Prognostic Precipitation in the Lokal-Modell (LM)
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1 Prognostic Precipitation in the Lokal-Modell (LM) Michael Baldauf, Günther Doms German Weather Service (DWD), Offenbach, Germany COSMO-Meeting, Mailand, COSMO, Work Package 2.1.1: Task: replacement of the diagnostic scheme for rain/snow in LM 3.5 by a prognostic scheme in operational use since (LM 3.9) Aim: improvement of the precipitation distribution in orographically structured areas due to horizontal drifting of rain/snow (solving the windward-lee-problem )
2 Conservation equation for humidity variables current LM: diagnostic scheme for rain/snow 0 columnequilibrium ρ [kg/m 3 ] density of air q x = ρ x /ρ [kg/kg] specific mass P x [kg/m 2 /s] sedimentation flux of x (only x=r,s) F x [kg/m 2 /s] turbulent flux of x S x [kg/m 3 /s] sources/sinks of x (cloud physics) x=v x=c x=i x=r x=s water vapour cloud water cloud ice rain drops, v sedim 5 m/s snow, v sedim 1..2 m/s
3 Mechanisms of orographic precipitation generation (Smith, 1979) Large-scale upslope precipitation Seeder-Feeder-mechanism Cumulonimbus in conditionally unstable airmass
4 Semi-Lagrange-schemes Advection-equation (1-dim.) or Numeric formulation 1.) determine the backtrajectory 2.) interpolate f at the starting point Properties: unconditionally stable (for u=const., without source terms) simple use in irregular grids avoids non-linear instabilities by advection Lit.: e.g. Staniforth, Côté (1991)
5 In LM 3.9 used for prognostic precipitation: Semi-Lagrange Advection backtrajectory in 2. order O( t 2 ) trilinear interpolation (about 80% comp. time) (about 20% comp. time) Properties: positive definite conservation properties sufficient for rain/snow relatively strong numerical diffusion
6 Test of Semi-Lagrange-Adv. in LM backtrajectory in 2. order O( t 2 ), trilinear interpolation plane, (u,v,w) = (30, 0, -2) m/s = const.
7 Test case: h total precipitation in 24 h LM with diagnostic precip. observations LM with progn. precip.
8 Test case: vertical cut (t=16:00) Prognostic precip. with v=0 Prognostic precip. ρ c ρ r ρ s
9 Numeric experiment: day h BONIE-Analysis
10 Numeric experiment: day h LM with diagnostic precipitation REGNIE-Analysis with prognostic precipitation
11 24 h - mean values of precipitation for Jan 2004 LM 3.5 with diagn. precip. Beobachtungen (REGNIE) LM 3.9 with progn. precip. Dr. B. Dietzer (VB HM1)
12 Monthly precipitation sum over Baden-Württemberg (SW Germany) in Mai 2004 LM 3.9 with prognostic precipitation Dr. U. Damrath, FE 14
13 Monthly precipitation sum over Baden-Württemberg (SW Germany) in October 2003 LM 3.5 with diagnostic precipitation Dr. U. Damrath, FE 14
14 Results from the actual numeric experiment (analysis over South-Germany in ) compared to the LM 3.5: Windward-Lee-distribution improved in most cases spatial averaged precipitation is reduced by about 15-25% precipitation maxima are reduced by about 20-40% computation time increased by about 20%
15 Verification BONIE (Bodenniederschlag) learning strategy derived from theory of artificial intelligence derivation of statistical properties of the spatial distribution patterns interpolation in analogy to Kriging-method data base: measurements at the stations of DWD and AWGeophysBDBw additional about 100 ombrometer measurements in Baden-Württemberg DWD, Geschäftsbereich VB/HM, Dr. T. Reich Homepage: REGNIE (Regionalisierung räumlicher Niederschlagsverteilungen) use of regionalised, monthly averaged precipitation values ( ) distance dependent interpolation (background field-method) data base: about 600 stations in Germany DWD, Geschäftsbereich VB/HM 1, Dr. B. Dietzer
16 Numeric experiment: day h BONIE-Analysis
17 Numeric experiment: day h LM 3.5 with diagnostic precipitation REGNIE-Analyse LM 3.9 with prognostic precipitation
18 Advection tests constant v solid body rotation LeVeque (1996) Courant numbers Courant numbers Courant numbers
19 Semi-Lagrange-advection, backtrajectory O(Dt), bilinear interpolation constant v solid body rotation LeVeque Min. = 0.0 Max. = rel. cons.= Min. = 0.0 Max.= 0.62 rel. cons. = Min. = 0.0 Max. = rel. cons. = computer time relative to upwind 1. order = 2.5
20 Semi-Lagrange-advection, backtrajectory O(Dt 2 ), bilinear interpolation constant v solid body rotation LeVeque Min. = 0.0 Max. = rel. cons.= Min. = 0.0 Max.= rel. cons. = Min. = 0.0 Max. = rel. cons. = computer time relative to upwind 1. order = 3.75
21 Semi-Lagrange-advection, backtrajectory O(Dt 2 ), biquadratic interpolation constant v solid body rotation LeVeque Min. = Max. = rel. cons.= Min. = Max.= rel. cons. = Min. = Max. = rel. cons. = computer time relative to upwind 1. order = 5.3
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