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ice_psd_Mcfar_97

PURPOSE ^

ice_psd_Mcfar_97 returns the particle size distribution in cirrus clouds.

SYNOPSIS ^

function [y]=ice_psd_Mcfar_97(T,IWC,D,mode);

DESCRIPTION ^

 ice_psd_Mcfar_97 returns the particle size distribution in cirrus clouds.
    
     Returns a vector with the particle size distribution for
     a given temperature and ice water content, for a tropical cirrus cloud.
     The parameterization is based upon the distribution of mass equivalent
     spheres with diameter Dm=(6M/(pi*rhoice))^(1/3), 
     where rhoice is the density
     of solid ice spheres, and M is the mass of the ice crystal. The
     parameterization can be applied over all sizes. 
     The particle size distribution is a bimodal distribution,
     and with the input "mode" there is an option of which mode
     that will be returned.

     The parameterization is taken from G.M McFarquhar and A.J Heymsfield,
     "Parameterization of tropical cirrus ice crystal size distribution
     and implications for radiative transfer: results from CEPEX",
     J. Atmos. Sci., 54, 2187-2200, 1997

 FORMAT   [y] = ice_psd_Mcfar_97(T,IWC,D,mode)     

 OUT      y is a vector with the particle size distribution [#/m^3/m]

 IN       T     Temperature [Kelvin]
          IWC   Ice water content [g/m^3]
          D     the size vector of the ice particles,
                (the mass equivalent sphere diameter [m]),
                where the concentration will be calculated  
          mode  1=both small and large mode
                2=only small mode
                3=only large mode

 History: 2004-07-19  Created by Bengt Rydberg

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

DOWNLOAD ^

ice_psd_Mcfar_97.m

SOURCE CODE ^

0001 % ice_psd_Mcfar_97 returns the particle size distribution in cirrus clouds.
0002 %
0003 %     Returns a vector with the particle size distribution for
0004 %     a given temperature and ice water content, for a tropical cirrus cloud.
0005 %     The parameterization is based upon the distribution of mass equivalent
0006 %     spheres with diameter Dm=(6M/(pi*rhoice))^(1/3),
0007 %     where rhoice is the density
0008 %     of solid ice spheres, and M is the mass of the ice crystal. The
0009 %     parameterization can be applied over all sizes.
0010 %     The particle size distribution is a bimodal distribution,
0011 %     and with the input "mode" there is an option of which mode
0012 %     that will be returned.
0013 %
0014 %     The parameterization is taken from G.M McFarquhar and A.J Heymsfield,
0015 %     "Parameterization of tropical cirrus ice crystal size distribution
0016 %     and implications for radiative transfer: results from CEPEX",
0017 %     J. Atmos. Sci., 54, 2187-2200, 1997
0018 %
0019 % FORMAT   [y] = ice_psd_Mcfar_97(T,IWC,D,mode)
0020 %
0021 % OUT      y is a vector with the particle size distribution [#/m^3/m]
0022 %
0023 % IN       T     Temperature [Kelvin]
0024 %          IWC   Ice water content [g/m^3]
0025 %          D     the size vector of the ice particles,
0026 %                (the mass equivalent sphere diameter [m]),
0027 %                where the concentration will be calculated
0028 %          mode  1=both small and large mode
0029 %                2=only small mode
0030 %                3=only large mode
0031 %
0032 % History: 2004-07-19  Created by Bengt Rydberg
0033 
0034 function [y]=ice_psd_Mcfar_97(T,IWC,D,mode);
0035 
0036 
0037 T=T-273.15;
0038 
0039 if T>0
0040    error('Only temperatures less than 273.15 K are allowed.')
0041 end
0042 if ((mode~=1) && (mode~=2) && (mode~=3))
0043    error('Only mode 1,2, or 3 are allowed.')
0044 end
0045 
0046 D=1e6*D; %micron
0047 
0048 a=0.252; %g/m^3
0049 b=0.837;
0050 IWC0=1; %g/m^3
0051 IWCs100=min(IWC,a*(IWC/IWC0)^(b));
0052 IWCl100=IWC-IWCs100;
0053 rhoice=0.91*1e6; %g/m^3
0054 
0055 %Gamma distribution component
0056 
0057 b=-4.99*1e-3;m=0.0494;
0058 alfas100=(b-m*log10(IWCs100/IWC0)); %miron^-1
0059 Ns100=6*IWCs100*alfas100^(5)/(pi*rhoice*gamma(5)); %micron^-5
0060 Nm1=Ns100*D.*exp(-alfas100*D); %micron^-4
0061 
0062 
0063 %Log normal distribution component
0064 
0065 aamu=5.20;
0066 bamu=0.0013;
0067 abmu=0.026;
0068 bbmu=-1.2*1e-3;
0069 amu=aamu+bamu*T; 
0070 bmu=abmu+bbmu*T;
0071 mul100=amu+bmu*log10(IWCl100/IWC0);
0072 
0073 aasigma=0.47;
0074 basigma=2.1*1e-3;
0075 absigma=0.018;
0076 bbsigma=-2.1*1e-4;
0077 asigma=aasigma+basigma*T;
0078 bsigma=absigma+bbsigma*T;
0079 sigmal100=asigma+bsigma*log10(IWCl100/IWC0);
0080 
0081 D0=1.0; %micron
0082 
0083 a1=6*IWCl100; %g/m^3
0084 a2=pi^(3/2)*rhoice*sqrt(2)*exp(3*mul100+9/2*sigmal100^(2))*sigmal100*D0^(3);
0085 %g/m^3/micron^3
0086 Nm2=a1/a2./D.*exp(-1/2*((log(D/D0)-mul100)/sigmal100).^(2)); %micron^-4
0087 
0088 %convert to m^-4
0089 Nm1=Nm1*1e24; 
0090 Nm2=Nm2*1e24;
0091 
0092 if mode==1
0093    y=Nm1+Nm2;
0094 end
0095 
0096 if mode==2
0097    y=Nm1;
0098 end
0099  
0100 if mode==3
0101    y=Nm2;
0102 end
0103

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