English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

High dimensional error covariance matrices and their inverses are used toweight the contribution of observation and background information in dataassimilation procedures. As observation error covariance matrices are oftenobtained by sampling methods, estimates are often degenerate orill-conditioned, making it impossible to invert an observation error covariancematrix without the use of techniques to reduce its condition number. In thispaper we present new theory for two existing methods that can be used to'recondition' any covariance matrix: ridge regression, and the minimumeigenvalue method. We compare these methods with multiplicative varianceinflation. We investigate the impact of reconditioning on variances andcorrelations of a general covariance matrix in both a theoretical and practicalsetting. Improved theoretical understanding provides guidance to usersregarding method selection, and choice of target condition number. The newtheory shows that, for the same target condition number, both methods increasevariances compared to the original matrix, with larger increases for ridgeregression than the minimum eigenvalue method. We prove that the ridgeregression method strictly decreases the absolute value of off-diagonalcorrelations. Theoretical comparison of the impact of reconditioning andmultiplicative variance inflation on the data assimilation objective functionshows that variance inflation alters information across all scales uniformly,whereas reconditioning has a larger effect on scales corresponding to smallereigenvalues. The minimum eigenvalue method results in smaller overall changesto the correlation matrix than ridge regression, but can increase off-diagonalcorrelations. Data assimilation experiments reveal that reconditioning correctsspurious noise in the analysis but underestimates the true signal compared tomultiplicative variance inflation.

Improving the condition number of estimated covariance matrices