Contents

• Contents
• 1. General Presentation
  • 1.1 Introduction
  • 1.2 The anelastic system
  • 1.3 Thermodynamic Variables
  • 1.4 Water
  • 1.5 Geographical Systems
  • 1.6 Vertical Coordinate
  • 1.7 References
• 2. Basic Equations
  • 2.1 A Family of Anelastic Approximations
  • 2.2 Preliminary Definitions
  • 2.3 Reference State
  • 2.4 Equation of State
  • 2.5 Anelastic Constraint
  • 2.6 Conservation of Momentum
  • 2.7 Hydrostatic Equation
  • 2.8 Thermodynamic Equation
  • 2.9 Conservation of Moisture
  • 2.10 Conservation of Passive Scalars
  • 2.11 Conservation of Total Mass
  • 2.12 Pressure Equation
  • 2.13 Boundary Conditions
  • 2.14 Energy and Potential Vorticity Conservation
  • 2.15 References
• 3. Coordinate Systems
  • 3.1 Conformal Projections and Terrain Following Coordinates
    • 3.1.1 Gal-Chen and Sommerville vertical coordinate
    • 3.1.2 Polar stereographic and Lambert Projections:
    • 3.1.3 Mercator Projection:
  • 3.2 Calculus in Non Orthogonal Coordinates
    • 3.2.1 Metric Coefficients
    • 3.2.2 Covariant Basis
    • 3.2.3 Jacobian
    • 3.2.4 Contravariant Basis
    • 3.2.5 Spatial derivatives of the Cartesian basis
    • 3.2.6 Gradient
    • 3.2.7 Divergence
    • 3.2.8 Divergence of a Tensor Product
    • 3.2.9 Coriolis Force
  • 3.3 Model Equations in Non Orthogonal Coordinates
    • 3.3.1 Prognostic Variables
    • 3.3.2 The contravariant components of the wind
    • 3.3.3 Momentum Equation
    • 3.3.4 Thermodynamic Equation
    • 3.3.5 Water and Other Scalars
    • 3.3.6 Continuity Equation
    • 3.3.7 Pressure Equation
  • 3.4 Degenerated Forms
    • 3.4.1 Thin shell approximation
    • 3.4.2 Cartesian Coordinate System
    • 3.4.3 Flagged Equations
  • 3.5 References
• 4. Discretization
  • 4.1 Stretching
  • 4.2 Location of the Variables on the Grid
  • 4.3 Schuman Operators
  • 4.4 Grid Generation
  • 4.5 Metric Coefficients and Jacobian
  • 4.6 Contravariant Velocity Components
  • 4.7 Time Derivatives
  • 4.8 Advection
  • 4.9 Curvature Terms
  • 4.10 Coriolis Force
  • 4.11 Pressure Gradient
  • 4.12 Buoyancy Term
  • 4.13 Thermodynamic Equation
  • 4.14 Continuity Equation
  • 4.15 Pressure Equation
• 5. Lateral Boundary Conditions
  • 5.1 Principles and equations
    • 5.1.1 Cyclic boundary condition (CLBCX or CLBCY = 'CYCL')
    • 5.1.2 Rigid wall lateral boundary condition ('WALL')
    • 5.1.3 Wave-radiation open boundary ('OPEN')
    • 5.1.4 Combinations of different types of l.b.c.
    • 5.1.5 The coupling
  • 5.2 Discretization and implementation
    • 5.2.1 Grid structure
    • 5.2.2 Cyclic l.b.c. ('CYCL')
    • 5.2.3 Rigid wall l.b.c. ('WALL')
    • 5.2.4 Wave-radiation open boundary ('OPEN')
• 6. Grid Nesting
  • 6.1 Principles
  • 6.2 Basic choices
  • 6.3 Averaging and interpolation procedures
    • 6.3.1 Interpolation operators
    • 6.3.2 Averaging operators
  • 6.4 Implementation of the nesting
  • 6.5 Preparation of a nested simulation (Spawning)
    • 6.5.1 Horizontal grid configuration
    • 6.5.2 Interpolation operators
    • 6.5.3 Specific treatments for spawning
• 7. Positive Advection Schemes For Scalar Variables
  • 7.1 Introduction
  • 7.2 Flux-Corrected Transport
    • 7.2.1 Description
    • 7.2.2 Discretization
    • 7.2.3 Boundary Conditions
  • 7.3 Multidimensional Positive Definite Advection Transport Algorithm (MPDATA)
    • 7.3.1 MPDATA Description
    • 7.3.2 Discretization
    • 7.3.3 Boundary Conditions
  • 7.4 Evaluation of FCT and MPDATA advection schemes
  • 7.5 References
• 8. Numerical diffusion terms
  • 8.1 Background diffusion
    • 8.1.1 Diffusion operator
    • 8.1.2 Choice of the diffusion coefficient
  • 8.2 Top absorbing layer
  • 8.3 Lateral sponge zone
• 9. The pressure problem
  • 9.1 Continuous pressure equation
    • 9.1.1 Full elliptic problem
    • 9.1.2 Conjugate gradient algorithm
    • 9.1.3 Richardson's method
    • 9.1.4 Flat operator
  • 9.2 Discrete pressure equation
    • 9.2.1 Full elliptic problem
    • 9.2.2 Flat operator
• 10. Initial Fields for Idealized Flows
  • 10.1 Input Atmospheric Profile
  • 10.2 Vertical Profile on the Model Grid
  • 10.3 Wind and Mass Fields in the absence of Orography
  • 10.4 Add a Perturbation
  • 10.5 Wind and Mass Fields with Orography
  • 10.6 Enforcement of the Anelastic Constraint
  • 10.7 Analytical 3D fields
• 11. Forced Mode Version
  • 11.1 Purpose
  • 11.2 Modified equations
  • 11.3 Interpolation
  • 11.4 Discretization
• 12. Examples of Idealized Simulations
  • 12.1 How to select the timestep length to perform a Meso-NH simulation?
