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

8.7.3.12. Iron chemistry¶

The tracer representing inorganic iron in darwin is total dissolved inorganic iron, FeT. Its source terms are

\[\begin{split}S_{\op{Fe}} &= \delta_{k,1} \frac{\alpha_{\op{Fe}}}{\Delta r_{\mathrm{F}}h_{\mathrm{C}}} F_{\op{Fe}} + \delta_{\op{bottom}} \delta_{|r|\le d_{\op{sed}}} \frac{1}{\Delta r_{\mathrm{F}}h_{\mathrm{C}}} F_{\op{Fe}}^{{\text{sed}}} \\ &+ \delta_{\op{bottom}} \delta_{|r|\ge d_{\op{vents}}} \frac{1}{\Delta r_{\mathrm{F}}h_{\mathrm{C}}} F_{\op{Fe}}^{{\text{vents}}} - r_{{\text{scav}}}\op{Fe}'\end{split}\]

where \(\delta_{\op{bottom}}\) selects the last ocean grid cell above the sea floor.

8.7.3.12.1. Dust deposition¶

The first term is iron input at the surface from dust deposition. The rate of dust deposition is read in from ironfile. \(\alpha_{\op{Fe}}\) (alpfe) is the solubility of iron dust; set it to 1 if the deposition rate in ironfile is already of soluble iron. darwin_inscal_iron can be used to convert units on the fly.

8.7.3.12.2. Sedimentation¶

The second term represents iron input from sediments at the ocean floor. It only occurs above depthfesed. The flux is either a fixed number, fesedflux or, if DARWIN_IRON_SED_SOURCE_VARIABLE is defined,

\[F_{\op{Fe}}^{{\text{sed}}}= \left[ F_{\op{Fe}}^{\op{sed pcm}} w^{\mathrm{C}}_{{{\text{sink}}}} \op{POC} - F_{\op{Fe}}^{\op{sed min}} \right]_0\]

For backwards compatibility, the variable sediment flux can be expressed in terms of POP if DARWIN_IRON_SED_SOURCE_POP is defined:

\[F_{\op{Fe}}^{{\text{sed}}}= F_{\op{Fe}}^{\op{sed pcm}} w^{\mathrm{P}}_{{{\text{sink}}}} R^{{\mathrm{C}}:{\mathrm{P}}}_{{\text{sed}}} \op{POP}^{\op{up}}\]

where \(\op{POP}^{\op{up}}\) is POP in the second-lowest wet grid cell of the water column.

8.7.3.12.3. Hydrothermal vents¶

The third term represents iron input from hydrothermal vents. To enable it, define DARWIN_ALLOW_HYDROTHERMAL_VENTS. This iron source is only active below depthFeVent. The flux is proportional to the Helium-3 flux \(F_{^3\text{He}}^{{\text{vents}}}\) given in ventHe3file in units of mmol ³He m^-2 s^-1,

\[F_{\op{Fe}}^{\text{vents}} = \alpha_{\op{Fe}}^{\op{vents}} R^{\op{Fe:^3He}}_{\op{vents}} F_{^3\text{He}}^{{\text{vents}}} \;.\]

Here, \(\alpha_{\op{Fe}}^{\op{vents}}\) (solFeVent) is the solubility of iron from vents and \(R^{\op{Fe:^3He}}_{\op{vents}}\) (R_FeHe3_vent) is the iron to Helium-3 ratio of the vents.

8.7.3.12.4. Scavenging¶

The fourth term represents losses due to particle scavenging. The scavenging rate for free iron is

\[\begin{split}r_{{\text{scav}}}= \begin{cases} r_{{\text{scav}}}I_{{\text{scav}}}\op{POC}^{e_{{\text{scav}}}} & \text{for POM-based scavenging,} \\ \op{scav} & \text{for constant scavenging.} \end{cases}\end{split}\]

To select POM-based scavenging, #define DARWIN_PART_SCAV. If DARWIN_PART_SCAV_POP is defined, \(\op{POC}\) is replaced by \(\op{POP}\!/R^{\op{POP}:\op{POC}}_{{\text{scav}}}\).

