Low-rank Approximations for Computing Observation Impact in 4D-Var Data Assimilation

TL;DR

This paper introduces a computational framework that efficiently quantifies the impact of individual observations in 4D-Var data assimilation using low-rank approximations and adjoint sensitivity analysis, applicable to data pruning and sensor fault detection.

Contribution

It develops a novel matrix-free, low-rank approximation method for observation impact in 4D-Var, enabling efficient analysis of large-scale data assimilation systems.

Findings

Effective in data pruning and sensor fault detection

Reduces computational cost of impact analysis

Demonstrated on shallow water test system

Abstract

We present an efficient computational framework to quantify the impact of individual observations in four dimensional variational data assimilation. The proposed methodology uses first and second order adjoint sensitivity analysis, together with matrix-free algorithms to obtain low-rank approximations of ob- servation impact matrix. We illustrate the application of this methodology to important applications such as data pruning and the identification of faulty sensors for a two dimensional shallow water test system.