ANALYSIS OF ERRORS IN THE HORIZONTAL DIVERGENCE DERIVED FROM HIGH TEMPORAL RESOLUTION OF THE WIND

The vorticity method is applied to determine horizontal divergence usi ng the dynamical balance of terms in the vorticity equation. The viabi lity of the method is analyzed in terms of dynamical approximations, s ensitivity to observation and truncation errors, and numerical experim ents. This analysis is also applied to the kinematic method, which cal culates the horizontal divergence by adding together the appropriate f inite-difference approximations of its individual terms. The analysis of errors in the vorticity and kinematic methods is based on the accur acy of the data. It is proven analytically that errors in the divergen ce derived from the vorticity method are smaller than those of the kin ematic method by a factor equal to the Rossby number, even though the former method involves higher-order derivatives. When a 10% random err or is included, the error of the large-scale divergence in the kinemat ic method exceeds 100%, whereas the error derived by the vorticity met hod is less than 30% and is comparable to the error in the horizontal wind as expected from the error analysis. An essential result is that the temporal variation of the vorticity is not adequately resolved by the 12-h rawinsonde observing systems and must instead be derived from high temporal resolution wind data such as those measured by the Wind Profiler Demonstration Network. Due to the unavailability of the prof iler data in the planetary boundary layer, the vorticity method is pri marily applicable to the free atmosphere.