BGBiogeosciencesBGBiogeosciences1726-4189Copernicus PublicationsGöttingen, Germany10.5194/bg-13-2823-2016A probabilistic assessment of calcium carbonate export and dissolution in the modern oceanBattagliaGiannabattaglia@climate.unibe.chhttps://orcid.org/0000-0002-6677-7969SteinacherMarcohttps://orcid.org/0000-0002-4795-1749JoosFortunathttps://orcid.org/0000-0002-9483-6030Climate and Environmental Physics, Physics Institute, University of Bern, Bern, SwitzerlandOeschger Centre for Climate Change Research, University of Bern, Bern, SwitzerlandGianna Battaglia (battaglia@climate.unibe.ch)13May20161392823284812November201521December201520April201621April2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://bg.copernicus.org/articles/13/2823/2016/bg-13-2823-2016.htmlThe full text article is available as a PDF file from https://bg.copernicus.org/articles/13/2823/2016/bg-13-2823-2016.pdf
The marine cycle of calcium carbonate (CaCO3) is an important
element of the carbon cycle and co-governs the distribution of carbon
and alkalinity within the ocean. However, CaCO3 export fluxes and
mechanisms governing CaCO3 dissolution are highly uncertain.
We present an observationally constrained, probabilistic assessment of
the global and regional CaCO3 budgets. Parameters governing
pelagic CaCO3 export fluxes and dissolution rates are sampled
using a Monte Carlo scheme to construct a 1000-member ensemble
with the Bern3D ocean model. Ensemble results are constrained by
comparing simulated and observation-based fields of excess dissolved
calcium carbonate (TA*). The minerals calcite and aragonite are
modelled explicitly and ocean–sediment fluxes are considered. For
local dissolution rates, either a strong or a weak dependency on CaCO3 saturation is assumed.
In addition, there is the option to have saturation-independent dissolution above the saturation horizon.
The median (and 68 % confidence
interval) of the constrained model ensemble for global biogenic CaCO3 export is 0.90
(0.72–1.05) Gt C yr-1, that is within the lower half of
previously published estimates
(0.4–1.8 Gt C yr-1). The spatial pattern of
CaCO3 export is broadly consistent with earlier
assessments. Export is large in the Southern Ocean, the tropical
Indo–Pacific, the northern Pacific and relatively small in the
Atlantic.
The constrained results are robust across a range of diapycnal mixing coefficients and, thus,
ocean circulation strengths. Modelled ocean circulation and transport
timescales for the different set-ups were further evaluated with CFC11
and radiocarbon observations. Parameters and mechanisms governing
dissolution are hardly constrained by either the TA* data or the
current compilation of CaCO3 flux measurements such that model
realisations with and without saturation-dependent dissolution achieve
skill. We suggest applying saturation-independent dissolution rates in
Earth system models to minimise computational costs.
Introduction
The cycling of calcium carbonate (CaCO3) forms an important
component of the marine carbon cycle. It co-governs the
surface-to-deep gradients of alkalinity and dissolved inorganic carbon (DIC)
in the ocean , dominates deep ocean alkalinity fluxes,
and influences the surface fields of DIC and
alkalinity, thereby providing the background conditions for the uptake
of excess anthropogenic carbon from the atmosphere. However, the
export and dissolution fluxes of CaCO3 are highly uncertain.
For example, current estimates of CaCO3 export diverge by
a factor of ∼40.4–1.8 GtCyr-1,
summarised in.
The CaCO3 cycle is driven by calcifying organisms such as
coccolithophorids, foraminifera, or pteropods, which remove calcium (Ca2+), alkalinity, and DIC from
the pelagic surface ocean waters to form shells and structures of CaCO3. These CaCO3 particles
are eventually exported out of the surface, gravitationally sink
through the water column, and dissolve at depth or get buried in ocean
sediments. The formation and dissolution of CaCO3 introduces
a vertical gradient in alkalinity and DIC. These gradients have been sustained against the counteracting
forces of physical mixing and transport, which would otherwise have
removed these gradients. This redistribution of alkalinity and carbon by biogenic and physical transport
affects the partitioning of carbon between the ocean and atmosphere
and a reduction, expected under ongoing ocean acidification, or even
a complete stop of CaCO3 export tend to decrease atmospheric
CO2 by a few ppm, and in the extreme case by up to ∼50ppm, on century timescales
.
There are different mineral forms of CaCO3 and solubility is
higher for high-magnesium calcite (typically present in fish) and
aragonite (typically present in free-swimming pelagic sea snails and
sea slugs; pteropods) than for calcite (typically present in
calcifying algae; coccolithophorids). Thermodynamic considerations
suggest that dissolution of CaCO3 particles occurs only when
the product of the calcium and carbonate ion concentrations in the
surrounding environment is below the saturation product. The
saturation product of all minerals increases with increasing pressure
. At depth, respiration of organic matter
additionally decreases the concentration of CO32-. As
a result, the bulk of the water in the deep ocean is undersaturated
with respect to CaCO3 minerals, generally enabling their
dissolution, and oversaturated in the upper ocean, thermodynamically
hindering their dissolution . Overall, the
quantitative understanding of dissolution kinetics is, however, low
and published estimates of saturation-dependent dissolution kinetic
parameters range over several orders of magnitude summarised
in. CaCO3 dissolution may nevertheless
still occur in the upper ocean in suitable, undersaturated
microenvironments which would be present for instance in the guts of
zooplankton, suspended organic aggregates, or fecal pellets
. There are in fact
several tracer-based studies reporting CaCO3 dissolution above
the saturation horizon of bulk seawater .
In a modelling study,
, nevertheless, demonstrated that the method which is often employed to derive these upper ocean
dissolution rates see Discussion section on TA* CFC age method, might not be applicable,
because this method neglects physical transport and mixing of
alkalinity. It is therefore still debated where and how fast settling
CaCO3 particles are dissolved in the water column. Another
complication, typically neglected in previous studies on open water
CaCO3 dissolution, arises from ocean–sediment interactions
and the influence of associated burial and redissolution fluxes on
alkalinity and carbon concentrations in the open ocean .
Here we propose an alternative, probabilistic assessment of the global
CaCO3 budget. We consider explicitly the transport and mixing
of alkalinity and account for ocean–sediment interactions to
probabilistically constrain the CaCO3 cycle with the
observation-based distribution of the TA* tracer. TA* reflects
the imprint of the CaCO3 cycle on alkalinity (see
Sect. ) and is therefore impacted by
CaCO3 export, water column dissolution, physical transport, and
mixing of the released alkalinity and DIC and ocean–sediment fluxes. For
the probabilistic flux assessment, a large range of calcite and
aragonite export and dissolution flux parameterisations are employed
within our Earth system model of intermediate complexity (EMIC) – the
Bern3D model – in a Monte Carlo set-up with 1000 members. The
Bern3D model calculates the corresponding modelled steady-state tracer
concentrations of TA*. The most probable export and dissolution
fluxes are then the ones resulting in modelled TA* fields that
match the observation-derived TA* distribution closely. The aim is
to assign uncertainty estimates that will be consistent with both the
observations and model equations – a classical data assimilation
problem (see Sect. ). It is expensive to perform
simulations with interactive sediments due to long spin-up times required to bring
ocean and sediments in equilibrium and we account a posteriori for the
influence of sediment burial and dissolution fluxes on TA* (see
Sect. ). This approach represents an alternative to the
interpretation of concentrations without a physical model or the
interpretation of flux/rate measurements within the water column,
which are generally much sparser (∼156 flux measurements in the
water column and ∼56 benthic dissolution flux
measurements , globally) and more difficult to
obtain. We apply the data compilation of water
column fluxes as an additional constraint for comparison. Additional
sensitivity analyses with respect to vertical diffusion (kdia, see
Sect. ) are illustrated. The results are compared and
contrasted to data-based estimates of export and dissolution (as
summarised in ). Finally, implications for the
parameterisation of CaCO3 dissolution in Earth system models
are discussed.
Overview of suggested ways of regression for TA0 either including
two (S, PO) or three (S, PO, T) explanatory variables and either as
a global or basin-wide fit. The last column shows the root mean square
error relative to the Global B3D estimate.
Equation (ueqkg-1)MeanRMSE from Global(molm-3)B3D (molm-3):TA0=(367.5+59.9psu-1⋅S+0.074kgµmol-1⋅PO)µeqkg-12.3770.012:TA0=148.7+61.36⋅S+0.0941⋅PO-0.582⋅Tpot2.390.0015:as Global B3D 2V:TA0=(297.51+56.399psu-1⋅S+0.1259kgumol-1⋅PO)ueqkg-12.3870.0022Global B3D:TA0=(345.64+56.03psu-1⋅S+0.069kgumol-1⋅PO-0.9∘C-1⋅T)ueqkg-12.3890Regional B3D:2.3850.0047AtlanticTA0=(688.15+44.97psu-1⋅S+0.129kgumol-1⋅PO+1.34∘C-1⋅T)ueqkg-1PacificTA0=(381.05+55.26psu-1⋅S+,0.049kgumol-1⋅PO-1.20∘C-1⋅T)ueqkg-1IndianTA0=(637.70+47.38psu-1⋅S+0.078kgumol-1⋅PO-0.54∘C-1⋅T)ueqkg-1
is the original, global regression based on two explanatory variables (based on their 1996
database). and are both taken from , also including temperature as an additional
explanatory variable and fitted to a Pacific subset. Global B3D 2V is a global regression with two explanatory variables
(based on WOA09 ) on the Bern3D grid
(32 × 40 × 41 grid cells). Global B3D includes three explanatory variables and Regional B3D further distinguishes each basin, separately.
