Computer Modelling In Atmospheric And Oceanic Sciences

by Muller, Peter; Von Storch, Hans; Hasselmann, Klaus; Storch, H. V.

• ISBN13: 9783540203537
• ISBN10: 3540203532
• Format: Hardcover
• Copyright: 2004-07-16
• Publisher: Springer Verlag

Summary

This textbook is about quasi-realistic models in atmospheric and oceanic sciences. Understanding the basis and limitations of these models is important since far reaching decisions about the environment are based on these models. It is novel in that it goes beyond a technical discussion of these quasi-realistic models and emphasizes their role and utility in generating new useful knowledge about the system. The book is written in a generally understandable way, with technical details relegated to a set of comprehensive appendices. The line of reasoning is illustrated by numerous examples, from both applied and fundamental research. It is a source of information for graduate students and scientists alike working in the field of environmental sciences.

Author Biography

Hans von Storch is the Director of the Institute of Coastal Research at the GKSS Research Centre and professor at the Meteorological Department of the University of Hamburg.

Table of Contents

Foreword	v
Preface	vii
Acknowledgements	ix
1 Introduction	1	(34)
1.1 Models	2	(2)
1.2 Environmental Systems	4	(2)
1.3 Tides	6	(9)
1.3.1 The Role of Tides Within Environmental Systems	6	(3)
1.3.2 Different Modeling Approaches	9	(6)
1.4 Climate	15	(9)
1.4.1 Historical Development	15	(5)
1.4.2 Quasi-realistic Climate Models	20	(1)
1.4.3 Societal Relevance of Climate	21	(3)
1.5 Quasi-realistic Computer Models	24	(2)
1.6 Applications	26	(4)
1.7 Issues	30	(5)
2 Computer Models	35	(20)
2.1 Dynamics	36	(6)
2.1.1 The Fundamental Laws	36	(1)
2.1.2 The Closure Problems	36	(4)
2.1.3 Parameterizations	40	(1)
2.1.4 Approximations and Representations	41	(1)
2.2 Numerics	42	(2)
2.3 Computers	44	(2)
2.4 Models as Dynamical Systems	46	(2)
2.5 Models as Stochastic Systems	48	(2)
2.6 Predictability	50	(5)
2.6.1 Limit of Predictability	51	(1)
2.6.2 Forecast of the First Kind	52	(1)
2.6.3 Forecast of the Second Kind	53	(2)
3 Models and Data	55	(14)
3.1 Validation	55	(7)
3.1.1 Validation as a Philosophical Problem	56	(1)
3.1.2 Some Common Approaches	57	(2)
3.1.3 Validation as a Statistical Problem	59	(3)
3.2 Data Assimilation	62	(2)
3.3 Calibration	64	(5)
4 The Dynamics of Tides and Climate	69	(22)
4.1 The Tidal System	70	(8)
4.1.1 The Nature of Tides	70	(1)
4.1.2 Laplace Tidal Equations	71	(2)
4.1.3 Tidal Loading and Self-attraction	73	(2)
4.1.4 The Tidal Inlet Problem	75	(3)
4.2 The Climate System	78	(13)
4.2.1 Components and Processes	78	(2)
4.2.2 Scales	80	(3)
4.2.3 The Primitive Equations	83	(2)
4.2.4 Fundamental Cognitive Models	85	(2)
4.2.5 Natural and Anthropogenic Climate Variability	87	(4)
5 Modeling in Applied Environmental Sciences - Forecasting, Analysis and Scenarios	91	(64)
5.1 Operational Forecasts	91	(26)
5.1.1 Forecast Versus Prediction	91	(2)
5.1.2 Tide and Storm Surge Forecasts	93	(1)
5.1.3 Weather Forecasts	94	(8)
5.1.4 El Niño Southern Oscillation Forecasts	102	(8)
5.1.5 The Skill of Forecasts	110	(4)
5.1.6 Post-processing Forecasts	114	(3)
5.2 Data Analysis	117	(27)
5.2.1 Global Reanalyses	118	(9)
5.2.2 Reconstruction of Regional Weather	127	(5)
