Influence of assimilating rainfall derived from WSR-88D radar on the rainstorm forecasts over the southwestern United States

In this study, the impact of rainfall assimilation on the forecasts of convective rainfall over the mountainous areas in the southwestern United States is investigated. The rainfall is derived from the U.S. Weather Surveillance Radar-1988 Doppler (WSR-88D) radar network, and the fifth-generation Mesoscale Model (MM5) Four-Dimensional Variational (4DVAR) system is employed in the study. We evaluate the rainfall assimilation skill through two rainstorm events (5-6 August and 11-12 September 2002) that occurred over the southwestern United States in 2002. A series of experiments for the two cases is conducted. The results show that the minimization process in the 4DVAR is sensitive to the length of assimilation window and error variance in the observation data. Assimilation of rainfall can produce a better short-range precipitation forecast. However, the time range of improved forecasts is limited to about 15 hours with the model resolution of 20 km. It is indicated that rainfall assimilation produces more realistic moisture divergence and temperature fields in the initial conditions for the two cases. Therefore the forecast of rainstorms is closer to observations in both quantity and pattern. Copyright 2006 by the American Geophysical Union

A Variational Assimilation Method for Satellite and Conventional Data: Development of Basic Model for Diagnosis of Cyclone Systems

A summary is presented of the progress toward the completion of a comprehensive diagnostic objective analysis system based upon the calculus of variations. The approach was to first develop the objective analysis subject to the constraints that the final product satisfies the five basic primitive equations for a dry inviscid atmosphere: the two nonlinear horizontal momentum equations, the continuity equation, the hydrostatic equation, and the thermodynamic equation. Then, having derived the basic model, there would be added to it the equations for moist atmospheric processes and the radiative transfer equation

AN EVALUATION OF HYBRID VARIATIONAL-ENSEMBLE DATA ASSIMILATION FOR THE NCEP GFS

Several variants of hybrid data assimilation algorithms have been developed and tested within recent years, particularly for numerical weather prediction (NWP). The hybrid algorithms are designed to combine the strengths of variational and ensemble-based techniques while at the same time attempting to mitigate their weaknesses. One such variational-based algorithm is under development for use with the National Centers for Environmental Prediction's (NCEP) global forecast system (GFS) model. In this work, we attempt to better understand the impact of utilizing a hybrid scheme on the quality of analyses and subsequent forecasts, as well as explore alternative extensions to make better use of the ensemble information within the variational solver. A series of Observing System Simulation Experiments (OSSEs) are carried out. It is demonstrated that analysis and subsequent forecast errors are generally reduced in a 3D-hybrid scheme relative to 3DVAR. Several variational-based 4D extensions are proposed and tested, including the use of a variety of dynamic constraints. A simple approach for hybridizing the 4D-ensemble with a time-invariant contribution is proposed and tested. The 4D variants are shown to be superior to the 3D-hybrid, with positive contributions from static B as well as the dynamic constraint formulations. It is clear from both the 3D and 4D experiments that more sophisticated methods for dealing with inflation and localization in the ensemble update are needed even within the hybrid paradigm. Lastly, a method for applying piecewise scale-dependent weights is proposed and successfully tested. The 3D OSSE-based results are also compared with results from an experiment using real observations to corroborate the findings. It is found that in general, most of the results are comparable, though the positive impact in the real system is more consistent and impressive

Doctor of Philosophy

dissertationA computationally efficient variational analysis system for two-dimensional meteorological fields is developed and described. This analysis approach is most efficient when the number of analysis grid points is much larger than the number of available observations, such as for large domain mesoscale analyses. The analysis system is developed using MATLAB software and can take advantage of multiple processors or processor cores. A version of the analysis system has been exported as a platform independent application (i.e., can be run on Windows, Linux, or Macintosh OS X desktop computers without a MATLAB license) with input/output operations handled by commonly available internet software combined with data archives at the University of Utah. The impact of observation networks on the meteorological analyses is assessed by utilizing a percentile ranking of individual observation sensitivity and impact, which is computed by using the adjoint of the variational surface assimilation system. This methodology is demonstrated using a case study of the analysis from 1400 UTC 27 October 2010 over the entire contiguous United States domain. The sensitivity of this approach to the dependence of the background error covariance on observation density is examined. Observation sensitivity and impact provide insight on the influence of observations from heterogeneous observing networks as well as serve as objective metrics for quality control procedures that may help to identify stations with significant siting, reporting, or representativeness issues