Observation-derived TA*
Total alkalinity data are from the GLODAP carbon climatology and salinity ,
temperature , oxygen, and phosphate data are from the World Ocean Atlas.
These gridded data products represent objectively analysed climatological fields of the respective oceanic variables and are based on samples taken during the previous decades.
They serve to split the alkalinity signal into its different physical and biogeochemical components such as TA*, our target variable in the data assimilation.
We first regridded all required gridded data sets to the Bern3D model grid (40 × 41 × 32 grid boxes) using the area-weighted regridding method of Ferret before deriving the other properties.
TA*, our target variable in the data assimilation, is a constructed tracer ()
to exclusively capture the imprint of
CaCO3 dissolution on alkalinity. TA* is, in this sense, one
of three components of measured total alkalinity (TA,
Eq. (), mean concentration
2.427 molm-3 based on the regridded GLODAP data set). TA* can be extracted from TA by
accounting for preformed (TA0, Eq. ) and remineralised
alkalinity (TAr, Eq. ):
TA=TA0+TAr+TA*.
TA0 is the
background or preformed concentration, set at the ocean surface, and
mixed conservatively in the ocean interior. Accordingly, TAr and
TA* are by definition zero in the surface ocean. To describe
TA0 in the ocean interior, one relies on a multilinear regression
relationship for surface ocean total alkalinity based on surface ocean
salinity (S) and PO
(PO =O2+r-O2:PO4⋅PO4, r-O2:PO4=170,
) and sometimes surface ocean temperature (T)
as explanatory variables (all conservative variables, see
Eq. (), ).
TA0=a0+a1⋅S+a2⋅T+a3⋅PO
The coefficients, ai, are estimated from observations of TA, S, T,
and PO in the surface ocean. The
linear regression fit is sometimes further subdivided to include only
specific basins . Table summarises different
regressions, including previously published regression estimates as
well as new estimates by us calculated on the Bern3D model grid
(B3D). The root mean squared errors (RMSEs) between these fits are smaller than
0.00465 molm-3 (i.e. smaller than 0.2 %, excluding
the equation, which relies on an older database
from 1996). From these different options, we accordingly chose the
Global B3D linear regression including three explanatory variables and global data sets as robust regression for TA0, which yields a mean concentration of ∼2.389molm-3.
TAr is linked
stoichiometrically to the apparent oxygen utilisation (AOU,
, Eq. ) and accounts for decreases in
TA due to the oxidation of organic nitrogen, phosphorous, and sulfur
(OM).
TAr=rAlk : OM⋅rNO3:-O2⋅AOU=1.26⋅16/170⋅AOU
We set rAlk : OM to 1.26 and
rNO3:O2 to 16/170 to
uniformly, and globally link AOU changes to changes in TA (as in
), which yields a mean concentration of -18 mmolm-3.
propose an
8 % higher value for rAlk : OM of 1.36, based on
a different sulfur to carbon ratio. In addition, we note that AOU has
been suggested to overestimate true oxygen utilisation by 20–25 %
. Accordingly, TAr might be associated
with an uncertainty of ∼20 %.
The TA* tracer captures exclusively the influence of CaCO3 dissolution on alkalinity.
An observationally based estimate of the TA* distribution (mmolm-3) yielding an inventory of ∼37.5PmolC
of which ∼41 % comes to lie above the calcite saturation horizon. The calcite (σcalcite=1) and
aragonite (σaragonite=1) saturation horizon are shown by the blue lines. Displayed are results for
a cross section through the Atlantic (25∘ W), across the Southern Ocean (58∘ S) into the Pacific,
and through the Pacific (175∘ W).
The remaining signal, then, is TA* (mean concentration ∼57mmolm-3 based on GLODAP and our reference choices to derive TA0 and TAr), the changes in alkalinity due only to the
CaCO3 cycle (Fig. ). The global average RMSE of any of the described
ways (16 in total) of accounting for TAr (25 % lower AOU or
different rAlk : OM) and TA0 (either two or three explanatory
variables, and either global or regional) from our reference choices
is ∼4mmolm-3 (average RMSE 3.9, 3.8,
3.1 mmolm-3 in the Atlantic, Pacific, and Indian Ocean,
respectively, i.e. ∼7 %). Note that this approach,
inherent to its empirical nature, yields slightly negative TA*
values in some places. TA* integrates to about 37.5 PmolC or
75 Pmol Alk-equivalents of which ∼41 % come to lie
above the calcite saturation horizon (similar to who find 44.7 % of the TA* inventory above the calcite saturation horizon). These estimates are robust
across the different sources of uncertainty.
TA* concentrations are
expressed in alkalinity equivalents throughout this paper and we do
not divide TA* concentrations by a factor of 2 as done in many
observational studies which express TA* in terms of carbon changes.
TA* inventories are in PmolC, and CaCO3 fluxes are given in carbon units
(GtCyr-1, mmolCm-3yr-1, mmolCm-2yr-1).
The modelling framework
To constrain the alkalinity fluxes associated with CaCO3
cycling, we introduce different export and dissolution fluxes (with
a total of 15 degrees of freedom) within the biogeochemistry
component of the Bern3D dynamic ocean model. The parameters of the new
formulations describing the export and dissolution fluxes of
CaCO3 are varied using a Monte Carlo sampling method and
the resulting model ensemble, including 1000 members, is run to
a pre-industrial steady state, producing a broad range of solutions
(see Sect. ). The alkalinity fluxes associated
with the CaCO3 cycle are then constrained by comparing
observation-based and simulated TA* data using a Bayesian approach
following ; a skill score is assigned to each
ensemble member and used as a weight for the computation of median
values and probability density functions from the ensemble
results. The sediment module is not included in the ensemble due to
extensive computational cost (∼150 vs. ∼8CPUh
for a single-member run with and without the
sediment, respectively). Instead, we reran the model configurations
which achieved the best skill scores with interactive sediments to
account for CaCO3 burial and sediment redissolution
a posteriori (see Sect. ).
The Bern3D model
The Bern3D model couples a dynamic ocean, sea ice, an energy-moisture
balance atmosphere, a marine biogeochemical cycle, a dynamic global
vegetation model, and an ocean sediment module. Here an ocean version with
a horizontal resolution of 41 by 40 grid cells and 32
logarithmically scaled vertical layers is used (see also
). The horizontal resolution is the same for the components atmosphere, ocean, sea ice, and sediments
of the Bern3D model.
Transport and mixing of tracers in the ocean is
based on and as
a three-dimensional frictional geostrophic model. The model has an
isopycnal diffusion scheme and Gent–McWilliams parameterisation for
eddy-induced transport . The NCEP/NCAR monthly
wind-stress climatology is prescribed at the
surface. Air–sea gas exchange for CO2 is implemented
according to OCMIP-2 protocols ().
The global mean air–sea transfer rate is reduced by 19% compared to OCMIP-2 to match observation-based estimates of natural and bomb-produced radiocarbon .
A two-dimensional energy moisture balance model represents the atmosphere
. The model is spun up to equilibrium under
preindustrial conditions, with atmospheric CO2 set to
278 ppm. The spin-up period is 4000 years without the
sediment module and 50 000 years with the sediment
module. Remaining model drifts are negligible.
The last year of the spin-up period is considered for all analyses (note that unforced interannual variability is generally negligible in our model).
We implicitly neglect potential changes in TA* over the industrial period by comparing model results for
preindustrial conditions with TA* data reconstructed from recent measurements.
Such changes are negligible in simulations with prescribed anthropogenic forcing in the Bern3D model.
The marine biogeochemical module computes the cycling of carbon,
alkalinity, phosphate, iron, oxygen, silica, and carbon isotopes. New
production of organic material in the model is limited by temperature,
light, phosphate, and iron following as described by
and . One-third (33 %) of
the new production is exported out of the euphotic zone (defined at
75 m) as particulate organic matter (POM), with the remainder
contributing to the dissolved organic matter pool. Within
biogeochemically similar regions, a parameter termed rain
ratio linearly scales the pattern of POM export to CaCO3
export (silica limitation is not considered here). We define eight such regions,
each assigned an independent value for the export rain-ratio parameter (mol inorganic carbon/mol organic carbon exported, later given in % inorganic to organic carbon exported). These
include the Pacific, Atlantic, and Indian sections of the Southern Ocean (<35∘ S, separated at 240∘ W, 63∘ W and 30∘ E), the tropical
(35∘ S to 30∘ N) Pacific, Atlantic, and Indian
Ocean, and the northern (>30∘ N) Atlantic (including the
Arctic) and Pacific Ocean. A global parameter (fcalc)
determines how much of the total CaCO3 export flux represents
calcite and how much represents aragonite (1-fcalc).
Abiotic CaCO3 precipitation is virtually absent in today's
ocean and not considered reviewed in.
In the model, we implemented TA* as an explicit, idealised
tracer . It captures the alkalinity equivalents of CaCO3
dissolution whenever it occurs and mixes this signal,
accordingly. TA* values are set to zero throughout the surface
ocean.
Results from sensitivity simulations applying three different illustrative dissolution schemes. Left column:
CaCO3 dissolution rates. Right column: the resulting steady-state TA* for these three contrasting
parameterisations of the CaCO3 dissolution rate. The dissolution rate is set to increase fast (top row),
slowly (middle row) with undersaturation of CaCO3, or is set constant throughout the water column (bottom row).
The standard version of the Bern3D model without the sediment module is applied, and the fraction of CaCO3 export in
the form of aragonite is set to 10 %. At least 43 % of the dissolution signal is simulated above the calcite
saturation horizon irrespective of whether dissolution is allowed to occur above the saturation horizon (bottom row)
or not (middle and top row). This points to the importance of physical transport in shaping the distribution of TA*.
