1 Mathematical Background and Methods of Ocean Modelling ....... 1
1.1 Classical Problems of Marine Dynamics: Equations,
Initial and Boundary Conditions ......................... 2
1.1.1 Equations, Initial and Boundary Conditions of
Ocean and Sea General Circulation ................ 2
1.1.2 Some Comments on the Boundary Conditions ......... 5
1.1.3 Some Comments on the Initial Conditions .......... 6
1.1.4 Total Energy Conservation ........................ 6
1.1.5 Parameterization of Subscale Physical
Processes ........................................ 7
1.2 Solvability of Ocean/Sea Dynamics Problems .............. 8
1.2.1 Linear Model of Small Oscillations in the Ocean
with Stable Stratification ....................... 8
1.2.2 Linear Stationary Model of Ocean Dynamics With
Turbulent Exchange Parameterization .............. 9
1.2.3 Prognostic Nonlinear Problem of Ocean General
Circulation ..................................... 10
1.2.4 Prognostic Nonlinear Problem of Ocean General
Circulation With Parameterization of Deep
Convection ...................................... 11
1.3 Alternative and Generalized Models of the General
Circulation in Oceans and Shelf Seas ................... 12
1.3.1 Model Based on the Nonlinear Shallow-Water
Equations ....................................... 12
1.3.2 Ocean General Circulation Model in the σ -
Coordinate System ............................... 13
1.3.3 Generalized Model of Sea Dynamics With a Free
Surface in the σ-Coordinate System .............. 15
1.4 Numerical Methods ...................................... 16
1.4.1 The Choice of a Differential Formulation of
the Problem ..................................... 17
1.4.2 Methods of Spatial Approximation ................ 18
1.4.3 Methods for Discrete Time Integration ........... 20
1.4.4 The Method of Weak Approximation (Splitting of
the Differential Problem) ....................... 21
1.5 Forward and Adjoint Models ............................. 22
1.5.1 Data Assimilation Problem ....................... 22
1.5.2 Initialization Problem .......................... 24
1.6 Advances and Trends in Mathematical Modelling of
Marine and Oceanic Currents ................................. 26
References .................................................. 27
2 Simple Linear Models for Diagnostic Calculation of Ocean
Climate Characteristics ..................................... 31
2.1 Basic Equations ........................................ 31
2.2 Simple Diagnostic Models for Ocean Characteristics
Calculation ............................................ 32
2.2.1 Geostrophic Flow ................................ 32
2.2.2 Simple Linear Model for Diagnostic Calculation
in the Ocean Equatorial Region (The Model D1) ... 34
2.2.3 Simple Linear Model for Diagnostic
Calculations in the Ocean Extraequatorial
Regions (The Model D1') ......................... 40
2.2.4 Final Formulation, Comparison and Qualitative
Analysis of Models D1 and D1' ................... 47
2.2.5 Simple Linear Model for Diagnostic
Calculations by Using Mass Transport Stream
Function (The Model D1'') ....................... 51
2.3 Are The Sverdrup Relation and the Dynamic (Reference-
Level) Method Still Up-To-Date? ........................ 53
2.3.1 Westward, Equatorward, Coastward and Other
Kinds of Intensifications in Baroclinic Basins
with Variable Depth ............................. 53
2.3.2 Contradiction Between the Dynamic (Reference
Level) Method and the Sverdrup Relation ......... 56
2.3.3 A Short Note on the Ocean Modelling First
Steps ........................................... 60
2.3.4 Brief List of the Main Results of Diagnostic
Calculations .................................... 63
References .................................................. 55
3 Nonlinear Models for Diagnostic, Prognostic and Adjustment
Calculations of Ocean Climate Characteristics ............... 67
3.1 Nonlinear Models Based on Sea Surface Height
Calculations ........................................... 67
3.1.1 The Equation of Vorticity ....................... 67
3.1.2 The Divergence Equation ......................... 70
3.2 Nonlinear Extraequatorial Model Based on the Mass
Transport Stream Function Calculation .................. 71
3.3 Quasianalytical Version of One Nonlinear Model ......... 76
3.4 Comments on Different Approaches and Different
Integral Equations Used in Ocean Modelling ............. 80
3.5 A Brief Analysis of Prognostic Calculations ............ 85
3.6 On the Intercalibration of Models ...................... 95
References .................................................. 99
4 Synthesis of Models and Observed Data ...................... 103
4.1 Energetics of Ocean's Hydrophysical Characteristics
Mutual Adjusting Processes ............................ 103
4.1.1 Introduction ................................... 103
