function [f] = fpaul(z);
%solar flux absorption profile functions as per Paulson & Simpson JGR, 86, 11044-11504, 1981
F=[.237 .360 .179 .087 .080 .0246 .025 .007 .0004];%solar fraction
G=[34.8 2.27 3.15e-2 5.48e-3 8.32e-4 1.26e-4 3.13e-4 7.82e-5 1.44e-5];%absorption length scale
fr=1-sum(F.*G./z.*(1-exp(-z./G)));%mean fraction absorbed in layer 
%fr={Integral{Fo-F(z)]dz}/z  from 0 to z
g=sum(F.*exp(-z./G));%fraction escaping below z
%g=F(z)  normalized profile of flux as function of water depth
f=[fr g];
