GMTB Common Community Physics Package (CCPP) Scientific Documentation  Version 1.0
GFS mfdeepcnv Main

This subroutine contains the entirety of the SAMF deep convection scheme. More...

Detailed Description

For grid sizes larger than threshold value, as in [28], the SAMF deep convection scheme can be described in terms of three types of "controls": static, dynamic, and feedback. The static control component consists of the simple entraining/detraining updraft/downdraft cloud model and is used to determine the cloud properties, convective precipitation, as well as the convective cloud top height. The dynamic control is the determination of the potential energy available for convection to "consume", or how primed the large-scale environment is for convection to occur due to changes by the dyanmics of the host model. The feedback control is the determination of how the parameterized convection changes the large-scale environment (the host model state variables) given the changes to the state variables per unit cloud base mass flux calculated in the static control portion and the deduced cloud base mass flux determined from the dynamic control.

For grid sizes smaller than threshold value, the cloud base mass flux in the SAMF scheme is determined by the cumulus updraft velocity averaged over the whole cloud depth ([33] ),which in turn, determines changes of the large-scale environment due to the cumulus convection.

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
cldwrk cloud_work_function cloud work function m2 s-2 1 real kind_phys out F
rn lwe_thickness_of_deep_convective_precipitation_amount deep convective rainfall amount on physics timestep m 1 real kind_phys out F
kbot vertical_index_at_cloud_base index for cloud base index 1 integer out F
ktop vertical_index_at_cloud_top index for cloud top index 1 integer out F
kcnv flag_deep_convection deep convection: 0=no, 1=yes flag 1 integer out 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
ud_mf instantaneous_atmosphere_updraft_convective_mass_flux (updraft mass flux) * delt kg m-2 2 real kind_phys out F
dd_mf instantaneous_atmosphere_downdraft_convective_mass_flux (downdraft 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 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 Deep Convection Scheme General Algorithm

  1. Compute preliminary quantities needed for static, dynamic, and feedback control portions of the algorithm.
  2. Perform calculations related to the updraft of the entraining/detraining cloud model ("static control").
  3. Perform calculations related to the downdraft of the entraining/detraining cloud model ("static control").
  4. For grid sizes larger than the threshold value (currently 8 km):
    1) Using the updated temperature and moisture profiles that were modified by the convection on a short time-scale, recalculate the total cloud work function to determine the change in the cloud work function due to convection, or the stabilizing effect of the cumulus.
    2) For the "dynamic control", using a reference cloud work function, estimate the change in cloud work function due to the large-scale dynamics. Following the quasi-equilibrium assumption, calculate the cloud base mass flux required to keep the large-scale convective destabilization in balance with the stabilization effect of the convection.
  5. For grid sizes smaller than the threshold value (currently 8 km):
    1) compute the cloud base mass flux using the cumulus updraft velocity averaged over the whole cloud depth.
  6. For scale awareness, the updraft fraction (sigma) is obtained as a function of cloud base entrainment. Then, the final cloud base mass flux is obtained by the original mass flux multiplied by the \((1-sigma)^2\).
  7. 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_deep::sasas_deep_run (im, ix, km, delt, delp, prslp, psp, phil, ql1, ql2, q1, t1, u1, v1, cldwrk, rn, kbot, ktop, kcnv, islimsk, garea, dot, ncloud, ud_mf, dd_mf, dt_mf, cnvw, cnvc, errmsg, errflg)
 

Function/Subroutine Documentation

subroutine sasas_deep::sasas_deep_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)  cldwrk,
real(kind=kind_phys), dimension(im), intent(out)  rn,
integer, dimension(im), intent(out)  kbot,
integer, dimension(im), intent(out)  ktop,
integer, dimension(im), intent(out)  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,km), intent(out)  ud_mf,
real(kind=kind_phys), dimension(im,km), intent(out)  dd_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 static, dynamic, 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.
  • 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 and downdraft mass fluxes to zero.
  • Determine maximum indices for the parcel starting point (kbm), LFC (kbmax), and cloud top (kmax).
  • Calculate hydrostatic height at layer centers assuming a flat surface (no terrain) from the geopotential.
  • Calculate interface height and the initial entrainment rate as an inverse function of height.
  • Convert prsl from centibar to millibar, set normalized mass fluxes 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 below index "kbm" for the level of maximum moist static energy.
  • Calculate the temperature, specific humidity, 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 and calculate \((1 - RH)\).
  • Search below the index "kbmax" 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.
  • Calculate the entrainment rate according to [31], equation 8, after [7], equation 2 given by:

    \[ \epsilon = \epsilon_0F_0 + d_1\left(1-RH\right)F_1 \]

    where \(\epsilon_0\) is the cloud base entrainment rate, \(d_1\) is a tunable constant, and \(F_0=\left(\frac{q_s}{q_{s,b}}\right)^2\) and \(F_1=\left(\frac{q_s}{q_{s,b}}\right)^3\) where \(q_s\) and \(q_{s,b}\) are the saturation specific humidities at a given level and cloud base, respectively. The detrainment rate in the cloud is assumed to be equal to the entrainment rate at cloud base.
  • 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.
  • 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. If the thickness of the calculated convection is less than a threshold (currently 200 hPa), then convection is inhibited, and the scheme returns to the calling routine.
  • To originate the downdraft, search for the level above the minimum in moist static energy. Return to the calling routine without modification if this level is determined to be outside of the convective cloud layers.
  • 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. The liquid water in the updraft layer is assumed to be detrained from the layers above the level of the minimum moist static energy into the grid-scale cloud water (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.
  • 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 above the mimimum in moist static energy.
  • Calculate updraft velocity square(wu2) according to [33] equation 7.
  • Calculate the mean updraft velocity within the cloud (wc).
  • Swap the indices of the convective cloud top (ktcon) and the overshooting convection top (ktcon1) to use the same cloud top level in the calculations of \(A^+\) and \(A^*\).
  • Separate the total updraft cloud water at cloud top into vapor and condensate.