In sensitivity simulations with the sediment module enabled, the flux
of CaCO3, and of other particles, reaching the seafloor is
passed to the sediment module from where a fraction potentially
redissolves back into the water column.
In simulations without the sediment module, the entire flux reaching the ocean floor redissolves back into the water column. Simulated TA* concentrations tend to be lower with the sediment module enabled than without the sediment module, because a fraction of the CaCO3 export flux is removed from the ocean and buried in the geosphere. The sediment diagenesis model
features the same
horizontal resolution as the ocean model and 10 layers resolving the
top 10 cm of the seafloor. It dynamically calculates the
transport, remineralisation/redissolution, and bioturbation of solid
material within the top 10 cm of the seafloor as well as
porewater chemistry and diffusion as described in detail in
. Solutes diffuse over a boundary layer of
1 cm between the sediment column and the lowermost ocean grid
cell. Four solid components (CaCO3, opal, POM, and clay) and
pore water substances (carbon and carbon isotopes, total alkalinity,
phosphate, nitrate, oxygen, and silicic acid) are modelled. The pore
water carbonate ion concentration determines whether, and at which
rate, CaCO3 dissolves. Aragonite and calcite are not
distinguished within the sediment module and CaCO3 is assumed
to be in the form of calcite. Any solid material that is pushed out of
the diagenetic zone disappears into the subjacent diagenetically
consolidated zone. During the spin up of the ocean–sediment model, the
net loss of alkalinity, and other tracers such as carbon and
nutrients, to the sediments is immediately replaced by corresponding
riverine inputs which are distributed uniformly along the coastlines
(and then taken to be part of TA0). The riverine input is diagnosed
at the end of the spin up.
The model features the main water masses and mixing timescales of the
ocean, an essential prerequisite to realistically simulate TA* and
other tracers. The simulated and observed distributions of the
ventilation tracers Δ14C and CFC11 are provided in
the Appendix along with a Taylor diagram
of CFC11, Δ14C, temperature, salinity, DIC, TA,
PO4, oxygen, and TA* (Figs. to ). Globally,
the correlation coefficient and standard deviation of the median
relative to the standard deviation of the observations
(σrel.obs.) are 0.94 and 0.99 for
Δ14C and 0.91 and 0.98 for CFC11.
CaCO3 dissolution within the water column
The dissolution equations for calcite and aragonite are implemented
using equations with identical functional forms, but with different
parameters for each mineral. In the following, we do not explicitly
distinguish the two minerals to ease notation. The dissolution of
calcite and aragonite below the euphotic zone is assumed to
be a function of the saturation state of the bulk seawater, Ω,
and the particle concentration per unit of water volume,
[CaCO3] (see for a discussion):
d[CaCO3]dt=-keff(Ω)×[CaCO3].keff denotes a first-order rate constant for either
calcite or aragonite. It is defined as
keff(Ω)=k0×(1-Ω)n×H(Ω-1)+kbg.k0 and kbg are rates in units of 1/time. H is the
Heaviside function, which is zero for supersaturated and 1 for
undersaturated water. The saturation state is defined by the ratio of the product of calcium
ion concentration times carbonate ion concentrations to the saturation
product, Ksp:
Ω=[Ca2+][CO32-]Ksp.Ω values larger than 1 correspond to oversaturated and
Ω values smaller than 1 to undersaturated conditions.
Ω and thus keff are grid-cell-specific. At supersaturation, the dissolution rate keff equals the
constant background rate kbg (which can be zero). With
increasing undersaturation, the dissolution rate increases towards
its maximum value (kbg+k0). n is a unitless parameter
and determines the deviation from linearity of this increase. For
simplicity and to avoid the addition of further free parameters,
a constant sinking velocity, v, is assumed and identical for both
calcite and aragonite particles. The flux profile of CaCO3
then takes the form
Fi,j(zk)=Fi,j(zk-1)⋅exp-keff(Ωi,j,k)v⋅Δzk,
where F is the downward flux of either calcite or aragonite
particles per unit area evaluated at the bottom of each tracer grid
cell at depth zk. i, j, and k are grid cell indices
indicating longitude, latitude, and depth. Δzk denotes grid
cell height. The export flux is set equal to F (z=75m) at
the depth of the euphotic zone. Particles are dissolved
instantaneously and sinking is not explicitly resolved in this
formulation, reducing computational costs. v/keff is in
units of m, and, if assumed constant, can be interpreted as the
dissolution length scale, i.e. the depth at which the flux has
decreased to 1/e (to ∼37 %) of the export flux at
75 m. Any particles reaching the sea floor are dissolved
completely in the appropriate lowermost box, except when the sediment
module is included.
Results from sensitivity simulations. CaCO3 export and TA* inventories for different
physical mixing (diapycnal mixing coefficient, kdia) and CaCO3 dissolution schemes.
For these illustrative simulations, calcite and aragonite particles were assigned equal parameter values
and 10 % of export is assumed to be in the form of aragonite. Fast: k0=10day-1, n=1,
fcalc=0.9, kbg=0; slow: k0=0.16day-1, n=2, fcalc=0.9,
kbg=0; constant: kbg/v=1/2900m-1.
kdia, lowkdia, refkdia, high0.1 × 10-4m2s-10.2 × 10-4m2s-10.5 × 10-4m2s-1Export at 75 m (Gt C yr-1)0.730.821.07TA* inventory (Pmol C)(fraction of which lies above Ωcalc=1)Fast47.8 (54 %)47.9 (52 %)44.5 (51 %)Slow62.5 (45 %)63.0 (44 %)58.9 (43 %)Constant38.1 (52 %)38.4 (51 %)35.4 (50 %)
In Fig. we illustrate three dissolution
cases to explore the sensitivity of TA* to dissolution profiles
which cover the sampled uncertainty in dissolution rate
parameters. The three dissolution rate profiles are selected to represent a case with constant,
saturation-independent dissolution (constant) and two cases where
this background dissolution rate is set to zero and CaCO3
dissolves only below the saturation horizon. In the fast (slow) case,
aragonite (chosen to represent 10 % of the total) and calcite
(90 % of total export) dissolves quickly (slowly) below the
saturation horizon. Aragonite and calcite dissolve within a few
hundred metres below the saturation horizon in the fast case, while
most CaCO3 dissolves on the ocean floor in the slow case.
The choice of the dissolution rate profile has a substantial influence
on the simulated TA* inventory (Fig. , Table , middle column, kdia, ref). The
global TA* inventory is 38 PmolC for the case with
a constant, saturation-independent dissolution and a rain ratio of
∼7 %, which is close to the observation-derived inventory of
37 PmolC. The simulated inventory is 48 and
63 PmolC for the fast and slow cases (where no dissolution
occurs above the saturation horizon), respectively, and by that
substantially higher. TA* accumulates in the deep ocean when all
CaCO3 is dissolved below the saturation horizon of aragonite
and calcite and no dissolution is permitted above. The TA*
inventory and concentrations are sensitive to the choice of the
dissolution rate profile, supporting our choice of TA* as a target
variable to constrain dissolution rates.
Ensemble simulations and metrics for skill assessmentThe Monte Carlo ensemble
Following and we run a 1000-member Latin hypercube
ensemble to constrain the export flux out of the surface ocean, and the dissolution
of aragonite and calcite within the water column.
Latin hypercube sampling is a statistical, Monte Carlo method to generate controlled
random samples from a multidimensional distribution (15 dimensions in our case).
The defined parameter ranges are divided into equally probable intervals (1000 in our case).
Random samples are then generated in each interval. This method ensures that the sampled
values are representative of the real variability, while minimising the number of required
samples and thus the computational costs.
We sample 15 parameters and apply uniform priors based on literature information.
The free parameters are the eight rain-ratio parameters (prior range: 0 to 18 % for the Pacific and South Indian regions,
prior range: 0 to 16 % for the tropical Indian, prior range: 0 to 7 % for the North and tropical Atlantic,
and prior range: 0 to 10 % for the South Atlantic), defining the total
amount of CaCO3 export for each of the six regions.
The prior ranges of the rain ratios for the three Atlantic regions are limited to maximal 10%.
This selection is based on results from previous ensemble set-ups that revealed an overestimation
of TA* for high rain ratios in the Atlantic domain.
Further we include the fraction fcalc (1–0.5) defining the split between
aragonite and calcite export, and 3 × 2 parameters governing
the dissolution kinetics for calcite and aragonite,
respectively. These are k0 (0.05–10 day-1) and n
(1–4), describing fast and slow dissolution kinetics as a function of
undersaturation, and kbg/v (0–1/2500 m-1),
the length scale associated with a constant, background dissolution
rate acting both above and below the saturation horizon. v is kept
constant at 100 mday-1.
The observation-based saturation state of the bulk seawater with
respect to aragonite and calcite
is prescribed for each model grid cell.
It was calculated with the carbonate chemistry package seacarb
from GLODAP
and World Ocean Atlas 2009 (WOA09; ).
Seacarb calculates carbonate chemistry based on pressure, temperature, salinity, alkalinity, DIC, silica, and phosphate.
This reduces computational costs as the carbonate chemistry package of the online model requires
substantial computational time. In addition, this avoids mismatches in the
modelled and observation-based saturation states, which are also due
to model deficiencies in the cycling of organic matter and physical
transport. Mismatches in modelled and observed saturation states are
particularly large in the North Pacific, where the modelled calcite saturation
horizon is up to 1.5 km too deep. The calcite saturation horizon is well represented in the South Pacific, Indian and Atlantic by the model. The results presented in Sect. suggest that estimated CaCO3 export production fields and dissolution rates are insensitive to the choice of the saturation field, because saturation-dependent and saturation-independent parameterisations of dissolution yield similar TA* fields.
