/**
\page RAD_CLD GFS Cloud-Radiation Interaction
\section des_radcld Description

The cloud-radiation interaction in the CCPP-Physics can be grouped in terms of three processes:
- horizontal coverage of cloud, normally referred to as \b cloud \b fraction
- cloud radii calculation
- vertical extent of the clouds (gethml())

In the CCPP-Physics, these cloud parameterization is followed by \ref GFS_RRTMG.

\section cld_fra  Cloud Fraction Calculation
The cloud fraction in the CCPP-physics suite with the Zhao-Carr scheme (progcld1()) is determined following 
Xu and Randall(1996) \cite xu_and_randall_1996, which is proportional to the grid-scale cloud condensate 
and relative humidity. It was modified ( Han and Pan (2011) \cite han_and_pan_2011 ) 
because it tends to produce too much low cloud over  the entire globe with the new shallow convection scheme. Following Xu and Randall (1996) \cite xu_and_randall_1996 ,
the fractional cloud cover within a grid box (\f$\sigma\f$) is given by:
\f[
\sigma=RH^{k_{1}}\left(1-exp\left\{-\frac{k_{2}q_{l}}{\left[(1-RH)q_{s}\right]^{k_{3}}}\right\}\right)
\f]
where \f$RH\f$ is relative humidity,\f$q_{l}\f$ is the cloud condensate, \f$q_{s}\f$ is saturation specific humidity,
\f$k_{1}\f$,\f$k_{2}\f$, and \f$k_{3}\f$ are empirical coefficients. Using data produced from explicit 
simulations of the observed tropical cloud systems, Xu and Randall(1996) \cite xu_and_randall_1996 have obtained
empirical values of \f$k_{1}\f$,\f$k_{2}\f$, and \f$k_{3}\f$ that are 0.25, 100 and 0.49, respectively. In the
previous GFS, values of \f$k_{1}=0.25\f$,\f$k_{2}=2000\f$, and \f$k_{3}=0.25\f$ are used to increase cloud
cover because the old shallow convection scheme is too efficient in destroying stratocumulus clouds. Now that the 
new shallow convection scheme can produce sufficient low clouds, the original empirical values of Xu and 
Randall (1996) \cite xu_and_randall_1996 (i.e., \f$k_{1}=0.25\f$,\f$k_{2}=100\f$, and \f$k_{3}=0.49\f$) are used.
Maximum-randomly cloud overlapping is used in both longwave radiation and shortwave radiation.

On the other hand, the convective cloudiness in the CCPP-Physics with the Zhao-Carr scheme is taken 
into account by detaining cloud water
from upper cumulus layers into the grid-scale cloud condensate, which helps to increase high cirrus clouds.
To take into account the convective cloudiness contribution from all the cumulus layers. The CCPP-Physics with the Zhao-Carr 
scheme adds the suspended cloud water in every cumulus layer into the grid-scale cloud condensate only 
for the cloud fraction and radiation computations. It has been shown (Fig.6 in Han et al.(2017) \cite han_et_al_2017
)that cloudiness enhancement by the suspended cloud water in the convective updraft is evident in the low
and middle clouds over the tropical convective regions. The impact of the suspended cloud water on convective
cloudiness enhancement appears to be rather small.

However, in the CCPP-Physics with the GFDL cloud MP, the calculation of cloud fraction calculation includes all cloud
hydrometeors:
\f[
\sigma=\max\left[0,\min\left(1,\frac{q_{plus}-q_{s}}{q_{plus}-q_{minus}}\right)\right]
\f]
where
\f[
q_{plus}=(q_{v}+q_{liq}+q_{sol})\times (1+h_{var})
\f]
\f[
q_{minus}=(q_{v}+q_{liq}+q_{sol})\times (1-h_{var})
\f]

where \f$h_{var}\f$ is the horizontal subgrid variability (see \ref GFDL_cloud)
and it is calculated in the last step of fast physics in Lagrangian to Eulerian step.

\section cld_radii Cloud Radii Calculation
Two methods have been used to parameterize cloud properties in the GFS model. The previous 
method made use of a diagnostic cloud scheme (diagcld1()),  in which cloud properties are determined based on model-predicted 
temperature, pressure, and boundary layer circulation from Harshvardhan et al. (1989) \cite harshvardhan_et_al_1989 . The
diagnostic scheme is now replaced with a prognostic scheme (progcld1() with the Zhao-Carr scheme and progcld4() with
the GFDL cloud MP scheme) that uses cloud condensate information instead (Heymsfield and McFarquhar (1996)
 \cite heymsfield_and_mcfarquhar_1996).

For the parameterization of effective radius of liquid cloud droplet,\f$r_{ew}\f$, we fix \f$r_{ew}\f$ to a value of \f$10\mu m\f$ over
the oceans. Over the land, \f$r_{ew}\f$ is defined as:
\f[
   r_{ew} = 5+5\times F
\f]
where 
\f[
F = \min\left[1.0,\max\left[0.0,(273.16-T)\times0.05\right]\right]
\f]
Thus, the effective radius of liquid cloud droplets will reach to a  minimum values of \f$5\mu m\f$ when F=0, and to a maximum value of 
\f$10\mu m\f$ when the ice fraction is increasing.

For ice clouds, following Heymsfield and McFarquhar (1996) \cite heymsfield_and_mcfarquhar_1996,
we have made the effective ice droplet radius to be an empirical function of ice water concentration (IWC) and environmental temperature as:
\f[
  r_{ei}=\begin{cases}(1250/9.917)IWC^{0.109} & T <-50^0C \\(1250/9.337)IWC^{0.080} & -50^0C \leq T<-40^0C\\(1250/9.208)IWC^{0.055} & -40^0C\leq T <-30^0C\\(1250/9.387)IWC^{0.031} & -30^0C \leq T\end{cases}
\f]

Currently, the effective radius of rain cloud and snow cloud is set to \f$1000\mu m\f$ and \f$250\mu m\f$,respectively.

*/