Introduction
Trace elements and isotopes (TEIs) are low-concentration components of the
ocean, but they contain decisive information for our understanding of its
dynamics. The international program GEOTRACES has been designed to improve
our knowledge on the TEI concentrations and the oceanic processes
controlling their distribution, by means of observations, modeling and
laboratory experiments. Since 2006, GEOTRACES cruises have been mapping the
global distribution of tens of these TEIs. Some of them are studied because
they constitute micronutrients for living organisms, like iron (Fe), or are
pollutants, like lead (Pb) and cadmium (Cd). Others are proxies of ocean
dynamics or of biogeochemical processes. For instance, neodymium (Nd) is a
proxy of the exchanges between seabed and seawater , and
thorium 234 (234Th) is related to the biological carbon pump
. Radium (Ra) isotopes are of
particular interest as they are proxies of all TEI fluxes from sediments and
continents toward the ocean. More specifically, radium isotopes have been
used to estimate a still poorly known pathway to the ocean: submarine
groundwater discharge (SGD).
SGD is defined as the flux of water from coastal aquifers to the ocean,
regardless of its composition and origin. Part of it is meteoric freshwater,
but the largest part is infiltrated seawater .
In these aquifers, water gets enriched in nutrients and trace elements,
released from soils and rocks or coming from land pollution, before flowing
back to the ocean. It has traditionally been considered that the main coastal
sources of terrestrial mineral elements to the ocean are rivers, but there is
growing evidence that SGD is in fact a source of nutrients of the same order
of magnitude, affecting the biogeochemistry at all scales, from coastal
regions to ocean basins
. SGD is a suspected cause of algal blooms,
including harmful algal blooms , and a pathway for
contamination. In spite of this, its contribution is still much less
precisely known than the river inputs. Because of the strong heterogeneity in
its distribution and intensity, properly estimating SGD by direct methods
requires an intense sampling, which is far from being fulfilled
. Indirect methods should then be used. Radium
isotopes offer a great potential due to their relation to SGD and their
simple chemistry.
All the four natural radium isotopes, 223Ra (T1/2=11.4 day), 224Ra (T1/2=3.6 d),
226Ra (T1/2=1602 years), and 228Ra (T1/2=5.75 years),
are produced within the rocks by the radioactive decay of thorium. Since
radium is far more soluble in water than thorium, its main source is not the
decay of dissolved thorium in the ocean, but dissolution from lithogenic
material. Therefore it is used as a tracer of boundary fluxes. This element
is released into the ocean by three main sources located on the continental
shelf: desorption from riverine particles, diffusion from seabed sediments,
and SGD, which are highly enriched. Dust inputs and dissolved riverine
228Ra each account for less than 1 % of all inputs
. In the ocean, Ra is almost conservative. It is removed by
radioactive decay and scavenging. Scavenging is associated with a residence
time of approximately 500 years , making it negligible for
all Ra isotopes except 226Ra. Then the distributions of the other three
isotopes, whose radioactive sinks are known, depend only on the source
distribution and transport by the ocean circulation. Since their half-life
timescales are small relative to the timescale of basin-wide horizontal
mixing, typically a few years to a few decades, 223Ra and 224Ra are
unsuitable for large-scale studies. Radium-228, whose half-life of 5.75 years
is short enough to neglect scavenging but long enough to consider the global
ocean, is suitable for global-scale analyses, and is thus considered here.
A simple way to use the information provided by this isotope is to make an
observation-based inventory of the ocean 228Ra. At steady state, the
supply of 228Ra must balance the loss from disintegration – i.e., 12 %
every year. According to , these total 228Ra fluxes
can be used to estimate fluxes of nutrients, iron, and rare earth elements.
Radium-228 fluxes are also a way to estimate the SGD by subtracting the
contribution from rivers and the release from sediments by diffusion and
bioturbation, and dividing the remaining flux by the mean 228Ra
concentration in groundwater. By this method SGD has been estimated at
0.03–0.48×1013 m3 yr-1 in the Mediterranean Sea
and 2–4×1013 m3 yr-1 in the
Atlantic Ocean . These direct approaches suffer from strong
potential biases when the data are sparse, because the total amount of
228Ra in the ocean is then roughly estimated, using regional averages
of observations or linear interpolations
. Therefore, they are suitable only in regions with dense
sampling, such as the Atlantic Basin.
Inverse modeling techniques represent an alternative and powerful approach to
estimate the fluxes, providing that the ocean circulation is known with
sufficient accuracy. Inverse modeling is based on three elements:
observations of the physical quantity of interest (here oceanic 228Ra
concentration), a forward prognostic model simulating the same quantity as a
function of the unknown variables to be assessed (here the shelf fluxes), and
an algorithm finding the values of the unknowns (fluxes) minimizing the
misfit between model and observations. The advantage of this method is that
no arbitrary averaging or interpolation is required: observed concentrations
are simply compared to model concentrations at the same points. It is
expected to be robust and consistent, since the model is based on physical
considerations. used such an inverse modeling approach to
produce a global estimate of 228Ra fluxes of 9.1–10.1×1023 atomsyr-1 between 60∘ S and 70∘ N,
corresponding to 9–15×1013 m3 yr-1 of SGD. Their study
is based on a data-constrained global ocean circulation model
, considering 50 source regions on the continental shelf,
and minimizing an ordinary least-squares cost function.
In this study, we estimate the radium fluxes from all continental shelves
around the world and localize the most intense sources, using an inverse
modeling technique with more data than previous studies . The
dataset has been augmented with data from two recent GEOTRACES cruises and
from the Southern Ocean, the North Pacific, the Mediterranean Sea, and the
Indonesian seas. It also contains data from the Arctic, a basin absent from
Kwon's study. The forward model is built on the ocean general circulation
model (OGCM) NEMO (Nucleus for European Modeling of the Ocean). Our main
improvement is a careful analysis of sensitivity and errors, which reveals
that the result depends on the model mathematical parameters, such as the
cost function and the number of regional sources that are considered. We have
performed several inversions and analyzed the residuals and uncertainties, to
determine the most appropriate mathematical parameters and evaluate the
precision of the flux estimates. This paper is organized as follows. In
Sect. 2, we describe the different aspects of the inversion technique – e.g.,
the global dataset, the forward model based on the NEMO OGCM, the different
cost functions, the choice of the source regions related to SGDs, and the
inverse method. Section 3 presents the main results – e.g., the global and
regional estimates of 228Ra supply, and the sensitivity of these
estimates to several parameters of our approach, such as the cost function or
the number of coastal 228Ra sources. Section 4 compares our results with
results obtained in previous studies, and discusses issues associated with
such an approach, with an emphasis on SGD.