Skill scores
Global skill scores, Sm, are assigned to each member, m, of
the Latin hypercube ensemble:
Sm=exp-0.5⋅MSErel.MSErel is the relative mean squared error of the
simulated TA* concentrations from member m with respect to observation-derived
TA*:
MSErel=∑jaj×TAj*model-TAj*obs-TAj*sedcorr2σ2.
The sum includes all grid cells (indexed j). TAj*model denotes simulated TA* concentrations for ensemble member m
and TAj*obs observation-based TA* concentrations
estimated by using the Global B3D regression
(Sect. ). TAj*sedcorr is
a correction term arising from CaCO3 burial in sediments,
further explained below. aj is the grid cell volume used as weight
in the sum.
σ2 represents the combined error of the
observation-based TA* estimates and of the model and sets the scale against which model deviations are evaluated. Model deviations from the observations are considered large or small relative to the magnitude of σ2. The total uncertainty in observation-derived gridded TA* data is difficult to estimate and includes uncertainties due to extrapolation of limited number of measurements, uncertainties in individual tracer measurements, and in the computation of TA* from tracer data.
The error associated with the procedure to compute TA* (average RMSE 3.9, 3.8, 3.1 mmolm-3
in the Atlantic, Pacific, and Indian Ocean, respectively; see Sect. ) is small
compared to the model error (the best run achieves a RMSE of 11, 18, and 18 mmolm-3 in the
Atlantic, Pacific, and Indian Ocean, respectively).
Following and , we estimate
σ2 as the (volume-weighted) variance of the model–data
discrepancy for the ensemble member with the lowest MSE
(this variance is 275 (mmolm-3)2); this corresponds to
MSErel close to unity for the best-fitting ensemble
member.
The skill scores Sm of the individual ensemble members are
likelihood-type functions corresponding to a Gaussian distribution
of the data–model discrepancy
(TA*model-TA*obs-TA*sedcorr) with zero mean and variance σ2.
Sm is an indication of the relative
performance/credibility of each individual model
configuration. Configurations which have relatively small deviations from
the data are judged more probable than configurations which differ greatly from the observations.
Sm are used as weight to compute probability density functions (PDFs) and
related measures such as the median (50th percentile) and the 16
and 84th percentiles defining the one standard deviation confidence
interval (1σ) of the ensemble results. PDFs represent weighted and
normalised histograms of the variables of interest. The normalisation is such
that the integral over a PDF equals 1. A cubic spline interpolation is used to
arrive at a continuous PDF from the discrete, normalised histogram. For the
computation of median and confidence ranges the histograms are converted to
cumulative distribution functions (CDFs). We interpolate linearly within the
discrete CDFs to arrive at the chosen percentiles (i.e. CDF = (0.16, 0.5, 0.68)).
The above explanations apply to any simulated quantity of interest. In the
following we will present PDFs, median values, and 1σ confidence
ranges for aragonite and calcite export and dissolution as well as for tracer
concentrations at individual grid cells or integrated over regions or the
whole ocean. Spatial integrations are done for each ensemble member
individually and before computing the PDFs and associated measures from the
full ensemble.
A first-order correction for ocean–sediment TA* fluxes
CaCO3 burial removes alkalinity from the ocean water column
and lowers concentrations and the overall TA* inventory relative to
a run without the sediment module. Riverine input compensates this
loss. This input of alkalinity is added to the surface ocean and by
that to the part of the preformed alkalinity component (TA0), leaving
TA* unchanged. CaCO3 export and dissolution within the
water column and the corresponding fluxes of alkalinity and TA*
remain largely unchanged between runs with and without sediments.
Mean sediment burial fluxes (GtCyr-1) and observation-based vs. simulated TA*
inventories (Pmol C). TA*sedcorr is estimated as the mean difference in TA* between runs with
and runs without the sediment module across the 14 best Bern3D simulations. The median estimate
is from the constrained 1000-member ensemble (without the sediment module).
AtlanticPacificIndianGlobalBurial flux (Gt C yr-1)0.0110.0620.0420.117TA* Inventory (Pmol C) TA*obs2.527.97.037.4TA*sedcorr0.94.61.46.9TA*obs+sedcorr3.432.48.444.1TA*median5.431.18.745.5
Ideally, the ensemble would be run fully interactively with the
sediment module enabled to account for all important processes within
the CaCO3 cycle. However, this is computationally too
expensive as the sediment module requires a long spin up to achieve
equilibrium. A first-order correction term TA*sedcorr that
accounts for the influence of CaCO3 burial and dissolution
fluxes on TA* is estimated as follows. First, the skill
scores are computed as described above with TA*sedcorr set
to zero. Then, the 14 best ensemble members are selected and rerun
with the sediment module enabled. The mean difference in the TA* fields
between the simulations with and without sediments yields the sediment
correction, TA*sedcorr.
Influence of ocean–sediment fluxes on TA*. The mean offset in TA* between simulations with and
without the sediment module is shown for the 14 ensemble members with the highest skill. Displayed are results for a cross section
through the Atlantic (25∘ W), across the Southern Ocean (58∘ S) into the Pacific, and through the
Pacific (175∘ W). Note the colour bar.
These simulations with sediments yield a mean global burial flux of
0.12 GtCyr-1 (see Table :
0.011 GtCyr-1 in the Atlantic,
0.062 GtCyr-1 in the Pacific, and
0.042 GtCyr-1 in the Indian Ocean). This is within
the estimate by of 0.1–0.14 GtCyr-1.
The sediment burial correction on TA* is largest in the Pacific and smallest in the Atlantic (Figs.
and ). The global TA* inventory in runs
with the sediment is 6.9 PmolC lower compared to the runs
without the sediment (see Table :
0.9 PmolC in the Atlantic, 4.6 PmolC in the
Pacific, and 1.4 PmolC in the Indian Ocean). This reduction
is equal to the inventory of the TA*sedcorr correction and
∼16 and ∼20 % of the observation-derived TA*
inventory of the Pacific and Indian Ocean, respectively. TA*
concentrations are affected relatively uniformly below 1 km
and differences in TA* between simulations with and without the sediment module tend to vanish toward the surface
ocean (Figs.
and ). Correspondingly, the spatial patterns of TA* are very
similar for simulations with and without sediments; correlation
coefficients are >0.99. We expect that the correction will tend to
increase the export flux of CaCO3 in the optimisation to
compensate for the loss by burial, but will not strongly affect
dissolution parameters as the spatial patterns of TA* remain
similar with or without correction.
Model ensemble vs. observation-based basin-mean TA* profiles. The grey shading shows the unconstrained
prior and the green shading shows the constrained (68 % confidence interval) distribution of the model ensemble.
Lines represent the median of the constrained ensemble (green), observation-based TA* (black dashes), and
observation-based TA* corrected for a sediment burial flux of 0.12 GtCyr-1 (black solid).
The corresponding Southern Ocean sector is included in the averaging.
A few caveats apply to this first-order estimate of
TA*sedcorr. First, our approach involves a few, likely
minor, technical inconsistencies. Aragonite is not treated explicitly
in the sediment module and all CaCO3 is assumed to be in the
form of calcite; this may tend to bias sediment burial high as calcite
is less soluble. The saturation state within the sediments is computed
interactively with modelled ocean boundary conditions; this may
locally lead to inconsistencies, as CaCO3 dissolution within
the ocean water column is computed using the prescribed,
observation-based saturation state. The alkalinity flux associated
with organic matter remineralisation within the sediment is not
explicitly distinguished and included in the flux of TA* from
sediments to the ocean; this results in a bias on order of 5 % in
the redissolution flux and a negligible influence on the sediment
correction.
ResultsObservation-derived vs. simulated TA*
Reconstructed TA* (Fig. , TA*obs) is – by
definition – close to zero at the ocean surface and correspondingly low within
the well-ventilated North Atlantic Deep Water (NADW), Antarctic Intermediate
and Mode Water, and within North Pacific Intermediate Water. TA*
concentrations in the deep ocean are increasing with the age of water
masses (see Fig. of Δ14C which is a proxy for water mass age) as the dissolution of CaCO3
continues to add TA*
along the flow path. TA* concentrations are around 40 to
50 mmolm-3 in the deep Atlantic (Antarctic bottom water, AABW)
and in the deep Southern Ocean and increase to
130 mmolm-3 in the northern Pacific. The reconstructed
basin-mean profiles in the Pacific and Indian basin
(Fig. ) show strong gradients in the upper
1500 m and relatively uniform values below that. Concentrations are generally much lower in the Atlantic than in the
Pacific.
The unconstrained model ensemble yields a large range of TA*
concentrations (Fig. , grey shading). The
optimisation procedure
greatly reduces this range in simulated TA* to a comparably narrow
confidence interval (Fig. , green shading
representing the 68 % confidence interval). For example,
basin-averaged concentrations in the deep Pacific (4000 m)
range between 11 and 287 mmolm-3 in the unconstrained
ensemble, while the corresponding 68 % confidence interval in
TA* is 73 to 122 mmolm-3 in the constrained
ensemble. The selected a priori parameter ranges are therefore wide
enough to result in a very broad range of TA* concentrations; the
Bayesian optimisation framework confines this initial range around or
close to the observation-based values.
Observation-based vs. simulated TA*. Left column: modelled (median) TA*, observed TA*, and their
difference in a cross section through the Atlantic (25∘ W), Southern Ocean (58∘ S), and Pacific
(175∘ W). Right column: the same for a cross section along 95∘ E in the Indian Ocean. The correlation
coefficient, relative standard deviation (σrel.obs.), and root mean square error (RMSE) between
the simulated and observation-based fields are 0.83, 1.09, and 17.7 mmolm-3 in the Atlantic; 0.88, 0.8, and
23.8 mmolm-3 in the Pacific; 0.87, 0.86, and 19.8 mmolm-3 in the Indian Ocean.
