Statistical Methods in the Atmospheric Sciences : An Introduction.

By: Wilks, Daniel SContributor(s): Wilks, Daniel SMaterial type: TextTextSeries: International Geophysics SerPublisher: Burlington : Elsevier Science & Technology, 2005Copyright date: ©2006Edition: 2nd edDescription: 1 online resource (649 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9780080456225Subject(s): Atmospheric physics | Atmospheric physics - Statistical methods | Atmospheric physics--Statistical methods | Statistical methodsGenre/Form: Electronic books.Additional physical formats: Print version:: Statistical Methods in the Atmospheric Sciences : An IntroductionDDC classification: 551.6302 LOC classification: QC874.5.W55 2006Online resources: Click to View
Contents:
Front Cover -- Statistical Methods in the Atmospheric Sciences -- Copyright Page -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- PART I: Preliminaries -- CHAPTER 1. Introduction -- 1.1 What Is Statistics? -- 1.2 Descriptive and Inferential Statistics -- 1.3 Uncertainty about the Atmosphere -- CHAPTER 2. Review of Probability -- 2.1 Background -- 2.2 The Elements of Probability -- 2.3 The Meaning of Probability -- 2.4 Some Properties of Probability -- 2.5 Exercises -- PART II: Univariate Statistics -- CHAPTER 3. Empirical Distributions and Exploratory Data Analysis -- 3.1 Background -- 3.2 Numerical Summary Measures -- 3.3 Graphical Summary Techniques -- 3.4 Reexpression -- 3.5 Exploratory Techniques for Paired Data -- 3.6 Exploratory Techniques for Higher-Dimensional Data -- 3.7 Exercises -- CHAPTER 4. Parametric Probability Distributions -- 4.1 Background -- 4.2 Discrete Distributions -- 4.3 Statistical Expectations -- 4.4 Continuous Distributions -- 4.5 Qualitative Assessments of the Goodness of Fit -- 4.6 Parameter Fitting Using Maximum Likelihood -- 4.7 Statistical Simulation -- 4.8 Exercises -- CHAPTER 5. Hypothesis Testing -- 5.1 Background -- 5.2 Some Parametric Tests -- 5.3 Nonparametric Tests -- 5.4 Field Significance and Multiplicity -- 5.5 Exercises -- CHAPTER 6. Statistical Forecasting -- 6.1 Background -- 6.2 Linear Regression -- 6.3 Nonlinear Regression -- 6.4 Predictor Selection -- 6.5 Objective Forecasts Using Traditional Statistical Methods -- 6.6 Ensemble Forecasting -- 6.7 Subjective Probability Forecasts -- 6.8 Exercises -- CHAPTER 7. Forecast Verification -- 7.1 Background -- 7.2 Nonprobabilistic Forecasts of Discrete Predictands -- 7.3 Nonprobabilistic Forecasts of Continuous Predictands -- 7.4 Probability Forecasts of Discrete Predictands.
7.5 Probability Forecasts for Continuous Predictands -- 7.6 Nonprobabilistic Forecasts of Fields -- 7.7 Verification of Ensemble Forecasts -- 7.8 Verification Based on Economic Value -- 7.9 Sampling and Inference for Verification Statistics -- 7.10 Exercises -- CHAPTER 8. Time Series -- 8.1 Background -- 8.2 Time Domain-I. Discrete Data -- 8.3 Time Domain-II. Continuous Data -- 8.4 Frequency Domain-I. Harmonic Analysis -- 8.5 Frequency Domain-II. Spectral Analysis -- 8.6 Exercises -- PART III: Multivariate Statistics -- CHAPTER 9. Matrix Algebra and Random Matrices -- 9.1 Background to Multivariate Statistics -- 9.2 Multivariate Distance -- 9.3 Matrix Algebra Review -- 9.4 Random Vectors and Matrices -- 9.5 Exercises -- CHAPTER 10. The Multivariate Normal (MVN) Distribution -- 10.1 Definition of the MVN -- 10.2 Four Handy Properties of the MVN -- 10.3 Assessing Multinormality -- 10.4 Simulation from the Multivariate Normal Distribution -- 10.5 Inferences about a Multinormal Mean Vector -- 10.6 Exercises -- CHAPTER 11. Principal Component (EOF) Analysis -- 11.1 Basics of Principal Component Analysis -- 11.2 Application of PCA to Geophysical Fields -- 11.3 Truncation of the Principal Components -- 11.4 Sampling Properties of the Eigenvalues and Eigenvectors -- 11.5 Rotation of the Eigenvectors -- 11.6 Computational Considerations -- 11.7 Some Additional Uses of PCA -- 11.8 Exercises -- CHAPTER 12. Canonical Correlation Analysis (CCA) -- 12.1 Basics of CCA -- 12.2 CCA Applied to Fields -- 12.3 Computational Considerations -- 12.4 Maximum Covariance Analysis -- 12.5 Exercises -- CHAPTER 13. Discrimination and Classification -- 13.1 Discrimination vs. Classification -- 13.2 Separating Two Populations -- 13.3 Multiple Discriminant Analysis (MDA) -- 13.4 Forecasting with Discriminant Analysis -- 13.5 Alternatives to Classical Discriminant Analysis.