Observed concentrations of 228Ra in the global ocean, averaged
when available on the ORCA2 cells used for inversion. Data plotted on
subfigures (b, c, d) are also vertically averaged in order to take
all layers into account.
Methods
228Ra dataset
Since the late 1960s tens of oceanographic
cruises have carried out measurements of 228Ra (e.g., articles listed in
Table S1 in the Supplement). The dataset used in this study includes, among
others, observations from three international programs sampling trace
elements. Data from the Indian Ocean cruise of GEOSECS (GEochemical Ocean
SECtions Study), in 1977–1978, are included. From 1981 to 1989, the TTO
(Transient Tracers in the Oceans) program produced a considerable number of
228Ra measurements in the Atlantic, from 80∘ N to
60∘ S, at all depths, making the Atlantic Ocean the best sampled
ocean by far. Currently, new data from all oceans are being produced by
GEOTRACES. In total, 6059 data from all basins are used, of which 2789 are
shallower than 10 m, 1107 are located between 10 and 200 m deep, 606
between 200 and 600 m deep, and 1557 deeper than 600 m. Our dataset
comprises 1359 more measurements than in Kwon et al. (2014): two GEOTRACES
sections, GA03 (United States–Cape Verde–Portugal) and GP16 (Ecuador–French Polynesia), and data from the Arctic, the Southern Ocean, the North
Pacific, the Mediterranean Sea, and the Indonesian seas have been added in the
present study (see Table S1). These supplementary observations extend the
data coverage to regions north of 70∘ N and around the Kerguelen
Islands. In a near future, other sections from the GEOTRACES program will
complete the global covering and may help in studying deeper sources.
For the purpose of our study, data have been averaged in each model grid cell
(see Sect. 2.2 for more details on the model configuration), leading to the
3076 cell averages shown in Fig. 1. The density of the measurement is
noticeably uneven. The Atlantic Ocean, north of 20∘ S, and the
Arctic, are the most densely covered basins and the only regions with a
significant number of data at depth deeper than 10 m. Other regions are
sparsely sampled, leaving wide areas with no or very few measurements, like
the western Indian Ocean, the equatorial Pacific, or the Pacific sector of the
Southern Ocean.
Data are expressed in concentration or activity units, with the following
conversion factor: 1 dpmm-3 = 4.36×106 atomsm-3. They range from 0.04 to
724.5 dpmm-3. The highest concentrations are found in the Bay of
Bengal and the coastal seas of eastern Asia, the lowest values are located in
the Southern Ocean. Concentrations are generally higher than
10 dpmm-3 in the Indian Ocean, the Atlantic, and the Pacific
north of 30∘ N, lower in the rest of the Pacific. In the Atlantic,
west of a line running from the Amazon Delta to Newfoundland, most
concentrations are higher than 30 dpmm-3.
Forward tracer model
The second requirement of the inversion technique is a 228Ra transport
model, allowing to link in situ observations to the boundary conditions or
shelf sources of 228Ra. The transport equation of tracer Ai
(originating from the source region i) is given by
∂Ai∂t=-U⋅∇Ai+∇⋅(K∇Ai)-λAi+Si.
U and K are the velocity field and the eddy diffusivity coefficient
respectively. The two first terms on the right together constitute transport.
They are derived from NEMO 3.6 model using OPA as a general
circulation component, coupled with the sea-ice model LIM3
, with an ORCA2 global configuration. The model has
a horizontal resolution of 2∘ × 2∘ cosϕ
(where ϕ is the latitude) enhanced to 0.5∘ near the equator. The
mesh is tripolar in order to overcome singularities, the North Pole being
replaced by two inland poles in the Northern Hemisphere. It has 31 vertical
levels, ranging from the surface to 6000 m deep, the upper layer covering
the first 10 m. The simulation is forced by a seasonal climatological
dataset, based on NCEP/NCAR reanalysis and satellite data.
λ is the radioactive decay constant, 0.12 yr-1, given by the
half-life of 228Ra which is 5.75 years. Decay is the sole sink. It is
known and does not depend on environmental parameters, leaving the source
term as the only unknown to be determined by the inversion technique.
Si is the source term specific to the ith region, representing riverine
inputs, sedimentary diffusive fluxes and groundwater discharge fluxes of
228Ra from region i. In this study, sources are assumed to be only on
the continental shelf, defined as the seabed shallower than 200 m. This
depth range, spanning 16 model levels, is chosen because it is where most
groundwater discharge outflows. However, diffusion from sediments also occurs
at larger depths .
Equation (1) shows that the Ai fields depend linearly on Si. That means
that any 228Ra distribution can be written as a linear combination of
the Ai fields. It is important to emphasize that the circulation is
supposed to be “perfect” – e.g., no correction of the U field is
looked for. Nevertheless, the simulated circulation obviously suffers from
deficiencies, and that point has to be kept in mind when interpreting the
results. From now, what we refer to as “model concentration”,
[228Ra]mod, is a linear combination of the tracer final
concentrations Ai, the coefficients being the source intensities xi:
[228Ra]mod=∑i=1nAixi.
A non-optimal model concentration was computed by assuming a uniform constant
flux per unit of surface everywhere, with a global fit using the average
concentration estimated from the observations: this defines the first guess
estimate before the inversion. The inversion undertaken in this study aims at
optimizing the parameters xi in order to minimize the total difference
between the observations and the model 228Ra distribution.
As a consequence of its coarse horizontal resolution, continental shelves are
only poorly resolved by the ORCA2 grid. The emitting surface is
underestimated and some regions with narrow continental shelves would be
completely omitted. To overcome that deficiency, sub-model grid-scale
bathymetric variations are accounted for by comparing the model grid to a
global 2′ resolution bathymetry ETOPO2 of the National Geophysical Data
Center (NGDC). The algorithm is detailed in . According to
this method, the total surface of continental shelf is 2.73×1013 m2, 73 % higher than the 1.58×1013 m2
obtained with the coarser bathymetry.