The median field from the constrained model ensemble generally
captures the observation-based TA* pattern
(Fig. ). The correlation coefficients (r) between
the two fields are 0.83, 0.88, and 0.87 in the Atlantic, Pacific, and
Indian Ocean, respectively, and the RMSEs between the two fields are
17.7, 23.8, and 19.8 mmolm-3 for the respective
basins. These deviations correspond, respectively, to 57, 28, and
28 % of their mean TA* concentration in each basin. Large
positive deviations are found in the intermediate waters of the
Pacific. This is also evident in the observation-derived basin-mean
profiles of TA*, which generally fall within the 68 %
confidence interval of the constrained model ensemble
(Fig. ). In the Atlantic, the ensemble median
concentrations are, on basin-average, higher than the
reconstructed ones. In the Pacific and Indian oceans, the median
clearly overestimates TA* in the thermocline (the 68 %
confidence range does not include the observations there) and somewhat
underestimates TA* in the deep ocean. This is likely linked to
known deficiencies in the model's circulation. Intermediate and mode
waters (with low TA* concentrations) do not penetrate far enough
towards the equator. As a consequence, mixing of TA* depleted
surface waters is too low and TA* concentrations are too high in
the thermocline. Alternatively, we cannot exclude that dissolution may
be overestimated in the thermocline of the Pacific and Indian Ocean.
This data–model mismatch could potentially be reduced by introducing
more than one background dissolution rate constant (kbg)
or a depth-dependent particle sinking velocity. However, this may
simply mask deficiencies in the circulation and we do not attempt such
a solution. Generally, the correlation between observed and modelled
TA* is remarkably high.
Constrained fluxes (median and 68 % confidence interval, c.i.) of biogenic
CaCO3 (GtCyr-1).
AtlanticPacificIndianGlobalmedianc.i.medianc.i.medianc.i.medianc.i.Export at 75 m 70–30∘ N0.021[0.007–0.037]0.081[0.027–0.134]30∘ N–35∘ S0.061[0.018–0.103]0.307[0.149–0.457]0.143[0.053–0.223]> 35∘ S0.041[0.014–0.07]0.174[0.057–0.254]0.088[0.03–0.14]70∘ N–90∘ S0.121[0.078–0.171]0.549[0.391–0.697]0.23[0.137–0.316]0.897[0.72–1.049]Dissolution in waters shallower than 1500 m 70–30∘ N0.006[0.002–0.011]0.048[0.015–0.086]30∘ N–35∘ S0.015[0.004–0.03]0.118[0.049–0.2]0.043[0.016–0.08]> 35∘ S0.01[0.003–0.021]0.043[0.013–0.082]0.02[0.006–0.042]70∘ N–90∘ S0.033[0.018–0.054]0.216[0.125–0.32]0.064[0.032–0.11]0.328[0.202–0.444]Deposition on sediments shallower than 1500 m 70–0∘ N0.003[0.001–0.005]0.008[0.002–0.014]30∘ N–35∘ S0.003[0.001–0.006]0.008[0.004–0.013]0.015[0.005–0.024]> 35∘ S0[0.0–0.001]0.007[0.002–0.011]0[0.0–0.001]70∘ N–90∘ S0.007[0.004–0.01]0.023[0.016–0.029]0.016[0.006–0.025]0.045[0.034–0.056]Dissolution in waters deeper or equal to 1500 m 70–30∘ N0.008[0.003–0.013]0.014[0.003–0.035]30∘ N–35∘ S0.03[0.011–0.048]0.133[0.068–0.2]0.053[0.022–0.087]> 35∘ S0.023[0.009–0.038]0.085[0.031–0.129]0.043[0.015–0.07]70∘ N–90∘ S0.06[0.039–0.083]0.233[0.165–0.305]0.097[0.061–0.139]0.395[0.32–0.469]Deposition on sediments deeper or equal to 1500 m 70–30∘ N0.003[0.0–0.007]0.002[0.001–0.007]30∘ N–35∘ S0.009[0.001–0.021]0.031[0.012–0.062]0.019[0.005–0.039]> 35∘ S0.005[0.001-0.011]0.02[0.006–0.041]0.016[0.005–0.03]70∘ N–90∘ S0.018[0.009–0.033]0.056[0.028–0.099]0.035[0.018–0.065]0.116[0.071–0.179]Deposition on all sediments 70–30∘ N0.006[0.001–0.012]0.011[0.003–0.021]30∘ N–35∘ S0.013[0.002–0.027]0.04[0.017–0.073]0.036[0.011–0.061]> 35∘ S0.005[0.001–0.012]0.028[0.008–0.051]0.016[0.005–0.03]70∘ N–90∘ S0.025[0.014–0.043]0.081[0.049–0.126]0.052[0.026–0.087]0.164[0.113–0.227]Probabilistic estimates of CaCO3 and alkalinity fluxes
The estimated global median export flux of CaCO3 at 75 m – with its
68 % confidence interval – is 0.90
(0.72–1.05) GtCyr-1 (Table and Fig. ). Basin-wide, we find
CaCO3 median export fluxes (and 68 % confidence intervals) of
0.12 (0.078–0.17) GtCyr-1 from the Atlantic,
0.55 (0.39–0.68) GtCyr-1 from the Pacific, and
0.23 (0.14–0.32) GtCyr-1 from the Indian Ocean
(Table and Fig. ).
Regionally, largest export fluxes are simulated in the Southern Ocean
sector of the Pacific, in the Pacific equatorial upwelling regions,
and in the northwestern Pacific (Fig. ). In the Indian
Ocean, export fluxes are highest in its eastern tropical regions and in
its section of the Southern Ocean. In the tropical and northern
Atlantic, export fluxes are generally low, consistent with the low
TA* values in the bulk of NADW and AABW.
Probability density functions of basin-wide and global CaCO3 fluxes as constrained by the
observation-based TA* distribution (corrected for a sediment burial flux of 0.12 GtCyr-1).
Note the different scaling of the x axes.
Median CaCO3 export production per unit area in the constrained ensemble is considerably lower in the Atlantic sector of the Southern Ocean
(135 mmolCm-2yr-1) as compared to the Pacific
(301 mmolCm-2yr-1) and Indian
(326 mmolCm-2yr-1) sectors (Fig. top).
This is attributable to the choice of the regional boundaries for the rain-ratio regions, and the assumption that the spatial pattern of
export within a region is identical to the pattern simulated by the standard version of the model. The standard model yields relatively
little zonal variation in the CaCO3 export fluxes in the Southern Ocean in contrast to the data assimilation with lower than zonally averaged export in the Atlantic.
This reflects the much lower TA* reconstructed in the deep Atlantic as compared to the deep Pacific and Indian (Fig. ).
A large export in the Atlantic sector of the Southern Ocean tends to yield high simulated TA* concentrations in the Antarctic bottom
water that fills the deep Atlantic. The Monte Carlo data assimilation therefore requires low CaCO3 export in the Atlantic sector
to minimise model–data mismatches in the deep Atlantic. It is difficult to correctly represent water mass formation and circulation in the
Southern Ocean and our model may be biased. A known bias is that the Atlantic bottom water circulation is too sluggish, also evidenced by
simulated low radiocarbon signatures (Figs. and ). The influence of a potential bias in South Atlantic export on global CaCO3 export is estimated to be relatively small;
assuming the same (median) CaCO3 export per unit area in the Atlantic sector as estimated for the Indian sector would yield
0.06 GtCyr-1 higher export than suggested by the ensemble median.
While our Monte Carlo approach is suitable to estimate export fluxes over larger regions, the detailed spatial patterns in CaCO3 export remain unconstrained.
Globally, the deposition flux on the respective deepest cells
integrates to 0.16 (0.11–0.23) GtCyr-1, i.e., ∼18 % of the export flux (Fig. ,
Table ). Local deposition depends on the local
CaCO3 export and on how much dissolution is occurring in the
water column, which itself depends on the saturation state and on the
depth of the water column. Particularly in the North Atlantic, along
coastlines, and in the Southern Ocean, high fluxes reach the ocean
floor. These are dissolved into the water column in the ensemble set-up
without the sediment module. Accordingly, ∼82 % of the global
median CaCO3 export dissolves in the water column. More
specifically, ∼37 % of the CaCO3 export dissolves in
the upper water column above 1500 m, ∼44 % below
1500 m depth, with the remaining ∼18 % dissolving at
the sea floor (Table ).
Top: median CaCO3 export, globally 0.90 (0.72–1.05) GtCyr-1.
Bottom: median CaCO3 fluxes reaching the ocean floor, globally 0.164 (0.113–0.227) GtCyr-1.
Note the different scaling of the colour bars.
Average dissolution profiles for aragonite (red) and calcite (olive)
in different ocean regions are displayed in
Fig. . A peak in aragonite and calcite dissolution is
located at or below the depth of the aragonite and calcite saturation
horizon, respectively. These dissolution peaks are associated with the
saturation-dependent dissolution rate coefficients
(Eq. ). As is the saturation horizon, these peaks
are located deep down in the water column of the north and tropical
Atlantic region (at 3–4 km depth for aragonite), at
intermediate depth of the South Atlantic, Indian, and Pacific
(1.5 km for aragonite) and at relatively shallow depth of the
tropical and north Pacific region (∼700m for
aragonite). As the calcite saturation horizon is found deeper in the
water column than the aragonite saturation horizon, so are these
dissolution peaks located deeper down in the water column for calcite
than for aragonite.
