GFS mfshalcnv Main

The subroutine contains the entirety of the SAMF shallow convection scheme. The scale-aware mass-flux shallow convection scheme is an updated version of the previous mass-flux shallow convection scheme with scale and aerosol awareness and parameterizes the effect of shallow convection on the environment. More...

Detailed Description

Argument Table

local_name	standard_name	long_name	units	rank	type	kind	intent	optional
im	horizontal_loop_extent	horizontal loop extent	count	0	integer		in	F
ix	horizontal_dimension	horizontal dimension	count	0	integer		in	F
km	vertical_dimension	vertical layer dimension	count	0	integer		in	F
delt	time_step_for_physics	physics time step	s	0	real	kind_phys	in	F
delp	air_pressure_difference_between_midlayers	pres(k) - pres(k+1)	Pa	2	real	kind_phys	in	F
prslp	air_pressure	mean layer pressure	Pa	2	real	kind_phys	in	F
psp	surface_air_pressure	surface pressure	Pa	1	real	kind_phys	in	F
phil	geopotential	layer geopotential	m2 s-2	2	real	kind_phys	in	F
ql1	cloud_ice_specific_humidity	cloud ice specific humidity	kg kg-1	2	real	kind_phys	inout	F
ql2	cloud_liquid_water_specific_humidity	cloud water specific humidity	kg kg-1	2	real	kind_phys	inout	F
q1	water_vapor_specific_humidity_updated_by_physics	updated vapor specific humidity	kg kg-1	2	real	kind_phys	inout	F
t1	air_temperature_updated_by_physics	updated temperature	K	2	real	kind_phys	inout	F
u1	x_wind_updated_by_physics	updated x-direction wind	m s-1	2	real	kind_phys	inout	F
v1	y_wind_updated_by_physics	updated y-direction wind	m s-1	2	real	kind_phys	inout	F
rn	lwe_thickness_of_shallow_convective_precipitation_amount	shallow convective rainfall amount on physics timestep	m	1	real	kind_phys	out	F
kbot	vertical_index_at_cloud_base	index at cloud base	index	1	integer		inout	F
ktop	vertical_index_at_cloud_top	index at cloud top	index	1	integer		inout	F
kcnv	flag_deep_convection	deep convection: 0=no, 1=yes	flag	1	integer		inout	F
islimsk	sea_land_ice_mask	landmask: sea/land/ice=0/1/2	flag	1	integer		in	F
garea	cell_area	grid cell area	m2	1	real	kind_phys	in	F
dot	omega	layer mean vertical velocity	Pa s-1	2	real	kind_phys	in	F
ncloud	number_of_hydrometeors	number of hydrometeors	count	0	integer		in	F
hpbl	atmosphere_boundary_layer_thickness	PBL top height	m	1	real	kind_phys	in	F
ud_mf	instantaneous_atmosphere_updraft_convective_mass_flux	(updraft mass flux) * delt	kg m-2	2	real	kind_phys	out	F
dt_mf	instantaneous_atmosphere_detrainment_convective_mass_flux	(detrainment mass flux) * delt	kg m-2	2	real	kind_phys	out	F
cnvw	convective_cloud_water_specific_humidity	convective cloud water specific humidity	kg kg-1	2	real	kind_phys	out	F
cnvc	convective_cloud_cover	convective cloud cover	frac	2	real	kind_phys	out	F
errmsg	error_message	error message for error handling in CCPP	none	0	character	len=*	out	F
errflg	error_flag	error flag for error handling in CCPP	flag	0	integer		out	F

GFS SAMF Shallow Convection Scheme General Algorithm

1. Compute preliminary quantities needed for the static and feedback control portions of the algorithm.
2. Perform calculations related to the updraft of the entraining/detraining cloud model ("static control").
3. The cloud base mass flux is obtained using the cumulus updraft velocity averaged ove the whole cloud depth.
4. Calculate the tendencies of the state variables (per unit cloud base mass flux) and the cloud base mass flux.
5. For the "feedback control", calculate updated values of the state variables by multiplying the cloud base mass flux and the tendencies calculated per unit cloud base mass flux from the static control.

Detailed Algorithm

Functions/Subroutines
subroutine	sasas_shal::sasas_shal_run (im, ix, km, delt, delp, prslp, psp, phil, ql1, ql2, q1, t1, u1, v1, rn, kbot, ktop, kcnv, islimsk, garea, dot, ncloud, hpbl, ud_mf, dt_mf, cnvw, cnvc, errmsg, errflg)

