I recently became interested in calculating water salinity from conductivity and temperature. I failed to find any theoretical model to how this is done, only empirical models derived from fitting to experimental data.
One such model (first Google hit) I found was this, of which if you look in the page source you find:
$r = \frac{C/42914}{c_0+T*(c_1+T*(c_2+T*(c_3+T*c_4)))}$
$ds_1 = b_0+r^2*(b_1+r^2*(b_2+r^2*(b_3+r^2*(b_4+r^2*b_5))))$
$ds_2 = ((T-15.0)/(1.0+0.0162*(T-15.0)))$
$d_s = ds_1 ds_2$
And finally:
$salinity=a_0+r^2*(a_1+r^2*(a_2+r^2*(a_3+r^2*(a_4+r^2*a_5))))+d_s$
where $a_i, b_i, c_i$ are fitted coefficients.
Without going into depth about the fysics of salinity, doesn't this model seem overly complicated? I mean whats the highest order of T? Alot.