function [eff_diameter_prime]=lidar_radar_eff_diameter(beta_a_backscat...
		,radar_backscat,depol,beta_a,p180_ice,h20_depol_threshold);
%[r_eff_prime]=lidar_radar_size(beta_a_backscat...
%		,radar_backscat,depol,beta_a,p180_ice,h20_depol_threshold);
%beta_a_backscat     = lidar backscatter cross section, (1/(m sr)
%radar_backscat      = radar backscatter cross section, (1/(m sr)
%depol               = lidar measured depolarization, this can be either
%                         linear or circular depolarization as long as
%                         h20_depol_threshold is set for proper pol type.
%beta_a              = scattering cross section array array computed from measured od.
%p180_ice            = p(180)/4pi = ice crystal backscatter phase function
%                      if p180_ice=[] (ie no number is supplied) beta_a computed from the measured
%                      od will be used, otherwise beta_a will be set
%                      equal to beta_a_backscat/p180_ice. This is useful
%                      because the measured beta_a is sensitive 
%                       averaging lengths and times, with short averages
%                       apt to have excessive noise and long averages apt
%                       to mix regions of low and high scattering the
%                       computed array can be replaced by a user supplied
%                       constant value. It is recomended that this be based 
%                       on an independent analysis of the data to determine an
%                       appropriate value for p(180)/4pi in ice regions
%                       of the cloud. 
%h20_depol_threshold = depol < h20_depol_threshold indicates liquid water cloud
%eff_diameter_prime  = lidar-radar effective diameter (microns)
%                    =(9*<Volume^2>/(pi*<Area>))^.25
%                      where <Volume^2> and <Area> refer to particle averages
%                      as defined by Donovan and Lammeren JGR,v106, D21,
%                      pp27425
%                    
% Assumptions:
%      - cloud at a given data point is either all water or all ice
%      - when depolarization is < h20_depol_threshold, cloud is water
%      - backscatter phase function for water droplets, p(180)/4pi = 0.05
%      - particles are large compared to the lidar wavelength such that
%              the optical scattering cross section is twice the
%              projected area of the particle.
%      - particles are small compared to the radar wavelength
%      - radar attenuation is negligible


k_sq_water=0.93;  %dielectric constant squared for water
k_sq_ice=  .176;   %dielectric constant squared for ice
lambda_radar=8.6e-3; %radar wavelength in meters.



% set separate constants for water and ice regions.
  %user supplied p(180)/4pi for ice regions
  [nprofiles,nalts]=size(beta_a_backscat);
  if ~isempty(p180_ice) %user over ride of internal beta_a computation;
    beta_a=beta_a_backscat/p180_ice; %compute beta_a with constant p180
  end
  
  %fixed value p(180)/4pi in water clouds.
    p180_array(depol< h20_depol_threshold)=.05;
 
    
 %dielectric constant
    k_sq_array=k_sq_ice*ones(size(beta_a_backscat));
    k_sq_array(depol< h20_depol_threshold)=k_sq_water;



 radar_factor_array=3*lambda_radar^4./(64*pi^4*k_sq_array);
 
 
 %eff_diameter_prime is the fundamental size dependent quantity derived 
 %from lidar and radar scattering cross sections.
 %<volume of particle^2>/<projected area of particle> = eff_diameter_prime^4 *pi/9
 %see Donovan and van Lammeran, JGR, Vol 106 no D21, Nov 16, 2001.
 %for more on this definition which we state in terms of diameter rather
 %than raduis. In the special case of monodisperse spherical particles
 %the effective_diameter_prime is equal to the effective diameter. 
 %In general, the converstion to effective diameter is a function of size
 %distribution parameters and ice crystal shape.
 

 beta_a_backscat(beta_a_backscat<=0)=nan;
 radar_backscat(radar_backscat<=0)=nan;
 
 
 eff_diameter_prime=2*((8*pi/3).*radar_factor_array.*radar_backscat...
       ./beta_a).^.25; 

 
%change units from meters to microns
eff_diameter_prime=real(eff_diameter_prime)*1e6;