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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.

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    You'd think they'd have tried simpler models first, no? In any event, I'm not sure what the *mathematical* question here is...2011-09-14
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    @J.M. - My point is that does it really add that much to have that many degrees of freedom?2011-09-14
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    Hard to tell. Were any physical justifications given for the polynomials in the expression?2011-09-14
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    No, I might try plotting salinity as a function of conductivity and temperature and see weather the function looks overfitted.2011-09-14

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