1. Page 1© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Variable resolution or lateral boundary conditions Terry Davies Dynamics Research Yongming Tang, Junichi Ishida

2. Page 2© Crown copyright 2006SRNWP 9-12 October 2006, Zurich UM Dynamical Core Fully compressible, non-hydrostatic deep atmosphere Semi-Lagrangian advection Semi-implicit time integration Horizontal C grid Vertical – Charney-Phillips Scheme Hybrid height coordinate Davies, Cullen, Malcolm, Mawson, Staniforth, White, Wood Quart. Journal Roy. Met. Soc 2005

3. Page 3© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Vertical and Horizontal Grid Staggering Horizontal staggering - Awakawa C-grid No grid decoupling Better geostrophic adjustment for wavelengths of gridsize less than Rossby radius of deformation Vertical staggering - Charney-Phillips No computational modes More consistent with thermal wind balance Can have complications in coupling with boundary layer parametrisation W, U,U, U i- 1 / 2,j V i,j + 1 / 2 V i,j- 1 / 2 U i+ 1 / 2,j i,j

4. Page 4© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Predictor - Corrector Solution Method Call some Physics at start of timestep Two time level semi-Lagrangian advection Add increments from boundary-layer and convection Predictor Corrector Linearise Equation of State and form Helmholtz eqn from other eqns Solve Helmholtz equation for (Exner) pressure using Generalised Conjugate Residual iterative technique Obtain other variables from Exner by back substitution

5. Page 5© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Physical Parametrizations Edwards-Slingo Radiation (Edwards & Slingo 1996) Mixed phase precipitation (Wilson & Ballard 1999) New Boundary Layer + 38L (Lock et al 2000) New GWD scheme + GLOBE orography smoothed (Raymond filter) Modern spectral database for gaseous absorption in the atmosphere + new H2O continuum - flexible configuration Multiple scattering included Better optical properties for clouds inc. non-spherical ice parametrisation

6. Page 6© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Physical Parametrizations Edwards-Slingo Radiation (Edwards & Slingo 1996) Mixed phase precipitation (Wilson & Ballard 1999) New Boundary Layer + 38L (Lock et al 2000) New GWD scheme + GLOBE orography smoothed (Raymond filter) Physically based transitions between vapour, liquid, ice and rain Ice content now a prognostic variable rather than diagnosed from cloud scheme

7. Page 7© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Physical Parametrizations Edwards-Slingo Radiation (Edwards & Slingo 1996) Mixed phase precipitation (Wilson & Ballard 1999) New Boundary Layer + 38L (Lock et al 2000) New GWD scheme + GLOBE orography smoothed (Raymond filter) Allows for non-local mixing in unstable regimes Scheme diagnoses 6 different mixing regimes in order to represent stable, well mixed and cumulus processes Scheme includes boundary layer top entrainment parametrisation Improved interaction with the convection scheme

8. Page 8© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Physical Parametrizations Edwards-Slingo Radiation (Edwards & Slingo 1996) Mixed phase precipitation (Wilson & Ballard 1999) New Boundary Layer + 38L (Lock et al 2000) New GWD scheme + GLOBE orography smoothed (Raymond filter) Simplified scheme Expression for linear 2D flow used to calculate total surface pressure drag Gravity wave amplitudes proportional to depth of sub-grid mountains above blocked layer Remainder of drag is attributed to flow blocking

9. Page 9© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Future Developments Dynamical core improvements More consistent treatment of moisture Conserving semi-Lagrangian advection scheme Variable resolution grid Resolution increases - (70 levels, 40km) New physical parametrizations New prognostic cloud scheme New convection scheme

10. Page 10© Crown copyright 2006SRNWP 9-12 October 2006, Zurich UM Operational Configurations Global 40 km N320L50 North Atlantic & European 12 km UK 12 km (retired) New UK 4 km

11. Page 11© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Convective scale NWP Variable Resolution / Nested models Case Studies with one-way nested UM NWP with variable resolution UM

