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GFS Deep and Shallow Cumulus Convection Schemes

GFS Deep and Shallow Cumulus Convection Schemes. Jongil Han. Introduction. (1). (2). Φ : θ , q, u, v , …. Tendency due to subgrid cumulus convection, turbulent mixing, and gravity wave drag. (2) All tendency terms due to advection and diabatic processes.

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GFS Deep and Shallow Cumulus Convection Schemes

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  1. GFS Deep and Shallow Cumulus Convection Schemes Jongil Han

  2. Introduction (1) (2) • Φ: θ, q, u, v, …. • Tendency due to subgrid cumulus convection, turbulent mixing, and gravity wave drag. • (2) All tendency terms due to advection and diabatic processes. NEMS/GFS Modeling Summer School

  3. Deep cumulus convection (sascnv): simplified Arakawa-Schubert (SAS) convection scheme • Use a bulk mass-flux scheme, which works well for a situation with well-organized updraft and complementary environment such as cumulus convection. • Updraft fraction over a grid size is assumed to be negligibly small. • To determine the cloud base mass flux, a quasi-equilibrium closure of Arakawa and Shubert (1974) is used, where the destabilization of an air column by the large-scale atmosphere is nearly balanced by the stabilization due to the cumulus. • For the cloud model, a entraining and detraining plume model is used. NEMS/GFS Modeling Summer School

  4. Cloud model (updraft) Moist static energy Rain Detrainment into grid scale liquid water η: normalized mass flux, ql: moist excess in updraft ε: entrainment rate, δ: detrainment rate NEMS/GFS Modeling Summer School

  5. Entrainment and detrainment rates in sub-cloud layers above cloud base NEMS/GFS Modeling Summer School

  6. Downdraft Downdraft is assumed to be saturated. z0: downdraft initiating level I1: normalized condensation I2: normalized evaporation 1-β: precipitation efficiency S: averaged vertical wind shear NEMS/GFS Modeling Summer School

  7. Quasi-equilibrium closure A: cloud work function, Mb: cloud base mass flux A0: reference cloud work function, : adjustment time scale (20-60 min) : cloud work function after modification of the thermodynamic fields by an arbitrary amount of mass flux, over a small time interval, . NEMS/GFS Modeling Summer School

  8. Convection trigger P(ks)-P(k1) < 120~180mb (proportional to w) P(k1)-P(k2) < 25mb k2 LFC k1 h* h ks h: moist static energy h*: saturation moist static energy NEMS/GFS Modeling Summer School

  9. Overshoot of the cloud top 0.1A A hs hc NEMS/GFS Modeling Summer School

  10. Convective momentum transport with convection-induced pressure gradient force effect C=0.55: effect of convection-induced pressure gradient force NEMS/GFS Modeling Summer School

  11. Shallow cumulus convection scheme (shalcnv) • Use a bulk mass-flux parameterization same as deep convection scheme. • Separation of deep and shallow convection is determined by cloud depth (currently 150 mb). • Entrainment rate is given to be inversely proportional to height (which is based on the LES studies) and much larger than that in the deep convection scheme. • Mass flux at cloud base is given as a function of the surface buoyancy flux (Grant, 2001). This differs from the deep convection scheme, which uses a quasi-equilibrium closure of Arakawa and Shubert (1974). NEMS/GFS Modeling Summer School

  12. Shallow convection scheme • It is assumed there exists only updraft (no downdraft). • Entrainment rate: • Siebesma et al.2003: • Detrainment rate = Entrainment rate at cloud base ce =0.3 NEMS/GFS Modeling Summer School

  13. Shallow convection scheme Mass flux at cloud base: Mb=0.03 w* (Grant, 2001) (Convective boundary layer velocity scale) NEMS/GFS Modeling Summer School

  14. Future development: a scale-aware cumulus convection scheme • Most of mass flux cumulus convection schemes have been developed under assumption that the updraft area is negligibly small over the grid box. • This assumption of small updraft area breaks down more and more often as the grid sizes get smaller and smaller (say less than 5 km). • Develop a scale-aware cumulus convection scheme that is applicable to any horizontal resolution. NEMS/GFS Modeling Summer School

  15. Scale-aware cumulus convection scheme (initial theoretical derivation by Hua-Lu Pan at EMC) For the cumulus updraft, σu: updraft area fraction (0~1.0) hu: moist static energy NEMS/GFS Modeling Summer School

  16. Scale-aware cumulus convection scheme Cloud model: • Mass flux can be directly derived from an updraft velocity equation rather than using the quasi-equilibrium assumption which may not be valid any longer as grid size becomes much smaller. NEMS/GFS Modeling Summer School

  17. Thank you !! NEMS/GFS Modeling Summer School

  18. ALBERTO

  19. Total precipitation (grid scale+convective) Revised package 24 h accumulated precipitation ending at 12 UTC, July 24, 2008 from (a) observation and 12-36 h forecasts with (b) control GFS and (c) revised model

  20. Siebesma & Cuijpers (1995, JAS) Siebesma et al. (2003, JAS) LES studies

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