Ocean data assimilation and the Kalman filter: spatial regularity.

Abstract

It is demonstrated by asymptotic analysis and numerical experiment that the Kalman filter gains converge if and only if the wave number spectrum of the system noise is suitably coloured. The analysis and experiments employ linear ocean models, and include the cases of data available continuously in time and discretely in time. The experiments show that, in the case of continuous data, the matrix Riccati equation for the streamfunction covariance matrix is numerically well conditioned provided the streamfunction system noise is coloured. The analysis shows that the covariance matrix is banded only in the case of discrete data and only if the system covariance greatly exceeds the measurement noise variance.