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 Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany 19.09.2006

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

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

Task 1: Looking at pressure bias 19.09.2006

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

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

Status: verifications carried out 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

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

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

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

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

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

(Förstner, Torrisi, Reinhardt, deMorsier) 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

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

Dynamic Bottom Boundary... “(Positive) Pressure Bias Problem” blue: Old Bottom Boundary Cond. red: Dynamic Bottom Boundary Cond. (Figures by Torrisi, CNMCA Rom) Dynamic Bottom Boundary... ... 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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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

Idealized 1D advection test 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

case study ‚25.06.2005, 00 UTC‘ total precipitation sum after 18 h Task 8: Improved vertical advektion for dynamic var. u, v, w, T, p‘ case study ‚25.06.2005, 00 UTC‘ 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

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 moist turbulence 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

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

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

contours: vertical velocity isolines: potential temperature Runge-Kutta new p*-T*-dynamics Runge-Kutta old p*-T-dynamics contours: vertical velocity isolines: potential temperature 19.09.2006

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

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 km³ lowest layer in 10 m above ground forecast duration: 18 h started 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