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8.7.3.12. Carbon chemistry

8.7.3.12.1. Carbon chemistry options

The following preprocessor options affect the computation of pH, \([\mathrm{CO}_2^*]\) and \([\mathrm{CO}_3^{2-}]\):

Table 8.42 CPP options for carbon chemistry

CPP option	description
DARWIN_ALLOW_CARBON	enable air-sea carbon exchange and ALK and O2 tracers
DARWIN_SOLVESAPHE	compile Munhoven “Solvesaphe” pH/pCO2 solver package
DARWIN_TOTALPHSCALE	consistently use the total pH scale for carbon chemistry coefficients
DARWIN_ALLOW_RADI	enable RADI sediment model

DARWIN_ALLOW_CARBON is required to enable the computation of pH, \([\mathrm{CO}_2^*]\) and \([\mathrm{CO}_3^{2-}]\) values. If DARWIN_SOLVESAPHE is defined, the coefficients for the carbon solver are computed following to Munhoven (2013) [Mun13], otherwise according to Follows et al. (2006) [FID06]. In this case, DARWIN_TOTALPHSCALE can be defined to ensure all computations consistently use the total pH scale. DARWIN_ALLOW_RADI activates the RADI sediment model following [SHW+22].

The run-time parameter selectPHsolver decides which pH solver to use:

selectPHsolver	meaning
0 (default)	use Follows et al. (2006) solver
1	use the GENERAL solver
2	use SEC solver
3	use FAST solver routine

All options except ‘0’ require DARWIN_SOLVESAPHE to be defined. Note that if the Follows et al. solver is selected with DARWIN_SOLVESAPHE, the dissociation coefficients from Solvesaphe will be used. More Solvesaphe parameters:

selectBTconst	estimates borate concentration from salinity
1 (default)	use default formulation of Uppström (1974) [Upp74] (same as S/R CARBON_COEFFS)
2	use new formulation from Lee et al (2010) [LKB+10]

selectFTconst	estimates fluoride concentration from salinity
1 (default)	use default formulation of Riley (1965) [Ril65] (same as S/R CARBON_COEFFS)
2	use new formulation from Culkin (1965) [Cul65]

selectHFconst	sets the first dissociation constant for hydrogen fluoride
1 (default)	use default Dickson and Riley (1979) [DR79] (same as S/R CARBON_COEFFS)
2	use new formulation of Perez and Fraga (1987) [PF87]

selectK1K2const	sets the 1rst and 2nd dissociation constants of carbonic acid
1 (default)	use default formulation of Millero (1995) [Mil95] with data from Mehrbach et al. (1973) [MCHP73] (same as S/R CARBON_COEFFS)
2	use formulation of Roy et al. (1993) [RRV+93]
3	use “combination” formulation of Millero (1995) [Mil95]
4	use formulation of Luecker et al. (2000) [LDK00]
5	use formulation of Millero (2010) [Mil10b]
6	use formulation of Waters, Millero, Woosley (2014) [WMW14, WM13]

The input parameters for the carbon solver are salinity, temperature, DIC, alkalinity, phosphate and silica. Limits are applied to all these quantities to ensure convergence. The corresponsing parameters are shown in Table 8.43. There is a separate set of parameters for the initialization phase which is treated differently from calls to the solver during the run: the Follows et al. solver is called 10 times in order to allow the solution to converge. The Munhoven solvers have a special initialization routine.

Table 8.43 Carbon parameters

Name	Symbol	Default	Units	Description
surfSaltMinInit		4.0	g/kg	limits for carbon solver input at initialization
surfSaltMaxInit		50.0	g/kg	…
surfTempMinInit		–4.0	°C
surfTempMaxInit		39.0	°C
surfDICMinInit		10.0	mmol C m-3
surfDICMaxInit		4000.0	mmol C m-3
surfALKMinInit		10.0	meq m-3
surfALKMaxInit		4000.0	meq m-3
surfPO4MinInit		1D-10	mmol P m-3
surfPO4MaxInit		10.0	mmol P m-3
surfSiMinInit		1D-8	mmol Si m-3
surfSiMaxInit		500.0	mmol Si m-3
surfSaltMin		4.0	g/kg	limits for carbon solver input during run
surfSaltMax		50.0	g/kg	…
surfTempMin		–4.0	°C
surfTempMax		39.0	°C
surfDICMin		400.0	mmol C m-3
surfDICMax		4000.0	mmol C m-3
surfALKMin		400.0	meq m-3
surfALKMax		4000.0	meq m-3
surfPO4Min		1D-10	mmol P m-3
surfPO4Max		10.0	mmol P m-3
surfSiMin		1D-8	mmol Si m-3
surfSiMax		500.0	mmol Si m-3

8.7.3.12.2. Calcite dissolution

The parameter darwin_disscSelect determines the calcite dissolution rate law. A value of ‘0’ gives a constant dissolution rate,

\[D_{\mathrm{PIC}} = \kappa^{\mathrm{diss}}_{\mathrm{C}} \cdot \op{PIC} \;.\]

