Abstract/Summary

Data assimilation is an inverse problem that seeks to optimally combine information from a set of observations with a first guess analysis to generate the best estimate of the current state of a dynamic system. It is an essential part of numerical weather prediction because the accuracy of a model forecast is closely tied to the accuracy of the initial conditions. Thus, the goal of this thesis is to enhance our ability to assimilate satellite brightness temperatures through development of bias correction (BC) methods to remove systematic errors from the observations and model background. In the first part of the thesis, we introduce an innovative BC method that uses a Taylor series polynomial expansion of the observation-minus-background (OMB) departures to remove linear and nonlinear conditional biases from all-sky satellite infrared brightness temperatures. Passive monitoring experiments reveal that variables sensitive to the cloud top height are the most effective BC predictors and that higher-order Taylor series terms are necessary to account for complex nonlinear biases in the OMB departures. Active data assimilation experiments using the nonlinear BC method show that the model background is most improved when higher-order cloud-sensitive predictors are employed. Following this work, we use the Lorenz-63 model to develop a model bias estimation method based on an asymptotic expansion of the model dynamics for small time scales and small perturbations in one of its parameters. The model bias estimators are subsequently used to improve the model background error covariance matrix used during the data assimilation step. It is shown that the combination of a static matrix with a dynamic matrix that varies with time leads to more accurate model analyses and forecasts. Together, results from this thesis demonstrate that bias predictors derived from polynomial expansions of modeled and observed variables can improve the performance of data assimilation systems.