Manually adjusting a numerical weather analysis using three-dimensional variational data-assimilation

A method is presented to manually adjust the analysis of a numerical weather forecasting model and study the impact of the adjustment on the ensuing forecast. The adjustment is made in terms of potential vorticity. The prime motivation for using potential vorticity is that within the constraints of hydrostatic and geostrophic balance the pressure, wind and temperature fields are adjusted whenever the potential vorticity field is adjusted. This is a consequence of the invertibility principle of potential vorticity. Another motivation is that potential vorticity usually correlates well with water vapour satellite images at midlatitudes. Obvious mismatches between the two fields are therefore indicative of errors and may, in actual practice, be a reason to adjust the analysis. The method is based on three-dimensional variational data-assimilation and utilizes the special properties of potential vorticity.

The potential vorticity of the analysis is manually adjusted by means of a graphical interface. The resulting modified potential vorticity field is treated as information that is to be incorporated into a new, modified, analysis. For this purpose we use three-dimensional variational data-assimilation, in which the observation term in the cost function is replaced by a potential vorticity term. In analogy with the observation term the potential vorticity term measures the difference between the modified potential vorticity and the potential vorticity of the model state. The extent to which the modified analysis reproduces the modified potential vorticity depends on the relative weights of the potential vorticity term and the background term in the cost function. An example is given of a modified analysis and its effect on a 24 hours forecast, using a limited area weather forecasting model.