The large-scale horizontal divergences computed from the kinematic and vorticity methods based on a four-dimensional least squares fit (4-D LSF) to the hourly wind measurements from the Wind Profiler Demonstration Network (WPDN) are compared to the divergence derived from a four-dimensional data assimilation (4-DDA) system. The kinematic method computes divergence by adding the appropriate terms of the velocity derivatives, while the vorticity method uses the dynamical balance of terms in the vorticity equation. The 4-D LSF method produces wind and vorticity analyses by approximating the analyzed wind field as a series of basis functions dependent on both space and time. The sensitivity of the basis functions is studied with an analytic solution and with real data. It is shown that the LSF results are not sensitive to the choice of basis functions as long as they include adequate variation to resolve the data. The high temporal resolution divergence and vorticity fields, which are obtained directly from hourly WPDN data, are used to independently validate the 4-DDA derived vorticity and divergence, which depend both on observational data and on the dynamics and physics in data assimilation models. For the initial case study, the relative errors between the 4-D LSF or the 4-DDA analysis and the WPDN measurements are essentially the same, and the smooth parts of the vorticity derived from these two analyses are similar. The large-scale divergence derived from the vorticity method is also in good agreement with that derived from the 4-DDA analysis. However, the divergence derived from the kinematic method shows little resemblance to those derived from the vorticity method and 4-DDA analysis.
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