Basic equations
To define the effect of the habitats of the different foraminifer species, we
first consider a subset of the growth functions derived by
from culture experiments (Fig. ) following the
original formulation of . For each foraminifer species
k considered, the growth function is written as
μT,k=μT1,k⋅expTAT1-TAT1+expTALkT-TALkTLk+expTAHkTHk-TAHkT,
where μ(T,k) is the growth rate at temperature T for the species k,
μ(T1,k) is the growth rate for a chosen reference temperature T1 (20 ∘C
or 293 K), TA is the Arrhenius temperature, TH(k) and TL(k) define
the upper and lower boundaries of the growth tolerance range for the species
k, and TAH(k) and TAL(k) are the Arrhenius temperatures for the decrease
in growth rate, respectively, above and below these boundaries for species k
. In the present study, we use the nominal values of
Eq. (1) parameters given in with the exception of TL
for G. bulloides. Indeed, comparing the output of FAME with
sediment-trap data from the subpolar North Atlantic showed that the
nominal value of TL=281.1 K was likely too high, causing an absence of
growth outside of the 3 summer months. In contrast, subpolar North Atlantic
sediment-trap data indicate that, on average over the 4 years of
observations, significant G. bulloides fluxes prevailed from the end
of June to the middle of November. We hence chose a value of TL closest to
the nominal value of that would allow the extension of the
growing season into the fall in agreement with the data pattern. Hence, a
value of TL=280 K was used for G. bulloides within FAME.
Growth functions corresponding to Eq. (1) over the full temperature range considered, replotted from
.
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We compute the μ(T,k) coefficient for all values of T(x,y,z,t) in the
World Ocean, T being a 4-D variable of space and time. This, in turn, gives
us the growth rate of the different foraminifer species considered in a
four-dimensional space as
μT,k=μTx,y,z,t,k.
To avoid numerical issues in the code, we limit the value of μ(T,k) on
the low end as follows:
μ′Tx,y,z,t,k=μT,kif μT,k≥0.1⋅maxTμT,k=0otherwise.
Given a four-dimensional input field for oceanic temperatures and δ18O
of seawater, the equilibrium inorganic calcite δ18O value can be
computed from the temperature equation of . Here, we use the
quadratic approximation of that equation given in :
T=T0-b⋅δ18Oc-δ18Osw+a⋅δ18Oc-δ18Osw2,
where T0=16.1 ∘C, b=-4.64 and a=0.09,
δ18Osw is the seawater δ18O. Since the seawater
temperature (∘C) and δ18Osw (permil) are
inputs, we can solve this equation to determine the value of
δ18Oc. With the discriminant of the second-degree equation being
Δ=b2-4a⋅T0-Tsw,
it becomes
δ18Oc,eq=-b-Δ2a+δ18Osw-0.27,
where the constant, 0.27, correction accounts for the
difference in the reference scales of seawater (permil versus Vienna mean standard ocean water – V-SMOW)
and calcite (permil versus V-PDB).
In previous studies, we and others computed the
above δ18O equilibrium value, averaged over time and the surface
layer (typically the first 50 m) to compare model results and
measured δ18Oc from planktonic foraminifers. In the following,
we will refer to this method as the “old method”, written formally as
δ18Oc,omx,y=1nt∑t=1nt1nz∑z=0zbδ18Oc,eqδ18Oswx,y,z,t,Tswx,y,z,t,
where nt is the number of time steps, nz the number of vertical levels
and zb the maximum depth.
The formalism used clearly expresses the fact that the old method is not
species-specific nor season-specific since all time steps and vertical levels
are averaged with the same weight. In contrast, the FAME method weighs the
δ18Oc both in time and in the horizontal and vertical space
according to the population abundances using the foraminifer growth formula (1). We thus write
δ18Oc,fmx,y,k=1nt∑t=1nt1nz∑z=0zb(k)δ18Oc,eqδ18Oswx,y,z,t,Tswx,y,z,tμ′T(x,y,z,t),k,
where zb(k) is dependent on the species and constrained by core-top data
(see below).
Using this set of equations, for any given seawater temperature and
δ18O provided as a four-dimensional field and a given species k, we
compute this species' δ18Oc over x,y (latitude, longitude)
coordinates.
It should be clearly understood that this approach is not able and does not
attempt to determine the relative abundances of the different species.
Instead FAME provides a simplified approach to compute the δ18Oc
of a generic population of foraminifers if environmental conditions permit
its growth. From a model–data perspective, this approach enables one to
compute the calcite δ18O for a given species, were it to exist in
the sedimentary record. Due to the limitations set by Eq. (),
no calcite isotopic content is computed if μ′ is zero, and hence
these areas will be masked out in the following.