A value of ‘1’ gives the power law of Keir (1980) [Kei80],

\[D_{\mathrm{PIC}} = \kappa_{\text{Keir}} (1 - \Omega_{\mathrm{C}})^{e_{\text{Keir}}} \cdot \op{PIC} \;,\]

a value of ‘2’ the double power law of Naviaux (2019) [NSD+19],

\[\begin{split}D_{\mathrm{PIC}} = \op{PIC} \cdot \begin{cases} 5.22\cdot 10^{-9} (1 - \Omega_{\mathrm{C}})^{0.11} &\text{for } \Omega_{\mathrm{C}} > 0.8272 \;, \\ 1.65\cdot 10^{-5} (1 - \Omega_{\mathrm{C}})^{4.7} &\text{for } \Omega_{\mathrm{C}} \le 0.8272 \;. \end{cases}\end{split}\]

Here,

\[\Omega_{\mathrm{C}} = \frac{[\op{Ca}^{2+}] [\op{CO}_3^{2-}]}{K_{\mathrm{sp}}^{\mathrm{calc}}}\]

and the concentration of calcium is parameterized as a function of salinity. With DARWIN_SOLVESAPHE,

\[[\op{Ca}^{2+}] = 0.010282\frac{S}{35} \;,\]

otherwise,

\[[\op{Ca}^{2+}] = 0.01028\frac{S}{35} \;.\]

Table 8.44 Calcite dissolution parameters

Name	Symbol	Default	Units	Description
darwin_disscSelect		0		choose calcite dissolution rate law
				0: constant
				1: Keir
				2: Naviaux
Kdissc	\(\kappa^{\mathrm{diss}}_{\mathrm{C}}\)	1/(300 days)	1/s	constant calcite dissolution rate
darwin_KeirCoeff	\(\kappa_{\text{Keir}}\)	e7.177 /100/86400	1/s	Keir rate factor
darwin_KeirExp	\(e_{\text{Keir}}\)	4.54		Keir rate exponent

8.7.3.12.3. Diagnostics

Diagnostics available with DARWIN_ALLOW_CARBON:

Table 8.45 Darwin package carbon diagnostic fields

Name	Code	Units	Description
apCO2	SM_P____L1	atm	atmospheric pCO2
apCO2sat	SM_P____L1	atm	atmospheric pCO2 sat
pH	SMR_____MR	1	pH
pCO2	SMRP____MR	atm	Partial Pressure of CO2 in the ocean
CO3	SMR_____MR	mol/kg	Concentration of carbonate
KspTPClc	SMR_____MR	mol2/kg2	Solubility product for calcite
OmegaC	SMR_____MR	1	Calcite saturation ratio
fugfCO2	SM_P____L1	1	Fugacity factor of CO2 at surface
fCO2	SM_P____L1	atm	Fugacity of CO2 (atm)
fluxCO2	SM______L1	mmol C/m2/s	Flux of CO2 - air-sea exch
fluxO2	SM______L1	mmol O2 /m2/s	Flux of O2 - air-sea exch
VfluxCO2	SM______L1	mmol C/m2/s	Virtual flux of CO2
VfluxAlk	SM______L1	meq/m2/s	Virtual flux of alkalinity
gDICsurf	SM______L1	mmol C/m3/s	Tendency of DIC due to air-sea exch + oldvirt.flux
gALKsurf	SM______L1	meq/m3/s	Tendency of ALK due to oldvirt.flux
gO2surf	SM______L1	mmol O2 /m3/s	Tendency of O2 due to air-sea exch
C_DIC	SMR_____MR	mmol C/m3/s	Consumption of DIC
C_DICPIC	SMR_____MR	mmol C/m3/s	Consumption of DIC due to PIC
respDIC	SMR_____MR	mmol C/m3/s	DIC due to respiration
rDIC_DOC	SMR_____MR	mmol C/m3/s	DIC due to remineralization of DOC
rDIC_POC	SMR_____MR	mmol C/m3/s	DIC due to remineralization of POC
dDIC_PIC	SMR_____MR	mmol C/m3/s	DIC due to dissolution of PIC
C_ALK	SMR_____MR	meq/m3/s	Consumption of alkalinity
S_ALK	SMR_____MR	meq/m3/s	Non-transport source of alkalinity
C_O2	SMR_____MR	mmol O2 /m3/s	Consumption of oxygen
S_O2	SMR_____MR	mmol O2 /m3/s	Non-transport source of oxygen

The sign convention for the fluxCO2, gDICsurf, gALKsurf and gO2surf diagnostics is such that positive values increase the concentration in the ocean. Note that the units vary: gDICsurf, gALKsurf and gO2surf are tracer tendencies, i.e., change rates of concentration, while fluxCO2 is a flux per area of sea surface.

Diagnostics available with DARWIN_ALLOW_RADI:

Table 8.46 RADI sediment model diagnostic fields

Name	Code	Units	Description
DICFsed	SM______U1	mmol C/m2/s	DIC sediment flux
ALKFsed	SM______U1	meq/m2/s	ALK sediment flux
O2Fsed	SM______U1	mmol O2 /m2/s	O2 sediment flux
POCFbur	SM______U1	mmol C/m2/s	POC buried flux
CALFbur	SM______U1	mmol C/m2/s	Calcite buried flux
sedFlPOC	SM_P____U1	mmol C/m2/s	POC flux from water column to sediment
sedFlPIC	SM_P____U1	mmol C/m2/s	PIC flux from water column to sediment
TcorrO2	SM_P____M1	1	Temperature correction factor for diffusive O2 flux
TcorrALK	SM_P____M1	1	Temperature correction factor for diffusive ALK flux
TcorrDIC	SM_P____M1	1	Temperature correction factor for diffusive DIC flux
OmegCbot	SM_P____M1	1	Calcite saturation ratio above the seabed