Accounting for model error in strong-constraint 4DVar data assimilation

The strong constraint formulation of four-dimensional variational data assimilation (4DVar) assumes that the model used in the process perfectly describes the true dynamics of the system. However, this assumption often does not hold and the use of an erroneous model in strong constraint 4DVar can lead to a sub-optimal estimation of the initial conditions. We show how the presence of model error can be correctly accounted for in strong constraint 4D-Var by allowing for errors in both the observations and the model when considering the statistics of the innovation vector. We demonstrate that when these combined model error and observation error statistics are used in place of the standard observation error statistics in the strong constraint formulation of 4DVar, a statistically more accurate estimate of the initial state is obtained. The calculation of the combined model error and observation error statistics requires the specification of model error covariances, which in practice are often unknown. We present a method to estimate the combined statistics from innovation data that does not require explicit specification of the model error covariances. Numerical experiments using the linear advection equation and a simple nonlinear coupled model demonstrate the success of the new methods in reducing the error in the estimate of the initial state, even in the case when only the uncorrelated part of the model error is accounted for

Data Assimilation Fundamentals

This open-access textbook's significant contribution is the unified derivation of data-assimilation techniques from a common fundamental and optimal starting point, namely Bayes' theorem. Unique for this book is the "top-down" derivation of the assimilation methods. It starts from Bayes theorem and gradually introduces the assumptions and approximations needed to arrive at today's popular data-assimilation methods. This strategy is the opposite of most textbooks and reviews on data assimilation that typically take a bottom-up approach to derive a particular assimilation method. E.g., the derivation of the Kalman Filter from control theory and the derivation of the ensemble Kalman Filter as a low-rank approximation of the standard Kalman Filter. The bottom-up approach derives the assimilation methods from different mathematical principles, making it difficult to compare them. Thus, it is unclear which assumptions are made to derive an assimilation method and sometimes even which problem it aspires to solve. The book's top-down approach allows categorizing data-assimilation methods based on the approximations used. This approach enables the user to choose the most suitable method for a particular problem or application. Have you ever wondered about the difference between the ensemble 4DVar and the "ensemble randomized likelihood" (EnRML) methods? Do you know the differences between the ensemble smoother and the ensemble-Kalman smoother? Would you like to understand how a particle flow is related to a particle filter? In this book, we will provide clear answers to several such questions. The book provides the basis for an advanced course in data assimilation. It focuses on the unified derivation of the methods and illustrates their properties on multiple examples. It is suitable for graduate students, post-docs, scientists, and practitioners working in data assimilation

Joint state and parameter estimation with an iterative ensemble Kalman smoother

International audienceBoth ensemble filtering and variational data assimilation methods have proven useful in the joint estimation of state variables and parameters of geophysical models. Yet, their respective benefits and drawbacks in this task are distinct. An ensemble variational method, known as the iterative ensemble Kalman smoother (IEnKS) has recently been introduced. It is based on an adjoint model-free variational, but flow-dependent, scheme. As such, the IEnKS is a candidate tool for joint state and parameter estimation that may inherit the benefits from both the ensemble filtering and variational approaches. In this study, an augmented state IEnKS is tested on its estimation of the forcing parameter of the Lorenz-95 model. Since joint state and parameter estimation is especially useful in applications where the forcings are uncertain but nevertheless determining, typically in atmospheric chemistry, the augmented state IEnKS is tested on a new low-order model that takes its meteorological part from the Lorenz-95 model, and its chemical part from the advection diffusion of a tracer. In these experiments, the IEnKS is compared to the ensemble Kalman filter, the ensemble Kalman smoother, and a 4D-Var, which are considered the methods of choice to solve these joint estimation problems. In this low-order model context, the IEnKS is shown to significantly outperform the other methods regardless of the length of the data assimilation win- dow, and for present time analysis as well as retrospective analysis. Besides which, the performance of the IEnKS is even more striking on parameter estimation; getting close to the same performance with 4D-Var is likely to require both a long data assimilation window and a complex modeling of the background statistics