Statistical Methods in the Atmospheric Sciences, Fifth Edition provides a structured exploration of the statistical techniques essential for analyzing atmospheric data. The book begins with foundational concepts in probability, setting the stage for more advanced topics. It then covers univariate statistics, including empirical distributions, parametric probability models, and both frequentist and Bayesian inference methods, offering tools for rigorous data analysis and interpretation. The text also addresses statistical forecasting and ensemble forecasting, along with methods for verifying forecast accuracy. In addition, time series analysis is explored in detail, enabling readers to understand temporal dependencies in atmospheric data.
The book advances into multivariate statistics, presenting matrix algebra and random matrices as mathematical foundations. It discusses the multivariate normal distribution, principal component analysis (EOF), and multivariate analysis of vector pairs to handle complex, multidimensional atmospheric datasets. Techniques for discrimination, classification, and cluster analysis are also examined, providing methods for categorizing and interpreting atmospheric patterns. Supplementary materials include example data sets, probability tables, and a glossary of symbols and acronyms, along with answers to exercises that reinforce learning.
1. Chapter 1. Introduction - p. 3 2. Chapter 2. Review of Probability - p. 7 3. Part II. Univariate Statistics - p. P2 4. Chapter 3. Empirical Distributions and Exploratory Data Analysis - p. 23 5. Chapter 4. Parametric Probability Distributions - p. 73 6. 4.1 Background - p. 73 7. 4.2 Discrete Distributions - p. 75 8. 4.3 Statistical Expectations - p. 85 9. 4.4 Continuous Distributions - p. 88 10. 4.5 Qualitative Assessments of the Goodness of Fit - p. 118 11. 4.6 Parameter Fitting Using Maximum Likelihood - p. 120 12. 4.7 Statistical Simulation - p. 129 13. 4.8 Exercises - p. 136 14. Chapter 5. Frequentist Statistical Inference - p. 139 15. 5.1 Background - p. 139 16. 5.2 Some Commonly Encountered Parametric Tests - p. 148 17. 5.3 Nonparametric Tests - p. 166 18. 5.4 Multiplicity and “Field Significance” - p. 186 19. 5.5 Analysis of Variance (ANOVA) and Comparisons among Multiple Means - p. 190 20. 5.6 Exercises - p. 198 21. Chapter 6. Bayesian Inference - p. 201 22. Chapter 7. Statistical Forecasting - p. 229 23. 7.1 Background - p. 229 24. 7.2 Linear Regression - p. 230 25. 7.3 Multiple Linear Regression - p. 247 26. 7.4 Predictor Selection in Multiple Regression - p. 252 27. 7.5 Regularization (“Shrinkage”) Methods for Multiple Regression - p. 260 28. 7.6 Nonlinear Regression - p. 266 29. 7.7 Nonparametric Regression - p. 273 30. 7.8 “Machine-Learning” Methods - p. 278 31. 7.9 Objective Forecasts Using Statistical Methods - p. 290 32. 7.10 Subjective Probability Forecasts - p. 296 33. 7.11 Exercises - p. 302 34. Chapter 8. Ensemble Forecasting - p. 305 35. 8.1 Background - p. 305 36. 8.2 Ensemble Forecasts - p. 311 37. 8.3 Univariate Ensemble Postprocessing - p. 319 38. 8.4 Multivariate Ensemble Postprocessing - p. 341 39. 8.5 Graphical Display of Ensemble Forecast Information - p. 347 40. 8.6 Exercises - p. 354 41. Chapter 9. Forecast Verification - p. 355 42. 9.1 Background - p. 355 43. 9.2 Nonprobabilistic Forecasts for Discrete Predictands - p. 360 44. 9.3 Nonprobabilistic Forecasts for Continuous Predictands - p. 378 45. 