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

  • First, in order to calculate the downdraft mass flux (as a fraction of the updraft mass flux), calculate the wind shear and precipitation efficiency according to equation 58 in [23] :

    \[ E = 1.591 - 0.639\frac{\Delta V}{\Delta z} + 0.0953\left(\frac{\Delta V}{\Delta z}\right)^2 - 0.00496\left(\frac{\Delta V}{\Delta z}\right)^3 \]

    where \(\Delta V\) is the integrated horizontal shear over the cloud depth, \(\Delta z\), (the ratio is converted to units of \(10^{-3} s^{-1}\)). The variable "edto" is \(1-E\) and is constrained to the range \([0,0.9]\).
  • Next, calculate the variable detrainment rate between the surface and the LFC according to:

    \[ \lambda_d = \frac{1-\beta^{\frac{1}{k_{LFC}}}}{\overline{\Delta z}} \]

    \(\lambda_d\) is the detrainment rate, \(\beta\) is a constant currently set to 0.05, implying that only 5% of downdraft mass flux at LFC reaches the ground surface due to detrainment, \(k_{LFC}\) is the vertical index of the LFC level, and \(\overline{\Delta z}\) is the average vertical grid spacing below the LFC.
  • Calculate the normalized downdraft mass flux from equation 1 of [66] . Downdraft entrainment and detrainment rates are constants from the downdraft origination to the LFC.
  • Set initial cloud downdraft properties equal to the state variables at the downdraft origination level.
  • Calculate the cloud properties as a parcel descends, modified by entrainment and detrainment. Discretization follows Appendix B of [28] .
  • Compute the amount of moisture that is necessary to keep the downdraft saturated.
  • Update the precipitation efficiency (edto) based on the ratio of normalized cloud condensate (pwavo) to normalized cloud evaporate (pwevo).
  • Calculate downdraft cloud work function ( \(A_d\)) according to equation A.42 (discretized by B.11) in [28] . Add it to the updraft cloud work function, \(A_u\).
  • Check for negative total cloud work function; if found, return to calling routine without modifying state variables.
  • Calculate the change in moist static energy, moisture mixing ratio, and horizontal winds per unit cloud base mass flux near the surface using equations B.18 and B.19 from [28], for all layers below cloud top from equations B.14 and B.15, and for the cloud top from B.16 and B.17.
  • If grid size is less than a threshold value (dxcrtas: currently 8km), the quasi-equilibrium assumption of Arakawa-Schubert is not used any longer.
  • If grid size is larger than the threshold value (i.e., asqecflg=.true.), the quasi-equilibrium assumption is used to obtain the cloud base mass flux. To begin with, calculate the change in the temperature and moisture profiles per unit cloud base mass flux.

Using the updated temperature and moisture profiles that were modified by the convection on a short time-scale, recalculate the total cloud work function to determine the change in the cloud work function due to convection, or the stabilizing effect of the cumulus.

  • Using notation from [66], the previously calculated cloud work function is denoted by \(A^+\). Now, it is necessary to use the entraining/detraining cloud model ("static control") to determine the cloud work function of the environment after the stabilization of the arbitrary convective element (per unit cloud base mass flux) has been applied, denoted by \(A^*\).
  • Recalculate saturation specific humidity.
  • As before, recalculate the updraft cloud work function.
  • As before, recalculate the downdraft cloud work function.
  • Following [7], the convective adjustment time (dtconv) is set to be proportional to the convective turnover time, which is computed 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 for the grid sizes where the quasi-equilibrium assumption of Arakawa-Schubert is not valid any longer. 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 the cases where the quasi-equilibrium assumption of Arakawa-Schubert is valid, first calculate the large scale destabilization as in equation 5 of [66] :

    \[ \frac{\partial A}{\partial t}_{LS}=\frac{A^+-cA^0}{\Delta t_{LS}} \]

    Here \(A^0\) is set to zero following [33] , implying that the instability is completely eliminated after the convective adjustment time, \(\Delta t_{LS}\).
  • Calculate the stabilization effect of the convection (per unit cloud base mass flux) as in equation 6 of [66] :

    \[ \frac{\partial A}{\partial t}_{cu}=\frac{A^*-A^+}{\Delta t_{cu}} \]

    \(\Delta t_{cu}\) is the short timescale of the convection.
  • The cloud base mass flux (xmb) is then calculated from equation 7 of [66]

    \[ M_c=\frac{-\frac{\partial A}{\partial t}_{LS}}{\frac{\partial A}{\partial t}_{cu}} \]

    Again when dtconv is larger than tauadv, the cloud base mass flux is further reduced in proportion to the ratio of tauadv to dtconv.

  • If the large scale destabilization is less than zero, or the stabilization by the convection is greater than zero, then the scheme returns to the calling routine without modifying the state variables.
  • 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.

  • 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 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.
  • If convective precipitation is zero or negative, reset the updated state variables back to their original values (negating convective changes).
  • Calculate and retain the updraft and downdraft mass fluxes for dust transport by cumulus convection.
  • Calculate the updraft convective mass flux.
  • save the updraft convective mass flux at cloud top.
  • Calculate the downdraft convective mass flux.