Principal Investigator: John F. Gamache
Collaborating Scientist:  Wen-Chau Lee [NCAR/ATD/RSF]

Objective : To improve dual- and multiple-Doppler analyses by incorporating the Doppler projection equations, the three-dimensional continuity equation, and filtering within a variational scheme. 
Rationale : The solution of a Doppler wind analysis involves two or more projection equations, and one continuity equation. The solution of these three simultaneously is difficult. In the past, the vertical wind was first assumed to be zero and then the projection equations were solved for the horizontal wind components. The divergence of the horizontal components was then integrated to determine the vertical wind. The new vertical wind was then used in the projection equations to determine a new horizontal wind field. This process was to be iterated to a solution. The process was unstable for Doppler radials more than approximately 45 degrees from horizontal. Thus these data must be thrown out if the process is to be iterated to a convergent solution. Throwing all three equations into a cost function, however, allows all three equations to be solved simultaneously, and thus Doppler radials above 45 degrees may be kept in the analysis. This is because the continuity equation is also solved in all three directions, and not just in the vertical. Another advantage is that since the filtering is included in the cost function at a much lower cost than continuity, a smoother wind field is found that still satisfies the continuity equation closely. 
Method : Several steps are required in determining the wind field from dual- or multiple-Doppler observations


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Last modified: 02/01/00