Our constrained ensemble includes non-zero values for the background
dissolution rate. Consequently, calcite and aragonite dissolve
throughout the water column, irrespective of the saturation state in
the Atlantic, Pacific, and Indian Ocean. The percentage of the export
flux, which dissolves in waters supersaturated with respect to calcite
are 72 (60–80), 43 (30–53), and 68 %
(55–78 %) in the Atlantic, Pacific, and Indian Ocean,
respectively. We will further investigate in
Sect. to which extent the finding that
a fraction of the CaCO3 export dissolves above the calcite
saturation horizon and our export and dissolution flux estimates are
robust.
Constrained open water dissolution rate profiles for aragonite (red) and calcite (olive). Ensemble medians
(solid lines) and 68 % confidence intervals (shadings) are for spatial averages across individual regions and
only include grid cells where the model water column extends to a depth of 5000 m.
Sensitivity of results to ocean–sediment interactions, and circulationOcean–sediment interactions
As discussed in Sect. , CaCO3 deposition on,
burial within, and redissolution from ocean sediments affects TA*
concentrations mainly in the Pacific and Indian Ocean in our model. To
assess uncertainties in CaCO3 fluxes arising from
uncertainties associated with the sediment correction, we set the
sediment correction (TA*sedcorr) of the TA* field to
zero to calculate potential skill scores (Eq. ). This
alternative case also illustrates the potential error due to the
neglect of ocean–sediment fluxes. Export fluxes of CaCO3 are
2, 12, 8, and 8 % smaller in the Atlantic, Pacific, Indian, and
global ocean, respectively, while the variance is about the same. This
is not surprising as we have already noted (Sect. ) that
a certain burial flux tends to decrease the TA* pattern uniformly,
i.e. the simulations with and without the sediment correlate highly in
terms of TA*. The PDF of fluxes is therefore shifted to higher
export fluxes, while the preference for dissolution parameters remains
the same. The CaCO3 that dissolves above 1500 m
is 4 % higher, 5 % lower, the same, and 4 % lower in the
Atlantic, Pacific, Indian, and global ocean, respectively, if sediment fluxes are neglected.
Implications of different diapycnal diffusivities illustrated for three dissolution rate profiles
The diapycnal diffusivity, kdia of the model is varied to
probe uncertainties related to the magnitude of the ocean overturning
circulation. kdia is either set to 0.1 (low), 0.2
(standard), or
0.5(high)× 10-4m2s-1. Increasing
kdia increases the strength of the overturning
circulation, and deep ocean ventilation. Maximum Atlantic Meridional
Overturning is 16, 18, and 23 Sv (Sverdrups), Southern Ocean overturning is -16, -14, and
-15 Sv, and maximal deep Pacific overturning is -13, -14,
and -20 Sv for the low, standard, and high kdia
simulations, respectively.
We compare the simulated (natural)
Δ14C of DIC and CFC11 distributions to their corresponding observations
to evaluate the physical transport (see Appendix). Both are
conservative tracers and are indicative of the ventilation timescales of the deep ocean and the thermocline, respectively. The
observation-based global mean (natural)
Δ14C of DIC is -151 ‰. The reference
simulation achieves a mean (natural) Δ14C of DIC of
-160 ‰. Correspondingly, ocean radiocarbon signatures
become too low (-176 ‰) with the low diapycnal mixing
rate and too high with the high (-126 ‰) diapycnal mixing
rate (see Fig. ). Simulated surface-to-deep Δ14C gradients are too low (high) relative to the observed gradients for the high (low) diapycnal diffusivity parameter, thereby indicating surface-to-deep water exchange that is too fast (slow) (Fig. ). The global
observation-based CFC11 inventory is estimated to 575 Mmol. The
reference simulation yields 513 Mmol CFC11 as the mean inventory over the modelled period between 1990 and 2000. In
the low mixing simulation, this inventory is even lower
(479 Mmol) and in the high mixing simulation it is too high
(631 Mmol). On a global scale, our reference choice is therefore
in better agreement with these physical tracers (see
Fig. ).
The simulated TA* inventory vs. the simulated CaCO3 export of each ensemble member, coloured
according to model skill (top) and background dissolution rate (bottom) for the Atlantic, Pacific, and Indian Ocean
(columns). Each circle represents results from an individual simulation. Green shadings show the
68 % confidence range in basin-wide TA* inventories and CaCO3 export of the constrained model
ensemble, and black dashed lines indicate the estimated TA* inventories based on the observations including the
sediment correction. Runs with low and high background dissolution can skillfully represent the TA* distribution.
Runs with a higher CaCO3 export tend to require a higher background dissolution to achieve a good skill.
We vary kdia for three illustrative dissolution rate
profiles introduced in Sect. (see
Fig. and Table ). In the
low diapycnal diffusivity case, CaCO3 export is 11 % lower
and in the high diapycnal diffusivity case, CaCO3 export is
30 % higher compared to the standard case. Larger overturning and
mixing yields more nutrient input into the euphotic zone and thus more
organic matter export. CaCO3 export is independent of
alkalinity in our model and does not depend on the choice of the
dissolution rate. The simulated TA* patterns remain similar, and
correlation between the patterns is at least 0.93. Basin-average profiles in TA* vary little in the upper ocean and the deep Pacific
(< 14 mmolm-3) and modestly in the deep Atlantic (< 44 mmolm-3) and deep Indian (< 18 mmolm-3)
when varying diapycnal diffusivity between 0.1 and 0.5 × 10-4m2s-1.
Perhaps somewhat surprisingly, the simulated TA* inventory is relatively weakly
affected by the choice of kdia; the global TA*
inventory varies by less than 7 % across the range of
kdia (Table ). In other words,
variations in the magnitude of ocean ventilation hardly affect the
TA* inventory for a given dissolution rate profile. Higher (lower)
export under higher (lower) mixing compensate each other. These
changes in TA* inventory are smaller than the influence of the
sediment correction (see Table ) or the choice of
the dissolution profile.
In conclusion, simulated TA* is only weakly affected by uncertainties in the diapycnal mixing coefficient.
The choice of the dissolution rate profile has a substantial influence
on the simulated TA* inventory (Table ). As
mentioned previously, TA* accumulates in the deep ocean when all
CaCO3 is dissolved below the saturation horizon of aragonite
and calcite and no dissolution is permitted above. This raises the
question whether surface-to-deep transport is too slow in our
model. As mentioned above, the radiocarbon signatures as well as CFC11
concentrations are on average close to observations
(Figs. and ). Increasing ocean
ventilation by increasing kdia results in radiocarbon signatures that are too young and CFC11
concentrations that are higher than observed. However, it does not substantially reduce the
overestimation of the TA* inventory in those cases.
How to parameterise CaCO3 dissolution in an Earth system model
An important question is how to formulate the dissolution rate of
calcite and aragonite particles in Earth system models. Should the
dissolution rate be a function of the simulated aragonite and calcite
saturation state of the surrounding water? Should dissolution above
the saturation horizon be permitted? We analyse the relationship
between model skill, dissolution parameterisation, CaCO3
export, and TA* inventories in the model ensemble (see
Fig. ) to address these questions. To achieve
a high skill (green-to-red coloured dots in the upper panels of
Fig. ), an individual ensemble member needs to
reproduce the observation-based TA* inventory (dashed line) within
a limited range. We identify an export range within which TA* can
be reproduced skillfully (vertical green range in the upper panels of
Fig. ). Surprisingly, a high skill is achieved
across the range of different dissolution schemes applied and for
a broad range of parameter values. In other words, neither the
dissolution scheme nor its parameters are well constrained by the
observation-based TA* field. This is illustrated by plotting the
value of the background dissolution rate, kbg (lower
panels of Fig. ), as a function of the TA*
inventory and export. Generally, the higher the global CaCO3
export flux, the higher the background dissolution rate required to
achieve a high skill. Likewise, lower export can be distributed
skillfully without dissolution in supersaturated waters
(kbg=0). Apparently, there are trade-offs between the
magnitude of export and the applied dissolution parameterisation in
terms of TA*, suggesting that export and dissolution parameters can
only be constrained simultaneously within limits when using TA* as
the only constraint.
These findings are in line with the results from our sensitivity
simulations (Fig. ,
Table ). The parameterisation with dissolution
above the saturation horizon (constant) yields the lowest TA*
inventory, followed by the scheme with fast dissolution below the
saturation horizon, and the scheme with dissolution near the ocean
floor (slow). A high (low) export is thus required for
parameterisations with high (low) dissolution above the saturation
horizon to simulate the observation-based TA*. Further, the
different dissolution schemes yield highly correlated TA* fields;
the correlation coefficient between the global fields from the fast
and slow dissolution scheme is 0.84, and between the fields from the
fast and constant scheme is 0.88 in simulations with the same
CaCO3 export (Fig. ).
The average RMSE between the fast and slow dissolution scheme is 43.2 mmolm-3 and between the fast and constant is 24.5 mmolm-3.
The high spatial correlation in simulated TA* and uncertainties in CaCO3 export make it difficult to
distinguish different dissolution parameterisations.
The magnitude of CaCO3 exports modulates absolute TA* concentrations and thus model–data bias and root mean square errors.
Given these uncertainties, we cannot objectively determine the preferred
dissolution scheme.
Flux measurements as additional constraint
Global sediment trap data represent another observational constraint
of the CaCO3 cycle. The database of see Fig.
includes 156 measurements globally and is an update of the
compilation. For comparison, we constrained the
model ensemble using these sediment trap data instead of the TA*
data as target (Figs. and ). Skill scores are
calculated individually for the Pacific, Atlantic, and Indian
Ocean. CaCO3 export fluxes, dissolution profiles, and
parameters constrained with the sediment trap data are consistent
within uncertainties with those constrained by the TA* data. The
sediment trap data, however, yield wider uncertainty ranges, as
illustrated in Fig. , and therefore do not
permit us to reduce uncertainty ranges any further.
