Characterization of conductivity fields through iterative ensemble smoother and improved correlation-based adaptive localization

Localization is critical to the effective use of an (iterative) ensemble Kalman filter or ensemble smoother to estimate uncertain quantities of interest. Here, we propose a novel, fully adaptive, correlation-based localization method (termed FBadap). We embed our FBadap approach within an iterative ensemble smoother to estimate three-dimensional spatially heterogeneous log-conductivity (Y) fields. The latter are characterized through a Generalized sub-Gaussian model, which includes the Gaussian distribution as a particular case. They constitute random fields within which head and concentration observations are collected at monitoring wells screened at multiple depths. To ensure transparent comparisons, we study and analyze the performance of our approach through a wide range of synthetic test cases. These comprise diverse configurations, including (a) various ensemble sizes, (b) various degrees of departure of the description of the spatial heterogeneity from a Gaussian model, as well as (c) different values of the mean and variance of the initial ensemble of Y. Our results show that (i) FBadap is robust adaptive approach enabling one to tackle a variety of settings; (ii) FBadap exhibits stronger adaptivity to cope with diverse ensemble sizes than FBconst, and can provide improved accuracy of conductivity estimates in comparison with traditional methods; and (iii) the quality of conductivity estimates is jointly impacted by the degree of departures of the reference Y field and of the initial ensemble of Y from a description based on a Gaussian model.