4.1.2 Characteristics of the Model and Numerical
Experiments .................................... 104
4.1.3 Results of Adjustment Calculation .............. 110
4.2 Ocean Modelling Experiments by General Adjustment
(OMEGA) ............................................... 116
4.3 Hydrodynamic Method for WOCE Data Processing and
Assimilation .......................................... 118
4.3.1 Synthesis of Model and Observation Data ........ 118
4.3.2 Results of Experiments ......................... 119
4.3.3 Computation Results ............................ 120
4.3.4 Discussion and Conclusions ..................... 124
4.4 Four-Dimensional Analysis of Hydrophysical Ocean and
Sea Fields ............................................ 127
4.4.1 Introduction ................................... 127
4.4.2 Differential Equations and the Kaiman Filter ... 128
4.4.3 Synchronization and Monitoring of
Hydrophysical Fields in the Newfoundland
Energy Active Zone ............................. 132
4.4.4 Numerical Experiments on the Estimation
Accuracy of the Four-Dimensional Analysis
Procedure ...................................... 135
4.4.5 Four-Dimensional Analysis of Hydrophysical
Fields in the Tropical Atlantic ................ 140
4.4.6 Algorithm for Altimeter Data Assimilation:
Numerical Experiments and Some
Reconstructions of Hydrophysical Fields in the
Black Sea from TOPEX/POSEIDON Altimetry ........ 143
References ................................................. l49
5 Modelling of Climate Variability in Selected Ocean
Basins ..................................................... 153
5.1 Numerical Simulation of in the Arctic-North Atlantic
System ................................................ 153
5.1.1 Introduction ................................... 153
5.1.2 Sea-Ice Dynamics ............................... 155
5.1.3 Simulation of the Coupled Arctic Ocean-North
Atlantic Circulation System .................... 161
5.1.4 Numerical Simulation of Tracer Propagation ..... 163
5.1.5 Propagation of Fresh Water from Siberian
Rivers and Pacific Waters of the Bering
Straits ........................................ 164
5.1.6 Conclusions .................................... 169
5.1.7 Latest Results of Arctic Ocean Modelling and
Intercomparison Project (AOMIP) ................ 170
5.2 The Gulf Stream ....................................... 175
5.2.1 Modelling the Gulf Stream in the DYNAMO
Experiment ..................................... 175
5.2.2 Crossing the Rubicon in Modelling the North
Atlantic Dynamics .............................. 178
5.3 Pacific Ocean Circulation and Tracer Transport
Modelling ............................................. 186
5.3.1 Water Circulation Modelling .................... 186
5.3.2 Numerical Modelling of Tracer Spreading in
the North Pacific Ocean ........................ 194
5.4 The Indian Ocean ...................................... 201
5.4.1 The Indian Ocean Descriptive
Hydrometeorology ............................... 201
5.4.2 Indian Ocean Climate Variability Modelling ..... 208
References ................................................. 219
6 Modelling Climate Variability of Selected Shelf Seas ....... 225
6.1 The North Sea ......................................... 225
6.1.1 Introduction ................................... 225
6.1.2 Special Features of North Sea Modelling ........ 227
6.1.3 Example of a Realistic Simulation: The
Variable Heat Budget of the North Sea .......... 232
6.2 The White Sea ......................................... 234
6.2.1 Introduction ................................... 234
6.2.2 Y. Semenov's Model ............................. 235
6.2.3 The Results of Calculations .................... 241
6.3 The Caspian Sea ....................................... 245
6.3.1 Introduction ................................... 245
6.3.2 Model Description .............................. 250
6.3.3 External Forcing ............................... 255
6.3.4 Seasonal Variability of the Caspian Sea
Dynamics ....................................... 261
6.3.5 Sensitivity Experiments ........................ 275
6.3.6 Summary and Conclusions ........................ 279
6.4 The Black Sea ......................................... 280
6.4.1 The Black Sea Descriptive Hydrophysics ......... 280
6.4.2 Modelling the Variability of Black Sea
Physical Characteristics ....................... 291
6.4.3 Modelling the Seasonal Variability of Black
Sea Climatic Characteristics by Means of
Four-Dimensional Analysis ...................... 301
6.4.4 Data Assimilation by the Method of Double
Correction ..................................... 313
References ............................................ 332
Color Plate Section ........................................... 339
Index ......................................................... 371
|
