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ice_psd_ellipsoids

PURPOSE ^

ice_psd_ellipsoids translates particle size distribution for a given

SYNOPSIS ^

function [y]=ice_psd_ellipsoids(T,IWC,D,a,b,psd,mode);

DESCRIPTION ^

 ice_psd_ellipsoids  translates particle size distribution for a given
                     particle size distribution into a distribution of
                     mass equivalent ellipsoids in cirrus clouds,
                     and returns the new distribution.
    
     Returns a vector with the particle size distribution 
     for a given temperature, ice water content, and particle
     size distribution, for a cirrus cloud.
     The ellipsoids "diameters" are D,Da,Db, where D is the
     major diameter,Da/D=a, and Db/D=b.   
     This function takes a given exponential or gamma bimodal size 
     distribution, which is based on the assumption of a certain
     habit of the ice crystals, and by using mass - diameter relations,
     translates the distribution into an exponential or gamma bimodal
     size distribution of mass equivalent ellipsoids.
     The particle size distributions are  bimodal distributions,
     and with the input "mode" there is an option of which mode
     that will be returned.
     
 
     The mass - diameter relations are taken from Donovan 
     "Ice cloud effective particle size parameterization based
     on combined lidar, radar reflectivity, and mean Doppler
     velocity measurements"
     J. of Geophys. res., vol. 108, NO. D18, 4573, 2003
 
     and Mitchell
     "Use of mass and area dimensional power laws for determining
     precipitation particle terminal velocities"
     J. of Atm. Sci., vol 53, No. 12, 1710-1723, 1996
    
 FORMAT   [y] = ice_psd_ellipsoids(T,IWC,D,a,b,psd,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 ellipsoid diameter [m]),
                where the concentration will be calculated        
          a     Aspect ratio 0<a<=1 
          b     Aspect ratio 0<b<=1 (a=b=1 for spheres)
          psd   The specific particle size distribution
                one wants to translate
                1=ice_psd_Donovan_03(complex polycrystals) 
                2=ice_psd_Donovan_03(compact polycrystals)
                3=ice_psd_Ivanova_01(planar polycrystals)
                4=ice_psd_Ivanova_01(bullet rosettes)
                5=ice_psd_Ivanova_01(hexagonal plates)
                6=ice_psd_Ivanova_01(hexagonal columns)
                7=ice_psd_Mitchell_99(planar polycrystals)
          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_ellipsoids.m

