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ice_psd_Donovan_03

PURPOSE ^

ice_psd_Donovan_2003 returns the particle size distribution in cirrus clouds.

SYNOPSIS ^

function [y]=ice_psd_Donovan_03(T,IWC,D,shape,mode)

DESCRIPTION ^

 ice_psd_Donovan_2003 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 midlatitude cirrus cloud.
     The uncertainty regarding the habits of the ice crystals is large.
     The parameterization here is based on the distribution of
     maximum dimension of complex polycrystals or compact
     polycrystals which are consistent with the average observed
     behaviour from the measurements. 
     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 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

 FORMAT   [y] = ice_psd_Donovan_03(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=complex polycrystals
                2=compact polycrystals
          mode  1=both small and large mode
                2=small mode
                3=large mode

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

DOWNLOAD ^

ice_psd_Donovan_03.m

SOURCE CODE ^

0001 % ice_psd_Donovan_2003 returns the particle size distribution in cirrus clouds.
0002 %
0003 %     Returns a vector with the particle size distribution for a
0004 %     given temperature, ice water content, and shape
0005 %     for a midlatitude cirrus cloud.
0006 %     The uncertainty regarding the habits of the ice crystals is large.
0007 %     The parameterization here is based on the distribution of
0008 %     maximum dimension of complex polycrystals or compact
0009 %     polycrystals which are consistent with the average observed
0010 %     behaviour from the measurements.
0011 %     The particle size distribution is a bimodal gamma distribution,
0012 %     and with the input "mode" there is an option of which mode
0013 %     that will be returned.
0014 %
0015 %     The parameterization is taken from Donovan.
0016 %     "Ice cloud effective particle size parameterization based
0017 %     on combined lidar, radar reflectivity, and mean Doppler
0018 %     velocity measurements"
0019 %     J. of Geophys. res., vol. 108, NO. D18, 4573, 2003
0020 %
0021 % FORMAT   [y] = ice_psd_Donovan_03(T,IWC,D,shape,mode)
0022 %
0023 % OUT      y is a vector with the particle size distribution [#/m^3/m]
0024 %
0025 % IN       T     Temperature [Kelvin]
0026 %          IWC   Ice water content [g/m^3]
0027 %          D     the vector with the maximum dimension of
0028 %                the ice particles [m],
0029 %                where the concentration will be calculated
0030 %          shape 1=complex polycrystals
0031 %                2=compact polycrystals
0032 %          mode  1=both small and large mode
0033 %                2=small mode
0034 %                3=large mode
0035 
0036 
0037 % History: 2004-07-19  Created by Bengt Rydberg
0038 
0039 
0040 function [y]=ice_psd_Donovan_03(T,IWC,D,shape,mode) 
0041 
0042 T=T-273.15;
0043 
0044 if T>0
0045    error('Only temperatures smaller than 273.15 K are allowed.')
0046 end
0047 if T<-70
0048    error('Only temperature larger or equal to 203.15 K are allowed.')
0049 end
0050 if IWC<0.001
0051    error('Only IWC larger than or equal to 0.001 are allowed.')
