function [DeltaF] = sulf(xx)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% SULFUR MODEL FUNCTION
%
% Authors: Sonja Surjanovic, Simon Fraser University
%          Derek Bingham, Simon Fraser University
% Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
%
% Copyright 2013. Derek Bingham, Simon Fraser University.
%
% THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
% FOR THE USE OF THIS SOFTWARE.  If software is modified to produce
% derivative works, such modified software should be clearly marked.
% Additionally, this program is free software; you can redistribute it 
% and/or modify it under the terms of the GNU General Public License as 
% published by the Free Software Foundation; version 2.0 of the License. 
% Accordingly, this program is distributed in the hope that it will be 
% useful, but WITHOUT ANY WARRANTY; without even the implied warranty 
% of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 
% General Public License for more details.
%
% For function details and reference information, see:
% http://www.sfu.ca/~ssurjano/
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% OUTPUT AND INPUT:
%
% DeltaF = direct radiative forcing by sulfate aerosols
% xx = [Tr, Ac, Rs, beta_bar, Psi_e, f_Psi_e, Q, Y, L]
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Tr       = xx(1);
Ac       = xx(2);
Rs       = xx(3);
beta_bar = xx(4);
Psi_e    = xx(5);
f_Psi_e  = xx(6);
Q        = xx(7);
Y        = xx(8);
L        = xx(9);

S0 = 1366;
A  = 5 * 10^14;

fact1 = (S0^2) * (1-Ac) * (Tr^2) * (1-Rs)^2 * beta_bar * Psi_e * f_Psi_e;
fact2 = 3*Q*Y*L / A;

DeltaF = -1/2 * fact1 * fact2;

end