The carbon isotopes were added as optional passive tracers, with the biotic
and abiotic implementations as two different options that can be set at the
compilation and build time. The abiotic 14C can be run with or
without the ocean ecosystem model, while the biotic 13C and
14C require the ocean ecosystem model to be turned on.
Abiotic 14C
In this implementation, DI14C is the model's normalized
concentration of total dissolved inorganic 14C, following the
OCMIP2 protocol . DI14C is used as normalized
concentration in order to minimize the numerical error of carrying very small
numbers. The normalization is done by dividing the real DI14C by
the standard ratio of 14C/12C=1.176×10-12
. To obtain comparable DI14C values as
measured, we multiply the simulated DI14C by this scaling factor of
1.176×10-12. Since the abiotic radiocarbon is designed to be run
without the ocean ecosystem active, we also carry an abiotic DI12C
tracer to calculate the isotope ratio
14R=DI14C/DI12C. For comparisons with
observations, we calculate Δ14C as a diagnostic variable:
Δ14C=(14R-1)⋅1000.
By construction, the abiotic DI12C and DI14C tracers only
depend on the solubility of carbon in seawater and neglect all biological
activity. The error in Δ14C due to neglecting biology activity
has been estimated to be on the order of 10 % .
Note that we do not multiply 14R by
14Rstd in Eq. (), as we are using a normalized
DI14C (following ). Given that this abiotic
implementation does not account for the fractionation during gas exchange, we
do not apply the correction for fractionation that is commonly applied to
observational measurements of 14C/12C ratios (as
well as for the biotic 14C implementation; see
Eq. () in Sect. ). The simulated
abiotic Δ14C is therefore directly comparable to observed data
reported as Δ14C seefor more
details.
Surface fluxes
We follow the abiotic OCMIP-2 protocol for most of the
implementation of the abiotic radiocarbon surface fluxes, with the following
notable differences.
We use a coefficient a of 0.31 cmh-1 instead of
0.337 cmh-1 as used in OCMIP-2. This is higher than what most recent estimates
suggest e.g.,, but makes it
consistent with the gas-transfer formulation used in other parts of the CESM.
We use the daily mean of the squared 10 m wind speed (either from the prescribed
CORE-II forcing or from the coupled atmospheric model) instead of the climatology of the squared
monthly average of the instantaneous SSMI velocity and its instantaneous variance as used in
OCMIP-2.
We use the daily mean of the ice fraction and atmospheric pressure (either from the data
models or the coupled sea ice and atmosphere models) instead of the monthly averaged climatology
used in OCMIP-2.
We use a constant reference value (1944 µmolm-3) for the virtual fluxes of
abiotic radiocarbon, rather than an annually updated average of the surface DI14C as
suggested in OCMIP-2. This is done to conserve total 14C in the model (in the absence of
radioactive decay).
To compute the partial pressure of CO2 from the abiotic DI12C, we require an
estimate of surface alkalinity. We follow again OCMIP-2, i.e., we estimate surface alkalinity
(Alk) by scaling the ocean mean alkalinity, Alkbar=2310 microeqkg-1 with
sea-surface salinity, SSS, i.e.,
Alk=Alkbar⋅ρsw⋅SSS/SRef
with SRef=34.7 and
ρsw=4.1/3.996 gcm-3 (these two are constants in
the CESM). We alter this calculation in the Baltic Sea and the Black Sea to
avoid unrealistic alkalinity values, following the procedure developed by K.
Lindsay for creating initial conditions for the marine ecosystem model: in
the Black Sea, the surface alkalinity is independent of SSS:
alkalinity=3300⋅ρsw. In the Baltic Sea, we
calculate alkalinity depending on the surface salinity, with alkalinity =119+196⋅SSS when SSS is equal to or below 7.3, and
alkalinity=1237+43⋅SSS when the SSS is above
7.3. The computation of pCO2 also requires an assumption about the
surface ocean concentrations of silicic acid and phosphate, for which we use
OCMIP-2's global constants, i.e., 7.5 µmolkg-1 for silicic
acid, Si(OH)4, and 0.5 µmolkg-1 for phosphate,
PO4.
