GFS Hybrid Eddy-diffusivity Mass-flux Scheme

The Hybrid EDMF scheme is a first-order turbulent transport scheme used for subgrid-scale vertical turbulent mixing in the PBL and above. It blends the traditional first-order approach that has been used and improved over the last several years with a more recent scheme that uses a mass-flux approach to calculate the countergradient diffusion terms. More...

Detailed Description

The PBL scheme's main task is to calculate tendencies of temperature, moisture, and momentum due to vertical diffusion throughout the column (not just the PBL). The scheme is an amalgamation of decades of work, starting from the initial first-order PBL scheme of Troen and Mahrt (1986) [93], implemented according to Hong and Pan (1996) [41] and modified by Han and Pan (2011) [34] and Han et al. (2015) [35] to include top-down mixing due to stratocumulus layers from Lock et al. (2000) [63] and replacement of counter-gradient terms with a mass flux scheme according to Siebesma et al. (2007) [89] and Soares et al. (2004) [90]. Recently, heating due to TKE dissipation was also added according to Han et al. (2015) [35].

This subroutine contains all of logic for the Hybrid EDMF PBL scheme except for the calculation of the updraft properties and mass flux. The scheme works on a basic level by calculating background diffusion coefficients and updating them according to which processes are occurring in the column. The most important difference in diffusion coefficients occurs between those levels in the PBL and those above the PBL, so the PBL height calculation is of utmost importance. An initial estimate is calculated in a "predictor" step in order to calculate Monin-Obukhov similarity values and a corrector step recalculates the PBL height based on updated surface thermal characteristics. Using the PBL height and the similarity parameters, the diffusion coefficients are updated below the PBL top based on Hong and Pan (1996) [41] (including counter-gradient terms). Diffusion coefficients in the free troposphere (above the PBL top) are calculated according to Louis (1979) [68] with updated Richardson number-dependent functions. If it is diagnosed that PBL top-down mixing is occurring according to Lock et al. (2000) [63] , then then diffusion coefficients are updated accordingly. Finally, for convective boundary layers (defined as when the Obukhov length exceeds a threshold), the counter-gradient terms are replaced using the mass flux scheme of Siebesma et al. (2007) [89] . In order to return time tendencies, a fully implicit solution is found using tridiagonal matrices, and time tendencies are "backed out." Before returning, the time tendency of temperature is updated to reflect heating due to TKE dissipation following Han et al. (2015) [35] .

