On the Interpolation of a Vector Field

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Abstract
By its very nature, interpolation in a vector field is ambiguous, owing to the somewhat arbitrary nature of the vector norm. Since a two-dimensional vector field cm be specified by two scalar quantities. which can be separately interpolated, the ambiguity can be resolved by forcing the interpolated wind field to preserve the vorticity and divergence fields associated with the raw data. A method to calculate divergence and vorticity directly from randomly spaced wind observations is developed and, using analytically generated data, shown to produce more accurate results than conventional computations. Two methods of retrieving the wind field from the analysed scalar fields are presented and also tested on the analytic field. Finally, total analysis, from wind observations to gridded wind fields, is demonstrated on real meteorological data. Abstract By its very nature, interpolation in a vector field is ambiguous, owing to the somewhat arbitrary nature of the vector norm. Since a two-dimensional vector field cm be specified by two scalar quantities. which can be separately interpolated, the ambiguity can be resolved by forcing the interpolated wind field to preserve the vorticity and divergence fields associated with the raw data. A method to calculate divergence and vorticity directly from randomly spaced wind observations is developed and, using analytically generated data, shown to produce more accurate results than conventional computations. Two methods of retrieving the wind field from the analysed scalar fields are presented and also tested on the analytic field. Finally, total analysis, from wind observations to gridded wind fields, is demonstrated on real meteorological data.

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