Air–sea gas exchange
As in OCMIP-2, the air–sea gas exchange flux of 12C is calculated as
F=PV⋅(Csat-Csurf)
with PV being the CO2 gas transfer velocity (called the piston velocity) in
ms-1, calculated as
PV=(1-aice)⋅a⋅u102⋅(660.0/ScCO2)-1/2.
The coefficient a is taken as 0.31 cmh-1 as mentioned earlier, aice is the fraction
of the ocean covered by sea ice, u102 is the squared 10 m wind speed from the coupler,
and ScCO2 is the Schmidt number of CO2. ScCO2 is
calculated as in the ecosystem model, following :
ScCO2=2073.1+SST⋅(-125.62+SST⋅(3.6276+SST⋅(-0.043219))).
Csurf in the gas flux calculation above is the surface aqueous
CO2 concentration in molm-3 (also called
CO2∗, which is the aqueous CO2 concentration in
molm-3 in the ocean in general). Csat is the
saturation concentration in molm-3, with
Csat=CO2∗+DCO2∗ and
DCO2∗ being the difference in CO2 concentration between
the surface ocean and the atmosphere. SST is the sea surface temperature.
CO2∗ and DCO2∗ in turn are calculated by the
carbonate solver from the ecosystem model, based on SST, SSS, ALK,
PO4, Si(OH)4, pH, atmospheric pCO2, atmospheric
pressure, and the abiotic DI12C and DI14C concentrations
in the surface water.
As in OCMIP-2, we do not account for fractionation during gas exchange in
this abiotic formulation, as the effect of isotopic fractionation is almost
completely accounted for by the standard correction made when calculating
Δ14C from observations seefor
details.
The gas flux of the normalized abiotic DI14C is calculated as
F14=PV⋅(Csat⋅R14Catm-Csurf⋅R14Cocn)
with
R14Catm=(1+Δ14Catm/1000)
and
R14Cocn=1000⋅(DI14C/DI12C-1).
The values of the atmospheric pCO2 and
Δ14Catm can be set to be constants or can be read
in from a file. For atmospheric pCO2, it can also be taken from the
coupler, to ensure the use of a consistent atmospheric pCO2 value
across model components. Currently the code is set up to read in three files
of Δ14Catm values, one each for the Northern
Hemisphere, the equatorial region (20∘ N–20∘ S), and the
Southern Hemisphere, in order to represent the spatial inhomogeneity of
Δ14Catm, for example, after the atmospheric
nuclear bomb tests.
Virtual fluxes
The CESM ocean model is a volume-conserving model where water fluxes at the
surface (from precipitation, evaporation, and river input) are added as
virtual fluxes. These virtual fluxes represent the dilution or concentration
effect from adding or removing freshwater. For the abiotic carbon isotope
tracers, we have a virtual DI12C and DI14C flux. As for
salinity and for DIC in the ecosystem model, we use a constant surface
reference DI12C and DI14C for the calculation of virtual
fluxes in order to conserve tracers. The reference values are 1944 µmolm-3 for both DI12C and normalized DI14C, the
same as for DIC in the ecosystem model of CESM.
Interior processes
In the interior of the ocean, the only additional term to the transport of
the tracers by the physical ocean model is the decay term for
DI14C, following the OCMIP-2 protocol:
d[DI12C]/dt=L([DI12C])
and
d[DI14C]/dt=L([DI14C])-λ⋅[DI14C],
with L being the 3-D transport operator and λ being the radioactive
decay constant for 14C in s-1, using a half-life of 5730
years :
λ=ln(2)/(5730⋅31 556 926).
The radiocarbon age (relative to AD 1950 =0 yr BP) is calculated from
Δ14C following
14Cage=-5730/ln2×ln(1+Δ14C/1000).
5730 years /ln2=8267 years is the mean life of 14C, which
differs from the often used mean life of 8033 years
e.g.,, which is based on the earlier Libby
half-life of 5568 .
