Coiffier, Jean.
Fundamentals of Numerical Weather Prediction. - 1 online resource (364 pages)
Cover -- Fundamentals of Numerical Weather Prediction -- Title -- Copyright -- Contents -- Foreword to the French Edition -- Foreword to the English Edition -- Preface -- Acknowledgments -- Partial list of symbols -- Latin letters -- Gothic letters -- Greek letters -- Generalized vectors, matrices, and operators -- Various mathematical notations -- 1 Half a century of numerical weather prediction -- 1.1 Introduction -- 1.2 The early days -- 1.3 Half a century of continual progress -- 1.3.1 The need to be fast and accurate -- 1.3.2 The use of filtered equations -- 1.3.3 Back to the primitive equations and initialization -- 1.3.4 Global processing and the spectral method -- 1.3.5 Limited area models -- 1.3.6 Algorithms for an increased time step -- 1.3.7 The move to nonhydrostatic equations -- 1.3.8 Physical processes -- 1.3.9 Objective analysis and data assimilation -- 1.4 Developments in computing -- 1.4.1 Computing power accompanies progress -- 1.4.2 From the ENIAC to scientific mainframes -- 1.4.3 Single and multiprocessor vector machines -- 1.4.4 Massively parallel computers -- 1.4.5 Software advances -- 2 Weather prediction equations -- 2.1 Introduction -- 2.2 The simplifications and the corresponding models -- 2.2.1 The general form of the equations -- 2.2.2 The traditional approximation and the nonhydrostatic equations -- 2.2.3 The hydrostatic assumption and the primitive equations -- 2.2.4 The primitive equations in the pressure coordinates -- 2.2.5 The shallow water model equations -- 2.2.6 The zero divergence model equation -- 2.3 The equations in various systems of coordinates -- 2.3.1 Vector operators in curvilinear coordinates -- 2.3.2 The equations in geographical coordinates -- 2.3.3 Formulation of the equations for a conformal projection -- 2.4 Some typical conformal projections -- 2.4.1 Polar stereographic projection. 2.4.2 The Mercator projection -- 2.4.3 The Lambert conical projection -- 2.4.4 The conformal transformation of the sphere onto itself -- 3 Finite differences -- 3.1 Introduction -- 3.2 The finite difference method -- 3.2.1 Computational principle, order of accuracy -- 3.2.2 Common notations for finite differences -- 3.2.3 The accuracy of finite difference schemes -- 3.3 The grids used and their properties -- 3.3.1 The primitive equations in conformal projection -- 3.3.2 The A-type grid -- 3.3.3 The B-type grid -- 3.3.4 The C-type grid -- 3.3.5 The D'-type staggered grid (Eliassen grid) -- 3.3.6 The properties of the various grids -- 3.3.7 Spatial filtering -- 3.4 Conclusion -- 4 Spectral methods -- 4.1 Introduction -- 4.2 Using series expansions in terms of functions -- 4.2.1 General remarks on Galerkin methods -- 4.2.2 Using finite elements for the advection equation -- 4.3 Spectral method on the sphere -- 4.3.1 General remarks -- 4.3.2 The basis of surface spherical harmonics -- 4.3.3 The properties of spherical harmonics -- 4.3.4 Expanding a spherical field -- 4.3.5 Truncating the expansion -- 4.3.6 Calculating linear terms and application to wind calculation -- 4.3.7 Calculating nonlinear terms -- 4.3.8 Practical implementation of the spectral method -- 4.4 Spectral method on a doubly periodic domain -- 4.4.1 Constructing a doubly periodic domain -- 4.4.2 Basis functions -- 4.4.3 Elliptical truncation -- 4.4.4 Calculating linear terms -- 4.4.5 Calculating nonlinear terms -- 4.4.6 The advantage of the method -- 5 The effects of discretization -- 5.1 Introduction -- 5.2 The linearized barotropic model -- 5.2.1 The equations for the perturbations -- 5.2.2 The analytical solutions of the linearized model -- 5.3 Effect of horizontal discretization -- 5.3.1 General principle -- 5.3.2 Application to the various grids. 