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miecoated_rain7

PURPOSE ^

Extinction, scattering, absorption, backscattering and

SYNOPSIS ^

function result = miecoated_rain7(fGHz, R, TK, coatmax, nr)

DESCRIPTION ^

 Extinction, scattering, absorption, backscattering and 
 asymmetric scattering coefficients in 1/km for Marshall-Palmer 
 (MP) drop-size distribution (Sauvageot et al. 1992),
 versus thickness 'coat' of ice-coated water spheres (freezing rain)
 assuming coat=min(coat,radius) for all spheres, using Mie Theory,
 the dielectric model of Liebe et al. 1991 for water and
 of M�zler (1998) for ice.
 Input:
 coat: thickness of coating in mm, 
 R: rain rate in mm/h, TK: Temp. in K, 
 fmin, fmax: minimum and maximum frequency in GHz
 nr: Number of coat-thickness values 
 C. M�zler, June 2002.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

DOWNLOAD ^

miecoated_rain7.m

SOURCE CODE ^

0001 function result = miecoated_rain7(fGHz, R, TK, coatmax, nr)
0002 
0003 % Extinction, scattering, absorption, backscattering and
0004 % asymmetric scattering coefficients in 1/km for Marshall-Palmer
0005 % (MP) drop-size distribution (Sauvageot et al. 1992),
0006 % versus thickness 'coat' of ice-coated water spheres (freezing rain)
0007 % assuming coat=min(coat,radius) for all spheres, using Mie Theory,
0008 % the dielectric model of Liebe et al. 1991 for water and
0009 % of M�zler (1998) for ice.
0010 % Input:
0011 % coat: thickness of coating in mm,
0012 % R: rain rate in mm/h, TK: Temp. in K,
0013 % fmin, fmax: minimum and maximum frequency in GHz
0014 % nr: Number of coat-thickness values
0015 % C. M�zler, June 2002.
0016 
0017 opt=1;
0018 nsteps=501;                  % number of drop-diameter values optimized for MP
0019 LA=4.1/R^0.21;               % MP paramter (with size unit in mm)
0020 N0=0.08/10000;               % original MP N0 in 1/mm^4
0021 nx=(1:nsteps)';
0022 c0=299.793;
0023 m1=sqrt(epswater(fGHz, TK)); % refractive index of pure water
0024 m2=sqrt(epsice(fGHz, TK));   % refractive index of pure ice
0025 dD=0.01*R^(1/6)/fGHz^0.05;   % diameter interval optimized for MP
0026 D=(nx-0.5)*dD;               % drop diameter in mm
0027 y=pi*D*fGHz/c0;
0028 dx=2*pi*coatmax*fGHz/c0/(nr-0.99999);
0029 for jr = 1:nr
0030     x=max(y-dx*(jr-1),0);
0031     coat=dx*(jr-1)*c0/(2*pi*fGHz);
0032     sigmag=pi*D.*D/4;        % geometric cross section
0033     NMP=N0*exp(-LA*D);       % MP distribution
0034     sn=sigmag.*NMP*1000000;  
0035     for j = 1:nsteps    
0036         a(j,:)=miecoated(m1,m2,x(j),y(j),opt);
0037     end;
0038     b(:,1)=D;             b(:,2)=a(:,1).*sn;   
0039     b(:,3)=a(:,2).*sn;    b(:,4)=a(:,3).*sn;
0040     b(:,5)=a(:,4).*sn;   b(:,6)=a(:,2).*a(:,5).*sn; 
0041     gext= sum(b(:,2))*dD;    gsca= sum(b(:,3))*dD;
0042     gabs= sum(b(:,4))*dD;    gb=   sum(b(:,5))*dD;
0043     gteta=sum(b(:,6))*dD;
0044     res(jr,:)=[coat gext gsca gabs gb gteta];
0045 end;
0046 output_parameters='Gext, Gsca, Gabs, Gb, Gsca<costeta>'
0047 semilogy(res(:,1),res(:,2:6))
0048 legend('Gext','Gsca','Gabs','Gb','Gsca<costeta>)')
0049 title(sprintf('Freezing Rain at R=%gmm/h, T=%gK, f=%gGHz',R,TK,fGHz))
0050 xlabel('Ice Coating (mm)');    ylabel('Gi(1/km)')
0051 result=res;

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