Optimization of Dynamic Retrievals from a Multiple-Doppler Radar Network

Alain Protat Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada

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Isztar Zawadzki J. S. Marshall Weather Observatory, Sainte Anne de Bellevue, Quebec, Canada

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Abstract

Recently, Protat and Zawadzki described an analysis method to retrieve the three wind components and their temporal derivatives from measurements collected by a bistatic multiple-Doppler radar network deployed around Montreal for nowcasting and research purposes. In the present paper, an extension of this method to retrieve the corresponding pressure and potential temperature perturbations is presented. The method consists of adding the three projections of the momentum equations as weak constraints to the minimization procedure, as is classically done. An evaluation of the performance of this basic constraining model indicates that, after minimization, the residuals of the horizontal momentum equations are of the same order of magnitude as the dominant terms of these equations. It is then shown that including the vorticity equation as an additional constraint substantially improves the perturbation pressure and temperature solutions, leading to negligible residuals of the horizontal momentum equations. This is due to the fact that the vorticity equation is equivalent to the condition that pressure derives from a potential (the second-order horizontal cross-derivatives of pressure are equal), which ensures that the problem has a mathematical solution.

Corresponding author address: Dr. Alain Protat, CETP/UVSQ/IPSL, 10–12, Avenue de l’Europe, 78140 Vélizy, France.

Email: protat@cetp.ipsl.fr

Abstract

Recently, Protat and Zawadzki described an analysis method to retrieve the three wind components and their temporal derivatives from measurements collected by a bistatic multiple-Doppler radar network deployed around Montreal for nowcasting and research purposes. In the present paper, an extension of this method to retrieve the corresponding pressure and potential temperature perturbations is presented. The method consists of adding the three projections of the momentum equations as weak constraints to the minimization procedure, as is classically done. An evaluation of the performance of this basic constraining model indicates that, after minimization, the residuals of the horizontal momentum equations are of the same order of magnitude as the dominant terms of these equations. It is then shown that including the vorticity equation as an additional constraint substantially improves the perturbation pressure and temperature solutions, leading to negligible residuals of the horizontal momentum equations. This is due to the fact that the vorticity equation is equivalent to the condition that pressure derives from a potential (the second-order horizontal cross-derivatives of pressure are equal), which ensures that the problem has a mathematical solution.

Corresponding author address: Dr. Alain Protat, CETP/UVSQ/IPSL, 10–12, Avenue de l’Europe, 78140 Vélizy, France.

Email: protat@cetp.ipsl.fr

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