Reference datasets
In an attempt to validate the FAME approach, we apply its methodology to
reference datasets, close to present-day observations. The first necessary
step is the computation of a reference δ18Oc field as obtained
when forced by climatological data.
For seawater temperature, we use the World Ocean Atlas 2013 (WOA13)
data at a monthly resolution. Considering that there is
no equivalent seawater oxygen-18 gridded dataset available in the World Ocean
Atlas fields and that the existing NASA Goddard Institute for Space Studies (GISS) gridded dataset
presents large deviations with respect to the seawater oxygen-18
(δ18Osw) raw data in numerous locations, we derived a
δ18Osw dataset based on seawater salinity to
δ18Osw relationships. This dataset is built in two steps: (a)
derivation of regional δ18Osw – salinity relationships from
GISS δ18Osw and salinity clustered by oceanic
regions, and (b) computation of a δ18Osw field based on the
World Ocean Atlas 2013 salinity fields. The resulting field
is at the World Ocean Atlas spatial resolution and is used as reference
seawater oxygen-18 in the following. Details on the derivation of the
δ18Osw dataset are given in Appendix .
Maximum depth per species as computed from
the optimization procedure. zb is the depth yielding the smallest
difference to the MARGO Late Holocene data . We computed
a confidence interval σzd↑,σzd↓ corresponding to a change of ±0.1 permil in the mean
error. The ∞ sign indicates that no value of zb within the range
0,-1500 yields the desired ±0.1 permil
change.
Species
zb (m)
σzd↑,σzd↓ (m)
No. of
Obs. living
References
points
range (m)
G. ruber
-10
0,-30
130
0–120
N. incompta
-65
-35,-150
60
0–200
T. sacculifer
-100
-75,-200
46
0–200
G. bulloides
-400
-100,-∞
123
0–300
N. pachyderma
-5501
-275,-900
244
0–500
1 An encrustation term of +0.1 permil is taken into account in
the case of N. pachyderma (see text).
As an independent test of the FAME results, we use the planktonic
δ18Oc measurements from the Multiproxy Approach
for the Reconstruction of the Glacial Ocean surface (MARGO) Late Holocene dataset
restricted to high chronozone quality levels (i.e.,
levels 1 to 4). A few errors have been corrected in the published dataset:
these concern the suppression of 10 Neogloboquadrina incompta (or
N. pachyderma right) data points from the Nordic Seas where only
Neogloboquadrina pachyderma should have been listed, and one outlier
N. pachyderma value with no age control that was erroneously listed
as having a level-4 chronozone quality. The corrected version of MARGO Late
Holocene planktonic oxygen-18 dataset is available in the Supplement.
As a result, the dataset used in the present study contains 248 values for
Neogloboquadrina pachyderma, 128 values for Globigerina bulloides, 59 values for Neogloboquadrina incompta, 135 values for
Globigerinoides ruber and 51 values for Globigerinoides sacculifer. In the remainder of the paper and following the genus
reassignment of , we will refer to the latter as
Trilobatus sacculifer.
Calculation of the best-fitting maximum depth per foraminifer species
In Eq. (), the maximum depth of integration per foraminifer
species, zb(k), is a free parameter and needs to be determined. We have
chosen to calculate it as the depth where the δ18Oc simulated by
FAME driven by the World Ocean Atlas 2013 temperature and derived seawater
δ18O datasets is closest on average to MARGO Late Holocene
δ18Oc data. The rationale behind this choice is to specifically
design FAME to enable model–data comparison with isotopic records from marine
sediment cores.
To determine the optimal value of zb(k), we repeated successive runs of
FAME with values of zb ranging from 1500 m to the surface along
the standard World Ocean Atlas vertical grid. The only difference between the
different species at this stage are the species-specific terms in the
equations presented and the data of each species from the MARGO Late Holocene
set. The results obtained through this optimization procedure are given in
Table . The maximum depths of calcification derived this
way are remarkably close to what is known from the ecology of G. ruber, N. incompta, T. sacculifer and G. bulloides . Only in the case of N. pachyderma, the computed value of
zb was much too deep (900 m) with respect to what studies based on
opening–closing plankton nets show. Also, plankton haul studies have
revealed that, whereas N. pachyderma seems to grow at relatively
shallow depth, i.e., where the chlorophyll maximum is found, a calcite crust
is added between ∼50 and 250 m, which greatly increases its mass
. As a consequence, the δ18O of
N. pachyderma collected in deep sediment traps and in surface
sediment is systematically heavier than that of living non-encrusted
N. pachyderma. To account for this effect, we have added a 0.1 permil “encrustation term” to our calculation of N. pachyderma calcite δ18O weighted by that species' culture-based
growth rates. The encrustation term value has been chosen in order to
simulate maximum depths in agreement with the literature. N. pachyderma simulated depth of maximum growth (Fig. e
and Table ) does indeed match very well the available
observations. For instance, Fig. 4e shows a deepening of N. pachyderma depth of maximum growth from 0 to 30 m in the Greenland Sea to
100–350 m in the Norwegian Sea, in agreement with the apparent calcification
depths reconstructed by .