12. Page 12© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Variable Resolution Grid Structure Grid varies from coarse resolution at the outer boundaries smoothly to a uniform fine resolution in the interior of the domain Uniform High Res zone Var-Res 2 Var-Res 1 Uniform Coarse Res 1 Uniform Coarse Res 2 Typically, there are 3 regions, and inflation ratio R 1 = R 2 = 5~10% e.g. = 1 km, R 1 = R 2 = 10 % N_vr = 34 / 24 / 15 points = 25 / 10 / 4 km R2R2 R1R1

13. Page 13© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Variable Resolution Grid Structure Grid varies from coarse resolution at the outer boundaries smoothly to a uniform fine resolution in the interior of the domain Uniform High Res zone Var-Res 2 Var-Res 1 Uniform Coarse Res 1 Uniform Coarse Res 2 Typically, there are 3 regions, and inflation ratio R 1 = R 2 = 5~10% e.g. = 1 km, R 1 = R 2 = 10 % N_vr = 34 / 24 / 15 points = 25 / 10 / 4 km R2R2 R1R1

14. Page 14© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Costs (relative to 4km) Area/ 2 km1.85km1.5 km 1 km 100% 8 10 19 64 25% 5 - 10 25 10% - - - 10

15. Page 15© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Convective scale NWP Forecasting precipitation from severe convection Parametrized convection – limited success Very high resolution models (over a small domain), with detailed controlling factors, such as surface forcing and orography – promising Nesting -- typically 3 - 5:1 Requires a smooth transition Mismatch of grids and model physics (e.g. coarse resolution model does not explicitly represent convection). Possible solution: variable resolution ?

16. Page 16© Crown copyright 2006SRNWP 9-12 October 2006, Zurich UM NWP Model Domains 1-Way Nested Limited Area Configuration HORIZONTAL VERTICAL (lowest km)

17. Page 17© Crown copyright 2006SRNWP 9-12 October 2006, Zurich NWP Model Orography 12 km4 km1 km Height of model orography (m)

18. Page 18© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Case Study 3 rd May 2002 case May 3 2002 case is a scattered convection case. To compare 1 km to 4 km variable resolution to a 1 km model nested inside a 4 km model. First, the conventional nested model.

19. Page 19© Crown copyright 2006SRNWP 9-12 October 2006, Zurich May 3 2002 Case ----- Nested model 1 km high resolution nested model and radar rainfall at 14 UTC 1 km4 km12 kmRadar

20. Page 20© Crown copyright 2006SRNWP 9-12 October 2006, Zurich May 3 2002 Case ----- Nested model 1 km high resolution nested model and radar rainfall at 15 UTC 1 km4 km12 kmRadar

21. Page 21© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Summary of nested model result 3 rd May 2002 case Nested models suffered two major problems: Spin up problem: at the inflow boundaries (northern) the nested model is too slow to produce convection. Transition problem: at the end of the run when finally the large convection cells are being advected in from the 4 km model, they remain as large cells in the north. How well will variable resolution model do ?

22. Page 22© Crown copyright 2006SRNWP 9-12 October 2006, Zurich May 3 2002 Case ----- variable resolution model Rainfall at 14 UTC. The three regions of the variable resolution domain are also shown Radar 1km

23. Page 23© Crown copyright 2006SRNWP 9-12 October 2006, Zurich May 3 2002 Case ----- variable resolution model Rainfall at 15 UTC. The three regions of the variable resolution domain are also shown Radar 1km

24. Page 24© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Summary In the variable resolution model, when the ratio of the minimum and maximum grid is the same as a conventional nesting ratio of 1 : 4, it performs better in resolving convective scale storms. In particular it has overcome the problems of spin up and transition, highlighted in the nested model. Further study is needed on the physical parametrization schemes if ratio > 4. We are currently working on a grid-scale dependent convection scheme.

25. Page 25© Crown copyright 2006SRNWP 9-12 October 2006, Zurich Lateral boundaries To run variable resolution LAM will still need lbcs. Current lbcs use standard merging technique Semi-Lagrangian advection applies lbcs naturally Apply appropriate lbcs to Helmholtz equation Need to filter small-scale outflow information For mpp, lateral boundary files do not need external halos

26. Page 26© Crown copyright 2006SRNWP 9-12 October 2006, Zurich The End