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Chiara Piccolo

Abstract

Numerical weather forecasting errors grow with time. Error growth results from the amplification of small perturbations due to atmospheric instability or from model deficiencies during model integration. In current NWP systems, the dimension of the forecast error covariance matrices is far too large for these matrices to be represented explicitly. They must be approximated.

This paper focuses on comparing the growth of forecast error from covariances modeled by the Met Office operational four-dimensional variational data assimilation (4DVAR) and ensemble transform Kalman filter (ETKF) methods over a period of 24 h. The growth of forecast errors implied by 4DVAR is estimated by drawing a random sample of initial conditions from a Gaussian distribution with the standard deviations given by the background error covariance matrix and then evolving the sample forward in time using linearized dynamics. The growth of the forecast error modeled by the ETKF is estimated by propagating the full nonlinear model in time starting from initial conditions generated by an ETKF. This method includes model errors in two ways: by using an inflation factor and by adding model perturbations through a stochastic physics scheme. Finally, these results are compared with a benchmark of the climatological error.

The forecast error predicted by the implicit evolution of 4DVAR does not grow, regardless of the dataset used to generate the static background error covariance statistics. The forecast error predicted by the ETKF grows more rapidly because the ETKF selects balanced initial perturbations, which project onto rapidly growing modes. Finally, in both cases it is not possible to disentangle the contribution of the initial condition error from the model error.

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Chiara Piccolo and Mike Cullen

Abstract

A natural way to set up an ensemble forecasting system is to use a model with additional stochastic forcing representing the model error and to derive the initial uncertainty by using an ensemble of analyses generated with this model. Current operational practice has tended to separate the problems of generating initial uncertainty and forecast uncertainty. Thus, in ensemble forecasts, it is normal to use physically based stochastic forcing terms to represent model errors, while in generating analysis uncertainties, artificial inflation methods are used to ensure that the analysis spread is sufficient given the observations. In this paper a more unified approach is tested that uses the same stochastic forcing in the analyses and forecasts and estimates the model error forcing from data assimilation diagnostics. This is shown to be successful if there are sufficient observations. Ensembles used in data assimilation have to be reliable in a broader sense than the usual forecast verification methods; in particular, they need to have the correct covariance structure, which is demonstrated.

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Stefano Migliorini, Chiara Piccolo, and Clive D. Rodgers

Abstract

Satellite observations are the most assimilated data type by operational meteorological centers. Spaceborne instruments can make measurements all over the globe and provide observations for assimilation even where the coverage of other data is poor. It is therefore most important that such observations, which are only indirectly related to the state of the atmosphere, are assimilated as optimally as possible. In this study, a detailed characterization of both retrievals and observed radiances for assimilation is provided, along with an error analysis. A method for assimilating remote sounding data while preserving its information content is presented. The main features of the technique are as follows: (i) the retrieval–forecast error cross covariance is removed even when the retrieval is severely constrained by a priori information, (ii) the radiative transfer calculations for radiance assimilation are done offline, and (iii) the number of assimilated quantities per observation is reduced to the number of effective degrees of freedom in the observation.

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