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 ATS 675 - Atmpospheric Data Assimilation This course will overview concepts of objective analysis methods relevant to atmospheric science, atmospheric data assimilation, and remote-sensing based data assimilation procedures. In the process of presenting the above three areas, in depth discussions of numerical weather prediction (NWP), the governing atmospheric dynamic equation sets, and the characteristics of the data sources used within NWP models will be provided. The goal of the course is to provide students in graduate level atmospheric science a broad background into atmospheric data assimilation, while focusing on several exercises of assimilation techniques. This is done through projects as a means of providing students hands-on examples to build expertise. Homework assignments will involve use of Fortran, C/C++, Matlab, and IDL. It is highly desirable for students to have or gain skills in programming compiled languages, like C, C++, and Fortran. Course Syllabus: 1. Overview:   a) Course Description   b) "Big Picture" of Data Assimilation 2. Matrix Methods:   a) Review: Matricies & Linear Algebra   b) Adjoints 3. Statistical Analysis:   a) Statistics: Variance & Correlations   b) Least Squares-Regression   c) Interpolation 4. Atmospheric NWP Models:   a) Governing Equation; Scale Representation   b) History   c) Filtering & Descritization; Errors   d) Initialization 5. Methods of Objective Analysis:   a) Cressman & The Barnes' Scheme   b) Function Fitting 6. The Assimilation of Data:   a) Conventional Data   b) Satellite & Remote Sensing   c) Assimilation & Data Types; Data Quality Controls 7. Applied Methods in Data Assimilation:   a) Data Replacement; "Hot Start" Initialization   b) Empirical Methods: Successive Correction & Nudging   c) Background Errors; Covariances   d) Multivariate Statistics and Optimal Interpolation   e) Least Square Methods: Least Square & Variational Approaches   f) Adjoints & Tangent Linear Models   g) Kalman Filters; Ensemble Kalman Filters 8. Advanced Topics:   a) Chaotic Dynamical Systems   b) Predictability & Error Growth   c) Singular Vectors; Error Growths   d) Ensemble Forecasting