5.4 Various time integration schemes -- 5.4.1 The Euler explicit scheme -- 5.4.2 The centred explicit scheme -- 5.4.3 The centred semi-implicit scheme -- 5.4.4 The centred semi-Lagrangian semi-implicit scheme -- 5.4.4.1 Implementation with perfect interpolation -- 5.4.4.2 Implicit treatment of the Coriolis parameter -- 5.4.4.3 The effects of interpolation in the semi-Lagrangian scheme -- 5.5 Time filtering -- 5.6 Effect of spatial discretization on stability -- 5.6.1 The case of finite difference models -- 5.6.2 The case of spectral models -- 6 Barotropic models -- 6.1 Barotropic models using the vorticity equation -- 6.1.1 The zero divergence model -- 6.1.2 Introducing a divergence term -- 6.1.3 Nonlinear instability and how to prevent it -- 6.2 The shallow water barotropic model -- 6.2.1 The properties of the shallow water model -- 6.2.2 Discretization of the equations on a C grid -- 6.2.3 The centred explicit scheme -- 6.2.4 The centred semi-implicit scheme -- 6.2.5 Semi-Lagrangian schemes -- 6.2.5.1 The centred scheme and determination of the particle origin point -- 6.2.5.2 Variants of semi-Lagrangian processing -- 6.3 Spectral processing of the shallow water model -- 6.3.1 Formulation of the equations -- 6.3.2 Semi-implicit processing -- 6.3.3 Semi-Lagrangian processing -- 6.4 Practical use of the shallow water model -- 7 Baroclinic model equations -- 7.1 Introduction -- 7.2 Introducing a general vertical coordinate -- 7.2.1 The transformation formulas -- 7.2.2 The total derivative expression -- 7.3 Application to the primitive equations -- 7.3.1 The hydrostatic equation -- 7.3.2 The pressure force term -- 7.3.3 The continuity equation -- 7.3.4 The surface pressure tendency equation -- 7.3.5 The vertical velocity equation -- 7.4 Various vertical coordinates -- 7.4.1 The drawbacks of the pressure coordinate -- 7.4.2 The sigma coordinate. 7.4.3 The progressive hybrid coordinate -- 7.5 Generalization to nonhydrostatic equations -- 7.5.1 The role of 'hydrostatic pressure' -- 7.5.2 The normalized 'hydrostatic pressure' hybrid coordinate -- 7.5.3 A comprehensive synthetic formulation of the equations -- 7.6 Conservation properties of the equations -- 7.6.1 The expression of global parameters -- 7.6.2 Conservation of mass -- 7.6.3 Conservation of angular momentum -- 7.6.4 The conservation of energy -- 7.7 Conclusion -- 8 Some baroclinic models -- 8.1 Introduction -- 8.2 The context of discretization -- 8.2.1 The equations -- 8.2.2 The layers, levels, and positions of variables -- 8.3 Vertical discretization of the equations -- 8.3.1 Vertical advection -- 8.3.2 Surface pressure evolution equation -- 8.3.3 Diagnostic equation for generalized vertical velocity -- 8.3.4 Diagnostic equation for geopotential -- 8.3.5 Pressure force term -- 8.3.6 Energy conversion term -- 8.3.7 Location of the pressure levels -- 8.3.8 Alternative solutions for vertical discretization -- 8.4 A sigma coordinate and finite difference model -- 8.4.1 Simplifications with the pure sigma coordinate -- 8.4.2 The location of variables on the C grid -- 8.4.3 The discretized equations -- 8.4.4 Explicit time integration of the model -- 8.4.5 Implementation of semi-implicit time integration -- 8.5 Formalization of the semi-implicit method -- 8.5.1 General formulation of the algorithm -- 8.5.2 Interpretation of the semi-implicit method -- 8.6 A variable resolution spectral model -- 8.6.1 The equations -- 8.6.2 Explicit time integration of the model -- 8.6.3 Implementation of semi-implicit time integration -- 8.7 Lagrangian advection in baroclinic models -- 9 Physical parameterizations -- 9.1 Introduction -- 9.2 Equations for a multi-phase moist atmosphere -- 9.2.1 Schematic framework of interaction among constituents. 