Biotic 13C and 14C
In the biotic implementation of 13C and 14C, we use the
ocean ecosystem model e.g., to compute the carbon
pools as well as all other biological variables (like silicic acid and
alkalinity). The ecosystem model currently has seven carbon pools: DIC, DOC
(dissolved organic carbon), CaCO3, diazotrophs, diatoms, small
phytoplankton, and zooplankton. We carry passive tracers for each of these in
the isotope-enabled version of the code. As 12C makes up over
98 % of the carbon earth and does not fractionate, we assume that the
ecosystem carries 12C. This means that the isotope ratio R can be
calculated as the ratio of the new isotopic carbon pools to the ecosystem
carbon pools. As for the abiotic radiocarbon, we use scaled variables for
13C and 14C in order to minimize the numerical error of
carrying very small numbers (particularly for 14C). The scaling
factor is the commonly used standard isoC/12C for
each isotope, i.e., 1.12372×10-8 for iso=13C
and 1.176×10-12 for iso=14C
. This means that we use 13RStd=1 and
14RStd=1 in the code, and that the model-simulated isotopic
carbon pools are multiplied by the respective scaling factor to compare them
with observations.
In the biotic formulation, we account for the fractionation of 13C
and 14C during gas exchange and during biological processes. The
fractionation (ϵ) of 14C is always twice that of
13C, as all relevant processes have a mass-dependent fractionation
for carbon . The isotopic fractionation
ϵ is related to the fractionation factor α through
ϵ=(α-1)⋅1000.
As diagnostic variables, we compute the δisoC values by
first computing the ratio isoR=DIisoC/DIC
and then using
δisoC=(isoR-1)⋅1000.
As for the abiotic Δ14C calculation in
Eq. (), we do not multiply by isoRStd
in the calculation of δisoC because we are using normalized
DIisoC.
Air–sea gas exchange of 13C
The air–sea flux of 13C is calculated based on :
F13=PV⋅αaqg⋅αk⋅(R13Catm⋅Csat-R13CDIC⋅Csurf/αDICg).
Here, Csat and Csurf are obtained from the ecosystem
model. αk=-0.99919 is the constant kinetic fractionation
factor from (with ϵ=-0.81 and
α=ϵ/1000+1). αaqg is the
temperature (TEMP, in ∘C) dependent isotopic fractionation factor
during gas dissolution, based on the equation for
ϵaqg from :
ϵaqg=-0.0049⋅TEMP-1.31.
The temperature and carbonate fraction (fCO3) dependent
fractionation factor (αDICg) between total DIC
and CO2 is based on the empirical relationship for
ϵDICg from :
ϵDICg=0.014⋅TEMP⋅fCO3-0.105⋅TEMP+10.53.
R13Catm is the 13C to 12C ratio
in atmospheric CO2, calculated using the atmospheric
δ13Catm record and
Ratm=1+δ13Catm/1000 (scaled by
13RStd). The values of δ13Catm can
be set to be a constant or it can be read in from a file. Currently
δ13Catm is assumed to be well mixed globally, so
only one global value is read in. With small code modifications globally
inhomogeneous δ13Catm values can easily be read in
instead. R13CDIC is the 13C to
12C ratio of dissolved inorganic carbon, calculated from the
simulated biotic DIC and DI13C.
Virtual fluxes of 13C
As stated in Sect. , we account for the
dilution and concentration effect of surface freshwater fluxes in the model
by adding a virtual flux, using a constant surface reference DI13C
(and DI14C) of 1944 µmolm-3 for the calculation of
virtual fluxes.
Biological fractionation of 13C
The isotopic carbon fixation by photosynthesis (photo13C) is
computed from the 12C fixation during photosynthesis (photoC, from
the ecosystem model), using
photo13C=photoC⋅Rp
with
Rp=1000⋅RCO2∗/(ϵp+1000)
and
RCO2∗=R13CDIC⋅αaqg/αDICg.
The strength of the biological fractionation of carbon during photosynthesis
(ϵp), as well as the key controlling parameters, are still
being debated in the literature e.g.,, and many of
the existing 13C implementations in models use different
parameterizations. We therefore implemented three different parameterizations
for ϵp to test the sensitivity of our results to the
choice of biological fractionation.
The simplest model for ϵp by gives the same
ϵp value for all types of autotrophs:
ϵp=1000⋅(δCO2∗-δCp)/(1000+δCp).