13.6 Exercises -- CHAPTER 14. Cluster Analysis -- 14.1 Background -- 14.2 Hierarchical Clustering -- 14.3 Nonhierarchical Clustering -- 14.4 Exercises -- APPENDIX A. Example Data Sets -- Table A.1. Daily precipitation and temperature data for Ithaca and Canandaigua, New York, for January 1987 -- Table A.2. January precipitation data for Ithaca, New York, 1933-1982 -- Table A.3. June climate data for Guayaquil, Ecuador, 1951-1970 -- APPENDIX B. Probability Tables -- Table B.1. Cumulative Probabilities for the Standard Gaussian Distribution -- Table B.2. Quantiles of the Standard Gamma Distribution -- Table B.3. Right-tail quantiles of the Chi-square distribution -- APPENDIX C. Answers to Exercises -- References -- Index.
Summary: Praise for the First Edition: "I recommend this book, without hesitation, as either a reference or course text...Wilks' excellent book provides a thorough base in applied statistical methods for atmospheric sciences."--BAMS (Bulletin of the American Meteorological Society) Fundamentally, statistics is concerned with managing data and making inferences and forecasts in the face of uncertainty. It should not be surprising, therefore, that statistical methods have a key role to play in the atmospheric sciences. It is the uncertainty in atmospheric behavior that continues to move research forward and drive innovations in atmospheric modeling and prediction. This revised and expanded text explains the latest statistical methods that are being used to describe, analyze, test and forecast atmospheric data. It features numerous worked examples, illustrations, equations, and exercises with separate solutions. Statistical Methods in the Atmospheric Sciences, Second Edition will help advanced students and professionals understand and communicate what their data sets have to say, and make sense of the scientific literature in meteorology, climatology, and related disciplines. * Presents and explains techniques used in atmospheric data summarization, analysis, testing, and forecasting * Features numerous worked examples and exercises * Covers Model Output Statistic (MOS) with an introduction to the Kalman filter, an approach that tolerates frequent model changes * Includes a detailed section on forecast verification New in this Edition: * Expanded treatment of resampling tests and coverage of key analysis techniques * Updated treatment of ensemble forecasting * Edits and revisions throughout the text plus updated references.
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Front Cover -- Statistical Methods in the Atmospheric Sciences -- Copyright Page -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- PART I: Preliminaries -- CHAPTER 1. Introduction -- 1.1 What Is Statistics? -- 1.2 Descriptive and Inferential Statistics -- 1.3 Uncertainty about the Atmosphere -- CHAPTER 2. Review of Probability -- 2.1 Background -- 2.2 The Elements of Probability -- 2.3 The Meaning of Probability -- 2.4 Some Properties of Probability -- 2.5 Exercises -- PART II: Univariate Statistics -- CHAPTER 3. Empirical Distributions and Exploratory Data Analysis -- 3.1 Background -- 3.2 Numerical Summary Measures -- 3.3 Graphical Summary Techniques -- 3.4 Reexpression -- 3.5 Exploratory Techniques for Paired Data -- 3.6 Exploratory Techniques for Higher-Dimensional Data -- 3.7 Exercises -- CHAPTER 4. Parametric Probability Distributions -- 4.1 Background -- 4.2 Discrete Distributions -- 4.3 Statistical Expectations -- 4.4 Continuous Distributions -- 4.5 Qualitative Assessments of the Goodness of Fit -- 4.6 Parameter Fitting Using Maximum Likelihood -- 4.7 Statistical Simulation -- 4.8 Exercises -- CHAPTER 5. Hypothesis Testing -- 5.1 Background -- 5.2 Some Parametric Tests -- 5.3 Nonparametric Tests -- 5.4 Field Significance and Multiplicity -- 5.5 Exercises -- CHAPTER 6. Statistical Forecasting -- 6.1 Background -- 6.2 Linear Regression -- 6.3 Nonlinear Regression -- 6.4 Predictor Selection -- 6.5 Objective Forecasts Using Traditional Statistical Methods -- 6.6 Ensemble Forecasting -- 6.7 Subjective Probability Forecasts -- 6.8 Exercises -- CHAPTER 7. Forecast Verification -- 7.1 Background -- 7.2 Nonprobabilistic Forecasts of Discrete Predictands -- 7.3 Nonprobabilistic Forecasts of Continuous Predictands -- 7.4 Probability Forecasts of Discrete Predictands.