9.2.2 The equations in conservative form -- 9.3 Radiation -- 9.3.1 General points -- 9.3.2 Allowance for the effects of radiation in the atmosphere -- 9.3.3 Two-flux approximation and integration over a layer -- 9.3.4 Calculating optical depths and spectral integration -- 9.3.4.1 The case of gases -- 9.3.4.2 The case of grey bodies -- 9.3.5 Integration over optical path and flux calculation -- 9.3.5.1 The case of solar fluxes -- 9.3.5.2 The case of thermal fluxes -- 9.3.6 Processing of clouds -- 9.3.6.1 The random overlap hypothesis -- 9.3.6.2 The maximum-random overlap hypothesis -- 9.3.6.3 Calculation of optical depths allowing for cloudiness -- 9.3.6.4 Calculating cloudiness -- 9.4 Boundary layer and vertical diffusion -- 9.4.1 General points -- 9.4.2 Parameterization of turbulent surface fluxes -- 9.4.3 Planetary boundary layer fluxes -- 9.4.4 Allowance for shallow convection -- 9.4.5 The evolution of surface parameters -- 9.4.5.1 Evolution of surface temperature -- 9.4.5.2 Evolution of soil moisture -- 9.4.6 Allowance for fluxes, vertical diffusion -- 9.5 Precipitation resolved at the grid scale -- 9.5.1 General points -- 9.5.2 Calculating precipitation in an atmospheric layer -- 9.5.3 Evaporation of precipitation during fall -- 9.5.4 The melting of snow as it falls -- 9.5.5 The calculation process in the various layers -- 9.5.6 The need for more detailed schemes -- 9.6 Convection -- 9.6.1 General points -- 9.6.2 The problem of causality for convection -- 9.6.3 The basic equations -- 9.6.4 The characteristic profiles of the cloud and the influence of microphysics -- 9.6.5 The triggering of instability -- 9.6.6 The closure relation -- 9.6.7 Prospects -- 9.7 Effect of sub-grid orography -- 9.7.1 The wave momentum flux induced by orography -- 9.7.2 Effects of resonance and trapping of the wave -- 9.7.3 Consequences of partial blocking of flow. 9.8 Horizontal diffusion.
A practical, accessible overview of weather forecasting and climate modeling techniques for graduate students, researchers and professionals in atmospheric science.
9781139185769
Numerical weather forecasting.
Weather forecasting -- Mathematical models.
Electronic books.
QC996 .C6513 2011
551.634
Fundamentals of Numerical Weather Prediction. - 1 online resource (364 pages)
Cover -- Fundamentals of Numerical Weather Prediction -- Title -- Copyright -- Contents -- Foreword to the French Edition -- Foreword to the English Edition -- Preface -- Acknowledgments -- Partial list of symbols -- Latin letters -- Gothic letters -- Greek letters -- Generalized vectors, matrices, and operators -- Various mathematical notations -- 1 Half a century of numerical weather prediction -- 1.1 Introduction -- 1.2 The early days -- 1.3 Half a century of continual progress -- 1.3.1 The need to be fast and accurate -- 1.3.2 The use of filtered equations -- 1.3.3 Back to the primitive equations and initialization -- 1.3.4 Global processing and the spectral method -- 1.3.5 Limited area models -- 1.3.6 Algorithms for an increased time step -- 1.3.7 The move to nonhydrostatic equations -- 1.3.8 Physical processes -- 1.3.9 Objective analysis and data assimilation -- 1.4 Developments in computing -- 1.4.1 Computing power accompanies progress -- 1.4.2 From the ENIAC to scientific mainframes -- 1.4.3 Single and multiprocessor vector machines -- 1.4.4 Massively parallel computers -- 1.4.5 Software advances -- 2 Weather prediction equations -- 2.1 Introduction -- 2.2 The simplifications and the corresponding models -- 2.2.1 The general form of the equations -- 2.2.2 The traditional approximation and the nonhydrostatic equations -- 2.2.3 The hydrostatic assumption and the primitive equations -- 2.2.4 The primitive equations in the pressure coordinates -- 2.2.5 The shallow water model equations -- 2.2.6 The zero divergence model equation -- 2.3 The equations in various systems of coordinates -- 2.3.1 Vector operators in curvilinear coordinates -- 2.3.2 The equations in geographical coordinates -- 2.3.3 Formulation of the equations for a conformal projection -- 2.4 Some typical conformal projections -- 2.4.1 Polar stereographic projection. 