Function/Subroutine Documentation

subroutine sasas_shal::sasas_shal_run	(	integer, intent(in)	im,
		integer, intent(in)	ix,
		integer, intent(in)	km,
		real(kind=kind_phys), intent(in)	delt,
		real(kind=kind_phys), dimension(ix,km), intent(in)	delp,
		real(kind=kind_phys), dimension(ix,km), intent(in)	prslp,
		real(kind=kind_phys), dimension(im), intent(in)	psp,
		real(kind=kind_phys), dimension(ix,km), intent(in)	phil,
		real(kind=kind_phys), dimension(ix,km), intent(inout)	ql1,
		real(kind=kind_phys), dimension(ix,km), intent(inout)	ql2,
		real(kind=kind_phys), dimension(ix,km), intent(inout)	q1,
		real(kind=kind_phys), dimension(ix,km), intent(inout)	t1,
		real(kind=kind_phys), dimension(ix,km), intent(inout)	u1,
		real(kind=kind_phys), dimension(ix,km), intent(inout)	v1,
		real(kind=kind_phys), dimension(im), intent(out)	rn,
		integer, dimension(im), intent(inout)	kbot,
		integer, dimension(im), intent(inout)	ktop,
		integer, dimension(im), intent(inout)	kcnv,
		integer, dimension(im), intent(in)	islimsk,
		real(kind=kind_phys), dimension(im), intent(in)	garea,
		real(kind=kind_phys), dimension(ix,km), intent(in)	dot,
		integer, intent(in)	ncloud,
		real(kind=kind_phys), dimension(im), intent(in)	hpbl,
		real(kind=kind_phys), dimension(im,km), intent(out)	ud_mf,
		real(kind=kind_phys), dimension(im,km), intent(out)	dt_mf,
		real(kind=kind_phys), dimension(ix,km), intent(out)	cnvw,
		real(kind=kind_phys), dimension(ix,km), intent(out)	cnvc,
		character(len=*), intent(out)	errmsg,
		integer, intent(out)	errflg
	)

Compute preliminary quantities needed for the static and feedback control portions of the algorithm.

• Convert input pressure terms to centibar units.
• Initialize column-integrated and other single-value-per-column variable arrays.
• Return to the calling routine if deep convection is present or the surface buoyancy flux is negative.
• determine aerosol-aware rain conversion parameter over land
• determine rain conversion parameter above the freezing level which exponentially decreases with decreasing temperature from [33] equation 8.
• Initialize convective cloud water and cloud cover to zero.
• Initialize updraft mass fluxes to zero.
• Determine maximum indices for the parcel starting point (kbm) and cloud top (kmax).
• Calculate hydrostatic height at layer centers assuming a flat surface (no terrain) from the geopotential.
• Calculate interface height and the entrainment rate as an inverse function of height.
• Find the index for the PBL top using the PBL height; enforce that it is lower than the maximum parcel starting level.
• Convert prsl from centibar to millibar, set normalized mass flux to 1, cloud properties to 0, and save model state variables (after advection/turbulence).
• Calculate saturation specific humidity and enforce minimum moisture values.
• Calculate moist static energy (heo) and saturation moist static energy (heso).

Perform calculations related to the updraft of the entraining/detraining cloud model ("static control").

• Search in the PBL for the level of maximum moist static energy to start the ascending parcel.
• Calculate the temperature, water vapor mixing ratio, and pressure at interface levels.
• Recalculate saturation specific humidity, moist static energy, saturation moist static energy, and horizontal momentum on interface levels. Enforce minimum specific humidity.
• Search below the index "kbm" for the level of free convection (LFC) where the condition \(h_b > h^*\) is first met, where \(h_b, h^*\) are the state moist static energy at the parcel's starting level and saturation moist static energy, respectively. Set "kbcon" to the index of the LFC.
• If no LFC, return to the calling routine without modifying state variables.
• Determine the vertical pressure velocity at the LFC. After [31] , determine the maximum pressure thickness between a parcel's starting level and the LFC. If a parcel doesn't reach the LFC within the critical thickness, then the convective inhibition is deemed too great for convection to be triggered, and the subroutine returns to the calling routine without modifying the state variables.
• The updraft detrainment rate is set constant and equal to the entrainment rate at cloud base.
• Calculate the normalized mass flux for subcloud and in-cloud layers according to [66] equation 1:

  \[ \frac{1}{\eta}\frac{\partial \eta}{\partial z} = \lambda_e - \lambda_d \]

