# Revising the stochastic iterative ensemble smoother

## TL;DR

This paper simplifies and improves the stochastic iterative ensemble smoother (EnRML) for large nonlinear inverse problems, addressing computational and noise issues while maintaining its accuracy.

## Contribution

It provides a streamlined formulation of EnRML, clarifies its linearization and subspace properties, and enhances its computational efficiency without altering the results.

## Key findings

- EnRML is made more computationally efficient and less noisy.
- The relation between ensemble linearizations and average sensitivity is clarified.
- Benchmark results show improved performance on the Lorenz-96 model.

## Abstract

Ensemble randomized maximum likelihood (EnRML) is an iterative (stochastic) ensemble smoother, used for large and nonlinear inverse problems, such as history matching and data assimilation. Its current formulation is overly complicated and has issues with computational costs, noise, and covariance localization, even causing some practitioners to omit crucial prior information. This paper resolves these difficulties and streamlines the algorithm, without changing its output. These simplifications are achieved through the careful treatment of the linearizations and subspaces. For example, it is shown (a) how ensemble linearizations relate to average sensitivity, and (b) that the ensemble does not lose rank during updates. The paper also draws significantly on the theory of the (deterministic) iterative ensemble Kalman smoother (IEnKS). Comparative benchmarks are obtained with the Lorenz-96 model with these two smoothers and the ensemble smoother using multiple data assimilation (ES-MDA).