A simple column model to explore anticipated problems in variational assimilation of satellite observations

We investigate a simplified form of variational data assimilation in a fully nonlinear framework with the aim of extracting dynamical development information from a sequence of observations over time. Information on the vertical wind profile, w(z), and profiles of temperature, T(z, t), and total water content, qt(z, t), as functions of height, z, and time, t, are converted to brightness temperatures at a single horizontal location by defining a two-dimensional (vertical and time) variational assimilation testbed. The profiles of T and qt are updated using a vertical advection scheme. A basic cloud scheme is used to obtain the fractional cloud amount and, when combined with the temperature field, this information is converted into a brightness temperature, using a simple radiative transfer scheme. It is shown that our model exhibits realistic behaviour with regard to the prediction of cloud, but the effects of nonlinearity become non-negligible in the variational data assimilation algorithm. A careful analysis of the application of the data assimilation scheme to this nonlinear problem is presented, the salient difficulties are highlighted, and suggestions for further developments are discussed