Can Gradient Information Be Used to Improve Variational Objective Analysis?

Abstract

A variational scheme for the analysis of scalar variables is developed and compared to two-pass and three-pass versions of the Barnes analysis scheme. The variational scheme, appropriate for diagnostic studies, is similar to a previously developed variational method in that scalar gradient ?observations??derived directly from the scalar observations?are used in addition to the scalar observations themselves. The current scheme is different in that the cost function does not require analyses of the scalar field and its gradient; it simply requires scalar and gradient observations at their native locations. For the evaluation, randomly selected model gridpoint data are chosen to serve as pseudo-observations for the analysis schemes. By choosing appropriate model gridpoint data to serve as pseudo-observations, artificial data networks can be generated so as to mimic the spatial characteristics of real observational networks. Results indicate that the proposed variational scheme is superior to both two-pass and three-pass Barnes schemes, increasingly so as the observations become more irregularly spaced. This is true even when the gradient information is not allowed to affect the variational analyses. When the observations are relatively sparse and irregularly distributed, further improvements in the variational analyses occur when the gradient information is properly included within the analysis scheme.