WSUB parameterization

Background

Ice cloud formation is very sensitive to the updraft velocity.

The characteristic updraft velocity for ice nucleation (w*) in the original ACME/CAM5 is parameterized a function of TKE and has an artificial upper bound of 0.2 m/s.

Based on parcel model simulations and in-situ aircraft measurements, we proposed a new treatment of w*, assuming the subgrid variation of vertical velocities follows the Gaussian distribution.

It has been implemented and tested in ACME, along with other improvements for ice cloud parameterizations.

 

Method

A new sub-grid parameterization of the characteristic updraft velocity (w*) for ice nucleation was proposed by Zhang et al. (in preparation). It is calculated by averaging the vertical velocities in the updraft portion of an assumed sub-grid distribution. In the present scheme, the subgrid variation of vertical velocities is assumed to follow the Gaussian distribution. The upper bound (0.2 m/s) in the original model was removed.

 

Implementation

A new subroutine is added in nucleate_ice_cam.F90:

subroutine subgrid_mean_updraft(ncol, w0, wsig, ww)

   !! interface

   integer,  intent(in) :: ncol              ! number of cols
   real(r8), intent(in) :: wsig(pcols,pver ) ! standard deviation (m/s)
   real(r8), intent(in) :: w0(pcols,pver ) ! large scale vertical velocity (m/s)
   real(r8), intent(out):: ww(pcols,pver) ! mean updraft velocity(m/s) -> characteristic w*

   !! local
   integer, parameter :: nbin = 50

   real(r8) :: wlarge,sigma
   real(r8) :: xx, yy
   real(r8) :: zz(nbin)
   real(r8) :: wa(nbin)
   integer  :: kp(nbin)
   integer  :: i, k
   integer  :: ibin

   !! program begins

   do k = 1, pver
   do i = 1, ncol

      sigma  = max(0.001_r8, wsig(i,k))
      wlarge = w0(i,k)

      xx = 6._r8 * sigma / nbin

      do ibin = 1, nbin
         yy = wlarge - 3._r8*sigma + 0.5*xx
         yy = yy + (ibin-1)*xx
         !! wbar = integrator < w * f(w) * dw >
         zz(ibin) = yy * exp(-1.*(yy-wlarge)**2/(2*sigma**2))/(sigma*sqrt(2*pi))*xx
      end do

      kp(:) = 0
      wa(:) = 0._r8

      where(zz.gt.0._r8)
         kp = 1
         wa = zz
      elsewhere
         kp = 0
         wa = 0._r8
      end where

      if(sum(kp).gt.0) then
         !! wbar = integrator < w * f(w) * dw >
         ww(i,k) = sum(wa)
      else
         ww(i,k) = 0._r8
      end if

      !!write(6,*) 'i, k, w0, wsig, ww : ', i, k, w0(i,k), wsig(i,k), ww(i,k)

  end do
  end do

end subroutine subgrid_mean_updraft

 

Results


Comparison between the parameterized w* and the inverted “true” w* derived from parcel model simulations and aircraft measurements.

 

Changes in longwave cloud forcing caused by using the new parameterization. 

 

It has a large impact on instantaneous ice nucleation events, but the change to the global annual mean cloud forcing is rather small.