  where \(\eta\) is the normalized mass flux, \(\lambda_e\) is the entrainment rate and \(\lambda_d\) is the detrainment rate. The normalized mass flux increases upward below the cloud base and decreases upward above.
• Set cloud properties equal to the state variables at updraft starting level (kb).
• Calculate the cloud properties as a parcel ascends, modified by entrainment and detrainment. Discretization follows Appendix B of [28] . Following [30], the convective momentum transport is reduced by the convection-induced pressure gradient force by the constant "pgcon", currently set to 0.55 after [89] .
• With entrainment, recalculate the LFC as the first level where buoyancy is positive. The difference in pressure levels between LFCs calculated with/without entrainment must be less than a threshold (currently 25 hPa). Otherwise, convection is inhibited and the scheme returns to the calling routine without modifying the state variables. This is the subcloud dryness trigger modification discussed in [31].
• Calculate additional trigger condition of the convective inhibition (CIN) according to [33] equation 13.
• Turn off convection if the CIN is less than a critical value (cinacr) which is inversely proportional to the large-scale vertical velocity.
• Calculate the cloud top as the first level where parcel buoyancy becomes negative; the maximum possible value is at \(p=0.7p_{sfc}\).
• Calculate the maximum value of the cloud base mass flux using the CFL-criterion-based formula of [31], equation 7.
• Set cloud moisture property equal to the enviromental moisture at updraft starting level (kb).
• Calculate the moisture content of the entraining/detraining parcel (qcko) and the value it would have if just saturated (qrch), according to equation A.14 in [28] . Their difference is the amount of convective cloud water (qlk = rain + condensate). Determine the portion of convective cloud water that remains suspended and the portion that is converted into convective precipitation (pwo). Calculate and save the negative cloud work function (aa1) due to water loading. Above the level of minimum moist static energy, some of the cloud water is detrained into the grid-scale cloud water from every cloud layer with a rate of 0.0005 \(m^{-1}\) (dellal).
• Calculate the cloud work function according to [66] equation 4:

  \[ A_u=\int_{z_0}^{z_t}\frac{g}{c_pT(z)}\frac{\eta}{1 + \gamma}[h(z)-h^*(z)]dz \]

  (discretized according to [28] equation B.10 using B.2 and B.3 of [3] and assuming \(\eta=1\)) where \(A_u\) is the updraft cloud work function, \(z_0\) and \(z_t\) are cloud base and cloud top, respectively, \(\gamma = \frac{L}{c_p}\left(\frac{\partial \overline{q_s}}{\partial T}\right)_p\) and other quantities are previously defined.
• If the updraft cloud work function is negative, convection does not occur, and the scheme returns to the calling routine.
• Continue calculating the cloud work function past the point of neutral buoyancy to represent overshooting according to [31] . Convective overshooting stops when \( cA_u < 0\) where \(c\) is currently 10%, or when 10% of the updraft cloud work function has been consumed by the stable buoyancy force. Overshooting is also limited to the level where \(p=0.7p_{sfc}\).
• For the overshooting convection, calculate the moisture content of the entraining/detraining parcel as before. Partition convective cloud water and precipitation and detrain convective cloud water in the overshooting layers.
• Calculate updraft velocity square(wu2) according to [33] equation 7.
• Calculate the mean updraft velocity within the cloud (wc).
• => Separate the total updraft cloud water at cloud top into vapor and condensate.

Calculate the tendencies of the state variables (per unit cloud base mass flux) and the cloud base mass flux.

• Calculate the change in moist static energy, moisture mixing ratio, and horizontal winds per unit cloud base mass flux for all layers below cloud top from equations B.14 and B.15 from [28], and for the cloud top from B.16 and B.17.
• Following [7], calculate the convective turnover time using the mean updraft velocity (wc) and the cloud depth. It is also proportional to the grid size (gdx).
• Calculate advective time scale (tauadv) using a mean cloud layer wind speed.
• From [33] equation 6, calculate cloud base mass flux as a function of the mean updraft velcoity. As discussed in [33] , when dtconv is larger than tauadv, the convective mixing is not fully conducted before the cumulus cloud is advected out of the grid cell. In this case, therefore, the cloud base mass flux is further reduced in proportion to the ratio of tauadv to dtconv.
• For scale-aware parameterization, the updraft fraction (sigmagfm) is first computed as a function of the lateral entrainment rate at cloud base (see [33] equation 4 and 5), following the study by [27].
• Then, calculate the reduction factor (scaldfunc) of the vertical convective eddy transport of mass flux as a function of updraft fraction from the studies by [4] (also see [33] equation 1 and 2). The final cloud base mass flux with scale-aware parameterization is obtained from the mass flux when sigmagfm << 1, multiplied by the reduction factor ([33] equation 2).

For the "feedback control", calculate updated values of the state variables by multiplying the cloud base mass flux and the tendencies calculated per unit cloud base mass flux from the static control.

• Recalculate saturation specific humidity.
• Calculate the temperature tendency from the moist static energy and specific humidity tendencies.
• Update the temperature, specific humidity, and horiztonal wind state variables by multiplying the cloud base mass flux-normalized tendencies by the cloud base mass flux.
• Accumulate column-integrated tendencies.
• Recalculate saturation specific humidity using the updated temperature.
• Add up column-integrated convective precipitation by multiplying the normalized value by the cloud base mass flux.
• Determine the evaporation of the convective precipitation and update the integrated convective precipitation.
• Update state temperature and moisture to account for evaporation of convective precipitation.
• Update column-integrated tendencies to account for evaporation of convective precipitation.
• Calculate shallow convective cloud water.
• Calculate convective cloud cover, which is used when pdf-based cloud fraction is used (i.e., pdfcld=.true.).
• Separate detrained cloud water into liquid and ice species as a function of temperature only.
• Calculate and retain the updraft mass flux for dust transport by cumulus convection.
• Calculate the updraft convective mass flux.
• save the updraft convective mass flux at cloud top.