Calculation of Consistent Flux and Advective Terms from Adjusted Vertical Profiles of Divergence

Abstract

A simple framework is presented for adjusting the normal wind components in a polygon of data points which produces a vanishing vertical integral of horizontal divergence, allows correct calculation of flux and advective terms, and permits virtually any choice of vertical profile of divergence adjustment. The procedure was used to estimate precipitation as a residual from vertically integrated heat and moisture budgets for SESAME data, in order to evaluate the uncertainty introduced by commonly used approximations in diagnostic studies. Although the method cannot be applied on a grid in its current form, the results remain valid for gridded calculations. Line integrals around the polygon were carried out analytically, allowing an exact calculation of eddy fluxes within the assumption of linearity along the edges. Finite difference approximations for nonlinear terms were shown to introduce significant errors, even under ordinary circumstances. It is common practice to neglect the horizontal advecting velocity adjustment brought about by the adjusted divergence. Such an assumption produced negligible median errors in the integrated heat and moisture budgets. The median differences in calculated precipitation caused by differing choices of the divergence adjustment profile reached 1.34 andO.35 cm day?1 in the heat and moisture budgets, respectively. Because the true divergence adjustment profile is unknown, these values represent median lower bounds on the errors in budget estimates of precipitation in middle latitude convection.