The ocean–continent interface, including the Arctic and the Antarctic, is
divided into 38 regions (Fig. 2). This first guess takes into account the
sampling coverage (very low in the Antarctic for instance, and higher in the
North Atlantic Basin or Bay of Bengal) and differences in the tracer
distributions Ai, which should be large enough to give independent
information. Delimitation is done by trial and error, using the posterior
covariance matrix of the inversion (see Sect. 2.3): the number of sources is
minimized by merging regions associated with negligible fluxes with close
highly correlated regions. Most islands are ignored, because the areas of
their continental shelf and thus their expected contributions to the
228Ra balance are small. In the inversion process, islands can give rise
to spurious fluxes to accommodate for other types of errors. The only islands
considered in this study are the Kerguelen and Crozet islands, in the
Southern Ocean, because many samples have been taken in their surroundings
which make it possible to constrain their contributions. Because of the lack
of measurements and the coarse model resolution, the Persian Gulf, the Red
Sea, the Baltic Sea, the North Sea, and the Hudson Bay are not taken into
account. The flux per unit of surface is assumed to be constant on each of
the 38 emitting regions. Model simulations last for the equivalent of
100 years in order to reach a quasi-steady state. It is more than 17 times
larger than the half-life of 228Ra, so that the total amount of
228Ra varies by less than 0.001 %. As there are not enough data
to study global interannual or seasonal variations, we do not take seasonal
variations of 228Ra concentrations into account. We implicitly assume
that radium concentration is constant over time, and work with average
concentrations over the 100th year of simulation.
Model 228Ra source regions.
Cost functions.
Cost function
Formula
Residuals
Ordinary least squares (ols)
Cols(x)=∑j=1p([228Ra]imod-[228Ra]iobs)2
ηols(x)=[228Ra]mod-[228Ra]obs
Logarithmic least squares (log)
Clog(x)=∑j=1p(log[228Ra]imod-log[228Ra]iobs)2
ηlog(x)=log[228Ra]mod-log[228Ra]obs
Proportional least squares (prp)
Cprp(x)=∑j=1p([228Ra]imod-[228Ra]iobs[228Ra]iobs)2
ηprp(x)=[228Ra]mod-[228Ra]obs[228Ra]obs
Inverse method
The last requirement of the inversion technique is to define a cost function
measuring the misfit between the data and the model. This cost is then
minimized by a method already used to assess air–sea gas fluxes
and oceanic heat fluxes
. If η represents the residuals, namely the
discrepancy between model results and observations:
Ax=[228Ra]obs+η.
Both sides are vectors, representing radium concentrations in each model cell
containing data. A is the matrix of
footprints, representing the circulation model and composed of the Ai at
each data point. x is the vector of unknowns, the flux of 228Ra
per unit of surface of each region. As only shelf sources are modeled and as
data coverage below 200 m is sparse, only data shallower than 200 m are
considered.
The distance between model concentrations and data is summed up in a scalar,
the cost function C(x). We look for the optimal flux vector
xopt minimizing the cost function. Different choices for C
are possible, depending on the assumed probability distribution for the prior
error on data and model footprints A. Errors due to biased sampling
are not considered here. All errors are supposed to be uncorrelated. In this
study, three different cost functions have been tested and minimized. They
all correspond to the sum of squares of a specific type of residuals. Their
respective equations are listed in Table 1. The first one is an ordinary
least-squares cost function, Cols. According to the Gauss–Markov
theorem, its minimization produces the best linear unbiased estimator when
prior errors have no correlation, zero expectation, and the same variance. It
is the simplest least-squares method, chosen in the study by
. This function gives the same weight to all observations.
However, the hypothesis of the homogeneity of the variance is questionable:
far offshore, where concentrations are lower and less sensitive to small
changes in coastal sources, observations and model errors can be expected to
be lower. Neglecting this fact means these data are not fully exploited, as
their contribution to the cost function is relatively small. Two other cost
functions with a higher weight for smaller values are then considered for
comparison. They are assuming heteroscedastic data, with higher variances for
higher concentrations. In the proportional least-squares cost function
Cprp, the error standard deviation is supposed to be proportional
to the observed concentrations. The logarithmic least-squares cost function
Clog works differently and assumes the logarithms of
concentrations have the same error variance. It is less sensitive than
Cprp to model overestimations and more to underestimations. It is
the only cost function which is not a quadratic function of the sources.
The residuals after inversion indicate what the inverse model cannot fit. In
a “perfect” inversion, these residuals should be assimilated to noise – e.g.,
small and without structure, due for instance to coarse resolution. In most
inversions, that is not the case, and the distribution of residuals
emphasizes biases or errors either in the chosen hypotheses (such as a
perfect circulation) or in the setting of the inversion (number and choice of
the regions). The posterior uncertainties on radium fluxes and correlations
between regions are computed following the method described in Appendix A. A
regional flux has a large uncertainty when it is constrained by few data or
correlated to other regions , and two regions are strongly
correlated when the 228Ra emitted by each is transported to the same
places and are then harder to differentiate. The computed posterior
uncertainties are precise only if all the preceding assumptions on prior
errors are correct. The coherence of error assumptions with the results has
to be checked (see Sect. 3.2). Along with the main inversion considering 38
regions, we performed four other inversions with a higher or lower number of
regions in order to estimate the sensitivity to this parameter (see
Sect. 3.3).
228Ra annual flux from each source within one standard
deviation, after minimization of three cost functions. Prior estimates,
proportional to shelf surfaces, are shown for comparison.
Results
228Ra fluxes
The 228Ra fluxes from each of the 38 regions, deduced by minimizing each
of the three cost functions, are shown in Fig. 3 with their confidence
intervals, and compared with the prior estimates. The global fluxes for each
method are also shown. As they are sums of local fluxes, their standard
deviations are proportionally lower.
Model surface 228Ra concentration after minimization of three
cost functions. Prior estimate is shown for comparison.
The global 228Ra flux within 1 standard deviation is 8.01–8.49×1023 atomsyr-1 according to the Clog
inversion. As we will explain in Sect. 3.2, this estimate is the most
accurate of the three. Fluxes are found to be comparatively high in the North
Atlantic (regions 5 to 16), in the western Pacific (22 to 27), and in the
Indian Ocean (28 to 34), together accounting for 62.6 % of the
continental shelf and 82.8 % of the global flux of 228Ra. The
highest fluxes are located in the China seas (23 and 25) and in the eastern
Indian Ocean (29 to 32), where the inversion process produces the largest
increase compared to prior estimates, and to a lesser extent on the east
coast of North America (10 and 13). Conversely, inversion significantly
reduces the prior estimates in the Arctic Ocean (35 to 37), in the Bering Sea
(21), and in the eastern Pacific Ocean (17 to 20). Fluxes are also quite low
in the Southern Ocean (1 and 38) and in the South Atlantic (2 to 4). The
newly estimated Arctic and Antarctic sources are in the range of 0.43 to
0.50 and 0.31 to 0.37×1023 atomsyr-1
respectively, accounting for 5 to 6.2 % and 3.6 to 4.6 % of the total
sources.