2.4.2 The Mercator projection -- 2.4.3 The Lambert conical projection -- 2.4.4 The conformal transformation of the sphere onto itself -- 3 Finite differences -- 3.1 Introduction -- 3.2 The finite difference method -- 3.2.1 Computational principle, order of accuracy -- 3.2.2 Common notations for finite differences -- 3.2.3 The accuracy of finite difference schemes -- 3.3 The grids used and their properties -- 3.3.1 The primitive equations in conformal projection -- 3.3.2 The A-type grid -- 3.3.3 The B-type grid -- 3.3.4 The C-type grid -- 3.3.5 The D'-type staggered grid (Eliassen grid) -- 3.3.6 The properties of the various grids -- 3.3.7 Spatial filtering -- 3.4 Conclusion -- 4 Spectral methods -- 4.1 Introduction -- 4.2 Using series expansions in terms of functions -- 4.2.1 General remarks on Galerkin methods -- 4.2.2 Using finite elements for the advection equation -- 4.3 Spectral method on the sphere -- 4.3.1 General remarks -- 4.3.2 The basis of surface spherical harmonics -- 4.3.3 The properties of spherical harmonics -- 4.3.4 Expanding a spherical field -- 4.3.5 Truncating the expansion -- 4.3.6 Calculating linear terms and application to wind calculation -- 4.3.7 Calculating nonlinear terms -- 4.3.8 Practical implementation of the spectral method -- 4.4 Spectral method on a doubly periodic domain -- 4.4.1 Constructing a doubly periodic domain -- 4.4.2 Basis functions -- 4.4.3 Elliptical truncation -- 4.4.4 Calculating linear terms -- 4.4.5 Calculating nonlinear terms -- 4.4.6 The advantage of the method -- 5 The effects of discretization -- 5.1 Introduction -- 5.2 The linearized barotropic model -- 5.2.1 The equations for the perturbations -- 5.2.2 The analytical solutions of the linearized model -- 5.3 Effect of horizontal discretization -- 5.3.1 General principle -- 5.3.2 Application to the various grids. 5.4 Various time integration schemes -- 5.4.1 The Euler explicit scheme -- 5.4.2 The centred explicit scheme -- 5.4.3 The centred semi-implicit scheme -- 5.4.4 The centred semi-Lagrangian semi-implicit scheme -- 5.4.4.1 Implementation with perfect interpolation -- 5.4.4.2 Implicit treatment of the Coriolis parameter -- 5.4.4.3 The effects of interpolation in the semi-Lagrangian scheme -- 5.5 Time filtering -- 5.6 Effect of spatial discretization on stability -- 5.6.1 The case of finite difference models -- 5.6.2 The case of spectral models -- 6 Barotropic models -- 6.1 Barotropic models using the vorticity equation -- 6.1.1 The zero divergence model -- 6.1.2 Introducing a divergence term -- 6.1.3 Nonlinear instability and how to prevent it -- 6.2 The shallow water barotropic model -- 6.2.1 The properties of the shallow water model -- 6.2.2 Discretization of the equations on a C grid -- 6.2.3 The centred explicit scheme -- 6.2.4 The centred semi-implicit scheme -- 6.2.5 Semi-Lagrangian schemes -- 6.2.5.1 The centred scheme and determination of the particle origin point -- 6.2.5.2 Variants of semi-Lagrangian processing -- 6.3 Spectral processing of the shallow water model -- 6.3.1 Formulation of the equations -- 6.3.2 Semi-implicit processing -- 6.3.3 Semi-Lagrangian processing -- 6.4 Practical use of the shallow water model -- 7 Baroclinic model equations -- 7.1 Introduction -- 7.2 Introducing a general vertical coordinate -- 7.2.1 The transformation formulas -- 7.2.2 The total derivative expression -- 7.3 Application to the primitive equations -- 7.3.1 The hydrostatic equation -- 7.3.2 The pressure force term -- 7.3.3 The continuity equation -- 7.3.4 The surface pressure tendency equation -- 7.3.5 The vertical velocity equation -- 7.4 Various vertical coordinates -- 7.4.1 The drawbacks of the pressure coordinate -- 7.4.2 The sigma coordinate. 