Articles | Volume 22, issue 4
Nonlin. Processes Geophys., 22, 403–411, 2015
https://doi.org/10.5194/npg-22-403-2015
Nonlin. Processes Geophys., 22, 403–411, 2015
https://doi.org/10.5194/npg-22-403-2015

Research article 24 Jul 2015

Research article | 24 Jul 2015

Verification against perturbed analyses and observations

N. E. Bowler, M. J. P. Cullen, and C. Piccolo N. E. Bowler et al.
  • Met Office, Fitzroy Road, Exeter, EX1 3PB, UK

Abstract. It has long been known that verification of a forecast against the sequence of analyses used to produce those forecasts can under-estimate the magnitude of forecast errors. Here we show that under certain conditions the verification of a short-range forecast against a perturbed analysis coming from an ensemble data assimilation scheme can give the same root-mean-square error as verification against the truth. This means that a perturbed analysis can be used as a reliable proxy for the truth. However, the conditions required for this result to hold are rather restrictive: the analysis must be optimal, the ensemble spread must be equal to the error in the mean, the ensemble size must be large and the forecast being verified must be the background forecast used in the data assimilation. Although these criteria are unlikely to be met exactly it becomes clear that for most cases verification against a perturbed analysis gives better results than verification against an unperturbed analysis.

We demonstrate the application of these results in a idealised model framework and a numerical weather prediction context. In deriving this result we recall that an optimal (Kalman) analysis is one for which the analysis increments are uncorrelated with the analysis errors.

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Short summary
It has long been known that verification of a forecast against the sequence of analyses used to produce those forecasts can under-estimate the magnitude of forecast errors. Here we show that under certain conditions the verification of a short-range forecast against a perturbed analysis coming from an ensemble data assimilation scheme can give the same root-mean-square error as verification against the truth. This means that a perturbed analysis can be used as a reliable proxy for the truth.