CLOUDPRP

Compiling cloudprp: f77 -O -o cloudprp cloudprp.f mieindsub.f

There are two modes of operation to cloudprp. One is for making a Mie scattering table of cloud optical properties. The other mode is to use a Mie table to produce an SHDOM property file. Because the Mie computations are time consuming it is useful to save these scattering tables. A Mie table lists the scattering properties (extinction, single scattering albedo, Legendre series coefficients for the phase function) as a function of droplet effective radius for a particular wavelength and gamma distribution width parameter. The table is made for a liquid water content of 1 g/m^3 and is easily scaled to other LWCs.

Input Parameters

Although the Mie calculations are done for a single wavelength, the wavelength range for a band is input. This is for performing a spectral integration across a band using a k-distribution for molecular absorption. If a range of wavelengths are input then the central wavelength is chosen by a weighted average using a Planck function. For solar wavelengths (< 4 um) the Planck function is for a solar temperature (5800 K), while for longer wavelengths an atmospheric temperature (270 K) is used. A weighted averaged is similarly done to define the band averaged index of refraction. The PARTTYPE='A' option allow one to make Mie tables and property files with a user specified index of refraction, such as for dirty cloud droplets, aerosols, etc.

The gamma distribution of cloud droplet sizes is n(r) = a r^alpha exp(-b*r) where r is the droplet radius, and a, b, alpha specify the gamma distribution. The number concentration of droplets is N = a Gamma(alpha+1)/ b^(alpha+1), where Gamma is the gamma function. The effective radius of the distribution is r_eff = (alpha+3)/b, while the effective variance is v_eff = 1/(alpha+3). A typical value for water clouds is v_eff=0.1 or alpha=7. For ice clouds a typical value is alpha=1. An exponential distribution is obtained with alpha=0. A large value of alpha gives close to a monodisperse distribution.

The lognormal distribution of cloud droplet sizes is n(r) = a/r exp( -[ln(r/r0)]^2 / (2*sigma^2) ) where r0 is the logarithmic mode of the distribution and sigma is the standard deviation of the log. The number concentration of droplets is N = sqrt(2*pi)*sigma*a. The effective radius of the distribution is r_eff = r0*exp(2.5*sigma^2) and the effective variance of the distribution is v_eff = exp(sigma^2)-1. A common value for water clouds is sigma=.35, or v_eff=0.130.

The cloud optical properties depend on the index of refraction and the gamma distribution of cloud droplets. The index of refraction of either water or ice is obtained from subroutines in the program and averaged over the wavelength range as described above. The width parameter of the gamma distribution, alpha, is given in the Mie table. The other parameters of the gamma distribution are determined from the cloud liquid water content and the effective radius. These are either both specified in the cloud LWC file or determined from the LWC. If only the LWC is in the cloud file then the droplet number concentration is assumed to be constant and the effective radius is calculated.

In order to save computing time, the integration over the droplet size distribution does not fully resolve the Mie scattering function. For large size parameters this may cause some small spurious wiggles on the phase function. If these bother you, then change the spacing (DELX) in MAKE_MIE_TABLE. Also the Mie code used does not determine if an integration point lands on a resonance spike, and so there is a small chance that this could effect the results in a minor way for nonabsorbing wavelengths.

The number of Legendre series terms needed for the phase function depends on the effective size parameter (x_eff = 2 pi r_eff/lambda) of the droplet size distribution. For visible wavelengths more than 1000 terms may be needed for a fully converged series. For some radiative transfer applications (outputting only fluxes in solar or for any thermal radiative transfer) a truncation of the series may be desired. The MAXTABLEG and MAXOUTLEG input parameters allow one to control how many Legendre terms are output.

Rayleigh scattering coefficient: The molecular scattering coefficient depends on the air density. Hence for a particular solar wavelength band a coefficient (k) may be defined which gives the extinction from the air pressure (p) and temperature (T): ext = k p/T. The Rayleigh scattering coefficient input to cloudprp may be derived from the molecular Rayleigh scattering optical depth. The Rayleigh optical depth at sea level as a function of wavelength (lambda in micron) is
    tau = 0.0088*lambda**(-4.15+0.2*lambda)
From this formula the cloudprp Rayleigh input coefficient is
    k = (2.97E-4 K mb^-1 km^-1) lambda**(-4.15+0.2*lambda)

Typically the high resolution cloud field occupies only small portion of the atmospheric profile and the other height levels are used to fill in the rest of the atmosphere. The other height levels should be chosen according to the needs of SHDOM, the aerosol profile, and the molecular absorption profile. SHDOM needs some vertical resolution to resolve the radiance field. If aerosols or molecular Rayleigh scattering are significant, then the other levels must exist in clear sky to put that scattering in the property file. Similarly, if a k-distribution file is giving the molecular absorption, then other levels must cover the range where the absorption is significant. For example, stratospheric levels need to be included for ozone absorption in the visible.

Cloud LWC File

   type         [1 or 2, for LWC only or LWC and Reff]
   Nx Ny Nz     [number of X, Y, Z grid points]
   delX delY    [X and Y grid spacing in km]
   Z1 ... Zn    [heights of cloud levels in km]
   T1 ... Tn    [temperatures in Kelvin]
  IX IY IZ LWC        [for 1 parameter file, for each grid point]
    . . .
  IX IY IZ LWC Reff   [for 2 parameter file]
    . . .

Aerosol Property File

   Height,  Extinction,  Eff. Radius,  alpha/sigma, Index of refraction
            at 0.55 um                              at 0.55 um and wavelenth
    (km)     (km^-1)      (micron)

The index of refraction and effective radius of the aerosols depends on their composition (e.g. sea salt, mineral, sulfate), degree of hydration, and wavelength.

An example aerosol file is given below (it has a total 0.55 micron optical depth of 0.4):

   0.0   0.10   0.9  0.7   1.5 -0.01  1.5 -0.02
   2.0   0.10   0.9  0.7   1.5 -0.01  1.5 -0.02
   4.0   0.02   0.6  0.7   1.5 -0.01  1.5 -0.02
  12.0   0.00   0.6  0.7   1.5 -0.01  1.5 -0.02