  • 12.2 Idealized 2D Mountain Waves
    • 12.2.1 Linear hydrostatic case:
    • 12.2.2 Non-Linear hydrostatic case:
    • 12.2.3 Non-hydrostatic case:
    • 12.2.4 Namelist Files
  • 12.3 Idealized 3D Mountain Waves
    • 12.3.1 Physical context
    • 12.3.2 The analytic solution
    • 12.3.3 Simulations
    • 12.3.4 Namelist Files
  • 12.4 Idealized 3D Baroclinic Waves
    • 12.4.1 Introduction
    • 12.4.2 Validation simulation
    • 12.4.3 Control simulation
    • 12.4.4 Namelist Files
    • 12.4.5 References
• 13. Initial Fields for Real Flows
  • 13.1 General Presentation
    • 13.1.1 Initialization for a one-model run, from operationel models
    • 13.1.2 Initialization for a one-model run, from a Meso-NH file
    • 13.1.3 Initialization for a nesting run
  • 13.2 The PREP_REAL_CASE algorithm
  • 13.3 Horizontal interpolation
    • 13.3.1 Introduction
    • 13.3.2 The interpolation algorithm
    • 13.3.3 Definition of interpolated fields
  • 13.4 The different grids
  • 13.5 Altitude of the Aladin points and conversion of the variables
  • 13.6 Interpolation to mixed grid
  • 13.7 The shifting process
  • 13.8 Vertical interpolation
  • 13.9 Reference State
  • 13.10 Computation of the total dry air mass
  • 13.11 Anelastic Constraint
• 14. Physiographic Data
  • 14.1 Introduction
  • 14.2 The surface cover types
    • 14.2.1 On the world, except Europe
    • 14.2.2 On Europe, for the 1km map
  • 14.3 Fields deduced from the surface cover types
    • 14.3.1 Sea, inland water, town and artificial surfaces, natural and cultivated landscape
    • 14.3.2 Artificial parameters
    • 14.3.3 Water parameters
    • 14.3.4 Main natural landscape parameters parameters
    • 14.3.5 Other natural landscape parameters parameters
  • 14.4 Soil characteristics
    • 14.4.1 Composition of the soil
    • 14.4.2 Color of the soil
  • 14.5 Orography
    • 14.5.1 Mean orography
    • 14.5.2 Envelope orography
    • 14.5.3 Silhouette orography
  • 14.6 Subgrid-scale orographic parameters
    • 14.6.1 Roughness length for momentum
    • 14.6.2 Subgrid-scale orography structure
  • 14.7 Appendix: default parameters for the ecosystems
  • 14.8 References
• 15. Surface Processes Scheme
  • 15.1 Introduction
  • 15.2 Fluxes over water surfaces
    • 15.2.1 Free water surfaces
    • 15.2.2 Sea ice
  • 15.3 Urban and artificial areas: the TEB surface cheme
  • 15.4 Soil and Vegetation
    • 15.4.1 Treatment of the soil heat content
    • 15.4.2 Treatment of the soil water
    • 15.4.3 Treatment of the intercepted water
    • 15.4.4 Treatment of soil ice
    • 15.4.5 Treatment of the snow
    • 15.4.6 The surface fluxes
    • 15.4.7 Summary of Useful Parameters
    • 15.4.8 Apendix A: Continuous formulation of the soil secondary parameters
    • 15.4.9 Appendix B: Gaussian formulation for the coefficient
  • 15.5 References
• 16. Convection Scheme
  • 16.1 Introduction
  • 16.2 Mass Flux equations
  • 16.3 Cloud Model
    • 16.3.1 Key cloud levels
    • 16.3.2 Trigger Function
    • 16.3.3 Updraft
    • 16.3.4 Downdraft
    • 16.3.5 Closure
  • 16.4 Discussion
  • 16.5 Appendix
    • 16.5.1 Definition of latent and specific heats
    • 16.5.2 Derivation of
    • 16.5.3 Definition of saturation mixing ratios
    • 16.5.4 Precipitation efficiency
  • 16.6 References
• 17. Microphysical Scheme for Warm Clouds
  • 17.1 Equations
  • 17.2 Raindrops characteristics
    • 17.2.1 Distribution
    • 17.2.2 Fall velocity
  • 17.3 Explicit sources
    • 17.3.1 Autoconversion
    • 17.3.2 Accretion
    • 17.3.3 Rain evaporation
    • 17.3.4 Rain sedimentation
  • 17.4 Implicit sources
  • 17.5 Global correction for negative values
  • 17.6 Practical implementation
  • 17.7 Available options and summary of the ajustable constants
  • 17.8 References
