# CLP

## Seminar

### A variance constraining Kalman filter for data assimilation

Seminar Room 1, Newton Institute

#### Abstract

Data assimilation aims to solve one of the fundamental problems of numerical weather prediction - estimating the optimal state of the atmosphere given a numerical model of the dynamics, and sparse, noisy observations of the system. A standard tool in attacking this filtering problem is the Kalman filter.We consider the problem when only partial observations are available. In particular we consider the situation where the observational space consists of variables which are directly observable with known observational error, and of variables of which only their climatic variance and mean are given. We derive the corresponding Kalman filter in a variational setting.

We analyze the variance constraining Kalman filter (VCKF) filter for a simple linear toy model and determine its range of optimal performance. We explore the variance constraining Kalman filter in an ensemble transform setting for the Lorenz-96 system, and show that incorporating the information on the variance on some un-observable variables can improve the skill and also increase the stability of the data assimilation procedure.

Using methods from dynamical systems theory we then investigate systems where the un-observed variables evolve deterministically (but chaotically) on a fast time scale.

This is joint work with Lewis Mitchell and Sebastian Reich.

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