SOURCE CODE ^

0001 % ice_psd_ellipsoids  translates particle size distribution for a given
0002 %                     particle size distribution into a distribution of
0003 %                     mass equivalent ellipsoids in cirrus clouds,
0004 %                     and returns the new distribution.
0005 %
0006 %     Returns a vector with the particle size distribution
0007 %     for a given temperature, ice water content, and particle
0008 %     size distribution, for a cirrus cloud.
0009 %     The ellipsoids "diameters" are D,Da,Db, where D is the
0010 %     major diameter,Da/D=a, and Db/D=b.
0011 %     This function takes a given exponential or gamma bimodal size
0012 %     distribution, which is based on the assumption of a certain
0013 %     habit of the ice crystals, and by using mass - diameter relations,
0014 %     translates the distribution into an exponential or gamma bimodal
0015 %     size distribution of mass equivalent ellipsoids.
0016 %     The particle size distributions are  bimodal distributions,
0017 %     and with the input "mode" there is an option of which mode
0018 %     that will be returned.
0019 %
0020 %
0021 %     The mass - diameter relations are taken from Donovan
0022 %     "Ice cloud effective particle size parameterization based
0023 %     on combined lidar, radar reflectivity, and mean Doppler
0024 %     velocity measurements"
0025 %     J. of Geophys. res., vol. 108, NO. D18, 4573, 2003
0026 %
0027 %     and Mitchell
0028 %     "Use of mass and area dimensional power laws for determining
0029 %     precipitation particle terminal velocities"
0030 %     J. of Atm. Sci., vol 53, No. 12, 1710-1723, 1996
0031 %
0032 % FORMAT   [y] = ice_psd_ellipsoids(T,IWC,D,a,b,psd,mode)
0033 %
0034 % OUT      y is a vector with the particle size distribution [#/m^3/m]
0035 %
0036 % IN       T     Temperature [Kelvin]
0037 %          IWC   Ice water content [g/m^3]
0038 %          D     the size vector of the ice particles,
0039 %                (the mass equivalent ellipsoid diameter [m]),
0040 %                where the concentration will be calculated
0041 %          a     Aspect ratio 0<a<=1
0042 %          b     Aspect ratio 0<b<=1 (a=b=1 for spheres)
0043 %          psd   The specific particle size distribution
0044 %                one wants to translate
0045 %                1=ice_psd_Donovan_03(complex polycrystals)
0046 %                2=ice_psd_Donovan_03(compact polycrystals)
0047 %                3=ice_psd_Ivanova_01(planar polycrystals)
0048 %                4=ice_psd_Ivanova_01(bullet rosettes)
0049 %                5=ice_psd_Ivanova_01(hexagonal plates)
0050 %                6=ice_psd_Ivanova_01(hexagonal columns)
0051 %                7=ice_psd_Mitchell_99(planar polycrystals)
0052 %          mode  1=both small and large mode
0053 %                2=only small mode
0054 %                3=only large mode
0055 %
0056 % History: 2004-07-19  Created by Bengt Rydberg
0057 
0058 function [y]=ice_psd_ellipsoids(T,IWC,D,a,b,psd,mode);
0059 
0060 
0061 if T>273.15
0062    error('Only temperatures smaller or equal to 273 K zero are allowed.')
0063 end
0064 if a<=0
0065 error('Only aspect ratio a larger than zero is allowed.')
0066 end
0067 if a>1
0068    error('Only aspect ratio a equal or smaller to one is allowed.')
0069 end
0070 if b<=0
0071    error('Only aspect ratio b larger than zero is allowed.')
0072 end
0073 if b>1
0074    error('Only aspect ratio b equal or smaller to one is allowed.')
0075 end
0076 if ((psd~=1) && (psd~=2) && (psd~=3) && (psd~=4) && (psd~=5) && (psd~=6) && (psd~=7))
0077    error('Only psd 1,2,3,4,5,6, and 7 are allowed.')
0078 end
0079 if ((mode~=1) && (mode~=2) && (mode~=3))
0080    error('Only mode 1,2, or 3 are allowed.')
0081 end
0082 
0083 if psd==1
0084    %complex polycrystals
0085    alfa1=102400;beta1=2.88;
0086    alfa2=32900;beta2=2.88;
0087    alfap2=6.94;betap2=1.88;
0088 end
0089 if psd==2
0090    %compact polycrystals
0091    alfa1=88800;beta1=2.88;
0092    alfa2=20000;beta2=2.88;
0093    alfap2=6.90;betap2=1.88;
0094 end
0095 if (psd==3 | psd==7)
0096    %planar polycrystals
0097    alfa1=36000;beta1=2.897;
0098    alfa2=587;beta2=2.45;
0099    alfap2=0;betap2=0;
0100 end
0101 if psd==4
0102    %bullet rosettes
0103    alfa1=8220;beta1=2.75;
0104    alfa2=alfa1;beta2=beta1;
0105    alfap2=0;betap2=0;
0106 end
0107 if psd==5
0108    %hexagonal plates
0109    alfa1=587;beta1=2.45;
0110    alfa2=alfa1;beta2=beta1;
0111    alfap2=0;betap2=0;
0112 end
0113 if psd==6
0114    %hexagonal columns
0115    alfa1=111000;beta1=2.91;
0116    alfa2=11.0;beta2=1.91;
0117 end
0118 
0119 rho=0.91*1e6;
0120 
0121 if (psd==1 | psd==2) 
0122    D11=linspace(1.01e-4,1e-3,1000);
0123    D22=(6/pi/rho/a/b*(alfa2*D11.^beta2+alfap2*D11.^betap2)).^(1/3);
0124    ypol=polyfit(D22,D11,2);
0125 end
0126 
0127 f1_D2= (rho*pi*a*b/6/alfa1*D.^3).^(1/beta1);
0128 
0129 if (psd==1 | psd==2)
0130     f2_D2=ypol(3)+ypol(2)*D+ypol(1)*D.^2;
0131 else 
0132     f2_D2= (rho*pi*a*b/6/alfa2*D.^3).^(1/beta2);
0133 end
0134 
0135 s=length(D);
0136 for i=1:s
0137     if f2_D2(i)<0
0138        f2_D2(i)=0;
0139     end
0140 end
0141 
0142 if psd==1
0143    [y1]=ice_psd_Donovan_03(T,IWC,f1_D2,1,2);
0144    [y2]=ice_psd_Donovan_03(T,IWC,f2_D2,1,3);
0145 end
0146 if psd==2
0147    [y1]=ice_psd_Donovan_03(T,IWC,f1_D2,2,2);
0148    [y2]=ice_psd_Donovan_03(T,IWC,f2_D2,2,3);
0149 end
0150 if psd==3
0151    [y1]=ice_psd_Ivanova_01(T,IWC,f1_D2,1,2);
0152    [y2]=ice_psd_Ivanova_01(T,IWC,f2_D2,1,3);
0153 end
0154 if psd==4
0155    [y1]=ice_psd_Ivanova_01(T,IWC,f1_D2,2,2);
0156    [y2]=ice_psd_Ivanova_01(T,IWC,f2_D2,2,3);
0157 end
0158 if psd==5
0159    [y1]=ice_psd_Ivanova_01(T,IWC,f1_D2,3,2);
0160    [y2]=ice_psd_Ivanova_01(T,IWC,f2_D2,3,3);
0161 end
0162 if psd==6
0163    [y1]=ice_psd_Ivanova_01(T,IWC,f1_D2,4,2);
0164    [y2]=ice_psd_Ivanova_01(T,IWC,f2_D2,4,3);
0165 end
0166 if psd==7
0167    [y1]=ice_psd_Mitchell_99(T,IWC,f1_D2,2);
0168    [y2]=ice_psd_Mitchell_99(T,IWC,f2_D2,3);
0169 end
0170 
0171 df1_dD2=3/beta1*(pi*rho*a*b/6/alfa1)^(1/beta1)*D.^(3/beta1-1); 
0172 
0173 if (psd==1 | psd==2)
0174    df2_dD2=ypol(2)+2*ypol(1)*D;
0175 else
0176    df2_dD2=3/beta2*(pi*rho*a*b/6/alfa2)^(1/beta2)*D.^(3/beta2-1);
0177 end
0178 
0179 ya=y1.*df1_dD2;
0180 yb=y2.*df2_dD2;
0181 
0182 if mode==1
0183    y=ya+yb;
0184 end
0185 
0186 if mode==2
0187    y=ya;
0188 end
0189  
0190 if mode==3
0191    y=yb;
0192 end
0193 
0194 
0195 
0196 
0197 
0198

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