An intermediate‐complexity model for four‐dimensional variational data assimilation including moist processes

This article presents a new Moist Atmosphere Dynamics Data Assimilation Model (MADDAM), an intermediate‐complexity system for four‐dimensional variational (4D‐Var) data assimilation. The prognostic model equations simulate nonlinear moisture advection, precipitation, and the impact of condensational heating on circulation. The 4D‐Var assimilation applies the incremental approach and uses transformed relative humidity as a control variable. In contrast to the model dynamical variables, which are analyzed in multivariate fashion using equatorial wave theory, moisture data are assimilated univariately. MADDAM is applied to study the extraction of wind information from time series of moisture observations in the Tropics, where the lack of wind information is most critical. Results show that wind tracing in the unsaturated atmosphere depends largely on the ability of the assimilation model to resolve spatial gradients in the moisture field, which is determined by the spatial density and accuracy of observations. In the saturated atmosphere, a combined assimilation of moisture and temperature data is shown to improve wind analyses significantly, as the intensity of the condensation process is susceptible to the slightest changes in saturation humidity and thus temperature. Moreover, a perfect‐model 4D‐Var with moisture observations can extract wind information even in precipitating regions and strongly nonlinear flow, provided sufficient observations of humidity gradients are available. MADDAM is envisaged to serve as a testbed for new developments in 4D‐Var assimilation, with a focus on interactions between moist processes and dynamics across many scales.