Adjoint of a parameterized moisture convection model

Adjoint models have found use as "dynamical tracers", helping to track a feature or phenomenon back to its origin. Their application to the study of atmospheric convection, however, is challenged by the complexity and nonlinearity of diabatic processes. Herein, the adjoint of a significantly simpler parameterized moisture (PM) model is described and tested. The PM model eliminates explicit moisture by making latent heating conditionally proportional to updraft velocity and providing a lower tropospheric heat sink mimicking rainwater evaporation. The PM adjoint, of course, is useful only if the parameterization can produce realistic results. Earlier work suggested that the PM framework possessed a fundamental flaw that made its storms have an excessive impact on their upstream environments. In fact, the adjoint was used to identify the origin of the discrepancies between PM and traditional cloud model storms, thereby leading to the parameterization improvements and dynamical insights recently discussed in Fovell (2002). The present paper is a companion to that study, describing how the adjoint model was constructed, tested and utilized. In addition, an even more realistic adjoint framework is described.