0052 end
0053 if IWC>1.0
0054    error('Only IWC smaller or equal to 1.0 are allowed.')
0055 end
0056 if ((shape~=1) && (shape~=2))
0057    error('Only shape 1 or 2 are allowed.')
0058 end
0059 if ((mode~=1) && (mode~=2) && (mode~=3))
0060    error('Only mode 1,2, or 3 are allowed.')
0061 end
0062 
0063 gammas=4.24;gammal=3.64;
0064 Rms=20.1623*1e-6;rms=Rms/(gammas+2);
0065 
0066 if shape==1
0067    %complex polycrystlas
0068    A0a=502.88;A1a=109.56;
0069    A0b=7.66;A1b=1.92;
0070    R0=A0a+A1a*log10(IWC);
0071    Ra=A0b+A1b*log10(IWC);
0072    Rml=(R0+Ra*T)*1e-6;
0073    rml=Rml/(gammal+2);
0074    Nl_Ns=[0.006409 0.007934 0.01089 0.01459 0.01851 0.02243 0.02625 0.02994;
0075           0.006119 0.007603 0.01222 0.01809 0.02402 0.02970 0.03510 0.04027;
0076           0.006078 0.007328 0.01350 0.02134 0.02894 0.03650 0.04279 0.04927;             0.006081 0.007068 0.01493 0.02478 0.03400 0.04256 0.05070 0.05859;             0.006000 0.006859 0.01627 0.02789 0.03851 0.04838 0.05783 0.06704;
0077           0.006000 0.006669 0.01773 0.03114 0.04321 0.05449 0.06536 0.07600;
0078           0.006000 0.006523 0.01909 0.03408 0.04747 0.06005 0.07226 0.08424];
0079    IWCv=[0.001 0.0033 0.01 0.033 0.10 0.33 1.0]';
0080    Tv=[-70:10:0];
0081    Nl_Ns=interp2(Tv,IWCv,Nl_Ns,T,IWC,'cubic');     
0082              
0083    alfa1=4.3;beta1=2.88;
0084    alfa2=1.38;beta2=2.88;
0085    alfap2=145.73;betap2=1.88;
0086 end
0087 
0088 if shape==2
0089    %compact polycrystlas
0090    A0a=718.74;A1a=164.49;
0091    A0b=10.56;A1b=2.74;
0092    R0=A0a+A1a*log10(IWC);
0093    Ra=A0b+A1b*log10(IWC);
0094    Rml=(R0+Ra*T)*1e-6;
0095    rml=Rml/(gammal+2);
0096    Nl_Ns=[0.003171 0.004194 0.005712 0.007455 0.009275 0.01110 0.01288 0.01461;
0097           0.002874 0.004195 0.006757 0.009670 0.01257  0.01534 0.01797 0.02050;
0098           0.002765 0.004196 0.007768 0.01172  0.01548  0.01901 0.0234  0.02555;          0.002739 0.004198 0.008876 0.01386  0.01846  0.02273 0.02681 0.03075;          0.002738 0.004199 0.009909 0.01577  0.02109  0.02605 0.03081 0.03546;
0099           0.002737 0.004200 0.01102  0.01776  0.02383  0.02953 0.03504 0.04043;
0100           0.002736 0.004201 0.01203  0.01955  0.02630  0.03269 0.03890 0.04497];
0101    IWCv=[0.001 0.0033 0.01 0.033 0.10 0.33 1.0]';
0102    Tv=[-70:10:0];
0103    Nl_Ns=interp2(Tv,IWCv,Nl_Ns,T,IWC,'cubic');     
0104              
0105    alfa1=3.73;beta1=2.88;
0106    alfa2=0.84;beta2=2.88;
0107    alfap2=144.96;betap2=1.88;
0108 end
0109 
0110 rho=0.91e-12;
0111 d1=linspace(1e-6,1e-3,1000);
0112 m1=rho*alfa1*(d1*1e6/2).^(beta1);
0113 m2=rho*(alfa2*(d1*1e6/2).^(beta2)+alfap2*(d1*1e6/2).^(betap2));
0114 N1=1/2/rms/gamma(gammas).*(d1/2/rms).^(gammas-1).*exp(-d1/2/rms);
0115 N2=Nl_Ns/2/rml/gamma(gammal).*(d1/2/rml).^(gammal-1).*exp(-d1/2/rml);
0116 Ntot=N1+N2;
0117 Ns=IWC/(1e-6*N1(1:1000)*m1(1:1000)'+1e-6*N2(1:1000)*m2(1:1000)');
0118   
0119 N1=(Ns/2/rms/gamma(gammas).*(D/2/rms).^(gammas-1).*exp(-D/2/rms));
0120 N2=(Nl_Ns*Ns/2/rml/gamma(gammal).*(D/2/rml).^(gammal-1).*exp(-D/2/rml));
0121 
0122 if mode==1
0123    y=N1+N2;
0124 end
0125 
0126 if mode==2
0127    y=N1;
0128 end
0129 
0130 if mode==3
0131    y=N2;
0132 end

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