Although having the same order of magnitude, uncertainties are generally
lower than fluxes. They are highest in the western Pacific and Indian oceans
(regions 22 to 34), because of data sparsity. It is lower in better sampled
oceans: the Arctic (35 to 37) and the Atlantic (2 to 16) oceans, except for
region 13 (Cape Hatteras to Newfoundland). The eastern Pacific (17 to 21)
also has low uncertainties in absolute values, probably due to the low
concentrations and prior errors there.
The two other inversions produce roughly similar results, although fluxes are
generally lower when derived from Cprp and generally have higher
uncertainties when derived from Cols. The global 228Ra flux
is estimated to 7.16–8.14×1023 atomsyr-1 with
Cols and 4.96–5.28×1023 atomsyr-1 with
Cprp. The three inversions agree on which basins and continents
have the largest and smallest sources. Yet, local disagreements occur.
Regions 5 (Amazon delta), 21 (Alaska and Bering Sea) and 33 (Arabian Sea)
have higher fluxes with Cols than with Clog, with
non-overlapping confidence intervals, whereas the contrary is true for
regions 12 (Mediterranean), 26 (Indonesian seas) and 34 (East Africa).
Cprp fluxes are generally lower, and in eight regions their
confidence intervals overlap with none of the other inversions. Discrepancies
happen because the fitting of the model to each observation implies different
and possibly opposite effects on the source intensities. Each inversion uses
different weights, which translates into different flux corrections. Fluxes
from each of the three inversions are most dissimilar for regions where
observations impose most dissimilar constraints, where the model fails to
reconstruct the pattern of the data and has to choose between fitting some
data or others in priority. In such cases, all the results should be
considered carefully. When the confidence intervals between the different
inversion techniques fail to overlap, it is likely that one or several
estimates are incorrect. As algorithms are built by assuming a prior error
statistics, it is likely that some rely on wrong assumptions.
Correlation between data and model concentration fields.
Model
Linear correlation
Logarithmic correlation
Prior
0.383
0.809
ols
0.813
0.883
log
0.797
0.902
prp
0.754
0.877
Model concentrations and residuals
The residuals – i.e., the differences between model concentrations and
observations – determine how well the model reproduces the observations and
quantify the improvements in the tracer distribution provided by the
inversion. They are also a basic tool to identify biases in the model and to
assess the quality of the assumptions.
Surface 228Ra logarithmic residuals after minimization of three
cost functions. Prior estimate is shown for comparison.
Radium fluxes obtained by the inverse method largely improve the model match
to observations compared to the prior radium flux (Figs. 4 and 5). The
improvement is quantified by the increase in the model–data correlations
(Table 2) and the decrease in the root mean square of the residuals
(Table 3), a proxy of the cost function. The correlation coefficient is
increased from 0.383 to 0.813 on a linear scale and from 0.809 to 0.902 on a
logarithmic scale. The correlation is higher on a logarithmic scale because
it is less sensitive to the few very high residuals associated with the
highest concentrations (see Fig. 6). On average, the inversion is able to
reduce the ordinary residuals (Cols) by a factor 2, logarithmic
residuals (Clog) by 1.4, and proportional residuals
(Cprp) by 3.5.
Root mean square of residuals before and after inversion
Model
Ordinary
Logarithmic
Proportional
residuals rms
residuals rms
residuals rms
(dpmm-3)
(no unit)
(no unit)
Prior
70.7
0.892
1.91
ols
36.6
0.703
1.10
log
37.9
0.636
1.02
prp
47.4
0.940
0.558
(a) Residuals, (b) logarithmic residuals,
(c) proportional residuals, and (d) model 228Ra
concentration as a function of observed 228Ra concentration. Lines of
zero residuals are drawn in black.
In spite of being smaller, the order of magnitude of the residuals remains
comparable to the data (Fig. 5). On the one hand, in all oceans, positive and
negative residuals are observed with no clear patterns at the scale of a few
grid cells. Because of the rather low model resolution (2∘, which is
not sufficient to reproduce medium- and small-scale processes) and of issues
associated with temporal (seasonal or higher frequency) variability of the
data, this kind of “noise” is expected. It is consistent with the
assumption of independent errors used when computing the error variances on
fluxes. On the other hand, in several regions, residuals can display coherent
large-scale patterns, which cannot be attributed to noise. These areas may
suffer from systematic overestimations, like in the Gulf Stream region, the
western Pacific between 20 and 40∘ N, and off eastern Siberia, or
underestimations, such as in the center of the North Atlantic Gyre. These
residuals point out to possible flaws in the model circulation. For instance,
228Ra is quite homogeneously distributed in the western North Atlantic
according to data, but in the model, the gradients are stronger, and no
combination of sources manages to reduce these gradients. This is probably
caused by a bias in the Atlantic circulation, with a too low exchange rate
between inshore and offshore waters. In a 2∘ resolution model,
mesoscale eddies are not represented and cannot transport 228Ra south
and east of the Gulf Stream or north of the North Brazil Current. Inversions
minimize the misfit by increasing the fluxes from regions 5 (northern Brazil), 8
(Caribbean), and 10 (southern east coast of the US), making the model
concentration too high close to the coast while still too low in the gyre.
Such large-scale biases are not consistent with the assumption of no prior
error correlation, which may lead to underestimation of flux uncertainties
around these basins.
Having assumed specific prior error statistics when choosing the cost
functions, we need to check that there is no a posteriori contradiction.
Figure 6 displays the residuals and model concentrations as a function of the
observations. If the residuals depend on the observed concentrations, it
means some observations are more precise than others, contain more
information, and should be given a higher weight in order to obtain the best
linear unbiased estimate. Figure 7 shows the probability density functions
(PDFs) of residuals after all three inversions and compares them with a
Gaussian curve representing the expected distribution given the root mean
square of residuals. Each PDF should look like a Gaussian curve for the
computed posterior uncertainties to be relevant descriptors of errors.
Model global 228Ra fluxes (1023 atomsyr-1)
with different numbers of source regions. The standard case with 38 regions is in bold.
Cost function
Case 1: 52 regions
Case 2: 38 regions
Case 3: 19 regions
Case 4: 12 regions
Case 5: 7 regions
ols
7.81–9.93
7.16–8.14
7.51–8.49
7.36–8.16
8.98–9.78
log
8.09–8.61
8.01–8.49
7.90–8.34
7.85–8.27
7.93–8.37
prp
5.15–5.47
4.96–5.28
4.70–4.98
4.25–4.49
3.75–4.01
Probability density functions (PDFs) of 228Ra
(a) ordinary residuals, (b) logarithmic residuals and
(c) proportional residuals after inversion, compared with a Gaussian
PDF (black full line) based on their standard deviations.
