%% Source: Microwave Radar and Radiometric Remote Sensing, http://mrs.eecs.umich.edu
%% These MATLAB-based computer codes are made available to the remote
%% sensing community with no restrictions. Users may download them and
%% use them as they see fit. The codes are intended as educational tools
%% with limited ranges of applicability, so no guarantees are attached to
%% any of the codes.
%%
%Code 4.8: Relative Dielectric Constant of Vegetation
%Description: Code computes the real and imaginary parts of the relative
%dielectric constant of vegetation material, such as corn leaves, in
%the microwave region.
%Input Variables:
%f: frequency in GHz
%mg: Gravimetric moisture content 0< mg< 1
%Output Products:
%eps_v_r: real part of dielectric constant
%eps_v_i: imaginary part of dielectric constant
%Book Reference: Section 4-9
%Example call: [A B] = RelDielConst_Vegetation(f,mg)
%Computes the real and imaginary components of the permitivity of
%vegetation vased on frequency and gravimetric moisture content.
%MATLAB Code
function [eps_v_r eps_v_i] = RelDielConst_Vegetation(f,mg)
S = 15; % salinity
%-- free water in leaves
sigma_i = 0.17.*S - 0.0013 .* S.^2;
eps_w_r = 4.9 + 74.4 ./( 1 + (f/18).^2);
eps_w_i = 74.4 .*(f/18) ./( 1 + (f/18).^2) + 18*sigma_i ./f ;
% bound water in leaves
eps_b_r = 2.9 + 55*(1+ sqrt(f/0.36))./( (1+ sqrt(f/0.36)).^2 + (f/0.36));
eps_b_i = 55*sqrt(f/0.36) ./ ( (1+ sqrt(f/0.36)).^2 + (f/0.36));
% empirical fits
v_fw = mg .*( 0.55 * mg - 0.076);
v_bw = 4.64 .*mg.^2 ./(1 + 7.36 * mg.^2);
eps_r = 1.7 - 0.74 *mg + 6.16 .* mg.^2;
eps_v_r = eps_r + v_fw .* eps_w_r + v_bw .*eps_b_r;
eps_v_i = v_fw .* eps_w_i + v_bw .*eps_b_i;
end