Computer Modelling in Atmospheric and Oceanic Sciences

1 Introduction.- 2 Computer Models.- 3 Models and Data.- 4 The Dynamics of Tides and Climate.- 5 Modeling in Applied Environmental Sciences — Forecasting, Analysis and Scenarios.- 6 Modeling in Fundamental Environmental Sciences — Simulation and Hypothesis Testing.- 7 Issues and Conclusions.- Appendices.- A Fluid Dynamics.- A.1 The Balance Equations.- A.1.1 Mass Balances.- A.1.2 Momentum Balance.- A.1.3 Energy Balance.- A.2 Thermodynamic Specification.- A.3 The Phenomenological Flux Laws.- A.4 Boundary Conditions.- A.5 A Closer Look at the Balance Equations.- A.5.1 Cloud Formation.- A.5.2 Radiation.- A.5.3 Photochemical Reactions.- A.6 Reynolds Decomposition.- A.7 Parameterization of Interior Fluxes.- A.7.1 Eddy Diffusivities.- A.7.2 Eddy Viscosities.- A.8 Parameterization of Boundary Layer Fluxes.- A.8.1 The Constant Flux Layer.- A.8.2 The Planetary Boundary Layer.- A.9 Approximations.- A.9.1 Anelastic Approximation.- A.9.2 Shallow Water Approximation.- A.10 Representations.- A.10.1 Vertical Coordinates.- A.10.2 Decoupling.- B Numerics.- B.1 Discretization.- B.2 Partial Differential Equations.- B.2.1 Elliptic Problems.- B.2.2 Parabolic Problems.- B.2.3 Hyperbolic Problems.- B.3 Staggered Grids.- B.4 Spectral Models.- B.5 Finite Element Models.- C Statistical Analysis.- C.1 Random Variables and Processes.- C.1.1 Probability Function.- C.1.2 Bivariate Random Variables.- C.1.3 Random Processes.- C.2 Characteristic Parameters.- C.2.1 Expectation Values.- C.2.2 Empirical Orthogonal Functions.- C.2.3 Decomposition of Variance.- C.2.4 Skill Scores.- C.3 Inference.- C.3.1 Basic Aspects of Estimation.- C.3.2 Estimation of Auto-covariance Functions.- C.3.3 Estimation of Spectra.- C.3.4 Estimation of EOFs.- C.3.5 Hypothesis Testing.- D Data Assimilation.- D.1 Estimation.- D.2 Filtering.- D.2.1 Kalman Filter.- D.2.2 Optimal or Statistical Interpolation.- D.2.3 Nudging.- D.2.4 Blending and Direct Insertion.- D.2.5 Minimization.- D.3 Smoothing.- D.3.1 Adjoint Method.- D.3.2 Inverse Method.- D.3.3 Parameter Estimation.- References.