\(\newcommand{\p}[1]{\frac{\partial }{\partial #1}}\) \(\newcommand{\pp}[2]{\frac{\partial #1}{\partial #2}}\) \(\newcommand{\dd}[2]{\frac{d #1}{d #2}}\) \(\newcommand{\h}{\frac{1}{2}}\) \(\newcommand{\op}[1]{\operatorname{#1}}\)

8.7.3.11. Air-sea exchanges

The preprocessor option DARWIN_ALLOW_CARBON is required to enable the computation of air-sea exchanges and the oxygen tracer.

The surface flux of DIC is

\[\mathcal{F}_{\mathrm{DIC}} = \rho_o K_{\text{g}}^{\mathrm{CO2}} \bigl( [\op{CO}_2^{\text{at}}] - [\op{CO}_2^*] \bigr)\]

with

\[K_{\text{g}}^{\mathrm{CO2}} = \frac{0.337\op{cm}\op{h}^{-1}}{\op{m}^2/\op{s}^2} w^2 \left(\frac{\op{Sc}_{\mathrm{CO2}}}{660}\right)^{-1/2} (1-f_{\text{ice}})\]
\[[\op{CO}_2^*] = [\op{CO}_2] + [\mathrm{H_2CO_3}]\]
\[[\op{CO}_2^{\text{at}}] = F p_{\op{CO}_2}^{\text{at}}\]
\[p_{\op{CO}_2}^{\text{at}} = p^{\text{at}} \cdot x_{\op{CO}_2}^{\text{at}}\]

where \(w\) is the wind speed and \(f_{\text{ice}}\) is the surface fraction covered by ice, read in from icefile or taken from the seaice package if useSEAICE is set to true. The Schmidt number for CO2, ScCO2, is parameterized according to Wanninkhof (1992) [Wan92], with values below 0.01 cut. \(F\) is computed following Weiss and Price (1980) [WP80]. The reference density of seawater, \(\rho_o\), is set via its inverse, m3perkg. The units of CO2 concentrations here are mol/kg. \([\mathrm{CO}_2^*]\) is computed in Carbon chemistry.

The surface flux of oxygen is

\[\mathcal{F}_{\mathrm{O2}} = K_{\text{g}}^{\mathrm{O2}} \bigl( [\op{O}_2^{\text{sat}}] - [\op{O}_2] \bigr)\]

with

\[K_{\text{g}}^{\mathrm{O2}} = \frac{0.337\op{cm}\op{h}^{-1}}{\op{m}^2/\op{s}^2} w^2 \left(\frac{\op{Sc}_{\mathrm{O2}}}{660}\right)^{-1/2} (1-f_{\text{ice}})\]
\[[\op{O}_2^{\text{sat}}] = p^{\text{at}} C_o^*\]

The saturated concentration of O2 at 1 atm, \(C_o^*\), is computed following Garcia and Gordon (1992) [GG92]. The Schmidt number of oxygen according to Keeling et al. (1998) [KSN+98]. The units of oxygen concentrations are mmol m-3.

Table 8.41 Air-sea exchange parameters

Name

Symbol

Default

Units

Description

m3perkg

\(1/\rho_o\)

1 / 1024.5

m3/kg

constant for converting per kg to per m3

darwin_useSEAICE

.FALSE.

whether to use ice area from the seaice package