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ice_psd_Mitchell_99

PURPOSE ^

ice_psd_Mitchell_99 returns the particle size distribution in cirrus clouds.

SYNOPSIS ^

function [y]=ice_psd_Mitchell_99(T,IWC,D,mode);

DESCRIPTION ^

 ice_psd_Mitchell_99  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. 
     This parameterization is based on the distribution
     of maximum dimension of planar polycrystals, 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 exponential
     distribution,  and with the input "mode" there is an option
     of which mode that will be returned.
         
     The parameterization is taken from Mitchell et al.
     "A GCM parameterization of bimodal size spectra for ice clouds"
     In Proceedings of the Ninth Atmospheric Radiation Measurement 
     (ARM) Science Team Meeting, U.S Department of Energy, 
     Washington, D.C. Available URL: 
     http://www.arm.gov/publications/proceedings/conf09/abstracts/
     mitchell2-99.pdf
     
 FORMAT   [y] = ice_psd_Mitchell_99(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 vector with the maximum dimension of
                the ice particles [m],
                where the concentration will be calculated
          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_Mitchell_99.m

SOURCE CODE ^

0001 % ice_psd_Mitchell_99  returns the particle size distribution in cirrus clouds.
0002 %
0003 %     Returns a vector with the particle size distribution
0004 %     for a given temperature and ice water content,
0005 %     for a tropical cirrus cloud.
0006 %     This parameterization is based on the distribution
0007 %     of maximum dimension of planar polycrystals, 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 exponential
0010 %     distribution,  and with the input "mode" there is an option
0011 %     of which mode that will be returned.
0012 %
0013 %     The parameterization is taken from Mitchell et al.
0014 %     "A GCM parameterization of bimodal size spectra for ice clouds"
0015 %     In Proceedings of the Ninth Atmospheric Radiation Measurement
0016 %     (ARM) Science Team Meeting, U.S Department of Energy,
0017 %     Washington, D.C. Available URL:
0018 %     http://www.arm.gov/publications/proceedings/conf09/abstracts/
0019 %     mitchell2-99.pdf
0020 %
0021 % FORMAT   [y] = ice_psd_Mitchell_99(T,IWC,D,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 %          mode  1=both large and small mode
0031 %                2=only small mode
0032 %                3=only large mode
0033 %
0034 % History: 2004-07-19  Created by Bengt Rydberg
0035 
0036 function [y]=ice_psd_Mitchell_99(T,IWC,D,mode);
0037 
0038 T=T-273.15;
0039 
0040 if T>0
0041    error('Only temperatures smaller or equal to 273.15 K are allowed.')
0042 end
0043 if ((mode~=1) && (mode~=2) && (mode~=3))
0044    error('Only mode 1,2, or 3 are allowed.')
0045 end
0046 
0047 
0048 Dlg=1031*exp(0.05522*(T-4))*1e-6;
0049 lambdalg=1/Dlg;
0050 lambdasm=(1.49*lambdalg+583*1e2);
0051 IWCsmn=0.025*(1-exp(-(Dlg*1e6/80)^2))+exp(-(Dlg*1e6/80)^2);
0052 IWCsm=IWC*IWCsmn;
0053 IWClg=IWC-IWCsm;
0054 
0055 rhosi=0.92*1e6;
0056 alfa1=1.21;alfa2=6.96;
0057 betasm=2.897;betalg=2.45;
0058 
0059 alfasm=alfa1*rhosi*1e-18*(1e6/2)^(betasm);
0060 alfalg=alfa2*rhosi*1e-18*(1e6/2)^(betalg);
0061 
0062 N0sm=IWCsm*lambdasm^(betasm+1)/(alfasm*gamma(betasm+1));
0063 N0lg=IWClg*lambdalg^(betalg+1)/(alfalg*gamma(betalg+1));
0064 
0065 Nsm=N0sm*exp(-lambdasm*D);
0066 Nlg=N0lg*exp(-lambdalg*D);
0067 
0068 if mode==1
0069    y=Nsm+Nlg;
0070 end
0071 
0072 if mode==2
0073    y=Nsm;
0074 end
0075 
0076 if mode==3
0077    y=Nlg;
0078 end

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