7.4.3 The progressive hybrid coordinate -- 7.5 Generalization to nonhydrostatic equations -- 7.5.1 The role of 'hydrostatic pressure' -- 7.5.2 The normalized 'hydrostatic pressure' hybrid coordinate -- 7.5.3 A comprehensive synthetic formulation of the equations -- 7.6 Conservation properties of the equations -- 7.6.1 The expression of global parameters -- 7.6.2 Conservation of mass -- 7.6.3 Conservation of angular momentum -- 7.6.4 The conservation of energy -- 7.7 Conclusion -- 8 Some baroclinic models -- 8.1 Introduction -- 8.2 The context of discretization -- 8.2.1 The equations -- 8.2.2 The layers, levels, and positions of variables -- 8.3 Vertical discretization of the equations -- 8.3.1 Vertical advection -- 8.3.2 Surface pressure evolution equation -- 8.3.3 Diagnostic equation for generalized vertical velocity -- 8.3.4 Diagnostic equation for geopotential -- 8.3.5 Pressure force term -- 8.3.6 Energy conversion term -- 8.3.7 Location of the pressure levels -- 8.3.8 Alternative solutions for vertical discretization -- 8.4 A sigma coordinate and finite difference model -- 8.4.1 Simplifications with the pure sigma coordinate -- 8.4.2 The location of variables on the C grid -- 8.4.3 The discretized equations -- 8.4.4 Explicit time integration of the model -- 8.4.5 Implementation of semi-implicit time integration -- 8.5 Formalization of the semi-implicit method -- 8.5.1 General formulation of the algorithm -- 8.5.2 Interpretation of the semi-implicit method -- 8.6 A variable resolution spectral model -- 8.6.1 The equations -- 8.6.2 Explicit time integration of the model -- 8.6.3 Implementation of semi-implicit time integration -- 8.7 Lagrangian advection in baroclinic models -- 9 Physical parameterizations -- 9.1 Introduction -- 9.2 Equations for a multi-phase moist atmosphere -- 9.2.1 Schematic framework of interaction among constituents. 9.2.2 The equations in conservative form -- 9.3 Radiation -- 9.3.1 General points -- 9.3.2 Allowance for the effects of radiation in the atmosphere -- 9.3.3 Two-flux approximation and integration over a layer -- 9.3.4 Calculating optical depths and spectral integration -- 9.3.4.1 The case of gases -- 9.3.4.2 The case of grey bodies -- 9.3.5 Integration over optical path and flux calculation -- 9.3.5.1 The case of solar fluxes -- 9.3.5.2 The case of thermal fluxes -- 9.3.6 Processing of clouds -- 9.3.6.1 The random overlap hypothesis -- 9.3.6.2 The maximum-random overlap hypothesis -- 9.3.6.3 Calculation of optical depths allowing for cloudiness -- 9.3.6.4 Calculating cloudiness -- 9.4 Boundary layer and vertical diffusion -- 9.4.1 General points -- 9.4.2 Parameterization of turbulent surface fluxes -- 9.4.3 Planetary boundary layer fluxes -- 9.4.4 Allowance for shallow convection -- 9.4.5 The evolution of surface parameters -- 9.4.5.1 Evolution of surface temperature -- 9.4.5.2 Evolution of soil moisture -- 9.4.6 Allowance for fluxes, vertical diffusion -- 9.5 Precipitation resolved at the grid scale -- 9.5.1 General points -- 9.5.2 Calculating precipitation in an atmospheric layer -- 9.5.3 Evaporation of precipitation during fall -- 9.5.4 The melting of snow as it falls -- 9.5.5 The calculation process in the various layers -- 9.5.6 The need for more detailed schemes -- 9.6 Convection -- 9.6.1 General points -- 9.6.2 The problem of causality for convection -- 9.6.3 The basic equations -- 9.6.4 The characteristic profiles of the cloud and the influence of microphysics -- 9.6.5 The triggering of instability -- 9.6.6 The closure relation -- 9.6.7 Prospects -- 9.7 Effect of sub-grid orography -- 9.7.1 The wave momentum flux induced by orography -- 9.7.2 Effects of resonance and trapping of the wave -- 9.7.3 Consequences of partial blocking of flow. 9.8 Horizontal diffusion.
A practical, accessible overview of weather forecasting and climate modeling techniques for graduate students, researchers and professionals in atmospheric science.
9781139185769
Numerical weather forecasting.
Weather forecasting -- Mathematical models.
Electronic books.
QC996 .C6513 2011
551.634