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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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Presentation Transcript
introduction
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

deep cumulus convection sascnv simplified arakawa schubert sas convection scheme
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

cloud model updraft
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

slide5

Entrainment and detrainment rates

in sub-cloud layers

above cloud base

NEMS/GFS Modeling Summer School

downdraft
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

quasi equilibrium closure
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

slide8

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

slide9

Overshoot of the cloud top

0.1A

A

hs

hc

NEMS/GFS Modeling Summer School

convective momentum transport with convection induced pressure gradient force effect
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

slide11

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

slide12

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

slide13

Shallow convection scheme

Mass flux at cloud base:

Mb=0.03 w* (Grant, 2001)

(Convective boundary layer velocity scale)

NEMS/GFS Modeling Summer School

slide14

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

slide15

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

slide16

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

slide17

Thank you !!

NEMS/GFS Modeling Summer School

slide19

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

slide20

Siebesma & Cuijpers

(1995, JAS)

Siebesma et al.

(2003, JAS)

LES studies