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Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany

Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany. COSMO Priority Project: Further developments of the Runge-Kutta Time Integration Scheme COSMO General Meeting Bukarest, 18.-21.09.2006. List of people contributing to the project: (alphabetical order) Michael Baldauf (DWD, D)

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Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany

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  1. Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany COSMO Priority Project:Further developments of the Runge-Kutta Time Integration SchemeCOSMO General MeetingBukarest, 18.-21.09.2006 19.09.2006

  2. List of people contributing to the project: • (alphabetical order) • Michael Baldauf (DWD, D) • Gabriella Ceci (CIRA, I) • Guy deMorsier (MeteoCH, CH) • Jochen Förstner (DWD, D) • Almut Gassmann (Univ. Bonn, D) (FTE not counted) • Paola Mercogliano (CIRA, I) • Thorsten Reinhardt (DWD, D) • Lucio Torrisi (CNMCA, I) • Pier Luigi Vitagliano (CIRA, I) • Klaus Stephan (DWD, D) (FTE not counted) • Matthias Raschendorfer (DWD, D) (FTE not counted) 19.09.2006

  3. Task 1: Looking at pressure bias (Torrisi, Förstner) verifications of LM 7 km runs showed a higher positive pressure bias for the RK core than for the Leapfrog core, whereas other variables show comparable behaviour. • Work done: • 5-day verifications were done for several model configurations • only little impact on PMSL by: • physics coupling • advection of qx (Bott, Semi-Lagrange) • most significant impact on PMSL: • new dynamical bottom boundary condition (DBBC) ( Task 6) • p‘T‘-dynamics in the RK-core • both measurements reduce the pressure bias verification area 19.09.2006

  4. Task 1: Looking at pressure bias 19.09.2006

  5. Task 1: Looking at pressure bias positive impact of p‘T‘-dynamics 19.09.2006

  6. Task 1: Looking at pressure bias positive impact of DBBC 19.09.2006

  7. Task 1: Looking at pressure bias Status: verifications carried out Work to do: longer verifications periods should be inspected Upper air verifications Lateral boundary conditions pressure bias improved by another fast waves solver?? ( --> task 10) 19.09.2006

  8. Task 2: Continue RK case studies (Torrisi, deMorsier) extensive verification of the other tasks Work done: case study 4.-8.Dez. 2004 (inversion in 800...1600m) was carried out: penetration of the stratus in Alpine valleys in 2km- sim. better performed by RK-core compared to LF-core Status: test case carried out; verifications were made Work to do: test cases should be continued 19.09.2006

  9. Task 3: Conservation (Baldauf) Tool for inspection of conservation properties will be developed. Integration area = arbitrarily chosen cubus (in the transformed grid, i.e. terrain-following) balance equation for scalar : temporal change flux divergence sources / sinks • Status: • integral over a volume (arbitrary square-stone): ready • Subr. init_integral_3D: define square-stone (in the transformed grid!), domain decomp. • Function integral_3D_total: calc. volume integral • Function integral_3D_cond: calc. vol. integral over individual processor • Work to do • flux integral over the surface 19.09.2006

  10. Task 4: Advection of moisture quantities in conservation form (Förstner) implementation of a Courant-number independent advection algorithm for the moisture densities Status: implemented schemes (Bott-2, Bott-4) behave well (Semi-Lagrange-scheme as a testing tool is also available) task finished 19.09.2006

  11. PP RK 2.1.4 + 2.1.3 Transport of Tracerin a Real Case Flow Field Bott (2nd)“Flux Form- DIV”+ Clipping init semi-Lagrange(tri-cubic)+ Clipping Bott (2nd)“Conserv. Form” 19.09.2006

  12. Task 5: investigation of convergence • (Ceci, Vitagliano, Baldauf) • determination of the spatial and temporal order of convergence of the RK-scheme in combination with advection schemes of higher order. • Planned test cases: • linear mountain flows (2D, 3D) • nonlinear mountain flows (dry case) • nonlinear mountain flows with precipitation Status: implementation of LM and test environment. First tests with linear mountain flow. Work to do: determine L2, L – errors of KE, w, ..., dependent from x, t, ... for the tests cases 19.09.2006

  13. Task 6: deep valleys (Förstner, Torrisi, Reinhardt, deMorsier) detection of the reason for the unrealistic ‚cold pools‘ in Alpine valleys Task 7: Different filter options for orography (Förstner) The reason for the cold pools was identified: metric terms of the pressure gradient Dynamical Bottom boundary condition (DBBC) (A. Gassmann (2004), COSMO-Newsl.) and a slope-dependent orography-filtering cures the problem to a certain extent. Status: the orography filtering is now sufficiently weak for DWD-LMK applications (max. slopes 30% allowed) • Proposal for future work: • inspect the limitations of the terrain following coordinate for steeper slopes, e.g. • for application of aLMo 2 (MeteoCH) in Alpine region • for future LMK ~1 km horizontal resolution 19.09.2006

