Implicit particle methods and their connection with variational data assimilation

TL;DR

This paper introduces a generalized derivation of implicit particle methods, connecting them with variational data assimilation, enabling improved estimates with uncertainty quantification and extending the approach to smoothing and perfect models.

Contribution

It establishes a theoretical link between implicit particle methods and variational data assimilation, allowing existing codes to be adapted for enhanced data assimilation.

Findings

Implicit particle methods can be derived from variational principles.

Existing variational codes can be converted into implicit particle methods at low cost.

The approach provides better estimates with quantitative uncertainty measures.

Abstract

The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. We present a new and more general derivation of this approach and extend the method to particle smoothing as well as to data assimilation for perfect models. We show that the minimizations required by implicit particle methods are similar to the ones one encounters in variational data assimilation and explore the connection of implicit particle methods with variational data assimilation. In particular, we argue that existing variational codes can be converted into implicit particle methods at a low cost, often yielding better estimates, that are also equipped with quantitative measures of the uncertainty. A detailed example is presented.