Fitting Microphysical Observations of Nonsteady Convective Clouds to a Numerical Model: An Application of the Adjoint Technique of Data Assimilation to a Kinematic Model

Rapid advances in the quality and quantity of atmospheric observations have placed a demand for the development of techniques to assimilate these data sources into numerical forecasting models. Four-dimensional variational assimilation is a promising technique that has been applied to atmospheric and oceanic dynamical models, and to the retrieval of three-dimensional wind fields from single-Doppler radar observations. This study investigates the feasibility of using space–time variational assimilation for a complex discontinuous numerical model including cloud physics. Two test models were developed: a one-dimensional and a two-dimensional liquid physics kinematic microphysical model. These models were used in identical-twin experiments, with observations taken intermittently. Small random errors were introduced into the observations. The retrieval runs were initialized with a large perturbation of the observation run initial conditions. The models were able to retrieve the original initial conditions to a satisfactory degree when observations of all the model prognostic variables were used. Greater overdetermination of the degrees of freedom (the initial condition being retrieved) resulted in greater improvement of the errors in the observations of the initial conditions but at a rapid increase in computational cost. Experiments where only some of the prognostic variables were observed also improved the initial conditions, but at a greater cost. To substantially improve the first guess of the field not observed, some spot observations are needed. The proper scaling of the variables was found to be important for the rate of convergence. This study suggests that scaling factors related to the error variance of the observations give good convergence rates. To show how this technique can be used when observations are general functions of the prognostic variables of the model (e.g., reflectivity or liquid water path), a form is derived that shows that this can be accomplished. This is considered to be an advantage of this technique over other assimilation techniques, since it is particularly suitable to remote-sensing systems where only integral parameters or derivatives of model prognostic variables are observed.