Figure 7a emphasizes that the ordinary residuals do not follow a Gaussian
distribution. On the contrary, most residuals are very close to zero, while a
small number of them are much higher than the standard deviation. Figure 6a
shows that these high residuals occur at high concentrations only, and that
error variance is not homogeneously distributed. Then high and low
concentrations should not be given the same weights, as in Cols,
but the highest concentrations should be given the lowest weights, as in
Clog and Cprp. Flux estimates based on
Cols are biased because the cost function puts more emphasis on
high concentrations, and this method then tries to fit more specifically the
misfits at high concentrations. Cols also produces very large
error bars because the error variance is assumed to be constant and its
computed value, influenced by a few very large residuals, is larger than the
actual error variances of the vast majority of data. Figures 6c and 7c show
that the proportional residuals are not normally distributed either. They are
not even symmetrical, as they cannot be smaller than -1 but they do not
have an upper limit. This asymmetry produces a bias in the flux estimate. The
algorithm based on Cprp is more sensitive to positive residuals
because underestimations are never associated to proportional residuals lower
than -1 whereas overestimations can produce residuals higher than 1. As a
consequence, this method tends to reduce the fluxes. The hypothesis of
constant variance is more realistic although the highest residuals occur at
low concentrations. Finally, the distribution of the logarithmic residuals
displayed in Figs. 6b and 7b is much closer to a Gaussian curve and much less
dependent on concentrations, which makes the logarithmic cost function more
relevant for this study.
Root mean square of residuals after inversions with different
numbers of source regions. The standard case with 38 regions is in bold.
Cost function
Case 1: 52 regions
Case 2: 38 regions
Case 3: 19 regions
Case 4: 12 regions
Case 5: 7 regions
ols
35.8
36.6
37.6
38.2
42.9
log
0.623
0.636
0.656
0.671
0.781
prp
0.545
0.558
0.581
0.597
0.665
Sensitivity to the number of regions
The choice of the regions (and their number) has been made rather
subjectively, although several criteria have been used (spatial distribution
of the observations, independence of the Ai fields). The global 228Ra
should ideally not depend upon the number of regions. Therefore, alternative
region geometries have been tested for comparison. The 228Ra fluxes are
shown on Table 4 and the root mean square of their residuals is presented on
Table 5. Case 1 inversion uses 52 regions: it was the original distribution
of regions before some of them were merged to define the 38 standard regions
of this study. It includes more regions in undersampled areas such as the
Arctic, the South Atlantic, the western Indian, or the equatorial Pacific oceans.
Case 5 has just one emitting region for each of the following ocean basins:
Southern, South Atlantic, North Atlantic, South Pacific, North Pacific,
Indian and Arctic. Case 3 and Case 4 are intermediate cases with source
regions built by merging regions from Case 2.
The root mean square of residuals is a proxy of the cost function. On the one
hand, this parameter should be as low as possible. Increasing the number of
regions always decreases it because the number of degrees of freedom
increases, which tends to improve the fit to the observations. In this
inversion, the largest decrease is found between 7 and 12 source regions.
Further increases in the number of regions have smaller impacts. On the other
hand, too many source regions may produce spurious results. Some regional
fluxes, with too few observations nearby to constrain them, would be computed
using observations farther away, already used by other fluxes. Because of the
lower sensitivity of the concentrations at these farther-off locations, this
process can create extreme fluxes, positive or even negative. The presence of
physically impossible negative values, set to zero by the constraint of
positivity, necessarily means such poor constraints exist. When 52 fluxes are
computed, 5 to 7 of them, according to the cost function, are so poorly
constrained that their fluxes have been set to zero to prevent them from
being negative. This number is reduced to 1 with Cols and zero
with Clog and Cprp when there are 38 regions, and
completely disappears with 19 or fewer regions. Regions with fluxes within
the error estimate are also very poorly constrained by the observations and
the circulation model: their number is also reduced from 26 out of 52 to 11
out of 38 with Cols, from 13 to 3 with Cprp and from
9 to 3 with Clog. All these fluxes have a low impact on the cost
function, but make the global 228Ra flux less precise. This analysis
shows that Case 1 (with 52 regions) is not constrained enough and that Cases
3 to 5 display too large residuals. Therefore, Case 2 (38 regions) is
considered to be the best choice.
The Cols-based global 228Ra flux is varying in a
non-monotonic way, with a difference of 23 % between the highest and the
lowest. The flux with 38 regions is lower than the fluxes computed with
either more or fewer regions. This high sensitivity may be related to the
high uncertainty associated with this inversion, certainly linked to the
relatively poor data coverage. All the confidence intervals within one
standard deviation from Case 1 to Case 4 overlap. The Cprp-based
global fluxes are always lower than the other fluxes, and they decrease as
the number of regions decreases. This is consistent with our previous
hypothesis on Cprp. This cost function tends to fit the lowest
data in priority. Larger regions suffer more from this bias because they are
constrained by more data, likely to be more dispersed. The confidence
intervals within 1 standard deviation based on Cprp fail to
overlap. Only the logarithmic least-squares method produces very similar
fluxes whatever the number of regions, with all confidence intervals
overlapping. The global flux based on Clog again seems to be the
most reliable.
Submarine groundwater discharge estimates
The shelf fluxes after inversion combine groundwater discharge, riverine
particles, diffusion from sediments, and bioturbation. Here we deduce the
contribution from groundwater discharge by using existing estimates of the
other sources of radium.
Rivers are poor in dissolved 228Ra and transport 228Ra mainly with
the sediments they carry . According to ,
the average dissolved 228Ra activity in rivers is 0.65–1.95×105 atomsl-1. As rivers annually discharge
35 000 km3 of freshwater , the dissolved
riverine source lies between 2.3 and 6.8×1021 atomsyr-1, which is less than 1 % of the total
flux. Nearly all the particulate radium is desorbed in the mixing zone,
because of the salinity increase. According to various studies
, the amount of 228Ra desorbed per
gram of sediment lies in the range of 2.9 to 8.7×106 atoms. In
this study, we follow who proposed a global river
sediment flux of 1.8×1016 g yr-1, divided into fluxes from
six basins: South Atlantic, North Atlantic, South Pacific, North Pacific,
Indian Ocean, and Arctic. This leads to a global 228Ra river flux
estimate of 0.53–1.60×1023 atomsyr-1, significant
but not dominant.
228Ra sources by basin, divided into riverine input, diffusion
from sediment and SGD. Only logarithmic least-squares results are shown.
