Estimation of vertical air motion from limited horizontal wind data—a numerical experiment

Abstract

The variational calculus and direct-differencing objective analysis procedures, which are formulated to produce mass conservative wind fields from horizontal wind data, were evaluated in numerical experiments. In the initial tests, the variational calculus procedure was evaluated using a test flow field generated by a land/sea breeze numerical model. The results indicated that this procedure reproduced the complex vertical flow field quite well if a minimum measurement density level was retained. A second set of numerical experiments employed the variational calculus procedure and direct-differencing method to generate a three-dimensional wind field for the Mikawa Bay area in Japan, using horizontal surface winds as input. The weighting parameter in the variational procedure, ( α 1 α 2 ) 2, affected both the resulting vertical motion and the residual divergence. The vertical motion was lower for smaller values of ( α 1 α 2 ) 2 and there was an optimum value of ( α 1 α 2 ) 2 to minimize the residual divergence. The direct-differencing method yielded quite similar flow patterns to those resulting from the variational method. However, this method requires very accurate horizontal wind field data as input to obtain vertical winds of reasonable magnitude.