Analysis of Errors in the Horizontal Divergence Derived from High Temporal Resolution of the Wind

Abstract

The vorticity method is applied to determine horizontal divergence using the dynamical balance of terms in the vorticity equation. The viability of the method is analyzed in terms of dynamical approximations, sensitivity to observation and truncation errors, and numerical experiments. This analysis is also applied to the kinematic method, which calculates the horizontal divergence by adding together the, appropriate finite-difference approximations of its individual terms. The analysis of errors in the vorticity and kinematic methods is based on the accuracy of the data. It is proven analytically that errors in the divergence derived from the vorticity method are smaller than those of the kinematic method by a factor equal to the Rossby number, even though the former method involves higher-order derivatives. When a 10% random error is included, the error of the large-scale divergence in the kinematic method exceeds 100%, whereas the error derived by the vorticity method 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 profiler data in the planetary boundary layer, the vorticity method is primarily applicable to the free atmosphere.