BGBiogeosciencesBGBiogeosciences1726-4189Copernicus PublicationsGöttingen, Germany10.5194/bg-13-1287-2016Decline of the Black Sea oxygen inventoryCapetArthurarthurcapet@gmail.comhttps://orcid.org/0000-0002-5939-3836StanevEmil V.BeckersJean-MarieMurrayJames W.GrégoireMarilaureOGS, National Institute of Oceanography and Experimental Geophysics, Trieste, ItalyMAST, MARE, University of Liège, Liège, BelgiumHZG, Helmholtz-Zentrum Geesthacht, Hamburg, GermanyGHER, GeoHydrodynamics and Environment Research, University of Liège, Liège, BelgiumSchool of Oceanography, University of Washington, Seattle, WA, USAArthur Capet (arthurcapet@gmail.com)1March20161341287129731August20152October201517February201619February2016This 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/13/1287/2016/bg-13-1287-2016.htmlThe full text article is available as a PDF file from https://bg.copernicus.org/articles/13/1287/2016/bg-13-1287-2016.pdf
We show that from 1955 to 2015, the inventory of oxygen in the Black Sea has
decreased by 44 % and the basin-averaged oxygen penetration depth has
decreased from 140 m in 1955 to 90 m in 2015, which is the shallowest
annual value recorded during that period.
The oxygenated Black Sea surface layer separates the world's largest
reservoir of toxic hydrogen sulfide from the atmosphere. The threat of
chemocline excursion events led to hot debates in the past decades arguing on
the vertical stability of the Black Sea oxic/suboxic interface. In the 1970s
and 1980s, when the Black Sea faced severe eutrophication, enhanced
respiration rates reduced the thickness of the oxygenated layer.
Re-increasing oxygen inventory in 1985–1995 supported arguments in favor of
the stability of the oxic layer. Concomitant with a reduction of nutrient
loads, it also supported the perception of a Black Sea recovering from
eutrophication. More recently, atmospheric warming was shown to reduce the
ventilation of the lower oxic layer by lowering cold intermediate layer (CIL)
formation rates.
The debate on the vertical migration of the oxic interface also addressed the
natural spatial variability affecting Black Sea properties when expressed in
terms of depth. Here we show that using isopycnal coordinates does not overcome the
significant spatial variability of oxygen penetration depth. By
considering this spatial variability, the analysis of a composite historical
set of oxygen profiles evidenced a significant shoaling of the oxic layer,
and showed that the transient “recovery” of the 1990s was mainly a result
of increased CIL formation rates during that period.
As both atmospheric warming and eutrophication are expected to increase in
the near future, monitoring the dynamics of the Black Sea oxic layer is
urgently required to assess the threat of further shoaling.
Introduction
The Black Sea deep waters constitutes the world's largest reservoir of toxic
hydrogen sulfide. 100 m of ventilated surface waters are all that separate
this reservoir from the atmosphere. This situation results from the permanent
halocline that separates the surface layer (of low salinity
due to river inflow) from the deeper layer (of high salinity due to inflowing
Mediterranean seawater), restraining ventilation to the upper layer
(Fig. ).
Typical profiles of temperature, salinity,
Brunt–Väisälä frequency (N), potential density anomaly
(σθ) and oxygen concentration in the central Black Sea (May).
Note the two peaks in the vertical stratification: the thermocline, which is
seasonal and corresponds roughly to the upper limit of the cold intermediate layer and the halocline, which is permanent, and correspond roughly to the
lower limit of the cold intermediate layer and the upper boundary of the
suboxic zone. Red dotted lines and shaded areas illustrate the diagnostic
values derived from each profile (Sect. ).
In the lower part of the halocline, a permanent suboxic layer separates the
Black Sea surface oxygenated waters ([O2] > 20 µM) from the
deep sulfidic waters ([H2S] > 20 µM)
. More precisely,
considered a threshold of 10 µM of oxygen because they analyzed
high-quality oxygen data. The threshold of 20 µM of oxygen was
applied later to analyze historical oxygen data of lower quality. The upper
(O2 disappearance) and lower (H2S onset) interfaces of this suboxic
layer are controlled by different biogeochemical and physical
processes , and undergo uncorrelated vertical
migrations . Sinking organic matter is mainly respirated
aerobically within the oxycline: the lower part of the oxygenated layer
where oxygen concentration decreases downwards to 20 µM. Increasing
flux of organic matter, induced by a period of high nutrient load from the
1970s to the late 1880s, resulted in higher oxygen consumption above the
suboxic layer and a shoaling of the upper suboxic interface
.
After reduction of nutrient inputs around 1990 , the Black
Sea was described as a recovering ecosystem . This
perspective was supported by improved eutrophication indices in the open sea
as well as the stabilization of the upper suboxic
interface in the 1990s . However, the timescale of the
expected recovery (i.e., the timescale associated with the chain of
biogeochemical mechanisms relating oxycline penetration depth to riverine
nutrient loads) is not quantitatively understood. Several processes cause the
oxycline depth to respond with a time lag to the reduction of riverine
nutrient inputs. First, nutrients are mainly delivered to the northwestern
shelf, where the accumulation of organic matter in the sediments buffers the
riverine inputs, with slow diagenetic processes controlling and delaying the
nutrient outflow across the seaward boundary . Second, the
intermediate oxidation–reduction cycling of nitrogen, sulfur, manganese,
iron and phosphorus that separates oxygen from hydrogen sulfide
can delay the
response of the lower suboxic interface to changing nutrient fluxes by
several years .
