| Numerical models and observations contain critical information regarding the earth-atmosphere system: they present a means of quantifying the system dynamics and provide evidence of the true system state, respectively. These two sources of information, however, are more valuable when combined into a single, dynamically consistent dataset. The objective of data assimilation in geosciences is to find an estimate of the model state that is statistically optimal, given all information known about the system, while preserving physical balances in the system dynamics. Another objective is to quantify the uncertainty in the resulting state estimate, which can be used for designing future observing networks, examining predictability limits, and initializing probabilistic model forecasts.;This dissertation provides an introduction to atmospheric data assimilation in the context of tropical cyclone modeling efforts at Penn State University using the Weather Research and Forecasting (WRF) model. The first chapter focuses on the role of forecast error covariance, and the necessity of using flow-dependent statistics from ensembles to initialize tropical cyclones with consistent inner-core structure. Chapter two presents an investigation on sampling errors in ensemble data assimilation systems, and discusses some of the major challenges for applying the Ensemble Kalman filter (EnKF) for mesoscale applications. An EnKF is applied in chapter three to explore the predictability and genesis of Hurricane Karl (2010), and study the impact of field observations in forecasting its track and intensity. The Hurricane Karl case study is revisited in chapter four to examine the impact of applying four-dimensional variational (4DVar) and hybrid ensemble- 4DVar (E4DVar) data assimilation methods for analyzing and forecasting genesis. The last chapter provides a more theoretical perspective on hybrid four-dimensional data assimilation. It compares the E4DVar approach used for the WRF model in chapter 4, with an alternative method that is being considered for operational use at several national forecast centers. This comparison is performed using a low-dimensional dynamical system to investigate several aspects of these methods in detail. |