Argument Table

local_name	standard_name	long_name	units	rank	type	kind	intent	optional
ix	horizontal_dimension	horizontal dimension	count	0	integer		in	F
im	horizontal_loop_extent	horizontal loop extent	count	0	integer		in	F
km	vertical_dimension	vertical layer dimension	count	0	integer		in	F
ntrac	number_of_vertical_diffusion_tracers	number of tracers to diffuse vertically	count	0	integer		in	F
ntcw	index_for_liquid_cloud_condensate	cloud condensate index in tracer array	index	0	integer		in	F
dv	tendency_of_y_wind_due_to_model_physics	updated tendency of the y wind	m s-2	2	real	kind_phys	inout	F
du	tendency_of_x_wind_due_to_model_physics	updated tendency of the x wind	m s-2	2	real	kind_phys	inout	F
tau	tendency_of_air_temperature_due_to_model_physics	updated tendency of the temperature	K s-1	2	real	kind_phys	inout	F
rtg	tendency_of_tracers_due_to_model_physics	updated tendency of the tracers	kg kg-1 s-1	3	real	kind_phys	inout	F
u1	x_wind	x component of layer wind	m s-1	2	real	kind_phys	in	F
v1	y_wind	y component of layer wind	m s-1	2	real	kind_phys	in	F
t1	air_temperature	layer mean air temperature	K	2	real	kind_phys	in	F
q1	tracer_concentration	layer mean tracer concentration, cf. GFS_typedefs.F90	kg kg-1	3	real	kind_phys	in	F
swh	tendency_of_air_temperature_due_to_shortwave_heating_on_radiation_time_step	total sky shortwave heating rate	K s-1	2	real	kind_phys	in	F
hlw	tendency_of_air_temperature_due_to_longwave_heating_on_radiation_time_step	total sky longwave heating rate	K s-1	2	real	kind_phys	in	F
xmu	zenith_angle_temporal_adjustment_factor_for_shortwave_fluxes	zenith angle temporal adjustment factor for shortwave	none	1	real	kind_phys	in	F
psk	dimensionless_exner_function_at_lowest_model_interface	dimensionless Exner function at the surface interface	none	1	real	kind_phys	in	F
rbsoil	bulk_richardson_number_at_lowest_model_level	bulk Richardson number at the surface	none	1	real	kind_phys	in	F
zorl	surface_roughness_length	surface roughness length in cm	cm	1	real	kind_phys	in	F
u10m	x_wind_at_10m	x component of wind at 10 m	m s-1	1	real	kind_phys	in	F
v10m	y_wind_at_10m	y component of wind at 10 m	m s-1	1	real	kind_phys	in	F
fm	Monin-Obukhov_similarity_function_for_momentum	Monin-Obukhov similarity function for momentum	none	1	real	kind_phys	in	F
fh	Monin-Obukhov_similarity_function_for_heat	Monin-Obukhov similarity function for heat	none	1	real	kind_phys	in	F
tsea	surface_skin_temperature	surface temperature	K	1	real	kind_phys	in	F
heat	kinematic_surface_upward_sensible_heat_flux	kinematic surface upward sensible heat flux	K m s-1	1	real	kind_phys	in	F
evap	kinematic_surface_upward_latent_heat_flux	kinematic surface upward latent heat flux	kg kg-1 m s-1	1	real	kind_phys	in	F
stress	surface_wind_stress	surface wind stress	m2 s-2	1	real	kind_phys	in	F
spd1	wind_speed_at_lowest_model_layer	wind speed at lowest model level	m s-1	1	real	kind_phys	in	F
kpbl	vertical_index_at_top_of_atmosphere_boundary_layer	PBL top model level index	index	1	integer		out	F
prsi	air_pressure_at_interface	air pressure at model layer interfaces	Pa	2	real	kind_phys	in	F
del	air_pressure_difference_between_midlayers	pres(k) - pres(k+1)	Pa	2	real	kind_phys	in	F
prsl	air_pressure	mean layer pressure	Pa	2	real	kind_phys	in	F
prslk	dimensionless_exner_function_at_model_layers	Exner function at layers	none	2	real	kind_phys	in	F
phii	geopotential_at_interface	geopotential at model layer interfaces	m2 s-2	2	real	kind_phys	in	F
phil	geopotential	geopotential at model layer centers	m2 s-2	2	real	kind_phys	in	F
delt	time_step_for_physics	time step for physics	s	0	real	kind_phys	in	F
dspheat	flag_TKE_dissipation_heating	flag for using TKE dissipation heating	flag	0	logical		in	F
dusfc	instantaneous_surface_x_momentum_flux	x momentum flux	Pa	1	real	kind_phys	out	F
dvsfc	instantaneous_surface_y_momentum_flux	y momentum flux	Pa	1	real	kind_phys	out	F
dtsfc	instantaneous_surface_upward_sensible_heat_flux	surface upward sensible heat flux	W m-2	1	real	kind_phys	out	F
dqsfc	instantaneous_surface_upward_latent_heat_flux	surface upward latent heat flux	W m-2	1	real	kind_phys	out	F
hpbl	atmosphere_boundary_layer_thickness	PBL thickness	m	1	real	kind_phys	out	F
hgamt	countergradient_mixing_term_for_temperature	countergradient mixing term for temperature	K	1	real	kind_phys	inout	F
hgamq	countergradient_mixing_term_for_water_vapor	countergradient mixing term for water vapor	kg kg-1	1	real	kind_phys	inout	F
dkt	atmosphere_heat_diffusivity	diffusivity for heat	m2 s-1	2	real	kind_phys	out	F
kinver	index_of_highest_temperature_inversion	index of highest temperature inversion	index	1	integer		in	F
xkzm_m	atmosphere_momentum_diffusivity_background	background value of momentum diffusivity	m2 s-1	0	real	kind_phys	in	F
xkzm_h	atmosphere_heat_diffusivity_background	background value of heat diffusivity	m2 s-1	0	real	kind_phys	in	F
xkzm_s	diffusivity_background_sigma_level	sigma level threshold for background diffusivity	none	0	real	kind_phys	in	F
lprnt	flag_print	flag for printing diagnostics to output	flag	0	logical		in	F
ipr	horizontal_index_of_printed_column	horizontal index of printed column	index	0	integer		in	F
xkzminv	atmosphere_heat_diffusivity_background_maximum	maximum background value of heat diffusivity	m2 s-1	0	real	kind_phys	in	F
moninq_fac	atmosphere_diffusivity_coefficient_factor	multiplicative constant for atmospheric diffusivities	none	0	real	kind_phys	in	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

Hybrid EDMF General Algorithm

1. Compute preliminary variables from input arguments.
2. Calculate the first estimate of the PBL height ("Predictor step").
3. Calculate Monin-Obukhov similarity parameters.
4. Update thermal properties of surface parcel and recompute PBL height ("Corrector step").
5. Determine whether stratocumulus layers exist and compute quantities needed for enhanced diffusion.
6. Calculate the inverse Prandtl number.
7. Compute diffusion coefficients below the PBL top.
8. Compute diffusion coefficients above the PBL top.
9. If the PBL is convective, call the mass flux scheme to replace the countergradient terms.
10. Compute enhanced diffusion coefficients related to stratocumulus-topped PBLs.
11. Solve for the temperature and moisture tendencies due to vertical mixing.
12. Calculate heating due to TKE dissipation and add to the tendency for temperature.
13. Solve for the horizontal momentum tendencies and add them to output tendency terms.

Detailed Algorithm

Functions/Subroutines
subroutine	hedmf::hedmf_run (ix, im, km, ntrac, ntcw, dv, du, tau, rtg, u1, v1, t1, q1, swh, hlw, xmu, psk, rbsoil, zorl, u10m, v10m, fm, fh, tsea, heat, evap, stress, spd1, kpbl, prsi, del, prsl, prslk, phii, phil, delt, dspheat, dusfc, dvsfc, dtsfc, dqsfc, hpbl, hgamt, hgamq, dkt, kinver, xkzm_m, xkzm_h, xkzm_s, lprnt, ipr, xkzminv, moninq_fac, errmsg, errflg)
subroutine	tridi2 (l, n, cl, cm, cu, r1, r2, au, a1, a2)
	Routine to solve the tridiagonal system to calculate temperature and moisture at \( t + \Delta t \); part of two-part process to calculate time tendencies due to vertical diffusion. More...
subroutine	tridin (l, n, nt, cl, cm, cu, r1, r2, au, a1, a2)
	Routine to solve the tridiagonal system to calculate u- and v-momentum at \( t + \Delta t \); part of two-part process to calculate time tendencies due to vertical diffusion. More...
subroutine	mfpbl (im, ix, km, ntrac, delt, cnvflg, zl, zm, thvx, q1, t1, u1, v1, hpbl, kpbl, sflx, ustar, wstar, xmf, tcko, qcko, ucko, vcko)
	This subroutine is used for calculating the mass flux and updraft properties. More...