Fluxes are divided the following way: Regions 1 and 38: Southern; 2–4: South
Atl; 5–16: North Atl; 17–18 and 26–27: South Pac; 19–25: North Pac;
28–34: Indian; 35–37: Arctic.
Estimates of 228Ra diffusive fluxes
(109 atomsm-2yr-1) from fine-grained sediments (muds) by
different methods. The studies which do not separate SGD and diffusion are in
bold.
Reference
Study area
Method
Flux
Narragansett Bay
Inventory
52
Amazon shelf
Inventory
110
North Inlet
Sediment profile
5
Zecks Lagoon
Benthic chamber
80
Sediment profile
80
Port Royal Sound Marsh
Krest formula
9
Greet Barrier Reef
Modeling
26
Radium-228 is released from the sediments by diffusion, bioturbation, and
advection, the latter being associated with the SGD. Like ,
we assume that the 228Ra fluxes by diffusion and bioturbation from
relict sands, composing 70 % of the total continental shelf area, is
weak, typically of the order of 109 atomsm-2yr-1
. Fluxes from continental shelf muds, which
correspond to the remaining 30 %, have been estimated by several studies
using different methods (Table 6), such as inventories ,
benthic chambers , sediment profiles ,
or modeling . But some of them were done at a time when
SGD were not considered to be an important source of radium and may have
included them in their estimates. These estimates should then be considered
as an upper limit. Furthermore, their locations are often very close to the
coast. Some recent studies, addressing diffusive fluxes (from muds or broader
regions containing both types) separately, in order to estimate local
groundwater discharge , used the simplified
equation of diffusion from (requiring only water diffusion,
sediment porosity, decay constants, and production rates) and pointed out to
significantly lower values, but may not be representative of all continental
shelves. So far, it is not possible to be very precise and a wide range has
to be considered: from the low recent values, close to 5×109 atomsm-2yr-1, to the higher values typically ranging
from 25 to 75×109 atomsm-2yr-1
. The full range is then 5–75×109 atomsm-2yr-1. As the continental shelf area in our
model is 2.73×1013 m2, this means a total flux due to
diffusion and bioturbation ranging from 0.43 to 6.51×1023 atomsyr-1. Then, using the logarithmic cost function,
the SGD 228Ra flux estimate varies between 0.62 and 6.82×1023 atomsyr-1: these two fluxes are within the same range.
Figure 8 shows the 228Ra fluxes for seven basins corresponding to the
Southern Ocean and the six basins used by to define
sediment inputs by rivers. The largest 228Ra fluxes are found in the
North Atlantic, the North Pacific, and the Indian Ocean, in roughly equal
proportions, whereas those from the South Atlantic, the South Pacific, and the
Arctic Ocean are far smaller. Fluxes from the last three regions are low
enough in fact to be within the confidence intervals of riverine and
diffusive sediment 228Ra fluxes, so that the SGD confidence intervals
include negative values, which are physically impossible.
SGD 228Ra end-member concentration varies considerably from one aquifer
to another, ranging from 0.04 to 125×106 atomsm-3
. Measurements so far have shown aquifer concentrations in
the Atlantic Ocean higher than the average by typically 30 %
. Following , we assume that the aquifer
concentrations are log-normally distributed with an average of 0.98 to
1.15×103 dpmm3. Taking a geometric mean rather than an
arithmetic mean is implicitly assuming that aquifers characterized by high
228Ra concentrations are emitting less water. It also suffers from wells
being concentrated in developed countries. Using the results from the
inversion technique based on the logarithmic cost function, the total SGD
flux is estimated to 1.3–14.7×1013 m3yr-1, to be
compared with the global river flow of 3.5×1013 m3yr-1 . As long as diffusion
cannot be separated from SGD more efficiently and is not shown to be
negligible, no precise SGD estimate based on 228Ra can be produced.
According to , there is only 2.6×1012 m3yr-1 of fresh groundwater discharge, representing
between 2 and 20 % of the SGD, and the remaining part is recirculated
seawater.
In total, 63 % of the 228Ra flows into the Indian and Pacific
basins, which is more than their share of the continental shelf (52 %).
As shown in Fig. 8, the estimated contributions of SGD to 228Ra fluxes
are in very similar proportions, with 68 % going to the Indian and
Pacific basins. This represents more than 70 % of all the groundwater
discharge when the differences in groundwater 228Ra concentration are
considered. However, uncertainties on SGD distribution are high, because
diffusion from sediment might not be identical in all basins. These results
contrast with the other source of water, nutrients and trace elements to the
ocean: 60 % of the global river discharge flows to the Atlantic and
Arctic basins .
Discussion
Comparisons with previous studies
Our inversion estimates are in good agreement with previous regional studies
of 228Ra based on inventories. The 228Ra inventory of the
Mediterranean Sea computed by led to a total flux due to
rivers, sediments and groundwater discharge of 1.86–2.48×1022 atomsyr-1. This is compatible with our estimate based
on Clog, 1.96–2.28×1022 atomsyr-1.
Other cost functions produce an underestimation in the model by a factor 2.5
(ols) or 3.8 (prp). In the Yellow Sea, estimated a flux of
3.3×1015 dpmyr-1, or 1.4×1022 atomsyr-1. Expressed per unit of surface, it
corresponds to 3.6×1010 atomsm-2yr-1. This is
slightly lower than our flux for the larger region 23 (Sea of Japan, Yellow
Sea, East China Sea) of 4.2–5.6×1010 atomsm-2yr-1 based on Clog, both these
fluxes being larger than the global average. At larger scale,
estimated the total 228Ra flux over the Atlantic
between 50∘ S and 80∘ N to be 2.8–4.2×1023 atomsyr-1. Restricting the inversion to the Atlantic
with Clog yields 2.64–2.92×1023 atomsyr-1, in the lower range but compatible. At least
two reasons can explain the difference. have included data
down to 1000 m, which allowed them to estimate 228Ra release
from sediments down to that depth. The authors have estimated the sources
between 200 and 1000 m deep to 0.13–0.37×1022 atomsyr-1. Furthermore, in order to compute the total
228Ra content of the Atlantic, they have performed a linear
interpolation of the data, potentially leading to errors, especially in areas
where measurements are sparse.
