SASS Wind Ambiguity Removal by Direct Minimization. Part II: Use of Smoothness and Dynamical Constraints

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  • 1 Atmospheric and Environmental Research, Inc., Cambridge, MA 02139
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Abstract

Variational analysis methods allow information from a variety of sources, including current observations and a priori statistics and constraints, to be combined by minimizing the lack of fit to the various sources of information. In this study, the ambiguity of the SASS winds is removed by a variational analysis method which combines the following information: a variety of current surface wind observations (radiosonde, ship, satellite scatterometer), earlier observations in the form of a forecast, smoothness constraints on the horizontal winds, its divergence and vorticity, and a dynamical constraint on the time rate of change of Vorticity of the surface wind. The constraints used are “weak” constraints in the sense of Sasaki. In an earlier work, constraints were not used. The scatterometer wind magnitudes are nearly unambiguous and are considered specially.

The lack of fit to data and constraints is measured by the so-called objective function. Here, a discrete form of the solution is assumed, the objective function is described in terms of discrete variables and a minimum is found by a conjugate gradient method. Global analyses are possible.

Compared to previous results, the use of constraints results in a more robust analysis procedure and produces better transitions between data-rich and data-poor regions, but the analyses, like all objective analyses, are still lacking common sense in some important respects.

The scatterometer data have been processed by two methods, one which bins and one which pairs the individual scatterometer values. Both data sets are analyzed for the case of an intense cyclone centered south of Japan at 0000 GMT 6 September 1978. Only slightly better results are obtained with the finer resolution winds produced by the pairing algorithm, although it is clear they contain far more detailed information.

Abstract

Variational analysis methods allow information from a variety of sources, including current observations and a priori statistics and constraints, to be combined by minimizing the lack of fit to the various sources of information. In this study, the ambiguity of the SASS winds is removed by a variational analysis method which combines the following information: a variety of current surface wind observations (radiosonde, ship, satellite scatterometer), earlier observations in the form of a forecast, smoothness constraints on the horizontal winds, its divergence and vorticity, and a dynamical constraint on the time rate of change of Vorticity of the surface wind. The constraints used are “weak” constraints in the sense of Sasaki. In an earlier work, constraints were not used. The scatterometer wind magnitudes are nearly unambiguous and are considered specially.

The lack of fit to data and constraints is measured by the so-called objective function. Here, a discrete form of the solution is assumed, the objective function is described in terms of discrete variables and a minimum is found by a conjugate gradient method. Global analyses are possible.

Compared to previous results, the use of constraints results in a more robust analysis procedure and produces better transitions between data-rich and data-poor regions, but the analyses, like all objective analyses, are still lacking common sense in some important respects.

The scatterometer data have been processed by two methods, one which bins and one which pairs the individual scatterometer values. Both data sets are analyzed for the case of an intense cyclone centered south of Japan at 0000 GMT 6 September 1978. Only slightly better results are obtained with the finer resolution winds produced by the pairing algorithm, although it is clear they contain far more detailed information.

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