9.4 Probability Forecasts for Discrete Predictands - p. 385 46. 9.5 Probability Distribution Forecasts for Continuous Predictands - p. 412 47. 9.6 Quantile Forecasts - p. 418 48. 9.7 Verification of Ensemble Forecasts - p. 420 49. 9.8 Nonprobabilistic Forecasts for Fields - p. 435 50. 9.9 Verification Based on Economic Value - p. 447 51. 9.10 Verification when the Observation Is Uncertain - p. 452 52. 9.11 Sampling and Inference for Verification Statistics - p. 454 53. 9.12 Exercises - p. 466 54. Chapter 10. Time Series - p. 471 55. 10.1 Background - p. 471 56. 10.2 Time Domain—I. Discrete Data - p. 473 57. 10.3 Time Domain—II. Continuous Data - p. 487 58. 10.4 Frequency Domain—I. Harmonic Analysis - p. 504 59. 10.5 Frequency Domain—II. Spectral Analysis - p. 514 60. 10.6 Time-Frequency Analyses - p. 533 61. 10.7 Exercises - p. 535 62. Part III. Multivariate Statistics - p. P3 63. Chapter 11. Matrix Algebra and Random Matrices - p. 541 64. 11.1 Background to Multivariate Statistics - p. 541 65. 11.2 Multivariate Distance - p. 544 66. 11.3 Matrix Algebra Review - p. 547 67. 11.4 Random Vectors and Matrices - p. 567 68. 11.5 Exercises - p. 574 69. Chapter 12. The Multivariate Normal Distribution - p. 577 70. 12.1 Definition of the MVN - p. 577 71. 12.2 Four Handy Properties of the MVN - p. 581 72. 12.3 Transforming To and Assessing Multinormality - p. 584 73. 12.4 Simulation from the Multivariate Normal Distribution - p. 587 74. 12.5 Inferences About a Multinormal Mean Vector - p. 592 75. 12.6 The Kalman Filter and Data Assimilation - p. 605 76. 12.7 Exercises - p. 611 77. Chapter 13. Principal Component (EOF) Analysis - p. 613 78. Chapter 14. Multivariate Analysis of Vector Pairs - p. 661 79. Chapter 15. Discrimination and Classification - p. 687 80. Chapter 16. Cluster Analysis - p. 711 81. Appendix A. Example Data Sets - p. 731 82. Appendix B. Probability Tables - p. 735 83. Appendix C. Symbols and Acronyms - p. 745 84. Appendix D. Answers to Exercises - p. 763 85. References - p. 773 86. Index - p. 796
Statistical Methods in the Atmospheric Sciences, Fifth Edition provides a structured exploration of the statistical techniques essential for analyzing atmospheric data. The book begins with foundational concepts in probability, setting the stage for more advanced topics. It then covers univariate statistics, including empirical distributions, parametric probability models, and both frequentist and Bayesian inference methods, offering tools for rigorous data analysis and interpretation. The text also addresses statistical forecasting and ensemble forecasting, along with methods for verifying forecast accuracy. In addition, time series analysis is explored in detail, enabling readers to understand temporal dependencies in atmospheric data.
The book advances into multivariate statistics, presenting matrix algebra and random matrices as mathematical foundations. It discusses the multivariate normal distribution, principal component analysis (EOF), and multivariate analysis of vector pairs to handle complex, multidimensional atmospheric datasets. Techniques for discrimination, classification, and cluster analysis are also examined, providing methods for categorizing and interpreting atmospheric patterns. Supplementary materials include example data sets, probability tables, and a glossary of symbols and acronyms, along with answers to exercises that reinforce learning.
