies on methods to characterize the source zone structure prior to remediation and subsequently to monitor the corresponding dissolved chemical levels. This paper develops and implements a new model-based approach to DNAPL source zone characterization based on the joint inversion of hydrological and geophysical data. To model the interaction of groundwater with the contaminant source zone, a fully three dimensional (3D) flow and transport model is used to provide the downstream contaminant concentrations associated to the source zone saturation distribution. As the geophysical modality we utilize electrical resistance tomography (ERT) where electric potential measurements related to the electrical properties of the medium are obtained cross gradient to the water flow direction. The inversion technique is based on the parametric level set method (PaLS) which provides for the recovery of the geometric profiles of the low and high saturation regions (corresponding to the ganglia and the pooling regions) and low order characterizations of the spatial variability within each region. The performance of our proposed algorithm is examined and discussed through the reconstruction of some challenging source zone architectures.