CONSERVATION OF MASS IN 3-DIMENSIONS IN GLOBAL ANALYSES

For a number of reasons, conservation of mass in the global analyses o n pressure coordinates is violated, yet this constraint is required fo r budget studies of all kinds. The imbalances arise from postprocessin g the variables onto pressure surfaces, problems of dealing with the l ower boundary and substituting an artificial atmosphere below ground, and diurnal pressure tendencies associated with the semidiurnal tide a nd the timing and distribution of observations. Methods are described and illustrated for May 1988 for adjusting the monthly mean global Eur opean Centre for Medium-Range Weather Forecasts analyses in three dime nsions on pressure surfaces so that the mass balance is achieved, but the problems are present in analyses on constant pressure surfaces fro m all centers. First, a correction is needed for the global mean verti cal motion. Second, it is shown that a local adjustment to the horizon tal divergent velocity held is needed for regions that are below groun d on constant pressure surfaces and nearby. Third, a change in the low er-boundary condition is required to remove diurnal and tidal influenc es, and this produces a barotropic adjustment in the horizontal veloci ty field as well as an adjustment in the vertical motion field that co mpares favorably with the semidiurnal tide in the analyses as a functi on of height. Solution of a three-dimensional Poisson equation is requ ired to provide a final adjustment that minimizes the changes in the t hree-dimensional flow held. A vertical coordinate change is required t o facilitate the solution, and the equation solves for the adjustment in the three-dimensional velocity potential using spherical harmonic e xpansions and finite differences in the vertical so that a matrix inve rsion is required for each wavenumber. Rather than any universal singl e-correction technique, this four-step process proves to be necessary to produce reasonable results. Even if the corrections noted here are not implemented, the diagnostic results serve as a warning to users of the analyses of potential substantial problems for certain applicatio ns. The results also indicate how operational centers could desirably alter their postprocessing procedures to ensure that the velocity fiel d archived on constant pressure surfaces in below-ground regions satis fies the constraint of conservation of mass.