At the global scale, have used a method which is quite
similar to ours and they have computed a total global 228Ra flux of
9.1–10.1×1023 atomsyr-1, of which between 4.2 and
7×1023 atomsyr-1 are released by SGD. This
corresponds to a global SGD flux of 9–15×1013 m3yr-1. The flux of 228Ra estimated by the
present study is thus significantly lower than the estimates by
, although our results include the Arctic and Antarctic
sources (0.43–0.50 and 0.28–0.35×1023 atomsyr-1
respectively). minimized an ordinary least-squares cost
function with 50 regions. We have shown here that both a high number of
source regions and the use of the ordinary least-squares cost function concur
to produce a higher estimate. However, this is at the expense of a higher
uncertainty and of producing unrealistic negative fluxes in some source
regions. Additional differences in Kwon's study may explain their higher
estimates such as a different ocean circulation model, a coarser vertical
resolution, and a bathymetry re-gridded onto the model domain. Finally, they
added dust deposition and removed data higher than 140 dpmm-3,
but these two factors should rather tend to reduce their fluxes.
As recently proposed by , shelf 228Ra fluxes can be
used as gauges of shelf fluxes of trace elements and isotopes, including
nutrients, iron, and rare earth elements. 228Ra is particularly relevant
because it is chemically conservative and integrates information over annual
to decadal timescales. At first approximation, the flux of TEIs is deduced
from the 228Ra flux and the ratio of the nearshore gradients. Limited
for now due to the lack of nearshore measurements, this method could be more
common in the future. As they are based on realistic assumptions on error
statistics and have low uncertainties, our radium fluxes are able to improve
the current estimates of all elements originating from the continental shelf.
In contrast, our uncertainties on groundwater discharge are large, even
when compared to previous estimates. These larger uncertainties stem from the
poor knowledge of the non-SGD sources of radium that we subtract from the
total flux. As diffusion and bioturbation are expressed in flux per area, the
mean SGD fluxes and their uncertainties depend to a large extent on the
radium-emitting area we consider. Based on a more realistic refined
bathymetry than (2.73×1013 m2 compared
to 1.5×1013 m2), our study also has a larger sedimentary
flux, with an upper range close to the total 228Ra flux. Thus, the lower
range of SGD fluxes, 1.3×1013 m3yr-1, is very low,
while the upper range, 14.7×1013 m3yr-1, is similar
to other studies. The use of this model provides an upper estimate but cannot
precisely compute the global SGD flux, and no inverse model can if the
surface diffusive flux and the area emitting radium are not clarified. Our
expectation is that the lower range of sedimentary flux is more likely,
because it comes from studies where SGD is also considered and because it
never produces negative regional fluxes. By contrast, the higher range is
very similar to the total bottom flux, as expected when no distinction is
made between diffusion and SGD.
Comparisons with local direct estimates of SGD
based on seepage meters and piezometers are also possible but less conclusive
because of the high spatial variability of SGD. Our global average SGD flux
lies between 0.5 and 5.5 myr-1. Values from seepage meters and
piezometers in the upper 200 m reported by and
range from 0.03 myr-1 in the Tokyo Bay
to 1790 myr-1 near Mauritius
. Most measurements have been performed in shallow coastal
areas, less than 10 m deep, and range from 1 to 50 myr-1, 1 order of magnitude higher than our averages on all the seafloor down to
200 m deep. Thus, this range is very wide and many local studies span
several orders of magnitude. At a global scale,
produced an estimate of the global SGD flux, 6.1–12.8×1013 m3yr-1, in the upper range of our global estimate, by
extrapolating seepage measurements. However, it suffers from most
measurements being concentrated in developed countries.
The spatial distribution of the fluxes in this study is consistent with
, with two-thirds of radium-228 flowing to the Indian and
Pacific basins and also quite high fluxes in the western North Atlantic. It
turns out that these basins have the highest riverine sediment loads
. However, we have shown that rivers could account for 7
to 20 % of 228Ra fluxes only, which does not exclude an indirect
impact on the other sources through the geology of the continental shelf. A
difference among basins in the quantity of radium diffusion, which is poorly
known, is also possible. If it is not the case, then the SGD are
significantly higher in East Asia than in other regions. SGD can be driven by
as many factors as storms, waves, tides, and thermal gradients, and depend on
the permeability and structure of coastal and shelf sediments
. Comparative data on these factors in several basins will
be necessary to explain the origin of the observed differences.
Model biases
Our model of 228Ra is based on a circulation model and assumptions on
the cycle of this isotope. Both are potential sources of errors.
Dust has not been included in the model. The model then replaces them with
other sources, potentially leading to an overestimation. At global scale, it
represents 1.7×1021 atomsyr-1 , less
than 0.2 % of the total flux and less than most individual source
regions, which cannot create large biases. Nevertheless, the largest dust
deposition is associated to Saharan dust transported to the North Atlantic,
in the Canary upwelling region . In this region, dust may
have some impact on the 228Ra distribution, since it brings this isotope
directly to the open ocean. Its absence in our study might explain the
overestimation by our model near the coast of region 6 and underestimation
offshore. Yet, the exclusion of dust deposition in our analysis cannot
explain the largest bias in the North Atlantic: the overestimation in the
Gulf Stream coupled with an underestimation just southeast (see Sect. 3.2),
because the area where the model cannot transport radium is located west of
the maximum of dust input and displays higher concentration.
Scavenging is a neglected potential sink in this study. As the residence time
related to scavenging is approximately 500 years , it
accounts for between 1 and 2 % of all sinks. Thus, its inclusion in our
computations would increase the source intensity necessary to maintain global
balance. Contrary to radioactivity, scavenging is highly heterogeneous, most
intense where primary productivity and particle concentrations are highest.
Fluxes from the high latitudes of the North Atlantic are thus potentially
more underestimated than fluxes in other regions, since they are areas of
intense biological activity during spring blooms. As the actual total
lifetime of 228Ra is overestimated when scavenging is not taken into
account, the gradient between coast and open ocean could be too low. However,
as the horizontal mixing timescale of the ocean is a few decades, the
relative overestimation of open ocean concentrations is less than 10 %.
The contribution of rivers to radium fluxes is considered when estimating the
SGD, but only at a basin-wide scale. As most riverine 228Ra travels
attached to particles and is desorbed in the mixing zone, we have based our
computation on the sediment loads of , which are
basin-wide. Although NEMO 3.6 takes rivers into account for their impact on
salinity , for now no information at the model grid scale is
available on their sediment loads. If this information existed, we would have
been able to estimate the contribution of rivers, and consequently sediments
and SGD, in the 228Ra fluxes for each of the 38 regions. Some local SGD
fluxes close to large rivers (Amazon, Congo, Yellow River, etc.) could then
appear to be significantly lower than their shares of the total 228Ra
fluxes suggest.