1. Chapter 1. Introduction - p. 3 2. Chapter 2. Review of Probability - p. 7 3. Part II. Univariate Statistics - p. P2 4. Chapter 3. Empirical Distributions and Exploratory Data Analysis - p. 23 5. Chapter 4. Parametric Probability Distributions - p. 73 6. 4.1 Background - p. 73 7. 4.2 Discrete Distributions - p. 75 8. 4.3 Statistical Expectations - p. 85 9. 4.4 Continuous Distributions - p. 88 10. 4.5 Qualitative Assessments of the Goodness of Fit - p. 118 11. 4.6 Parameter Fitting Using Maximum Likelihood - p. 120 12. 4.7 Statistical Simulation - p. 129 13. 4.8 Exercises - p. 136 14. Chapter 5. Frequentist Statistical Inference - p. 139 15. 5.1 Background - p. 139 16. 5.2 Some Commonly Encountered Parametric Tests - p. 148 17. 5.3 Nonparametric Tests - p. 166 18. 5.4 Multiplicity and “Field Significance” - p. 186 19. 5.5 Analysis of Variance (ANOVA) and Comparisons among Multiple Means - p. 190 20. 5.6 Exercises - p. 198 21. Chapter 6. Bayesian Inference - p. 201 22. Chapter 7. Statistical Forecasting - p. 229 23. 7.1 Background - p. 229 24. 7.2 Linear Regression - p. 230 25. 7.3 Multiple Linear Regression - p. 247 26. 7.4 Predictor Selection in Multiple Regression - p. 252 27. 7.5 Regularization (“Shrinkage”) Methods for Multiple Regression - p. 260 28. 7.6 Nonlinear Regression - p. 266 29. 7.7 Nonparametric Regression - p. 273 30. 7.8 “Machine-Learning” Methods - p. 278 31. 7.9 Objective Forecasts Using Statistical Methods - p. 290 32. 7.10 Subjective Probability Forecasts - p. 296 33. 7.11 Exercises - p. 302 34. Chapter 8. Ensemble Forecasting - p. 305 35. 8.1 Background - p. 305 36. 8.2 Ensemble Forecasts - p. 311 37. 8.3 Univariate Ensemble Postprocessing - p. 319 38. 8.4 Multivariate Ensemble Postprocessing - p. 341 39. 8.5 Graphical Display of Ensemble Forecast Information - p. 347 40. 8.6 Exercises - p. 354 41. Chapter 9. Forecast Verification - p. 355 42. 9.1 Background - p. 355 43. 9.2 Nonprobabilistic Forecasts for Discrete Predictands - p. 360 44. 9.3 Nonprobabilistic Forecasts for Continuous Predictands - p. 378 45. 9.4 Probability Forecasts for Discrete Predictands - p. 385 46. 9.5 Probability Distribution Forecasts for Continuous Predictands - p. 412 47. 9.6 Quantile Forecasts - p. 418 48. 9.7 Verification of Ensemble Forecasts - p. 420 49. 9.8 Nonprobabilistic Forecasts for Fields - p. 435 50. 9.9 Verification Based on Economic Value - p. 447 51. 9.10 Verification when the Observation Is Uncertain - p. 452 52. 9.11 Sampling and Inference for Verification Statistics - p. 454 53. 9.12 Exercises - p. 466 54. Chapter 10. Time Series - p. 471 55. 10.1 Background - p. 471 56. 10.2 Time Domain—I. Discrete Data - p. 473 57. 10.3 Time Domain—II. Continuous Data - p. 487 58. 10.4 Frequency Domain—I. Harmonic Analysis - p. 504 59. 10.5 Frequency Domain—II. Spectral Analysis - p. 514 60. 10.6 Time-Frequency Analyses - p. 533 61. 10.7 Exercises - p. 535 62. Part III. Multivariate Statistics - p. P3 63. Chapter 11. Matrix Algebra and Random Matrices - p. 541 64. 11.1 Background to Multivariate Statistics - p. 541 65. 11.2 Multivariate Distance - p. 544 66. 11.3 Matrix Algebra Review - p. 547 67. 11.4 Random Vectors and Matrices - p. 567 68. 11.5 Exercises - p. 574 69. Chapter 12. The Multivariate Normal Distribution - p. 577 70. 12.1 Definition of the MVN - p. 577 71. 12.2 Four Handy Properties of the MVN - p. 581 72. 12.3 Transforming To and Assessing Multinormality - p. 584 73. 12.4 Simulation from the Multivariate Normal Distribution - p. 587 74. 12.5 Inferences About a Multinormal Mean Vector - p. 592 75. 12.6 The Kalman Filter and Data Assimilation - p. 605 76. 12.7 Exercises - p. 611 77. Chapter 13. Principal Component (EOF) Analysis - p. 613 78. Chapter 14. Multivariate Analysis of Vector Pairs - p. 661 79. Chapter 15. Discrimination and Classification - p. 687 80. Chapter 16. Cluster Analysis - p. 711 81. Appendix A. Example Data Sets - p. 731 82. Appendix B. Probability Tables - p. 735 83. Appendix C. Symbols and Acronyms - p. 745 84. Appendix D. Answers to Exercises - p. 763 85. References - p. 773 86. Index - p. 796
