Use of Uncertainty Inflation in OSTIA to Account for Correlated Errors in Satellite-Retrieved Sea Surface Temperature Data

Abstract

Sea surface temperature (SST) analysis systems such as the Operational Sea Surface Temperature and Ice Analysis (OSTIA) use statistical methods to combine observations together with a first guess field to create spatially complete maps of SST. These commonly assume that observation errors are uncorrelated, yet some errors (such as due to retrieval issues) can be correlated. Information about errors is used by the analysis system to determine the weighting to apply to the observations, hence this incorrect assumption could degrade the analysis. A common technique to mitigate for this is to inflate the observation uncertainties. Using information on observation error correlations provided with data produced by the European Space Agency (ESA) SST Climate Change Initiative (CCI) project, idealised tests were carried out to determine how this inflation technique can best be applied. These showed that applying inflation in situations where the observation errors are correlated over similar or larger distances to the errors in the background can cause unpredictable and sometimes negative results. However, in situations where the observation error correlation length scale is relatively small, inflation should improve the analysis. These findings were adapted to the OSTIA system and various configurations were tested. It was found that the inflation methods did not affect statistics of differences between the analyses and independent Argo reference data. However, the SST gradients were affected, particularly if some observation uncertainties were inflated but others were not. The results from both the idealised tests and the application to the real system therefore highlight that it is challenging to implement the inflation method in the case of an SST analysis system and show the need for assimilation schemes that can make full use of observation error correlation information.

Impact of correlated observation errors on the conditioning of variational data assimilation problems

“…Taking M to be an even number allows us to split T −M = T −M∕2 T −M∕2 and hence to derive a simple 'square-root' factorization of Equation (9). The 'square-root' operator is convenient for generating random correlated samples and has been used for this purpose for the numerical experiments in Section 4.…”

“…However, when observation error is correlated over distances similar to or greater than those of the background error, inflation can actually degrade the analysis. 9 While these methods can alleviate to some extent the inaccuracies associated with a diagonal R, they still lead to sub-optimal solutions since potentially valuable observations are excluded and any remaining error correlations from the pre-processed observations are ignored. 10 Several studies have examined the impact from using non-diagonal representations of R to account for spatially correlated errors.…”

“…Furthermore, the observation‐error variances are often multiplied by an ‘inflation’ factor in order to prevent the analysis from overfitting observations that may still have a substantial component of correlated error. However, when observation error is correlated over distances similar to or greater than those of the background error, inflation can actually degrade the analysis 9 . While these methods can alleviate to some extent the inaccuracies associated with a diagonal $$$ \mathbf{R} $$$, they still lead to sub‐optimal solutions since potentially valuable observations are excluded and any remaining error correlations from the pre‐processed observations are ignored 10 …”