DiscussionExport of CaCO3
summarised current estimates of CaCO3
export out of the euphotic zone (based on models and data) to
0.4–1.8 GtCyr-1 (spanning factor ∼4). Our
constrained median estimate of ∼0.90 (ensemble range:
0.72–1.05) GtCyr-1 therefore lies at the lower
end of these previously published estimates. In the end, these authors
suggest that global CaCO3 export must be higher than
1.6 GtCyr-1. This estimate is based on sediment trap
data and other information constraining the flux to the deep ocean (>2000m) to 0.6±0.4GtCyr-1 and results obtained with the so-called
TA* CFC age method, suggesting an upper ocean dissolution of
1 GtCyr-1. The TA* CFC age method is heavily criticised by and tends to bias estimates systematically towards high values . This method and its shortcomings are further discussed in the next section on upper ocean dissolution. While our estimated flux to the deep ocean
of 0.52 (0.43–0.61) GtCyr-1 is roughly consistent
with the budget of , their export estimate, and
upper ocean dissolution, is in clear conflict with our results and
those of other studies that
apply a range of different methodologies. We attribute this mismatch
to deficiencies in the TA* CFC age method, implying that the export estimate by
is biased high.
Observationally constrained CaCO3 export fields as estimated by different studies. Global total
export is estimated to be 0.5 by , 1.14 by , 1.1 by , and
0.90 GtCyr-1 by this study.
Global-scale CaCO3 export has been previously estimated (see Fig. ).
diagnosed a global CaCO3 export of 1.1 GtCyr-1
by restoring annual-mean potential alkalinity to observations
in the euphotic zone and in the whole water column
within the Modular Ocean Model. Sediment burial and sediment–ocean
fluxes are included implicitly in this approach. They provide
a relatively small uncertainty range of 0.8 to
1.2 GtCyr-1 which falls within our range. Most of the
uncertainty is attributed to uncertainties in the alkalinity data by
these authors. estimated CaCO3 export
(∼0.5GtCyr-1) by combining satellite NPP (as
a mean of the three algorithms; ) with the organic particle export model of
and the rain-ratio estimate of
.
derived net CaCO3
production (∼0.92±0.3GtCyr-1) from seasonal
potential alkalinity decreases. Both approaches focus on information
of the surface ocean without taking advantage of information displayed
in the full biogeochemical depth profile. In addition, used an ensemble Kalman filter
approach to assimilate total alkalinity and phosphate data into their model and determined a global CaCO3 export
flux of 1.2 GtCyr-1.
On average, these four
studies yield a global mean CaCO3 export of
0.93 GtCyr-1, close to our median estimate of
0.90 GtCyr-1.
We find peaks in zonally averaged export in the North Pacific, the
tropical Pacific and Indian, and in the Southern Ocean and low export
fluxes in the subtropics and the tropical Atlantic
(Fig. ). This is in agreement with the results
of and , with the exception that
suggested little CaCO3 export in all tropical
regions. A significant CaCO3 export in the tropics is
consistent with deep ocean sediment trap data . As noted by , the low estimates of
for tropical regions are likely related to small
signals in seasonal alkalinity in the tropics, hampering their
calculations. Concerning the magnitude of the export, our
zonally averaged values are similar to these two studies in the
Pacific sector of the Southern Ocean, and smaller in the Atlantic and
Indian Southern Ocean sectors as well as in the North Pacific.
Interestingly, found significant CaCO3 export
in the North Atlantic, in contrast to ,
, and this study. The relatively low North
Atlantic export suggested by these latter studies appears to be in
conflict with the occurrence of coccolithophorid blooms in this region
. On the other hand, the low TA* inventory in the
Atlantic (Fig. ) argues for a limited export of
CaCO3 in this basin.
Zonally integrated export fluxes of the constrained Bern3D model ensemble (median and 68 % confidence
interval) compared to estimates by , , and .
defined another alkalinity tracer, termed Alk*,
that isolates the portion of the alkalinity signal that varies in
response to calcium carbonate cycling and exchanges with terrestrial
and sedimentary environments from the portion that varies in response
to freshwater and organic matter cycling. These authors compiled
a riverine input of alkalinity into the low-latitude Atlantic
(>40∘ S and <40∘ N) equivalent to
0.057 GtCyr-1, which is ∼40 % of the global
continentally derived alkalinity. Their Alk* tracer in the Atlantic
has the lowest open-ocean surface concentrations despite this large
riverine source. They conclude that these large riverine inputs must
therefore be more than balanced by strong net CaCO3 formation.
For comparison, our estimates of CaCO3 export between
35∘ S and 30∘ N in the Atlantic are 0.06
(0.018–0.1) GtCyr-1. We note, however, that
a direct comparison between these two studies remains difficult. The
river input does not strictly have to be compensated by the export
flux but rather by the burial flux. In addition, the river input gets mixed
and is subducted and transported southward by North Atlantic Deep
Water, and the interpretation of concentrations without explicit
consideration of transport and mixing is always difficult.
Regional patterns of CaCO3 export (Fig. ) vary
among the different studies. In our approach CaCO3 export
fluxes are scaled by a rain ratio to simulated export of particulate
organic carbon within each of the eight considered regions. Thus, the
total export for the three Southern Ocean sectors, the Indian Ocean,
the tropical and northern Pacific, and the tropical and northern
Atlantic is constrained by the TA* data, but not the pattern within
each of these regions.
Dissolution rates of biogenic CaCO3 [GtCyr-1] in the upper water column
(200–1500 m depth levels) based on the TA* CFC age method as summarised in ,
and as constrained by TA* data in our Latin hypercube ensemble (including the sediment correction, median
and 68 % c.i.). The dissolution estimates by were assigned an estimated uncertainty of ∼50 %.
LocationBerelson et al.This study(2007)medianc.i.Atlantic> 40∘ N0.0600.006[0.002–0.011]40∘ N–40∘ S0.0100.02[0.008–0.036]> 40∘ S0.0400.009[0.003–0.017]Pacific> 40∘ N0.0700.039[0.013–0.067]40∘ N–5∘ N0.3300.063[0.032–0.099]5∘ N–5∘ S0.0200.035[0.015–0.058]5∘ S–40∘ S0.0000.039[0.019–0.066]> 40∘ S0.1600.034[0.011–0.061]Indian40∘ N–40∘ S0.1600.062[0.026–0.104]> 40∘ S0.1400.021[0.009–0.038]Total1.00.346[0.225–0.461]CaCO3 dissolution in the upper ocean
The CaCO3 leaving the surface ocean dissolves within the water
column, at the sea floor, or gets buried. get to
global dissolution rates of ∼1GtCyr-1 within
upper level waters, clearly higher
than our TA*-based estimate of
0.35 (0.26–0.46) GtCyr-1. On a regional level, only
two out of ten regional estimates by are within our uncertainty ranges; these are the
estimates for the tropical Pacific (taken as 5∘ N to
5∘ S) and the low- and mid-latitude Atlantic (40∘ S
to 40∘ N) (Table ).
High dissolution rates in the range of ∼ 0.1 to 0.4 mmolCm-3yr-1 are estimated by
for a transect in the upper tropical and northern North Atlantic. These values are much larger
than our estimates of order 0.01 mmolCm-3yr-1 for the upper tropical and northern Atlantic.
These high estimates are based on the measured decrease of suspended CaCO3 particles with depth multiplied
by a CaCO3 particle settling velocity of 80 mday-1 and neglecting any temporal trend in the CaCO3
particle concentration. These estimates may be affected by uncertainties in the assumed particle settling velocity.
CaCO3 particles settling velocities are reported by , to vary greatly (0.15 to 3440 mday-1)
and to be typically of the order of 1 mday-1 for coccolitophorides and several 100 mday-1 for foraminifera and
pteropods. Our dissolution rates would be
consistent with the measured depth gradient in suspended biogenic CaCO3 particles
for an average settling velocity of a few mday-1.
As mentioned above, we link the differences between the estimates of and this study to
methodological problems associated with the TA* CFC
age method that very likely introduce a high bias in the results of . The TA* CFC age method relies on deduced, observation-derived
TA* concentrations and estimates of water mass age, typically
derived from measurements of chlorofluorocarbons (CFCs) and their
known atmospheric history. TA* concentrations are plotted against
their CFC age and a line is fitted to this data.
The higher the TA* concentration for
a given water mass, the more TA* must have been added by
dissolution to this particular water parcel according to this method. The slope of the
relationship between TA* and age is in this sense the CaCO3
dissolution rate (mol volume-1 time-1).
The method has been criticised for its neglect of explicit transport
and mixing processes. In particular, noted that
TA* signals ended up above the saturation horizon in their model
run, even though there was explicitly no dissolution allowed to occur
there. This is confirmed by our sensitivity simulations with no
dissolution above the saturation horizon
(Fig. ). This finding does not depend on the
choice of the numerical model, as mixing within the ocean must spread
the TA* signal within the ocean and establish a surface-to-deep
gradient in TA* in the upper ocean even when all CaCO3
dissolves at great depth. The TA* CFC age method does not account
for such processes and assigns dissolution rates in the waters above
the saturation horizon irrespective of whether or not the signal stems
from the deep ocean. Our approach to combine TA* data within an
ocean transport model and the approach by or
avoid this shortcoming.
