\(\newcommand{\p}[1]{\frac{\partial }{\partial #1}}\) \(\newcommand{\pp}[2]{\frac{\partial #1}{\partial #2}}\) \(\newcommand{\dd}[2]{\frac{d #1}{d #2}}\) \(\newcommand{\h}{\frac{1}{2}}\) \(\newcommand{\op}[1]{\operatorname{#1}}\)
8.7.3.13. Iron chemistry¶
The tracer representing inorganic iron in darwin is total dissolved inorganic iron, FeT. Its source terms are
where \(\delta_{\op{bottom}}\) selects the last ocean grid cell above the sea floor.
8.7.3.13.1. 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.
8.7.3.13.2. 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,
For backwards compatibility, the variable sediment flux can be expressed in terms of POP if DARWIN_IRON_SED_SOURCE_POP is defined:
where \(\op{POP}^{\op{up}}\) is POP in the second-lowest wet grid cell of the water column.
8.7.3.13.3. 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,
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.
8.7.3.13.4. Scavenging¶
The fourth term represents losses due to particle scavenging. The scavenging rate for free iron is
To select particle-based scavenging following Parekh et al. (2005) [PFB05], define DARWIN_PART_SCAV. POM is the concentration of particulate organic matter in units of mg/L. It is parameterized in terms of POC, POSi and PIC,
The value for \(w^{\text{scav}}_{\text{POC}}\) is taken from Rios et al. (1998) [RFPF98] as the weight of as detritus without opal per mol of carbon. \(w^{\text{scav}}_{\text{POSi}}\) and \(w^{\text{scav}}_{\text{PIC}}\) are just the molecular weights of opal (per mol Si) and calcium carbonate, see Table 8.47.
deprecated formulations
The old (and deprecated) formulation of scavenging in terms of POP can be recovered by defining DARWIN_PART_SCAV_POP, in which case \(\op{POM}\) is replaced by \(\op{POP}\!/R^{\op{POP}:\op{POC}}_{{\text{scav}}}\). Parameter names and defaults are different in this case, see Table 8.48. For comparison: this formulation with its default parameters could also be recovered in the new formulation (with new default parameters) by setting \(\op{POM}=w^{\text{scav}}_{\text{POP}} \op{POP}\) where \(w^{\text{scav}}_{\text{POP}}\approx 15.274\) g/mmol P.
The faulty formulation in terms of POC only that existed before 2022-12-05 can be recovered by setting scav_POC_wgt=1, scav_PIC_wgt=0 and scav_POSi_wgt=0 and making sure the product scav_tau*scav_inter has the same value as scav_rat*scav_inter before.
The concentration of free iron, Fe’, is determined following Parekh et al. (2004) [PFB04] and Dutkiewicz et al. (2005) [DFP05]. Free dissolved iron is assumed to be in equilibrium with dissolved iron bound to ligands, FeL,
At equilibrium,
Using \(\op{FeL}+\op{Fe}'={\op{FeT}}\) and \(\op{FeL}+L'={L_{{\mathrm{T}}}}\), the solution is obtained as
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.
Parameter |
Symbol |
Default |
Units |
Description |
|---|---|---|---|---|
\(\alpha_{\op{Fe}}\) |
0.04 |
solubility of Fe dust |
||
\(d_{\op{sed}}\) |
-1.0 |
m |
depth above which to add sediment source |
|
fesedflux |
1E-3 / day |
mmol Fe /m2/s |
fixed iron flux from sediment |
|
\(F_{\op{Fe}}^{\op{sed pcm}}\) |
0.68E-3 |
mmol Fe / mmol C |
iron input per POC sinking into bottom for DARWIN_IRON_SED_SOURCE_VARIABLE |
|
\(F_{\op{Fe}}^{\op{sed min}}\) |
0.5E-3 / day |
mmol Fe /s |
minimum iron input rate subtracted from fesedflux_pcm*wc_sink*POC |
|
\(R^{\op{C:P}}_{\op{sed}}\) |
106 |
mmol C / mmol P |
POC:POP conversion for DARWIN_IRON_SED_SOURCE_VARIABLE |
|
\(d_{\op{vents}}\) |
750 |
m |
depth below which iron from hydrothermal vents is added |
|
\(\alpha_{\op{Fe}}^{\op{vents}}\) |
0.002 |
solubility of iron from hydrothermal vents |
||
\(R^{\op{Fe:^3He}}_{\op{vents}}\) |
4.5E8 |
mol Fe / mol 3He |
Fe:3He ratio for hydrothermal vents |
|
scav |
0.4/year |
1/s |
fixed iron scavenging rate |
|
\(\tau_{\op{scav}}\) |
0.2 |
factor for converting Th scavenging rates to iron ones |
||
\(I_{\op{scav}}\) |
0.079 / day |
Le mg-e s-1 |
intercept of scavenging power law (e=escav) |
|
\(e_{\op{scav}}\) |
0.58 |
exponent of scavenging power law |
||
\(w^{\op{scav}}_{\op{POC}}\) |
0.02173 |
g/mmol C |
weight POC contributes to POM |
|
\(w^{\op{scav}}_{\op{POSi}}\) |
0.069 |
g/mmol Si |
weight POSi contributes to POM |
|
\(w^{\op{scav}}_{\op{PIC}}\) |
0.100 |
g/mmol C |
weight PIC contributes to POM |
|
\(L_{\op{T}}\) |
1E-3 |
mmol/m3 |
total ligand concentration |
|
\(\beta_{\op{stab}}\) |
0.2E6 |
m3/mmol |
ligand stability rate ratio |
|
\(\op{Fe}'_{\op{max}}\) |
0.4E-3 |
mmol/m3 |
max concentration of free iron |
Parameter |
Symbol |
Default |
Units |
Description |
|---|---|---|---|---|
\(\tau_{\op{scav}}\) |
0.005 / day |
1/s |
rate factor |
|
\(I_{\op{scav}}\) |
0.079 |
Le mg-e |
intercept of scavenging power law (e=escav) |
|
\(e_{\op{scav}}\) |
0.58 |
exponent of scavenging power law |
||
\(R^{\op{POP:POC}}_{\op{scav}}\) |
1.1321E-4 |
mmol P / g |
POP:POC ratio |