5.2.3 Transport and Deposition of Lead in Europe	132	(6)
5.2.4 Altimeter Data and the Tides	138	(6)
5.3 Scenarios	144	(8)
5.4 Secondary Applications	152	(3)
6 Modeling in Fundamental Environmental Sciences - Simulation and Hypothesis Testing	155	(36)
6.1 Hypothesis Testing	155	(16)
6.1.1 Tides and the Coriolis Force	157	(1)
6.1.2 The Sun and the Late Maunder Minimum	158	(4)
6.1.3 The Stochastic Climate Model at Work	162	(4)
6.1.4 Validating Stommel's Theory of the Thermohaline Circulation	166	(3)
6.1.5 Validating Theories of Alpine Lee Cyclogenesis	169	(2)
6.2 Specification of Reduced Models	171	(9)
6.2.1 Heat Flux and Sea Surface Temperature	172	(6)
6.2.2 A Conceptual Zero-dimensional Climate Model	178	(2)
6.3 Simulating the Unobservable	180	(11)
6.3.1 Circulation Regimes in the North Sea	181	(1)
6.3.2 Multimodality in Atmospheric Dynamics	182	(2)
6.3.3 Tidal Dissipation	184	(7)
7 Issues and Conclusions	191	(10)
7.1 Reduction of Information	192	(1)
7.2 New and Old Models	193	(1)
7.3 Trustworthiness	194	(2)
7.4 Model Builder and Model User	196	(1)
7.5 Social and Psychological Conditioning	197	(1)
7.6 Final Conclusions	198	(3)
Appendices
A Fluid Dynamics	201	(32)
A.1 The Balance Equations	201	(3)
A.1.1 Mass Balances	201	(2)
A.1.2 Momentum Balance	203	(1)
A.1.3 Energy Balance	203	(1)
A.2 Thermodynamic Specification	204	(2)
A.3 The Phenomenological Flux Laws	206	(3)
A.4 Boundary Conditions	209	(1)
A.5 A Closer Look at the Balance Equations	210	(6)
A.5.1 Cloud Formation	211	(1)
A.5.2 Radiation	212	(3)
A.5.3 Photochemical Reactions	215	(1)
A.6 Reynolds Decomposition	216	(3)
A.7 Parameterization of Interior Fluxes	219	(4)
A.7.1 Eddy Diffusivities	219	(2)
A.7.2 Eddy Viscosities	221	(2)
A.8 Parameterization of Boundary Layer Fluxes	223	(4)
A.8.1 The Constant Flux Layer	223	(2)
A.8.2 The Planetary Boundary Layer	225	(2)
A.9 Approximations	227	(3)
A.9.1 Anelastic Approximation	227	(2)
A.9.2 Shallow Water Approximation	229	(1)
A.10 Representations	230	(3)
A.10.1 Vertical Coordinates	231	(1)
A.10.2 Decoupling	231	(2)
B Numerics	233	(18)
B.1 Discretization	233	(3)
B.2 Partial Differential Equations	236	(8)
B.2.1 Elliptic Problems	237	(2)
B.2.2 Parabolic Problems	239	(1)
B.2.3 Hyperbolic Problems	240	(4)
B.3 Staggered Grids	244	(1)
B.4 Spectral Models	245	(4)
B.5 Finite Element Models	249	(2)
C Statistical Analysis	251	(24)
C.1 Random Variables and Processes	252	(7)
C.1.1 Probability Function	252	(3)
C.1.2 Bivariate Random Variables	255	(1)
C.1.3 Random Processes	256	(3)
C.2 Characteristic Parameters	259	(6)
C.2.1 Expectation Values	259	(2)
C.2.2 Empirical Orthogonal Functions	261	(2)
C.2.3 Decomposition of Variance	263	(1)
C.2.4 Skill Scores	264	(1)
C.3 Inference	265	(10)
C.3.1 Basic Aspects of Estimation	265	(3)
C.3.2 Estimation of Auto-covariance Functions	268	(1)
C.3.3 Estimation of Spectra	269	(1)
C.3.4 Estimation of EOFs	270	(1)
C.3.5 Hypothesis Testing	271	(4)
D Data Assimilation	275	(10)
D.1 Estimation	276	(1)
D.2 Filtering	276	(5)
D.2.1 Kalman Filter	277	(2)
D.2.2 Optimal or Statistical Interpolation	279	(1)
D.2.3 Nudging	279	(1)
D.2.4 Blending and Direct Insertion	280	(1)
D.2.5 Minimization	280	(1)
D.3 Smoothing	281	(4)
D.3.1 Adjoint Method	281	(1)
D.3.2 Inverse Method	282	(1)
D.3.3 Parameter Estimation	283	(2)
References	285	(10)
Index	295