In addition, we notice, that in most regions the upper ocean TA*
distribution remains remarkably similar within our ensemble, even for
very different dissolution rate profiles (see
Fig. ). Remarkably, for a given
export, kslow dissolution rate profiles, with most of the
dissolution at or near the ocean bottom, tend to reach highest values
of TA* both in the deep ocean and the thermocline (see also
inventories in Table ). In these cases, most of the
TA* source is added to slowly ventilated waters in the deep where
it accumulates over time along deep water flow paths. This high TA*
signal is brought to the thermocline and eventually to the
surface where TA* is reset to its preformed value of zero. As
a result, a larger TA* gradient is established across the
thermocline for deep compared to shallow dissolution. The TA* CFC
age method would therefore have a tendency to assign higher
dissolution rates in the wrong cases. This further illustrates the
difficulty to uniquely relate upper ocean tracer concentrations to
either dissolution or mixing processes.
CaCO3 dissolution in the deep ocean
Turning to the deep ocean, suggest, based on
sediment trap and benthic dissolution data, that the particle flux
below 2000 m is 0.6±0.3GtCyr-1, sea
floor dissolution for sites >2000m averages 0.4±0.3GtCyr-1, and carbonate burial in deep marine
sediments is 0.1 GtCyr-1. Our estimate of the
particle flux below 1500 m is 0.52 (0.43–0.61) GtCyr-1.
Thus, the compilation of
sediment trap data by roughly supports our
particle flux at 1500 m. However, the split between sea floor
dissolution and open water dissolution in the deep is different. We
estimate that most of the deep ocean particle flux dissolves within
the water column (0.40 (0.32–0.47) Gt C yr-1 below
1500 m). The steady-state burial flux for the runs with
interactive sediments is 0.12 GtCyr-1, corresponding
to the burial of 1.95 × 1013molAlk,yr-1; this
is comparable in magnitude but smaller than the total alkalinity input
by rivers estimated to be
2.3 × 1013molyr-1 by
or the burial flux estimated by of 0.121 GtCyr-1. We note that CaCO3 formation by coral
reefs and burial in shallow coastal waters is not considered in our
coarse-resolution model.
Parameterisations of CaCO3 within Earth system models
Uncertainties appear too large to objectively determine well-defined
parameter ranges for the dissolution rates of calcite and aragonite
(judging from both the TA* and the flux data compilation). A good
agreement between simulated and observed TA* fields can be achieved,
irrespective of whether dissolution is assumed to depend on the
calcite or aragonite saturation state or whether dissolution rates are
assumed to be constant throughout the water column. We recall that the
computation of the saturation state by carbonate chemistry routines
across all grid cells and for each model time step poses
a considerable computational burden. For simplicity, and to minimise
computational costs, we therefore recommend describing CaCO3
dissolution by a constant dissolution rate in Earth system models as
long as these uncertainties exist. This yields an exponential particle
flux profile when assuming constant settling velocities throughout the
water column. This approach is used in previous studies . A shortcoming of the
application of an exponential particle flux profile for CaCO3 is that it is not easy to account for the
potential influence on dissolution of changes in environmental variables, including a decrease in saturation state
as expected under ongoing ocean acidification, or in the quality, form, and size distribution of exported CaCO3 particles.
Summary and conclusions
Constraining the CaCO3 cycle comes down to three fundamental
questions: how much CaCO3 is exported from the surface ocean?
Where does CaCO3 dissolve in the water column? How much is buried in sediments? Here, we set up a probabilistic framework to
constrain the CaCO3 budget within the Bern3D EMIC with
observationally based TA* as a robust target variable. The saturation state of water with respect to calcite and aragonite is prescribed using observational estimates to provide realistic boundary conditions for the CaCO3 dissolution parameterisation. In addition to
the uncertainty estimates obtained by our Bayesian framework, we also consider uncertainties related to the choice of
metrics to define the assimilation target, including flux measurements as an alternative target variable,
uncertainties in ocean transport, and ocean–sediment interactions.
We estimate that 0.72–1.05 Gt C with a best estimate of 0.90 Gt C
are exported out of the surface ocean each year in the form of biogenic CaCO3. Of this, about
37 % (0.33 (0.2–0.4) GtCyr-1) is estimated to
dissolve in the open water column above 1500 m, and 44 %
(0.40 (0.32–0.47) GtCyr-1) in the open water column
below, with the remainder (0.16 (0.113–0.23) GtCyr-1)
deposited on open ocean sediments, globally.
Sensitivity simulations with interactive sediments suggest that about 30 % of the
deposition flux dissolves back into the ocean and 70 % gets
buried in consolidated sediments.
We find that the higher the export fluxes within the constrained,
likely ranges, the more likely dissolution above the saturation
horizon is needed to distribute TA* skillfully in the
model. Different kinds of dissolution schemes (with and without
dissolution above saturation) achieve realistic TA* distributions
within the export ranges identified. Therefore, background dissolution
above the saturation horizon cannot be ruled out from this
Latin hypercube ensemble evaluated within the Bern3D EMIC. Future
progress likely depends on a better observational characterisation of
particle concentrations, size distribution, and settling within the water
column. Physical transport and mixing reduces concentration gradients
such that conceptually different dissolution schemes (e.g. dissolution
permitted above saturation or not) cannot be distinguished
statistically. This implies that concentrations cannot be used to
infer dissolution rates directly. It also implies that dissolution
parameterisations remain uncertain. For simplicity and to minimise
computational costs, we suggest using saturation-independent
parameterisations of CaCO3 dissolution within Earth system
models.
Model evaluation and additional constraints
It is an essential prerequisite for the model to feature the main
water masses and mixing timescales of the ocean to realistically
simulate biogeochemical tracers such as TA*. In this Appendix, we
graphically document ocean model performance by comparing simulated
and observation-based distributions for a range of tracers. Results
are for a pre-industrial steady state of the Bern3D ocean model configuration with a horizontal
resolution of 40 by 41 grid cells and 32 vertical layers as coupled to
an energy balance and sea ice module without the sediment
module. The atmospheric history of CFC11 is prescribed according to .
Here we do not account for potential changes in ocean circulation and CFC11 solubility over the industrial period.
Figure provides a Taylor diagram
of CFC11, Δ14C, temperature,
salinity, DIC, TA, PO4, oxygen, and TA* of the standard
model configuration with a constant rain ratio of 7 % and of the
median TA* of the weighted model ensemble. Modelled and observed
distributions of the ventilation tracers Δ14C and
CFC11 are compared along a section through the Atlantic, Southern
Ocean, and Pacific (Figs. and ). Simulated and observation-based basin-mean
vertical gradients of CFC11 and natural Δ14C are
compared in Fig. for three simulations
where diapycnal mixing is set to a low, the standard, and a high value
(kdia=(0.1,0.2,0.5)×10-4m2s-1). Results bracket observation-based
profiles with best agreement between model and observations for the
standard set-up.
Taylor diagram for global and basin-wide volume-weighted oceanic tracer distributions as
simulated by the Bern3D standard set-up with kdia=0.2×10-4m2s-1.
Observation-derived fields are taken from GLODAP and the World Ocean Atlas 2009
.
Top: distributions of (natural) Δ14C of DIC (‰) as simulated with a standard
kdia of 0.2×10-4m2s-1 at steady state. Bottom: as estimated from
Δ14C measurements . The correlation coefficient, σrel.obs.
and RMSEs are 0.89,1.46, 23.77 ‰ in the Atlantic; 0.95, 0.97, 16.28 ‰ in the Pacific; 0.9, 0.78,
21.1 ‰ in the Indian Ocean. The section displayed is through the Atlantic (25∘ W), the Southern
Ocean (58∘ S), and the Pacific (175∘ W).
Top: distributions of CFC11 (nmolm-3) as simulated with a standard kdia of
0.2×10-4m2s-1 averaged over the model years 1990–2000 and (bottom) as observed
. The correlation coefficient, σrel.obs. and RMSEs are 0.9, 1.01,
0.45 nmolm-3 in the Atlantic; 0.94, 1, 0.29 nmolm-3 in the Pacific; 0.83, 0.92,
0.54 nmolm-3 in the Indian Ocean. The section displayed is through the Atlantic (25∘ W),
the Southern Ocean (58∘ S), and the Pacific (175∘ W).
Basin-wide average profiles for (natural) Δ14C of DIC (‰) at steady state (top)
and for CFC11 (nmolm-3) averaged over the model years 1990–2000 (bottom). Results are for simulations
with a low (green dotted), standard (green solid), and high (green dashes) value of the diapycnal mixing
coefficient kdia (0.1, 0.2 and 0.5×10-4m2s-1). Observation-based estimates
are in black. The corresponding Southern Ocean sector is included in the averaging.
The global sediment trap data collection of see their auxiliary material at
doi:10.1029/2012GB004398 on the Bern3D grid.
The measurements are located at different depths (>1500m). If more than one measurement was
assigned to the same cell, the mean was chosen.
As Fig. but coloured according to model skill with respect to the sediment
trap database evaluated by basin. This target variable constrains export and dissolution to wider ranges
(yellow to red colours) as compared to the TA* target (light green shading). Generally, high skill scores
with respect to regional, sediment-corrected TA* are also associated with high skill scores with respect
to regional fluxes. Only few models are in good agreement with the few flux measurements in the Indian Ocean.
Acknowledgements
Many thanks to an anonymous reviewer and Wolfgang Koeve for their critical and constructive reviews.
Also, thanks to Kitack Lee, Xin Jin, and Niki Gruber for sharing their
data, and to Raphael Roth for his contributions to the modelling
framework. This work was supported by the Swiss National Science
Foundation and the European Project CARBOCHANGE (264879) which
received funding from the European Commission's Seventh Framework
Programme (FP7/20072013).
We acknowledge the support from the International Space Science Institute (ISSI).
This publication is an outcome of the ISSI's Working Group on “Carbon Cycle Data Assimilation:
How to consistently assimilate multiple data streams”.
Edited by: Victor Brovkin
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