7.5 Probability Forecasts for Continuous Predictands -- 7.6 Nonprobabilistic Forecasts of Fields -- 7.7 Verification of Ensemble Forecasts -- 7.8 Verification Based on Economic Value -- 7.9 Sampling and Inference for Verification Statistics -- 7.10 Exercises -- CHAPTER 8. Time Series -- 8.1 Background -- 8.2 Time Domain-I. Discrete Data -- 8.3 Time Domain-II. Continuous Data -- 8.4 Frequency Domain-I. Harmonic Analysis -- 8.5 Frequency Domain-II. Spectral Analysis -- 8.6 Exercises -- PART III: Multivariate Statistics -- CHAPTER 9. Matrix Algebra and Random Matrices -- 9.1 Background to Multivariate Statistics -- 9.2 Multivariate Distance -- 9.3 Matrix Algebra Review -- 9.4 Random Vectors and Matrices -- 9.5 Exercises -- CHAPTER 10. The Multivariate Normal (MVN) Distribution -- 10.1 Definition of the MVN -- 10.2 Four Handy Properties of the MVN -- 10.3 Assessing Multinormality -- 10.4 Simulation from the Multivariate Normal Distribution -- 10.5 Inferences about a Multinormal Mean Vector -- 10.6 Exercises -- CHAPTER 11. Principal Component (EOF) Analysis -- 11.1 Basics of Principal Component Analysis -- 11.2 Application of PCA to Geophysical Fields -- 11.3 Truncation of the Principal Components -- 11.4 Sampling Properties of the Eigenvalues and Eigenvectors -- 11.5 Rotation of the Eigenvectors -- 11.6 Computational Considerations -- 11.7 Some Additional Uses of PCA -- 11.8 Exercises -- CHAPTER 12. Canonical Correlation Analysis (CCA) -- 12.1 Basics of CCA -- 12.2 CCA Applied to Fields -- 12.3 Computational Considerations -- 12.4 Maximum Covariance Analysis -- 12.5 Exercises -- CHAPTER 13. Discrimination and Classification -- 13.1 Discrimination vs. Classification -- 13.2 Separating Two Populations -- 13.3 Multiple Discriminant Analysis (MDA) -- 13.4 Forecasting with Discriminant Analysis -- 13.5 Alternatives to Classical Discriminant Analysis.

13.6 Exercises -- CHAPTER 14. Cluster Analysis -- 14.1 Background -- 14.2 Hierarchical Clustering -- 14.3 Nonhierarchical Clustering -- 14.4 Exercises -- APPENDIX A. Example Data Sets -- Table A.1. Daily precipitation and temperature data for Ithaca and Canandaigua, New York, for January 1987 -- Table A.2. January precipitation data for Ithaca, New York, 1933-1982 -- Table A.3. June climate data for Guayaquil, Ecuador, 1951-1970 -- APPENDIX B. Probability Tables -- Table B.1. Cumulative Probabilities for the Standard Gaussian Distribution -- Table B.2. Quantiles of the Standard Gamma Distribution -- Table B.3. Right-tail quantiles of the Chi-square distribution -- APPENDIX C. Answers to Exercises -- References -- Index.

Praise for the First Edition: "I recommend this book, without hesitation, as either a reference or course text...Wilks' excellent book provides a thorough base in applied statistical methods for atmospheric sciences."--BAMS (Bulletin of the American Meteorological Society) Fundamentally, statistics is concerned with managing data and making inferences and forecasts in the face of uncertainty. It should not be surprising, therefore, that statistical methods have a key role to play in the atmospheric sciences. It is the uncertainty in atmospheric behavior that continues to move research forward and drive innovations in atmospheric modeling and prediction. This revised and expanded text explains the latest statistical methods that are being used to describe, analyze, test and forecast atmospheric data. It features numerous worked examples, illustrations, equations, and exercises with separate solutions. Statistical Methods in the Atmospheric Sciences, Second Edition will help advanced students and professionals understand and communicate what their data sets have to say, and make sense of the scientific literature in meteorology, climatology, and related disciplines. * Presents and explains techniques used in atmospheric data summarization, analysis, testing, and forecasting * Features numerous worked examples and exercises * Covers Model Output Statistic (MOS) with an introduction to the Kalman filter, an approach that tolerates frequent model changes * Includes a detailed section on forecast verification New in this Edition: * Expanded treatment of resampling tests and coverage of key analysis techniques * Updated treatment of ensemble forecasting * Edits and revisions throughout the text plus updated references.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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