A new procedure for generating data covariance inflation factors for ensemble smoother with multiple data assimilation

Evaluating the Impact of the Inflation Factors Generation for the Ensemble Smoother With Multiple Data Assimilation

“…Opposite to the left-hand side of Equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15), the right-hand side of the same equation displays a matrix problem of size N d × N d , which is more feasible when N d N m , as explained before. Therefore, one may compute m map as follows:…”

“…This section presents a brief background of regularization for nonlinear inverse problems [21] and how we can link this theory to the ES-MDA update equation [10,15]. The concept of regularization is crucial to yielding a significant analysis of the influence of the inflation factors selection in the ES-MDA performance from a mathematical perspective.…”

“…The concept of regularization is crucial to yielding a significant analysis of the influence of the inflation factors selection in the ES-MDA performance from a mathematical perspective. Moreover, it was the base of the studies of Le et al (2016) [7], Rafiee and Reynolds (2017) [10], Emerick (2019) [12], and [15] to present novel methods to generate ES-MDA inflation factors efficiently.…”

“…5. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) and (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) for different ensembles.…”

“…In contrast with the study of Rafiee and Reynolds (2017) [10], Emerick (2019) [12] tests the resulting first inflation factor using a standard discrepancy principle function [14]. Recently, Silva et al (2021) [15] proposed a new method to compute the ES-MDA inflation factors by computing the first and the last factors using the formula of Rafiee and Reynolds (2017) [10]. The other inflation factors are selected geometrically in decreasing order.…”