The other part of the model is the circulation model. The climatological
circulation of NEMO 3.6 was not optimized in this study. However, the
residuals after inversion show that some regions are associated with
spatially structured residuals. There are good reasons to incriminate the
ocean circulation. Because of the low resolution of the model (2∘),
isopycnal diffusion has been used to parameterize sub-grid processes and
mixing with a constant eddy diffusivity of
2000 m2s-1. Nevertheless, in very energetic regions, such as
the western boundary currents (WBCs; e.g., the Gulf Stream and the Kuroshio),
higher eddy diffusivity might be needed to enhance the exchanges with the
open ocean, possibly improving the fit with the observations. Furthermore, it
is well known that the mean currents are also dependent on this low
resolution (impacting for instance the position and intensity of the WBCs).
Although it cannot solve all the flaws of the circulation, improvements could
thus be brought by an increase of the resolution towards eddy resolving
models. However, as 100 years of simulation are needed at a global scale for
each source region, this would be computationally expensive.
Other sources of errors are the four statistical assumptions on the errors:
errors are assumed to have zero expectation, no correlation, a normal
distribution, and variances depending on the concentrations in a way specific
to each cost function. Systematic biases on data or model are not corrected
by least-squares algorithms. They increase or decrease values without leaving
clues. However, the model conserves mass: the quantity of radium present in
the ocean from each model tracer is precisely known and if concentration is
too high at some place, it will be too low elsewhere. As for the
measurements, their uncertainty is generally around 10 % or lower, and
cruises take them independently from each other, making the assumption of
zero expectation on the observational errors reasonable. The second
assumption is the absence of prior correlation. If prior uncertainties of
neighboring data are correlated, it means that the errors are likely to be of
the same sign whatever the solution, and that multiplying measurements in
this area does not multiply information proportionally. Where measurements
are dense, with residuals far from the expected white noise, for instance in
the North Atlantic, there may be correlation and uncertainties may be
underestimated. The last assumptions are about the structure of variance. We
have shown that logarithmic residuals were almost normally distributed and
independent from concentrations (see Sect. 3.2), justifying the choice of
Clog as a cost function. Cols leads to higher
uncertainties, especially for small sources, and Cprp to
systematic underestimation, but both are useful for comparison, in order to
identify regions where physical assumptions are inaccurate (see Sect. 3.1).
What new data would be most useful?
Observations are not evenly distributed. Some coastal regions cannot be
constrained properly because 228Ra data are lacking. Improving the
coverage would increase the quality of the inversion in two ways: it would
reduce the uncertainties and make it possible to divide wide regions into
smaller regions as long as they have distinct footprints. For instance, the
Philippines, Papua, or the Gulf of Guinea, whose footprints are very
different from the Indonesian seas and the southwestern coast of Africa,
could be considered as independent regions. More samples in the Indian Ocean,
the South Atlantic (south of 30∘ S), the Southern Ocean, and the
western equatorial Pacific are priorities. All these regions will be sampled
by upcoming GEOTRACES cruises shown in Fig. 9. At the same time, deep samples
will be taken outside of the Atlantic, enabling a more comprehensive global
inversion with extra source regions at greater depths. This would improve our
knowledge of the contribution of deeper sediments.
Map of GEOTRACES cruises (from
http://www.geotraces.org/cruises/cruise-summary). Planned sections are
in red, completed sections in yellow, International Polar Year sections in
black. Names in rectangles correspond to cruises potentially bringing the
largest extra information on 228Ra fluxes because they are performed in
places lacking measurements.
Most direct submarine groundwater discharge measurements have been performed
in developed countries, with a focus on the North Atlantic and the
Mediterranean Sea . At the same time, measurements are
completely lacking over large regions. More SGD studies in areas where they
are potentially the highest, namely the Bay of Bengal, the Indonesian seas
and the China seas, would produce more representative estimates of the
228Ra content of SGD around the world and direct estimates of local SGD
magnitude to be compared with regional inversion results. They have begun
more recently and are still sparse.
Information contained in 228Ra might be completed with 226Ra
concentrations, measured during the same campaigns and for this reason
available with a similar coverage. Associated with the same source as
228Ra, but with a much longer half-life, 1602 year, 226Ra would
constrain deeper sources and would help in assessing the quality of the
thermohaline circulation and deep ventilation of the circulation model.
However, inverting 226Ra data would require a precise modeling of
scavenging, which is not negligible at these longer timescales, as well as a
much longer integration duration in order to get steady state distribution.
Conclusions
Based on inverse modeling, we have computed a global 228Ra flux from
continental shelves of 8.01–8.49×1023 atomsyr-1,
with the largest sources in the western Pacific, the western North Atlantic,
and the Indian oceans and the smallest sources in the eastern Pacific. The
Arctic and Antarctic sources have been estimated for the first time,
accounting for 0.43–0.50 and 0.28–0.35×1023 atomsyr-1 respectively. These precise estimates are
obtained by minimizing the squared differences between model and observed
concentrations on a logarithmic scale. We think this cost function is more
realistic than a linear least-squares one because it assumes that the error
standard deviation is proportional to 228Ra concentration, rather than
constant, which proves to be more accurate. It is also better than a
“proportional” cost function, weighted by the inverse of the observed
concentration, which tends to produce underestimations of concentrations and
fluxes. Given the number of available measurements, we were able to constrain
38 regional fluxes. The shelf fluxes produced using these optimal parameters
are around 20 % lower than previous estimates. In a near future, they
will enable us to quantify continental shelf fluxes of trace elements and
isotopes to the oceans at any place where nearshore gradients are measured
. The estimated global SGD is far less precise, ranging
between 1.3 and 14.7×1013 m3yr-1, because of the
very large uncertainty on the two other sources of 228Ra – i.e.,
riverine particles and most of all diffusion from bottom sediments, also
located on the continental shelf. Only the upper range is compatible with
previous estimates. These results mean that all the studies which have used
or will use 228Ra to estimate SGD will suffer from a very high
uncertainty until diffusion is properly estimated or proven to be negligible.
After inversion, we were able to reproduce the basin-scale patterns of
228Ra distribution with nevertheless systematic biases in several
regions, especially in the Arctic, and west of the subtropical gyres.
Shortcomings in the circulation model are the most probable explanation of
these biases (too weak exchanges between continental shelves and open ocean).
Extensive regions are lacking observations, mostly in the Southern Hemisphere
(Pacific, Indian, and mostly Southern Ocean, as well as western equatorial
Pacific Ocean), and better coverage in basins where
SGDs are known to be influential and to produce large horizontal gradients is
also needed (such as in South Asia). But the main impediment to achieve
precise estimates of global Ra SGD fluxes comes from the very poor knowledge
of diffusive sedimentary fluxes: without a proper way to separate diffusion
and SGD, inversions can compute the total bottom flux but are not able to
precisely evaluate these two components.