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A Reduced Rank Estimate of Forecast Error Variance Changes due to Intermittent Modifications of the Observing Network

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  • 1 Centre National de Recherches Météorologiques, Météo-France, Toulouse, France, and European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom
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Abstract

A new tool for planning adaptive observations is introduced. Different modifications of the observing network can be compared prior to the time of modification. The method predicts the variance of forecast errors projected into a low-dimensional subspace. Tangent-linear error evolution is assumed and the contribution of model errors to the forecast error is neglected. Singular vectors of the propagator of the tangent-linear version of the forecast model are used to define a relevant subspace. The method employs the Hessian of the cost function of a variational assimilation scheme to obtain information on the distribution of initial errors. Thus, this technique for planning adaptive observations can be made consistent with operational variational assimilation schemes. The application of the method is currently limited to intermittent modifications of the observing network as changes of the background error distribution due to modifications of the network in previous assimilation cycles are not accounted for. The predicted changes of forecast error variance are identical to those that the ensemble transform Kalman filter method would yield if applied to a set of Hessian singular vectors.

The reduced rank estimate has been implemented in the Integrated Forecasting System of the European Centre for Medium-Range Weather Forecasts. To illustrate the scope of the method, it is applied to the 2-day forecast of an extratropical cyclone. The expected reduction of the total energy of forecast error is computed for various hypothetical adaptive networks that differ by spatial coverage, observation density, and the type of observation.

Corresponding author address: Martin Leutbecher, European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, Berkshire RG2 9AX, United Kingdom. Email: m.leutbecher@ecmwf.int

Abstract

A new tool for planning adaptive observations is introduced. Different modifications of the observing network can be compared prior to the time of modification. The method predicts the variance of forecast errors projected into a low-dimensional subspace. Tangent-linear error evolution is assumed and the contribution of model errors to the forecast error is neglected. Singular vectors of the propagator of the tangent-linear version of the forecast model are used to define a relevant subspace. The method employs the Hessian of the cost function of a variational assimilation scheme to obtain information on the distribution of initial errors. Thus, this technique for planning adaptive observations can be made consistent with operational variational assimilation schemes. The application of the method is currently limited to intermittent modifications of the observing network as changes of the background error distribution due to modifications of the network in previous assimilation cycles are not accounted for. The predicted changes of forecast error variance are identical to those that the ensemble transform Kalman filter method would yield if applied to a set of Hessian singular vectors.

The reduced rank estimate has been implemented in the Integrated Forecasting System of the European Centre for Medium-Range Weather Forecasts. To illustrate the scope of the method, it is applied to the 2-day forecast of an extratropical cyclone. The expected reduction of the total energy of forecast error is computed for various hypothetical adaptive networks that differ by spatial coverage, observation density, and the type of observation.

Corresponding author address: Martin Leutbecher, European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, Berkshire RG2 9AX, United Kingdom. Email: m.leutbecher@ecmwf.int

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