| Summary: | 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 ...
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