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Analysis of Blackbody Radiation and Angstrom Exponent in Remote Sensing | EET 3132

This homework assignment explores blackbody radiation principles and the Angstrom Exponent's calculation using MATLAB. It includes plotting the blackbody radiation curves for Earth, Sun, and Alpha Centauri B, utilizing constants such as Planck's constant and Stefan-Boltzmann constant. Additionally, it demonstrates the analysis of aerosol optical depths (AOD) at various wavelengths and time through data importation and processing from a CSV file. The findings are illustrated in numerous plots showcasing AOD versus time, wavelength, and the Angstrom Exponent's trend over time.

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Analysis of Blackbody Radiation and Angstrom Exponent in Remote Sensing | EET 3132

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  1. Homeworks Antonio Aguirre EET 3132 Fall 2011 NYCCT/CUNY

  2. HW1 • % EET 3132:Remote Sensing, Instr: VivianaVladutescu, Student: Antonio Aguirre • % Sept. 23, 2011 @ New York City College of Technology (CUNY) • % contact: sadykov1@yahoo.com • close all,clear all • %%% Showing a Blackbody radiation plot (lambda vs. blackbody radiation) • % Constants • h=6.626E-34; % Planck's constant (J*s) • c=3E8; % speed of light (m/s) • k=1.38E-23; % Boltzmann's constant (J/K) • sigma=5.67E-8; % Stefan–Boltzmann constant: http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_constant • lambda=.001e-6:0.01e-6:20e-6; % Lambda in microns • T1=245; % Temperature of Earth in (K) • T2=6000; % Temperature of Sun in (K) • T3=5260; % Temperature of Alpha Centauri B in (K) • % Blackbody radiation equation in 3 parts: for simplicity • A1=(h*c)./(k*T1.*lambda); • A2=(h*c)./(k*T2.*lambda); • A3=(h*c)./(k*T3.*lambda); • B=(2*h*c^2)./lambda.^5; • BB1=B.*(1./(exp(A1)-1)); • BB2=B.*(1./(exp(A2)-1)); • BB3=B.*(1./(exp(A3)-1));

  3. % Plot of the radiation curve for the Earth, Sun, and Alpha Centauri B. • subplot(2,1,1) • plot(lambda,BB1,lambda,BB2,lambda,BB3) • % semilogy(lambda,BB1,lambda,BB2,lambda,BB3) • xlabel('Wavelength in microns') • ylabel('Radiance in W*m^-2') • legend('earth bb','sunbb','alpha centaury') • subplot(2,1,2) • plot(lambda,BB1) • % semilogy(lambda,BB1,lambda,BB2,lambda,BB3) • xlabel('Wavelength in microns') • ylabel('Radiance in W*m^-2') • legend('earth bb') • %%% Showing that B(lambda,T)=sigma*T^4 • lambda2=300E-9:10E-9:4000E-9; • Asun=(h*c)./(k*T2.*lambda2); • Bsun=(2*h*c^2)./(lambda2.^5); • BBsun=Bsun.*(1./(exp(Asun)-1)); • display ('B(lambda2,T2)=zz and sigma*T2^4=zz1') • zz=trapz(BBsun) • zz_aBB2=trapz(BB2) • zz1=sigma*(T2^4)

  4. HW2 • % EET 3132:Remote Sensing, Instr: VivianaVladutescu, Student: Antonio Aguirre • % Sept. 23, 2011 @ New York City College of Technology (CUNY) • % contact: sadykov1@yahoo.com • clc,clear all • cd('E:\Remote Sensing') % Sets the directory, not necessary. • file='111010_111010_CCNY.lev15'; % Names the file to load • data=importdata(file,','); % Reads the file and seperates data (commas=diff columns) • data_1=data.textdata; % defines the location of the data within the structure • [s,d]=size(data_1); % defines the size in [x,y] dimensions (rows, columns) • for k=6:s % loop for reading from row 6 to the last row. • aod_440(k-5)=str2num(data_1{k,16}); % turning characters to actual numbers from desired column • aod_500(k-5)=str2num(data_1{k,13}); % (k-5) is so that the values are stored starting at 1 and not 6 • aod_675(k-5)=str2num(data_1{k,7}); % {k,n} k is for the row determined by the loop state • aod_870(k-5)=str2num(data_1{k,6}); % {k,n} n is for the column of interest • time(k-5)=str2num(data_1{k,3}); • end

  5. time_round=fix(time); % rounding time down to establish whole days • time_fraction=time-time_round; % determining the fraction of the time of day • time_hour=time_fraction*24; % turning it into actual hours • t=time_hour; %UTC • % Vectors for plotting all AOD's vs. time • wav=[440,500,675,870]; • aod=[aod_440(7),aod_500(7),aod_675(7),aod_870(7)]; • % Calculating the Angstrom Exponent • top=log(aod_870/aod_440); • bottom=log(870/440); • angstrom=-(top./bottom) • %plot of AOD vs. Time • subplot(3,1,1) • plot(t,aod_440,'b*-',t,aod_500,'g+-',t,aod_675,'rx-',t,aod_870,'k^-') • legend('AOD 440','AOD 500','AOD 675','AOD 870',0) % the '0' places the legend in the best spot • xlabel('UTC') • ylabel('AOD') • title('AOD vs. Time') • hold on • % Plot AOD vs. Lambda • subplot(3,1,2) • plot(wav,aod,'b*-') • xlabel('Wavelength in (nanometer)') • ylabel('AOD') • title('AOD vs. Wavelength') • legend('AOD',0) • hold on • % Plot Angstrom vs. Time • subplot(3,1,3) • plot(t,angstrom,'m^-') • xlabel('UTC') • ylabel('Angstrom Exponent') • legend('Angstrom Values',0) • title('Angstrom vs. Time')

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