Concerning T. sacculifer, although this species bears symbionts, and
thus lives in the photic zone like G. ruber, it is known to produce
calcite with higher δ18O values than G. ruber. These
heavier δ18O values are thought to result from the accretion of
gametogenetic calcite (for a certain unknown fraction of the shell mass) or
from the precipitation of its final sac-like chamber deeper in the water
column . This characteristic explains the deeper habitat
depth computed for T. sacculifer versus G. ruber (maximum
calcification depth estimates range from -200 to -75 m, best estimate of
-100 m). Note that a deeper habitat for T. sacculifer than G. ruber is in agreement with observations (Table 1).
Evaluation of the model performance
Error distribution
Since the depth parameter was constrained using the MARGO Late Holocene
dataset by error minimization, it is not surprising that the errors obtained
with FAME are very small on average for each species considered (Fig. ). The error distribution obtained with FAME is very
similar to the one obtained with the simple surface equilibrium assumption
for the two species closest to the surface (G. ruber and N. incompta). For deeper dwellers (T. sacculifer, G. bulloides & N. pachyderma), FAME results are better than those
obtained with the old method, as expected, since deeper layers in the ocean
are accounted for.
Error distribution for the “old method”
(grey) and the “FAME method” (orange) using climatological datasets as
compared to MARGO Late Holocene dataset . Best-fitting
distributions are calculated and plotted as a solid line for the FAME
method and as a dashed line for the old method, except for T. sacculifer, for which the small number of available data points yields a
poor fit both for FAME and the old method. The mean and deviation are given
for FAME and the old method at the top of each panels.
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Robustness of results
To test the robustness of our calibration in depth or error distribution, we
performed a full set of additional analyses using the lower and upper growth
functions as presented in Fig. , introduced
here above.
Regarding depth calibration, we find our results to be largely insensitive to
the use of these upper-bound and lower-bound values for the growth functions.
Specifically, the uncertainty in the maximum growth depth is largest on
N. pachyderma (range of 475 to 600 m) and G. bulloides
(400 to 450 m). It is somewhat smaller for T. sacculifer (100
to 125 m) and N. incompta (60 to 65 m). There is no impact
for G. ruber.
Another method to check the impact of the uncertainty in the growth functions
on our δ18Oc results is by keeping maximum computed depths
constant and looking at the impact of the growth function on the mean
difference between simulated and MARGO δ18Oc values shown in
Fig. . When doing so (not shown), the resulting
change is lower than 0.1 permil for all individual species. It therefore
shows that our results are very robust and largely insensitive to the errors
arising in the growth functions used .
Model–data comparison of species' abundances.
Ocean regions where FAME predicts that the species is present at some time of
the year (μ′>0) are plotted in blue, with shades of blue
indicating the number of months of presence. Overlaid are the MARGO Late
Holocene data (quality levels 1–4) species' abundance data, plotted using
the yellow–white to dark red color bar and given in percent. A qualitative
correspondence between simulated FAME presence/absence and the occurrence of
10 % level in the difference species is noted.
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Geographical distribution
To further check our methodology against the MARGO Late Holocene dataset, we
compare the zone of presence of each species predicted by FAME (grossly
determined by μ′) with the observed reported abundances in the
MARGO dataset (restricted to chronology quality values 1–4). As noted above,
we cannot predict the relative abundance of each species. However, the method
determines the species' absence or presence.
Depth of maximum growth for the species
considered for the month of July. The color scale shows the depth in meters.
Oceanic areas left in white correspond to areas where growth rates are below
the threshold defined in Eq. (3).
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The results presented in Fig. show that, despite the
exceptional simplicity of our approach, FAME predicts relatively well the
spatial limits of the area occupied by each species. The two species whose
presence distribution is best predicted are again G. bulloides and
N. pachyderma, both showing a quite remarkable model–data match of
the transition zones from presence to absence. N. incompta and
G. ruber also show quite satisfactory results, with only a few
outliers in specific areas: FAME computes overextended coverage of
N. incompta in the Gulf of Guinea and of G. ruber along the
coast of Namibia.
The computed spatial coverage of T. sacculifer is slightly too
extended towards high northern and possibly southern latitudes. The
very low number of high-quality dated data points in the latter area prevents
a definitive conclusion. Also, specific zones, consistent for several
species, may be noted, such as the Benguela upwelling regions where FAME fails
to predict the absence of T. sacculifer and G. ruber.