• 18. Microphysical scheme for atmospheric ice
  • 18.1 Introduction
    • 18.1.1 Purpose of the parameterization
    • 18.1.2 Representation of the ice categories
    • 18.1.3 General characteristics of the ice crystals
    • 18.1.4 Nomenclature
    • 18.1.5 Outlines of the microphysical scheme for mixed phase clouds
  • 18.2 Microphysical processes
    • 18.2.1 Summary of the scheme
    • 18.2.2 Warm processes
    • 18.2.3 Heterogeneous nucleation
    • 18.2.4 Homogeneous Nucleation
    • 18.2.5 Deposition(Sublimation) of water vapor
    • 18.2.6 Bergeron-Findeisen effect
    • 18.2.7 Autoconversion of primary ice crystal to form aggregates
    • 18.2.8 Contact freezing of raindrops to form graupeln
    • 18.2.9 Collection growth of the aggregates
    • 18.2.10 Wet/dry growth of the graupeln:
    • 18.2.11 Melting of ice crystals
    • 18.2.12 Sedimentation rates
  • 18.3 Integration of the equations of conservation
    • 18.3.1 System of equation
    • 18.3.2 Positivity adjustments
    • 18.3.3 Ordering the integration of the microphysical sources
    • 18.3.4 Water vapor adjustments
  • 18.4 References
• 19. Turbulence Scheme
  • 19.1 Introduction
  • 19.2 Turbulent fluxes in a cartesian frame
  • 19.3 Turbulence kinetic energy equation
  • 19.4 Closure by Mixing Length
    • 19.4.1 The grid-size
    • 19.4.2 Bougeault-Lacarrère mixing length
    • 19.4.3 Qualitative Behaviour of the 1D dry system with BL length
  • 19.5 Closure by dissipation equation
  • 19.6 Terrain-following coordinate system
  • 19.7 Spatial Discretization
  • 19.8 Boundary conditions
    • 19.8.1 Lateral Boundary Conditions
    • 19.8.2 Upper Boundary Condition
    • 19.8.3 Surface Boundary Conditions
    • 19.8.4 Extrapolation of gradients
  • 19.9 Semi-implicit time discretization
• 20. Sub-Grid Condensation Scheme
  • 20.1 Introduction
  • 20.2 Definition of conservative variables
  • 20.3 Retrieval of cloud water mixing ratio
  • 20.4 Flux of liquid water
  • 20.5 Closure of the scheme
  • 20.6 Buoyancy flux
  • 20.7 Modification to the mixing length
  • 20.8 Spatial Discretization
  • 20.9 Practical implementation
  • 20.10 References
• 21. The radiation parameterization
  • 21.1 Introduction to the radiation code
    • 21.1.1 Purpose
    • 21.1.2 The Fouquart-Morcrette radiation code and its Méso-NH interface
    • 21.1.3 Outline of the scheme
  • 21.2 Longwave radiation^21.4
    • 21.2.1 First glance
    • 21.2.2 Vertical integration
    • 21.2.3 Spectral integration
    • 21.2.4 Incorporation of the effects of clouds
  • 21.3 Solar radiation^21.6
    • 21.3.1 First glance
    • 21.3.2 Spectral integration
    • 21.3.3 Vertical integration
    • 21.3.4 Multiple reflections between layers
    • 21.3.5 Cloud shortwave optical properties
  • 21.4 Additional features of the radiation computations
    • 21.4.1 Solar astronomy
    • 21.4.2 Surface slope angles
    • 21.4.3 Upper level extensions
  • 21.5 Intermittent radiation call
  • 21.6 References
• 22. Budget Analysis
  • 22.1 Introduction
  • 22.2 Budget definition
    • 22.2.1 Equations
    • 22.2.2 Average operators
• 23. Atmospheric Chemistry
  • 23.1 Overview
  • 23.2 Basic equations
  • 23.3 Stiff solvers
  • 23.4 Modification of the reaction scheme
  • 23.5 0-D box model
  • 23.6 Dry deposition of trace species
    • 23.6.1 Meso-NH surface for dry deposition
    • 23.6.2 Aerodynamic resistance
    • 23.6.3 Quasi-laminar resistance
    • 23.6.4 Surface Resistance
    • 23.6.5 Dry deposition velocity formulation
  • 23.7 Photolysis rates
    • 23.7.1 Background
    • 23.7.2 Cloud Attenuation
  • 23.8 Cloud Dynamics and Chemistry
    • 23.8.1 Model description
    • 23.8.2 Subgrid Convective Cloud Scheme
    • 23.8.3 Resolved Cloud Scheme
  • 23.9 References
• 24. The Regional Atmospheric Chemistry Mechanism RACM