You have measured $O_2$ and $Ar$ concentrations in the surface ocean over the course of a month during the summer. Average water temperature and salinity were $25C$ and $35$ psu, respectively for the period of observation. Average $O_2$ and Ar concentrations were $225$ moles $kg$ and $10\mathrm{.}7$ moles$/$kg respectively. Both concentrations appeared to be at steady state.

$($a$)$ Calculate the air$-$sea gas exchange using the stagnant boundary layer model. Assume that $D{O}_2=2\mathrm{.}3{10}^{-5}c{m}^2{s}^7,$DAr$=1\mathrm{.}7{10}^{-3}c{m}^2{s}^{-4},$ and $z($the stagnant boundary layer thickness$)=30m,F=-\frac{D}{Z}$ film $($Ceq $-Cs)$

$($b$)$ Determine the magnitude of the biological oxygen signal.

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