Optimal allocation of computational resources in hydrogeological models under uncertainty

We analyze solute transport in a radially converging 3‐D flow field in a porous medium with spatially heterogeneous hydraulic conductivity (K). The aim of the paper is to analyze the impact of heterogeneity and the mode of injection on BreakThrough Curves (BTCs) detected at a well pumping a contaminated aquifer. The aquifer is conceptualized as an ensemble of blocks of uniform but contrasting K and the analysis makes use of the travel time approach. Despite the approximations introduced, the model reproduces a laboratory experiment without calibration of transport parameters. Our results also show excellent agreement with numerical simulations for different levels of heterogeneity. We focus on the impact on the BTC of both heterogeneity in K and solute release conditions. It is shown that the injection mode matters, and the differences in the BTCs between uniform and flux‐proportional injection increase with the heterogeneity of the K‐field. Furthermore, we study the effect of heterogeneity and mode of injection on early and late arrivals at the well.

Section: Introductionmentioning

confidence: 99%

Radial solute transport in highly heterogeneous aquifers: Modeling and experimental comparison

Dato

Fiori

Barros

et al. 2017

“…A two-dimensional regularly spaced grid is considered for the K-fields with discretization size in both directions. We mimic the numerical setup based on the grid and statistical convergence analyses performed in Moslehi et al (2015). The length of the generated fields in each direction is denoted by L. The properties of the K-fields for the ensemble and the reference field, along with their values, are listed in Table 2.…”

Section: Illustrative Examplementioning

confidence: 99%

Using Color Coherence Vectors to Evaluate the Performance of Hydrologic Data Assimilation

Moslehi

Barros

2019

Self Cite

An inadequate characterization of hydrogeological properties can significantly decrease the trustworthiness of subsurface flow and transport model predictions. A variety of data assimilation methods have been proposed in order to estimate hydrogeological parameters from spatially scarce data by incorporating them into the governing physical models. In order to quantify the accuracy of the estimations, several metrics have been used such as Rank Histograms, root-mean-square error (RMSE), and Ensemble Spread. However, these commonly used metrics do not regard the spatial correlation of the aquifer's properties. This can cause permeability fields with very different spatial structures to have similar histograms or RMSE. In this paper, we propose an approach based on color coherence vectors (CCV) for evaluating the performance of these estimation methods. CCV is a histogram-based technique for comparing images that incorporate spatial information. We represent estimated fields as digital three-channel images and use CCV to compare and quantify the accuracy of estimations. The appealing feature of this technique is that it considers the spatial structure embedded in the estimated fields. The sensitivity of CCV to spatial information makes it a suitable metric for assessing the performance of data assimilation techniques. Under various factors, such as numbers of measurements and structural parameters of the log conductivity field, we compare the performance of CCV with the RMSE. 10.1029/2018WR023533Key Points: • We introduce the use of CCV to test the performance of data assimilation techniques • The CCV-based metric outperforms the RMSE metric • The CCV-based metric accounts for the spatial correlation of the estimated attributeCorrespondence to:

“…It is noted that, multi-fidelity simulation methods, that is, using paired simple and complex models to achieve a balance between accuracy and efficiency, have become increasingly popular in hydrologic science (Doherty & Christensen, 2011;Linde et al, 2017;Lu et al, 2016;Moslehi et al, 2015;Watson et al, 2013), while the application of these methods in Bayesian inference is very limited. Here we adopt the method originally developed by Kennedy and O'Hagan (2000) to build the multifidelity GP system.…”

Section: Research Articlementioning

confidence: 99%

Inverse Modeling of Hydrologic Systems with Adaptive Multifidelity Markov Chain Monte Carlo Simulations

Zhang

Man

Lin

et al. 2018

Markov chain Monte Carlo (MCMC) simulation methods are widely used to assess parametric uncertainties of hydrologic models conditioned on measurements of observable state variables. However, when the model is CPU‐intensive and high dimensional, the computational cost of MCMC simulation will be prohibitive. In this situation, a CPU‐efficient while less accurate low‐fidelity model (e.g., a numerical model with a coarser discretization or a data‐driven surrogate) is usually adopted. Nowadays, multifidelity simulation methods that can take advantage of both the efficiency of the low‐fidelity model and the accuracy of the high‐fidelity model are gaining popularity. In the MCMC simulation, as the posterior distribution of the unknown model parameters is the region of interest, it is wise to distribute most of the computational budget (i.e., the high‐fidelity model evaluations) therein. Based on this idea, in this paper we propose an adaptive multifidelity MCMC algorithm for efficient inverse modeling of hydrologic systems. In this method, we evaluate the high‐fidelity model mainly in the posterior region through iteratively running MCMC based on a Gaussian process system that is adaptively constructed with multifidelity simulation. The error of the Gaussian process system is rigorously considered in the MCMC simulation and gradually reduced to a negligible level in the posterior region. Thus, the proposed method can obtain an accurate estimate of the posterior distribution with a small number of the high‐fidelity model evaluations. The performance of the proposed method is demonstrated by three numerical case studies in inverse modeling of hydrologic systems.