Hans-Joachim Herzog, Gerd Vogel DWD, FE14, Potsdam. COSMO meeting -, Milano September 2004

Transcription

1 A radiative uer boundary condition of the Klem-Durran-Bougeault-tye and its alication to a comressible nonhydrostatic model -resent state toards LM-imlementation- Hans-Joachim Herzog, Gerd Vogel DWD, FE14, Potsdam COSMO meeting -, Milano Setember 004

2 Contents. Simulations ith a fast-mode LM toy-model demonstrating that the successful alication of the KDB-RUBC in a nonhydrostatic comressible model is feasible.. First alication of the KDB-RUBC in the LM-code. Summary and outlook

3 A sectral toy-model ith time-difference scheme adoted from the LM fast- mode art = v f k t u u = u f t v v = z z t µ 1 θ θ g c g s = c g t c s s 1 1 u k z z 1 1 θ θ θ g N t = ε ε = = 1 1, 1 1 = 0.4 ε = z u k c t s d : α =0.3 α d Λ = π k - horizontal ave number Time-level eights to determine the degree of imlicity Divergence daming in the ressure gradient term - differing from LM default-value =0.1, Method of model simlification as in Arakaa and Konor 1996 cf. Herzog, 004, Internal aer, reared for a COSMO Techn.Paer

4 The Radiative Uer Boundary Condition of Klem - Durran - Bougeault KDB - RUBC Limiting assumtions for the validity of the KDB-RUBC : - hydrostatic aroximation µ = 0 - condition of incomressibility - isothermal basic state - no rotation f = Boussinesq - aroximation c s 1 >>, n z H >> H 1 - reduced frequency equation ω n = ± N k Physical radiative condition > 0 t to KDB-RUBC N to = to to k t

5 lid-condition KDB-RUBC Process of disersion from defined initial erturbance of otential temerature chosen as in Arakaa und Konor1996. Simulation over 48 h. Sectral erturbation amlitude associated to horizontal avelength L=50km. L-grid CP-grid

6 Simulation exeriments ith the fast-mode LM toy-model have shon that the KDB-RUBC can be imlemented successfully in a nonhydrostatic comressible model ith the given semi-imlicit time-scheme, from hich vertically roagating acoustic aves are effectively filtered out and horizontally roagating acoustic aves are sufficiently suressed due to a divergence daming aroach. We have found out to equally successful methods ho to imlement the KDB-RUBC: Method 1: A judicious idea from D.R. Durran 1999 to incororate this RUBC in the vertically imlicit time-scheme. It is functioning ith our toy-model, but needs reformulations of the given algorithm ith lid-condition. Method : A direct method, hich is easily imlemented ithout interventions in the given model algorithm and is indeendent of a given time-scheme. It oerates satisfactory, too, and leads to results equivalent to the Durran-method. Further strategy : - steise generalisation in the LM-orld - first ste reetition of the given exerimental set-u for the toy-model no ith the LM

7 First exeriment ith the LM 1. Horizontal integration domain: 84 x 84 gridoints, D x=.8km. Number of vertical layers: 35 ke = Double-eriodic continuation in the horizontal leri=.true. 4. Slo tendencies are set equal to zero in subroutine fast_aves 5. Physics and Rayleigh-daming deleted 6. Isothermal basic state olytroic state also ossible 7. Definition of initial state - u = v = = = 0 - temerature disturbance T i, k 0 0 = A sin i 1 k A ν πν Nλ k= 0 = 0.5K, =,4,... A, N k = 1 = 84 = 0.5K Λ = 11,56,... km λ 8. Alication of KDB-RUBC after Method, no including discrete Fourier-transform and its inverse oeration, ith adatation to the C-grid staggering. We failed ith Method 1!

8 The KDB -RUBC - oerations 1. be extraolated hydrostatically from k=1 to k =1 to : = FT,,. Fourier-transform k l to i j to 3. KDB - RUBC : k l : = k, l to, k l to N to mit sin k = a cosϕ 0 π N λ λ k, l = π sin l N a ϕ ϕ, k [ 0, N 1], l [ 0, N 1] 1 : = FT, 4. Inverse Fourier - transform i, j to k l to λ ϕ

9 lid-condition KDB-RUBC Time-height cross-section of erturbation amlitude for T and, resectively, at zonal gridoint i = 11, associated to horizontal avelength L =56km. T

10 Pressure gradient term error test ith LMK for isothermal atmoshere at rest ith bell-shaed mountain lid-condition Kelvin to i, j, k T i T, j, k 0 KDB-RUBC hours hours a / H = 6 s / 1000m, s =. 8km

11 Summary and outlook for further ork - On rincile, e ere able to sho that the KDB-RUBC is alicable in a model-tye like the LM, and it orks in the right ay. - What follos is a straightforard engineering ork - Diverse generalisations of exerimentation toards real cases... - Relacing FT by FFT - Introducing an aeriodic integration domain - Taking advantage from exeriences ith DM / SM / HRM - Co-oeration ith MeteoSiss : real-case - studies and otimisation!...

12 Further investigations concerning CP - grid advantages versus L - grid shortcomings by Hans-Joachim Herzog, DWD, Potsdam A reort about is unfortunately not ossible here, but a COSMO Technical Reort is being reared instead. A note to the COSMO meeting in Milano, Italia, Set. 004