Integrating multiple scales of hydraulic conductivity measurements in training image-based stochastic models

Abstract

Hydraulic conductivity is one of the most critical and at the same time one of the most uncertain parameters in many groundwater models. One problem commonly faced is that the data are usually not collected at the same scale as the discretized elements used in a numerical model. Moreover, it is common that different types of hydraulic conductivity measurements, corresponding to different spatial scales, coexist in a studied domain, which have to be integrated simultaneously. Here we address this issue in the context of Image Quilting, one of the recently developed multiple-point geostatistics methods. Based on a training image that represents fine-scale spatial variability, we use the simplified renormalization upscaling method to obtain a series of upscaled training images that correspond to the different scales at which measurements are available. We then apply Image Quilting with such a multiscale training image to be able to incorporate simultaneously conditioning data at several spatial scales of heterogeneity. The realizations obtained satisfy the conditioning data exactly across all scales, but it can come at the expense of a small approximation in the representation of the physical scale relationships. In order to mitigate this approximation, we iteratively apply a kriging-based correction to the finest scale that ensures local conditioning at the coarsest scales. The method is tested on a series of synthetic examples where it gives good results and shows potential for the integration of different measurement methods in real-case hydrogeological models.

Groundwater Simulations and Uncertainty Analysis Using MODFLOW and Geostatistical Approach with Conditioning Multi-Aquifer Spatial Covariance

“…One of the most influential parameters in groundwater simulation is hydraulic conductivity (K), which is a soil property that measures the ability of soil to transmit fluid through pore spaces and fractures [1] (e.g., the ratio of velocity to hydraulic gradient). Previous studies [2][3][4][5] have demonstrated that hydrogeological parameters, such as transmissivity and hydraulic conductivity, exhibit log-normal distributions.…”

“…However, though hydraulic conductivity in soil and rock exhibits large spatial heterogeneity, with likely variations of several orders of magnitude within a short distance [7,8], only a small number of measurements can be made due to the prohibitively expensive cost. It is thus suggested that hydraulic conductivity should be addressed within a stochastic framework, and the uncertainty should be quantified in groundwater simulations in multiple aquifers [1,7,9].…”

“…Hydraulic conductivity is one of the most critical and uncertain parameters in numerous groundwater models [1]. The high degree of spatial variability in hydraulic conductivity and the complexity of causes of this variability are widely recognized as major impediments to making precise predictions [8].…”

“…The high degree of spatial variability in hydraulic conductivity and the complexity of causes of this variability are widely recognized as major impediments to making precise predictions [8]. Stochastic methods are widely applied to estimate, simulate, and delineate representative heterogeneous field distributions of hydrogeological properties for groundwater models based on a limited number of groundwater samples [1,[9][10][11]. Stochastic analysis allows a quantitative evaluation of the effects of variability and thereby provides a means of addressing uncertainty in the resultant heads and flows that are caused by uncertainty in the hydraulic conductivity field [10,12].…”

“…Geostatistical simulation, including lower upper (LU) decomposition, turning bands, sequential gaussian (SG) simulation and simulated annealing (SA) simulation, is a well-known technique for modeling the spatial uncertainty of a regionalized variable [1,2,10,11,[16][17][18] such as hydraulic conductivity. The typical geostatistical simulation is performed using a semivariogram model and a simulation algorithm to generate many realizations (conditional or unconditional) of the random function model [18].…”