Preface ........................................................ xi
Acronyms and abbreviations ................................... xiii
Principal symbols ........................................... xviii
1 Introduction ................................................. 1
2 The governing systems of equations ........................... 6
2.1 The basic equations ..................................... 6
2.2 Reynolds' equations: separating unresolved turbulence
effects ................................................. 7
2.3 Approximations to the equations ........................ 10
3 Numerical solutions to the equations ........................ 17
3.1 Overview of basic concepts ............................. 17
3.2 Numerical frameworks ................................... 23
3.3 Finite-difference methods .............................. 51
3.4 Effects of the numerical approximations ................ 58
3.5 Lateral-boundary conditions ............................ 96
3.6 Upper-boundary conditions ............................. 114
3.7 Conservation issues ................................... 116
3.8 Practical summary of the process for setting up
a model ............................................... 116
4 Physical-process parameterizations ......................... 119
4.1 Background ............................................ 119
4.2 Cloud microphysics parameterizations .................. 121
4.3 Convective parameterizations .......................... 129
4.4 Turbulence, or boundary-layer, parameterizations ...... 140
4.5 Radiation parameterizations ........................... 155
4.6 Stochastic parameterizations .......................... 166
4.7 Cloud-cover, or cloudiness, parameterizations ......... 166
5 Modeling surface processes ................................. 171
5.1 Background ............................................ 171
5.2 Land-surface processes that must be modeled ........... 172
5.3 Ocean or lake processes that must be modeled .......... 185
5.4 Modeling surface and subsurface processes over land ... 187
5.5 Modeling surface and subsurface processes over
water ................................................. 192
5.6 Orographic forcing .................................... 192
5.7 Urban-canopy modeling ................................. 194
5.8 Data sets for the specification of surface
properties ............................................ 196
6 Model initialization ....................................... 198
6.1 Background ............................................ 198
6.2 Observations used for model initialization ............ 199
6.3 Continuous versus intermittent data-assimilation
methods ............................................... 210
6.4 Model spinup .......................................... 215
6.5 The statistical framework for data assimilation ....... 216
6.6 Successive-correction methods ......................... 227
6.7 Statistical interpolation (optimal interpolation) ..... 230
6.8 Three-dimensional variational analysis ................ 231
6.9 Diabatic-initialization methods ....................... 233
6.10 Dynamical balance in the initial conditions ........... 236
6.11 Advanced data-assimilation methods .................... 242
6.12 Hybrid data-assimilation methods ...................... 248
6.13 Initialization with idealized conditions .............. 249
7 Ensemble methods ........................................... 252
7.1 Background ............................................ 252
7.2 The ensemble mean and ensemble dispersion ............. 254
7.3 Sources of uncertainty, and the definition of
ensemble members ...................................... 257
7.4 Interpretation and verification of ensemble
forecasts ............................................. 261
7.5 Calibration of ensembles .............................. 269
7.6 Time-lagged ensembles ................................. 271
7.7 Limited-area, short-range ensemble forecasting ........ 272
7.8 Graphically displaying ensemble-model products ........ 273
7.9 Economic benefits of ensemble predictions ............. 280
8 Predictability ............................................. 284
8.1 Background ............................................ 284
8.2 Model error and initial-condition error ............... 284
8.3 Land-surface forcing's impact on predictability ....... 287
8.4 Causes of predictability variations ................... 288
8.5 Special predictability considerations for limited-
area and mesoscale models ............................. 290
8.6 Predictability and model improvements ................. 292
8.7 The impact of post processing on predictability ....... 293
9 Verification methods ....................................... 294
9.1 Background ............................................ 294
9.2 Some standard metrics used for model verification ..... 295
9.3 More about reference forecasts and their use .......... 299
9.4 Truth data sets: observations versus analyses of
observations .......................................... 300
9.5 Special considerations ................................ 301
9.6 Verification in terms of probability distribution
functions ............................................. 306
9.7 Verification stratified by weather regime, time of
day, and season ....................................... 307
9.8 Feature-based, event-based, or object-based
verification .......................................... 309
9.9 Verification in terms of the scales of atmospheric
features .............................................. 312
9.10 The use of reforecasts for model verification ......... 317
9.11 Forecast-value-based verification ..................... 317
9.12 Choosing appropriate verification metrics ............. 317
9.13 Model-verification toolkits ........................... 318
9.14 Observations for model verification ................... 318
10 Experimental design in model-based research ................ 321
10.1 Case studies for physical-process analysis ............ 321
10.2 Observing-system simulation experiments ............... 323
10.3 Observing-system experiments .......................... 328
10.4 Big-Brother-Little-Brother experiments ................ 329
10.5 Reforecasts ........................................... 330
10.6 Sensitivity studies ................................... 331
10.7 Predictive-skill studies .............................. 338
10.8 Simulations with synthetic initial conditions ......... 339
10.9 The use of reduced-dimension and reduced-physics
models ................................................ 339
10.10 Sources of meteorological observational data ......... 340
11 Techniques for analyzing model output ...................... 343
11.1 Background ............................................ 343
11.2 Graphical methods for displaying and interpreting
model output and observations ......................... 343
11.3 Mathematical methods for analysis of the structure
of model variable fields .............................. 352
11.4 Calculation of derived variables ...................... 356
11.5 Analysis of energetics ................................ 356
12 Operational numerical weather prediction ................... 358
12.1 Background ............................................ 358
12.2 Model reliability ..................................... 360
12.3 Considerations for operationallimited-area models ..... 361
12.4 Computational speed ................................... 361
12.5 Postprocessing ........................................ 362
12.6 Real-time verification ................................ 363
12.7 Managing model upgrades and developments .............. 363
12.8 The relative role of models and forecasters in the
forecasting process ................................... 364
13 Statistical post processing of model output ................ 366
13.1 Background ............................................ 366
13.2 Systematic-error removal .............................. 367
13.3 Weather generators .................................... 375
13.4 Downscaling methods ................................... 376
14 Coupled special-applications models ........................ 378
14.1 Background ............................................ 378
14.2 Wave height ........................................... 381
14.3 Infectious diseases ................................... 382
14.4 River discharge, and floods ........................... 386
14.5 Transport, diffusion, and chemical transformations
of gases and particles ................................ 389
14.6 Transportation safety and efficiency .................. 393
14.7 Electromagnetic-wave and sound-wave propagation ....... 394
14.8 Wildland-fire probability and behavior ................ 396
14.9 The energy industry ................................... 396
14.10 Agriculture .......................................... 399
14.11 Military applications ................................ 399
15 Computational fluid-dynamics models ........................ 401
15.1 Background ............................................ 401
15.2 Types of CFD models ................................... 401
15.3 Scale distinctions between mesoscale models and LES
models ................................................ 402
15.4 Coupling CFD models and mesoscale models .............. 403
15.5 Examples of CFD-model applications .................... 405
15.6 Algorithmic approximations to CFD models .............. 405
16 Climate modeling and downscaling ........................... 407
16.1 Global climate prediction ............................. 408
16.2 Reanalyses of the current global climate .............. 431
16.3 Climate downscaling ................................... 432
16.4 Modeling the climate impacts of anthropogenic
landscape changes ..................................... 451
Appendix Suggested code structure and experiments for
a simple shallow-fluid model ............................... 456
References .................................................... 461
Index ......................................................... 523
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