Improving pseudo-optimal Kalman-gain localization using the random shuffle method

Hyper-Parameter Optimization for Improving the Performance of Localization in an Iterative Ensemble Smoother

“…An alternative to distance-based localization is correlation-based localization (Lacerda et al, 2019;Luo et al, 2018;Luo and Bhakta, 2020;Ranazzi et al, 2022), in which a tapering matrix is formulated based on sample correlations -rather than physical distances -between ensembles of model variables and simulated observation data points. As elaborated in Luo et al (2018Luo et al ( , 2019, correlation-based localization is able to overcome or mitigate the aforementioned long-standing issues arising in distance-based localization, and can be used in certain situations, e.g., when model variables and/or observations do not possess physical locations (Luo et al, 2018) or when localization needs to be done for an ensemble of gradients projected onto ensemble subspaces (Luo and Cruz, 2022), where the conventional distance-based localization does not seem to be straightforwardly applicable.…”

“…In the meantime, by applying the random shuffle method multiple times, one can also generate a number of substitute sampling errors for ''global'' parameters, making it possible to estimate the threshold value 𝜃 𝐺 𝑘 ,𝑠 for a ''global'' parameter based on the first line of Eq. ( 15) (Ranazzi et al, 2022).…”

“…To alleviate the adversarial effects of the small ensemble size, a common practice in the community is to equip an ensemble data assimilation algorithm with a localization scheme, which in effect modifies the model update formula in the ensemble data assimilation algorithm. Various localization techniques have been developed from different perspectives, and been applied for different purposes (Anderson, 2012;Anderson and Lei, 2013;Arroyo et al, 2008;Bishop and Hodyss, 2007;Oliver, 2010, 2017;Emerick and Reynolds, 2011;Fertig et al, 2007;Hamill et al, 2001;Lacerda et al, 2019;Luo et al, 2018;Luo and Bhakta, 2020;Ranazzi et al, 2022;Soares et al, 2021).…”

“…In light of these challenges, there have been some recent efforts (Anderson, 2012;Furrer and Bengtsson, 2007;Lacerda et al, 2019;Luo et al, 2018;Luo and Bhakta, 2020;Ranazzi et al, 2022;Soares et al, 2021) dedicated to tackling the above-mentioned issues, which use sample correlations between model variables and simulated observations (or between model variables themselves), rather than the distances between their physical locations, to compute the tapering coefficients, and which are thus referred to as correlation-based localization hereafter. For reservoir data assimilation problems, it has been shown that correlation-based localization is able to avoid or mitigate the aforementioned issues (Luo et al, 2019), works reasonably well in both synthetic (Lacerda et al, 2019;Luo et al, 2018;Luo and Bhakta, 2020;Ranazzi et al, 2022;Soares et al, 2021) and real field (Luo et al, 2019;Lorentzen et al, 2020) case studies.…”

“…Most of the existing localization schemes, being either distanceor correlation-based, have some inherent hyper-parameters that need to be determined in one way or another. The type of the hyperparameters could be localization length scale (Chen and Oliver, 2010;Emerick and Reynolds, 2011;Hamill et al, 2001;Luo and Bhakta, 2020;Soares et al, 2021), localization radius (Chen and Oliver, 2017), certain threshold values (Lacerda et al, 2019;Luo et al, 2018), or coefficients inside the tapering functions (Anderson, 2012;Bishop and Hodyss, 2007;Ranazzi et al, 2022).…”