Preparing for GPM: Inclusion of linearized moist physics in NASA's Data Assimilation Tools
Part of the reason that assimilating observations of clouds can be difficult is because it challenges many of the assumptions that assimilation algorithms are based on. For example that covariance structures are homogeneous and that model error growth through the assimilation window is small. When dealing with clouds these assumptions can break down. The algorithms used in variational data assimilation, especially 4D-Var, rely on the linearized version of the forecast model. In 4D-Var the linear model is used to propagate model sensitivities between observation and analysis times. In 3D-Var, 4D-Var and most operational ensemble methods the adjoint of the observation operator, that translates between model and observation space, is required. For an all sky assimilation system it is essential that the moist processes in the atmosphere are represented in this linear model. Linearization of the schemes that are used to model convection and large scale condensation are required.
Linearizing these moist physics schemes can be rather challenging. Moist processes are inherently nonlinear, for example the sudden onset of convection or sudden re-evaporation of falling rain. As a result the nonlinear moist physics schemes tend to make use of numerous conditional statements. When linearizing the forecast model it is important to capture as much of the nonlinear perturbation trajectory as possible whilst not attempting to model anything that is too nonlinear. If functions are very steep or contain many discontinuities then the linear approximation will be a poor one. When linearizing moist physics a careful balance is required. Often there are parts of the nonlinear scheme that need to be smoothed in some way before a useful approximation is obtained.
A linearization of the convection and large scale cloud schemes has been developed and implemented in NASA's GEOS-5 data assimilation tools and in the Gridded Statistical Interpolation (GSI) data assimilation observation operator. The benefits of including detailed linearized moist physics is demonstrated by comparing with the nonlinear perturbation trajectory, through observation impact experiments, through sensitivity studies and through an improvement in the analysis produced by GSI.