  14. cold pool – problem in narrow valleys is essentially induced by pressure gradient term T (°C) starting point after 1 h after 1 h modified version: pressure gradient on z-levels, if |metric term| > |terrain follow. term| 19.09.2006

  15. “(Positive) Pressure Bias Problem” blue: Old Bottom Boundary Cond. red: Dynamic Bottom Boundary Cond.(Figures by Torrisi, CNMCA Rom) Dynamic BottomBoundary... ... Condition... ... for metric pressure gradient term in equation for u- and v-component.Gaßmann (COSMO Newsletter No. 4) 19.09.2006

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  18. Task 8: Higher order discretization in the vertical for RK-scheme (Baldauf) Improved vertical advection for the dynamic var. u, v, w, T (or T‘), p‘ motivation: resolved convection • vertical advection has increased importance => use scheme of higher order (compare: horizontal adv. from 2. order to 5. order) • => bigger w (~20 m/s) => Courant-crit. is violated =>implicit scheme or CNI-explicit scheme up to now: implicit (Crank-Nicholson) advection 2. order (centered differences) new: implicit (Crank-N.) advektion 3. order  LES with 5-banddiagonal-matrix but: implicit adv. 3. order in every RK-substep; needs ~ 30% of total computational time!  planned: use outside of RK-scheme (splitting-error?, stability with fast waves?) Status: implicit scheme of 3. order implemented (5-banddiagonal solver, ...) Work to do: best combination with time integration scheme? test suite; verification 19.09.2006

  19. Task 8: Improved vertical advektion for dynamic var. u, v, w, T, p‘ analytic sol. implicit 2. order implicit 3. order implicit 4. order C=1.5 80 timesteps Idealized 1D advection test C=2.5 48 timesteps 19.09.2006

  20. case study ‚25.06.2005, 00 UTC‘ Task 8: Improved vertical advektion for dynamic var. u, v, w, T, p‘ total precipitation sum after 18 h with vertical advection 2. order difference total precpitation sum after 18 h ‚vertical advection 3. order – 2. order‘ 19.09.2006

  21. Task 9: Physics coupling scheme (Förstner, Stephan, Raschendorfer) original task: problems with reduced precipitation could be due to a nonadequate coupling between physics scheme and dynamics Problems in new physics-dynamics coupling (NPDC): • Negative feedback between NPDC and operational moistturbulence parameterization (not present in dry turbulence parameterization) • 2-z - structures in the specific cloud water field (qc) • 2-z - structures in the TKE field, unrealistic high values, where qc > 0 Status: NPDC-scheme analogous to WRF was implemented.Problems occuring  reduced variant is used now Work to do: what are the reasons for the failure of the WRF-PD-scheme in LM? (turbulence scheme?)  test tool (Bryan-Fritsch-case) is developed in PP ‚QPF‘, task 4.1 19.09.2006

  22. Physics-Dynamics-Coupling n = (u, v, w, pp, T, ...)n Descr. of Advanced Research WRF Ver. 2 (2005) • Physics (I) • Radiation • Shallow Convection • Coriolis force • Turbulence ‚Physics (I)‘-Tendencies: n(phys I) + n-1(phys II) Dynamics Runge-Kutta [ (phys) +(adv)  fast waves ] * = (u, v, w, pp, T, ...)* - n-1(phys II) • Physics (II) • Cloud Microphysics ‚Physics (II)‘-Tendencies: n(phys II) n+1 = (u, v, w, pp, T, ...)n+1 19.09.2006

  23. Task 10: Testing of alternative fast wave scheme • (Gassmann, Förstner, Baldauf) • p‘T‘-RK-scheme • ‚shortened-RK2‘-scheme (Gassmann) • this allows the use of the ‚radiative upper boundary condition‘ (RUBC) • Status: • p‘T‘-RK-scheme is already tested and is used now in LMK • ‚shortened RK2‘-scheme works • RUBC is tested in idealized and one real test case • Work to do: • implement ‚shortened RK2‘ version in official LM version • experiments especially with RUBC • tests both versions in CLM-application (dx=18 km) 19.09.2006

  24. Runge-Kuttanew p*-T*-dynamics Runge-Kuttaold p*-T-dynamics contours: vertical velocity isolines: potential temperature 19.09.2006

  25. Choose CN-parameters for buoyancy in p‘T‘-dynamics from stability analysis =0.6 =0.7 =0.5 (‚pure‘ Crank-Nic.) =0.8 =0.9 =1.0 (purely implicit)  choose =0.7 as the best value 19.09.2006

  26. LMK (Lokal-Modell Kürzestfrist) • grid length: x = 2.8 km • direct simulation of the coarser parts of deep convection • interactions with fine scale topography • timestep t=30 sec. • 421 x 461 x 50 grid points~ 1200 * 1300 * 22 km³lowest layer in 10 m above ground • forecast duration: 18 hstarted at 0, 3, 6, 9, 12, 15, 18, 21 UTC • center of the domain 10° E, 50° N • boundary values from LME(x = 7 km) in pre-operational mode at DWD since 14.08.2006 19.09.2006

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