Computational Statistics in Climatology

Contents......Page 12
1.1 Gauss-Markov Theory......Page 18
1.2 Polynomial Approximations......Page 21
1.3 Variance of the Point Estimates......Page 30
1.4 The Fourier Set......Page 36
1.5 Examples......Page 38
1.6 Smoothing Digital Filters......Page 39
1.7 Regressive Filters......Page 43
1.8 Harmonic Filters......Page 54
1.9 Applications of Digital Filters......Page 55
1.10 Differentiating Filters......Page 59
1.11 Two-Dimensional Filters......Page 66
1.12 Multidimensional Filters......Page 73
2.1 Correlated Observations......Page 76
2.2 The Mean and the Linear Trend......Page 81
2.3 Nonoptimal Estimation......Page 90
2.4 Spatial Averaging......Page 94
2.5 Smoothing of Correlated Observations......Page 102
2.6 Filters of Finite Differences......Page 106
2.7 Regression and Instrumental Variable......Page 114
2.8 Nonlinear Processes......Page 122
3. RANDOM PROCESSES AND FIELDS......Page 125
3.1 Stationary Process......Page 126
3.2 Cross-Statistical Analysis......Page 132
3.3 Nonstationary Processes......Page 137
3.4 Nonergodic Stationary Process......Page 142
3.5 Time Series with Missing Data......Page 144
3.6 Two-Dimensional Fields......Page 146
3.7 Multidimensional Fields......Page 153
3.8 Examples of Climatological Fields......Page 162
3.9 Anisotropy of Climatological Fields......Page 175
4. VARIABILITY OF ARMA PROCESSES......Page 177
4.1 Fundamental ARMA Processes......Page 178
4.2 AR Processes......Page 180
4.3 AR(1) and AR(2) Processes......Page 182
4.4 Order of the AR Process......Page 189
4.5 MA(1) and MA(2) Processes......Page 194
4.6 ARMA(1,1) Process......Page 198
4.7 Comments......Page 201
4.8 Signal-Plus-White-Noise Type Processes......Page 205
4.9 Process with Stationary Increments......Page 213
4.10 Modeling the Five-Year Mean Surface Air Temperature......Page 216
4.11 Nonstationary and Nonlinear Models......Page 219
5.1 Fundamental Multivariate AR Processes......Page 223
5.2 Multivariate AR(1) Process......Page 227
5.3 Algorithm for Multivariate Model......Page 233
5.4 AR(2) Process......Page 238
5.5 Examples of Climate Models......Page 240
5.6 Climate System Identification......Page 249
6.1 Linear Trends......Page 254
6.2 Climate Trends over Russia......Page 260
6.3 Periodograms......Page 262
6.4 Spectral and Correlation Analysis......Page 266
6.5 Univariate Modeling......Page 274
6.6 Statistics and Climate Change......Page 278
7. THE GCM VALIDATION......Page 281
7.1 Objectives......Page 282
7.2 Data......Page 283
7.3 Zonal Time Series......Page 286
7.4 Multivariate Models......Page 294
7.5 The Diffusion Process......Page 300
7.6 Latitude-Temporal Fields......Page 306
7.7 Conclusion......Page 314
8. SECOND MOMENTS OF RAIN......Page 317
8.1 GATE Observations......Page 318
8.2 PRE-STORM Precipitation......Page 346
8.3 Final Remarks......Page 359
References......Page 363
D......Page 370
M......Page 371
S......Page 372
Y......Page 373