This relationship is based on the empirical relationship found by
between the isotopic composition of the autotroph
(δCp) and CO2∗:
δCp=-0.8⋅CO2∗-12.6,
limiting δCp to values between -18 and -32 ‰ .
assumed that CO2 enters the cell by diffusion and that the
fractionation depends on the rate of photosynthesis, and therefore parameterized
ϵp as a function of CO2∗ and the specific photosynthesis rate of
each phytoplankton group (μ, in s-1, calculated by the ecosystem model):
13ϵp=(μ/CO2∗⋅86 400-0.371)/(-0.015).
Parameters used in the parameterization of ϵp
for the implementation following . The values for
small phytoplankton are based on E. huxleyi, the value for diatoms
are based on P. tricornumtum, and the values for diatoms are based
on Synechococcus sp. .
Small phytoplankton
Diatom
Diazotroph
Qc (molCcell-1)
69.2×10-14
63.3×10-14
3×10-14
cellpermea (ms-1)
1.8×10-5
3.3×10-5
3.0×10-8
cellsurf (m2)
87.6×10-12
100.6×10-12
5.8×10-12
Cup
2.2
2.3
7.5
ϵfix
25.3
26.6
30
argued that only considering diffusive CO2
transport into cells and assuming a linear relationship between
ϵp and CO2∗ concentration and the specific
growth rate (μ) does not agree with laboratory and field data, citing
work by , , and
. therefore proposed to use
phytoplankton type-specific (constant) cell parameters (see
Table ) to compute the fractionation during
photosynthesis:
13ϵp=ϵdiff+(Cup/(Cup+1/var))⋅δd13C+θ⋅(ϵfix-ϵdiff)
where
θ=(1+(Cup-1)⋅var)/(1+Cup⋅var)
and
var=μ/CO2∗⋅1000⋅Qc/(cellpermea⋅cellsurf),
with Qc being the cell carbon content, cellpermea being
the cell wall permeability to CO2 (aq),
cellsurf being the surface areas of cells,
Cup being the ratio of active carbon uptake to carbon
fixation, ϵfix being a constant phytoplankton
type-dependent fractionation effect of carbon fixation,
ϵdiff=0.7 representing the fractionation by diffusion
, and δd13C=-9.0 being the difference
between the isotopic compositions of the external CO2 and the organic
matter pools .
While the fractionation during calcium carbonate formation is much smaller
than the fractionation during photosynthesis , we include
a small constant fractionation of 2 ‰ for calcium carbonate
formation, based on work by that found a range of
3 ‰ to -2 ‰ for different species. Other implementations
of 13C in ocean models have used values of 1 ‰
e.g., or have assumed no
isotopic fractionation for calcification
e.g.,. However, as shown by
, the effect of the calcium carbonate pump on
δ13C is small, so the choice of the value for the
fractionation during calcium carbonate formation is not expected to have a
big impact on the results in the current ecosystem model with one species of
calcium carbonate.
Biotic 14C
The 14C air–sea flux is calculated in the same way as shown in
Eq. () for 13C, but with the fractionation
for 14C being twice as large as for 13C
(ϵ14=2⋅ϵ13, ) and
with R14Catm and R14CDIC
instead of R13Catm and R13CDIC.
The biological fractionation is also the same as for 13C, except
that ϵ14=2⋅ϵ13 everywhere in
Sect. . The surface reference value for DI14C
for the virtual flux calculation is 1944 µmolm-3, the same as for DI13C (and DI12C).
In contrast to 13C, 14C decays in all carbon pools, following the decay equation
(see Eq. () in Sect. ).
To compare the model-simulated δ14C values that we save as
diagnostics (see Eq. ) with published observations of
Δ14C, we apply the same fractionation correction to it that is
used for observations to convert δ14C to Δ14C:
Δ14C=δ14C-2(δ13C+25)(1+δ14C/1000).
In the following we always show Δ14C.
As for the abiotic 14C implementation, the value of Δ14Catm can
be set to be a constant or it can be read in from three files (one for the Northern Hemisphere, one
for the equatorial region, and one for the Southern Hemisphere).