Comparison of the depth of maximum
growth for N. pachyderma and G. bulloides for January and July. Color scale
is as in Fig. 3.
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One possible explanation for this mismatch could be the impact of increased
nutrient availability on observed abundances as a consequence of the
upwelling systems, whereas nutrients are at present ignored in the FAME
approach. Another possibility could be the quality of the vertical oceanic
structure obtained from the World Ocean Atlas in those upwelling regions.
Finally, it should be noted that our comparison ignores the natural
interannual variability since we are using climatologies. The interannual
variability involves changes in the location of the fronts and currents, and
thus bears the potential of shifting the spatial boundaries between the
different foraminifer species.
Further discussion of the abundance comparison including all data points from
the MARGO Late Holocene dataset regardless of the dating quality is given in
Appendix .
To further investigate the functioning of the FAME model, it is useful to
consider the spatial distribution of the depth at which each species'
growth is maximum. An example is given for the month of July in Fig. . It clearly shows that even though the maximum depth
allowed for each species is fixed through the zb(k) parameter, the
predicted/computed calcification depth varies according to the location in
the World Ocean. Except for G. ruber which always calcifies in the
topmost ocean layers, the depth of maximum growth exhibits large spatial
variations, notably at the edge of the species' domains; in July, this is
particularly marked in the case of G. bulloides and N. pachyderma (Fig. d and e).
Likewise, it is useful to consider the seasonal variations in the depth of
maximum growth for a given species. We propose to highlight this aspect for
the two species that show the largest variations: N. pachyderma and
G. bulloides at two extreme months (January and July) (Fig. ). For both species, the area of computed non-zero
contribution varies along the year, with an expansion (reduction) of the area
occupied by N. pachyderma in the Northern Hemisphere in January
(July), while the regions occupied by G. bulloides shift towards
higher (lower) latitudes in the Northern Hemisphere in July (January). These
seasonal changes are a direct response of these species' preferred habitat to
temperature. FAME thus mechanistically predicts the adaptation of planktonic
foraminifer depth habitat to maintain optimal living conditions. For
instance, Fig. b and d clearly show that G. bulloides is
predicted to dwell deeper at low latitudes when surface temperature rises
above its preferred temperature range. Similarly, Fig. b and d show that
G. bulloides is present at higher northern latitudes in July than in
January, so that the growing season actually tracks the species' preferred
living conditions, as observed .
Effect of a large climatic change on the computed oxygen-18 content of the calcite
Though FAME gives realistic results when forced by atlas data, it is mostly
designed to retrieve the species-specific effect of climate change on the
recorded δ18Oc. To highlight the effect of seasonal and vertical
weighting of the δ18Oc signal computed by FAME, we have
performed a simplified experiment showing the effect of a change in the
foraminifers' living conditions on their δ18Oc signal.
To simulate a change in climatic conditions, we apply a homogeneous
4 ∘C decrease to the WOA13 sea temperature dataset and compute
the anomaly in δ18Oc between that new cold state and the
original one for each species, as well as for the surface equilibrium approach
(Fig. ). This anomaly is noted Δ18Oc in
what follows.
Applying a spatially homogeneous temperature change should result is a
quasi-homogeneous temperature change in the equilibrium calcite
Δ18Oc, following Eq. (). It is indeed what is
obtained in Fig. e, with Δ18Oc
values between 0.8 in the tropics and 1 permil at high latitudes.
When applying the FAME equations, we obtain large spatial variations in
Δ18Oc with values down to -0.75 and up to 1 permil. All
species share a common pattern of lower Δ18Oc at the border of
their living domain and close to equilibrium values at the center of their
living domain. More specifically, the smallest differences to the equilibrium
are recorded by N. pachyderma and the largest, negative, differences
are computed for G. bulloides. The species with the smallest
vertical living range, G. ruber, has the most homogeneous
distribution. The range of values (minimum to maximum) is always close to 1
permil with the exception of G. bulloides that presents a
total range of 1.6 permil. This large range of Δ18Oc
for G. bulloides is a consequence of its growth over a large range
of temperatures (Eq. ). In general, the maximum
simulated Δ18Oc values are systematically 0.1 to 0.2 permil
lower than the equilibrium value.
This simple scenario, though unrealistic with respect to actual climatic
applications, shows the potential of FAME to unravel the climatic signal
embedded in multispecies isotopic records and thus opens the door to
transient climate–data intercomparison where the species' specific
behavior is taken into account.
δ18Oc response to a horizontally
and vertically homogeneous 4 ∘C cooling applied to the WOA13
dataset, Δ18Oc. Results are expressed in permil for
each species (a–d) and for the equilibrium surface calcite
approach.
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