1. GFS Deep and Shallow Cumulus Convection Schemes
Jongil Han

2. NEMS/GFS Modeling Summer School
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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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.
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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
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5. Entrainment and detrainment rates
in sub-cloud layers
above cloud base
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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
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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, .
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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
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Overshoot of the cloud top
0.1A A hs hc
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Convective momentum transport with convection-induced pressure gradient force effect
C=0.55: effect of convection-induced pressure gradient force
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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).
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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
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13. Shallow convection scheme
Mass flux at cloud base:
Mb=0.03 w* (Grant, 2001)
(Convective boundary layer velocity scale)
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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.
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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
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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.
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Thank you !!
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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 h forecasts with (b) control GFS and (c) revised model

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