Diagonal Approximations to the Observation Error Covariance Matrix in Sea Ice Thickness Data Assimilation

Abstract

Data assimilation is a statistical technique for combining observations of a physical system with the state of a numerical model of that system. The procedure yields a new and ideally improved state estimate called the analysis. A critical component of data assimilation is the observation error covariance matrix, which describes the magnitude and the correlation of the errors in the observations. When the observation error correlation structure is unknown, an approximation can yield a poor analysis and an incorrect estimate of the quality of the analysis.

Little is known about the error correlation structure of remotely-sensed sea ice thickness observations. However, sea ice prediction centres are beginning to move forward with ice thickness assimilation under the simplifying assumption that the observation errors are uncorrelated. The assumption of uncorrelated observation errors is attractive because the errors can be represented by a diagonal observation error covariance matrix, which is inexpensive to invert. The purpose of this thesis was to develop an understanding of how the diagonal approximation might affect the quality of the sea ice state estimate.

This thesis describes a set of twin assimilation experiments that were conducted using a one-dimensional sea ice model. The twin experiment design enabled an investigation of the differences between the estimated and actual errors in the analysis state. The first part of this investigation explored how the diagonal approximation can impact the estimated mean analysis error standard deviation. The second component of the investigation explored the spatial scales of the errors present in the analysis.

The experimental results indicated that the diagonal approximation can be used without increasing the mean analysis error standard deviation so long as the observation error variances are multiplied by a sufficiently-large inflation factor. The results also indicated that the inflation factor can be conservatively overestimated without adversely impacting the analysis. For some of the experiments, the diagonal approximation resulted in an increase in the analysis error spectral variance at lower wavenumbers. The approximation had little effect at higher wavenumbers.

The main finding of this thesis is that diagonal approximations to the ice thickness observation error covariance matrix can likely be incorporated into ice prediction systems without adverse effects. One caveat of this statement is that an inflation factor should be used to increase the observation error variance estimates. A second caveat is that the analysis error covariance matrix may underestimate the correlation of analysis errors at the largest spatial scales. A final finding is that large improvements in analysis quality may be obtained if better approximations to the ice thickness observation error covariance matrix can be found and used in the analysis.