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ice_psd_Ivanova_01

PURPOSE ^

ice_psd_Ivanova_01 returns the particle size distribution in cirrus clouds.

SYNOPSIS ^

function [y]=ice_psd_Ivanova_01(T,IWC,D,shape,mode);

DESCRIPTION ^

 ice_psd_Ivanova_01 returns the particle size distribution in cirrus clouds.
    
     Returns a vector with the particle size distribution 
     for a given temperature, ice water content, and shape
     for a mid-latitude cirrus cloud. 
     This parameterization is based on the distribution
     of maximum dimension of the particle shapes, and are based on 
     measurements of ice crystals in the range 10^-6 m to 10^-3 m.  
     The particle size distribution is a bimodal gamma distribution,
     and with the input "mode" there is an option of which mode
     that will be returned.
    
     The parameterization is taken from Ivanova et al.
     "A GCM parameterization for bimodal size spectra and ice mass 
     removal rates in mid-latitude cirrus clouds"
     Atmospheric Research 59-60, 89-113, 2001
     
 FORMAT   [y] = ice_psd_Ivanova_01(T,IWC,D,shape,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 vector with the maximum dimension of
                the ice particles [m],
                where the concentration will be calculated
          shape 1=planar polycrystals
                2=bulett rosettes
                3=hexagonal plates
                4=hexagonal columns
          mode  1=both large and small 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_Ivanova_01.m

SOURCE CODE ^

0001 % ice_psd_Ivanova_01 returns the particle size distribution in cirrus clouds.
0002 %
0003 %     Returns a vector with the particle size distribution
0004 %     for a given temperature, ice water content, and shape
0005 %     for a mid-latitude cirrus cloud.
0006 %     This parameterization is based on the distribution
0007 %     of maximum dimension of the particle shapes, and are based on
0008 %     measurements of ice crystals in the range 10^-6 m to 10^-3 m.
0009 %     The particle size distribution is a bimodal gamma distribution,
0010 %     and with the input "mode" there is an option of which mode
0011 %     that will be returned.
0012 %
0013 %     The parameterization is taken from Ivanova et al.
0014 %     "A GCM parameterization for bimodal size spectra and ice mass
0015 %     removal rates in mid-latitude cirrus clouds"
0016 %     Atmospheric Research 59-60, 89-113, 2001
0017 %
0018 % FORMAT   [y] = ice_psd_Ivanova_01(T,IWC,D,shape,mode)
0019 %
0020 % OUT      y is a vector with the particle size distribution [#/m^3/m]
0021 %
0022 % IN       T     Temperature [Kelvin]
0023 %          IWC   Ice water content [g/m^3]
0024 %          D     the vector with the maximum dimension of
0025 %                the ice particles [m],
0026 %                where the concentration will be calculated
0027 %          shape 1=planar polycrystals
0028 %                2=bulett rosettes
0029 %                3=hexagonal plates
0030 %                4=hexagonal columns
0031 %          mode  1=both large and small mode
0032 %                2=only small mode
0033 %                3=only large mode
0034 %
0035 % History: 2004-07-19  Created by Bengt Rydberg
0036 
0037 function [y]=ice_psd_Ivanova_01(T,IWC,D,shape,mode);
0038 
0039 T=T-273.15;
0040 
0041 if T>0
0042    error('Only temperatures smaller than 273.15 K are allowed.')
0043 end
0044 
0045 if ((shape~=1) && (shape~=2) && (shape~=3) && (shape~=4))
0046    error('Only shape 1,2,3,or 4 are allowed.')
0047 end
0048 
0049 if ((mode~=1) && (mode~=2) && (mode~=3))
0050    error('Only mode 1,2, or 3 are allowed.')
0051 end
0052 
0053 D=1e6*D; %micron
0054 
0055 musm=3.24;
0056 mulg=2.64;
0057 Dsm=27.4; %micron
0058 lambdasm=(musm+1)/Dsm;
0059 Dlg=337.7*exp(0.01754*T); %micron
0060 lambdalg=(mulg+1)/Dlg;
0061 
0062 if shape==1
0063    %constants for planar polycrystals
0064    alfa1=36000;beta1=2.897;
0065    alfa2=587;beta2=2.45;
0066    IWCsmn=0.11+0.89*exp(-(Dlg/50)^2);
0067 end
0068 
0069 if shape==2
0070    %constants for bulett rosettes
0071    alfa1=8220;beta1=2.75;
0072    alfa2=alfa1;beta2=beta1;
0073    L=-0.00009524*Dlg+0.1200;
0074    IWCsmn=L+(1-L)*exp(-(Dlg/45)^2);
0075 end
0076 
0077 if shape==3
0078    %constants for hexagonal plates
0079    alfa1=587;beta1=2.45;
0080    alfa2=alfa1;beta2=beta1;   
0081    IWCsmn=0.11+0.89*exp(-(Dlg*1e6/50)^2);
0082 end
0083 
0084 if shape==4
0085    %constants for hexagonal columns
0086    alfa1=111000;beta1=2.91;
0087    alfa2=11.0;beta2=1.91;
0088    L=0.0009722*Dlg-0.05833;
0089    IWCsmn=L+(1-L)*exp(-(Dlg/85)^2);
0090 end
0091 
0092 IWClgn=1-IWCsmn;
0093 IWCsm=IWC*IWCsmn; %g/m^3
0094 IWClg=IWC*IWClgn; %g/m^3
0095 
0096 Nosm=IWCsm*(lambdasm*1e6)^(beta1+musm+1)/(alfa1*gamma(beta1+musm+1)); 
0097 Nolg=IWClg*(lambdalg*1e6)^(beta2+mulg+1)/(alfa2*gamma(beta2+mulg+1));
0098 
0099 Nmsm=Nosm*(1e-6*D).^(musm).*exp(-lambdasm*D); %m^-4
0100 Nmlg=Nolg*(1e-6*D).^(mulg).*exp(-lambdalg*D); %m^-4
0101 
0102 if mode==1
0103    y=Nmsm+Nmlg;
0104 end
0105 if mode==2
0106    y=Nmsm;
0107 end
0108 if mode==3
0109    y=Nmlg;
0110 end

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