1. Geophysical Modelling: Climate Modelling How advection, diffusion, choice of grids, timesteps etc are defined in state of the art models

2. Example: The UK Met Office “Unified Model” Same basic model is used for Global numerical weather prediction (i.e. operational weather forecasting) Regional NWP Climate modelling

3. Model dynamics: Solves the “primitive equations” (Navier- Stokes Equations) on a rotating sphere. Prognostic equations for (u,v,w), θ, q, hydrometeors, etc. Mass continuity equation. Variables are “initialised” (at t=0), and are functions of (x,y,z,t), so prognostic equations are used to march forward in time and space.

4. Model physics: Many processes are “sub grid scale” and hence cannot be resolved These are parameterised…

5. Model physics: Many processes are “sub grid scale” and hence cannot be resolved These are parameterised… – convection – Cloud microphysics, precipitation etc – Turbulence and heat exchange within boundary layer – Radiative transfer (interactions with trace gases etc) – Drag by mountains, gravity waves,etc – Land surface processes

6. Dynamical equations:

9. Old DynamicsNew Dynamics HydrostaticNon-hydrostatic Pressure based hybrid coordinateHeight based hybrid coordinate Charney Phillips grid staggering Arakawa-B gridArakawa-C grid Semi-implicit eulerian advection2 time level semi-lagrangian advection Richardson number based boundary layer scheme Equilibrium stable boundary layer scheme Mass flux convection scheme with buoyancy closure Mass flux convection scheme with cape closure Linear hydrostatic GWD schemeWarner and McIntyre type gravity wave drag scheme Met Office Surface Exchange Scheme MOSES I Surface hydrology and soil model MOSES II Standard Smith cloud scheme with prognostic cloud ice

10. Model Grid

11. UM Horizontal grid

12. UM Vertical Grid

13. A climate simulation from climateprediction.net