Fitting microphysical observations to a numerical model through an optimal control theory technique

March 26, 1992.Also issued as author's dissertation (Ph.D.) -- Colorado State University, 1992.Includes bibliographical references.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 also to the retrieval of three-dimensional wind fields from single Doppler radar observations. This study investigates the feasibility of using four-dimensional variational assimilation for a complex discontinuous numerical model. Three test models were developed, a positive definite advection scheme, a one-dimensional liquid physics kinematic microphysical model with a positive definite advection scheme, 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. All 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 observe also improved the initial conditions, but at a greater cost. To substantially improve tie 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 suggest 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 which shows that this can be accomplished. This is considered to be an advantage of this technique over others, since it is particularly suitable to remote sensing systems where only integral parameters or derivatives of model prognostic variables are observed.Sponsored by the South African Weather Bureau, Dept of Environment Affairs; the National Science Foundation ATM-8814913; and the Army Research Office DAAL03-86-K-017