The concentration of free iron is determined following Parekh et al. (2004) [PFB04] and Dutkiewicz et al. (2005) [DFP05]. Free dissolved iron, Fe’, is assumed to be in equilibrium with dissolved iron bound to ligands, FeL,

\[\op{Fe}' + L' \rightleftharpoons \op{FeL}\]

At equilibrium,

\[\frac{[\op{FeL}]}{[\op{Fe}'][L']} = {\beta_{{\text{stab}}}}\;,\]

Using \(\op{FeL}+\op{Fe}'={\op{FeT}}\) and \(\op{FeL}+L'={L_{{\mathrm{T}}}}\), the solution is obtained as

\[ \begin{align}\begin{aligned}L' &= \frac{ {\beta_{{\text{stab}}}}({L_{{\mathrm{T}}}}- {\op{FeT}}) - 1 +\sqrt{(1 - {\beta_{{\text{stab}}}}({L_{{\mathrm{T}}}}- {\op{FeT}}))^2 + 4 {\beta_{{\text{stab}}}}{L_{{\mathrm{T}}}}}} {2 {\beta_{{\text{stab}}}}}\\\op{FeL} &= {L_{{\mathrm{T}}}}- L'\\\op{Fe}' &= \op{FeT} - \op{FeL}\;.\end{aligned}\end{align} \]

If DARWIN_MINFE is defined, Fe’ will be constrained to be no more than Fe’_max, and FeT adjusted accordingly, assuming that excess free iron is scavenged away. This is done before and after each biogeochemical subtimestep.

Table 8.42 Iron parameters set in DARWIN_PARAMS¶
Parameter	Symbol	Default	Units	Description
alpfe	\(\alpha_{\op{Fe}}\)	0.04		solubility of Fe dust
depthfesed	\(d_{\op{sed}}\)	-1.0	m	depth above which to add sediment source
fesedflux	fesedflux	1E-3 / day	mmol Fe /m²/s	fixed iron flux from sediment
fesedflux_pcm	\(F_{\op{Fe}}^{\op{sed pcm}}\)	0.68E-3	mmol Fe / mmol C	iron input per POC sinking into bottom for DARWIN_IRON_SED_SOURCE_VARIABLE
fesedflux_min	\(F_{\op{Fe}}^{\op{sed min}}\)	0.5E-3 / day	mmol Fe /s	minimum iron input rate subtracted from fesedflux_pcmwc_sinkPOC
R_CP_fesed	\(R^{\op{C:P}}_{\op{sed}}\)	106	mmol C / mmol P	POC:POP conversion for DARWIN_IRON_SED_SOURCE_VARIABLE
depthFeVent	\(d_{\op{vents}}\)	750	m	depth below which iron from hydrothermal vents is added
solFeVent	\(\alpha_{\op{Fe}}^{\op{vents}}\)	0.002		solubility of iron from hydrothermal vents
R_FeHe3_vent	\(R^{\op{Fe:^3He}}_{\op{vents}}\)	4.5E8	mol Fe / mol ³He	Fe:³He ratio for hydrothermal vents
scav	scav	0.4/year	1/s	fixed iron scavenging rate
scav_rat	\(r_{\op{scav}}\)	0.005 / day	1/s	rate of POM-based iron scavenging
scav_inter	\(I_{\op{scav}}\)	0.079		intercept of scavenging power law
scav_exp	\(e_{\op{scav}}\)	0.58		exponent of scavenging power law
scav_R_POPPOC	\(R^{\op{POP:POC}}_{\op{scav}}\)	1.1321E-4	mmol P / mmol C	POP:POC ratio for DARWIN_PART_SCAV_POP
ligand_tot	\(L_{\op{T}}\)	1E-3	mmol/m³	total ligand concentration
ligand_stab	\(\beta_{\op{stab}}\)	.2E6	m³/mmol	ligand stability rate ratio
freefemax	\(\op{Fe}'_{\op{max}}\)	0.4E-3	mmol/m³	max concentration of free iron