Temporal distribution of the ship-based oxygen profiles merged from
the World Ocean Database, R/V Knorr 2003 and R/V Endeavor
2005 campaigns. Only the profiles containing at least five observation depths,
one observation above 30 m depth and one record with
[O2] < 20 µM were considered.
In addition to these biogeochemical factors, the dynamics of the upper and
lower interfaces of the suboxic layer are controlled by physical processes
. In the Black Sea, dense waters formed by
winter cooling and mixing do not sink to the deepest
layer, as in the Mediterranean Sea, but accumulate on top of the permanent
halocline (Fig. ). The resulting cold intermediate layer (CIL)
is a major feature of the Black Sea vertical structure. Cold intermediate
water formation and advection by the cyclonic basin-wide Rim Current
ventilate the oxycline and thereby influence
variability in the depth of the upper suboxic interface
. Recently, atmospheric warming was
shown to reduce the ventilation of the lower oxic layer
. At deeper levels, the dense sinking plume
formed by the Mediterranean inflow through the Bosporus, which entrains water
from the overlying CIL, injects fingers of oxygenated water directly into the
deeper part of the suboxic layer and upper sulfidic layer and thus acts to
control the depth of the lower suboxic interface
.
Previous long-term analyses of the vertical migration of the suboxic
interfaces either ended (1955–1995; ) or started
(1985–2015; ) with the eutrophication period,
excluding the large–scale overview required to grasp the interactions of
eutrophication and climate factors. Those analyses lacked a comprehensive
consideration of the natural spatial and seasonal variability of the vertical
distribution of oxygen.
In the presence of large gradients, uneven data distribution may induce
artificial signals when interannual trends are assessed from direct annual
averages. In the stratified Black Sea, properties expressed in terms of depth
coordinates (m) present a high spatial variability due to mesoscale
features and to the general curvature of Black Sea
isopycnals . As an alternative, using density
(isopycnal levels, σθ) as vertical coordinate is generally
considered a stable solution to assess the vertical migration of the
chemocline on a decadal scale .
However, the spatial confinement of the lateral oxygen injections associated
with the Bosporus plume, as well as the spatial variability of diapycnal
ventilating processes , imposes a horizontal structure
to the oxygen penetration depth when expressed in terms of density
. As this spatial gradient might scale with the
temporal variations (a range of 0.17 kgm-3 was observed during
the Knorr 2003 campaign, ), it has to be considered when
deriving interannual trends.
The present study describes the application of the DIVA (Data-Interpolating
Variational Analysis) detrending procedure
to untangle the temporal and spatial variability of three indices related to
the Black Sea oxygenation status: the depth and density level of oxygen
penetration and the oxygen inventory. These values were diagnosed from a
composite historical data set of oxygen vertical profiles. We review the
evolution of those indices through the past 60 years and discuss the
respective controls of eutrophication and climate factors.
We gathered a composite set of 4385 ship-based vertical profiles (oxygen,
temperature and salinity) obtained between 1955 and 2005 in the Black Sea
using CTD rosette bottles, continuous pumping profilers
and in situ analyzers from the World Ocean Database
(http://www.nodc.noaa.gov/OC5/SELECT/dbsearch/dbsearch.html), and R/V
Knorr 2003 and R/V Endeavor 2005 campaigns
(http://www.ocean.washington.edu/cruises/Knorr2003/,
http://www.ocean.washington.edu/cruises/Endeavor2005/). Only the
profiles containing at least five observation depths, one observation above
30 m depth and one record with [O2] < 20 µM were retained
for analysis. The temporal and spatial distribution of the selected
ship-based profiles are displayed in Figs. and
, respectively.
To complement the analysis of ship-based casts, we considered profiles
originating from 10 Argo autonomous profilers (May 2010–December 2015).
Only good quality-checked real-time data were considered .
Two of these floats (Argo ID 7900465 and 7900466) have been presented and
discussed by , where the consistence and comparability of
Argo and historical profiles is asserted within a 1 µM error range.
Several studies address the error of Argo real-time oxygen data
e.g.,. Demonstrating that the
Black Sea real-time Argo data are precisely (i.e., at fine scales) comparable
with historical Winkler data, or identifying the relevant correction, is
beyond the scope of the present study which addresses monthly to decadal timescales. Evenly distributed small-scale error (e.g., difference between
ascending and descending profiles due to sensor time response) were thus
filtered by the temporal smoothing. However, a systematic error is not
strictly excluded which could reach an underestimation of 10 µM
(Virginie Thierry, IFREMER, personal communication, January 2016). Therefore,
we evaluated a “worst-case” scenario in the analysis of Argo data by
considering a systematic underestimation of oxygen concentration by
10 µM.
Although most of the floats drifted along the basin periphery, some were also
advected in the central part (Fig. ). These trajectories
highlight the range of spatial variability for the diagnostics described in
Sect. .
The investigation time frame was divided into periods according to data
availability and to dissociate known phases of eutrophication and CIL dynamics – see also
for decadal cycles in the Black Sea: 1955–1975 (1575
ship-based profiles), 1976–1985 (1350 ship-based profiles), 1986–1998 (1324
ship-based profiles) and 1999–2015 (136 ship-based profiles and 1393 Argo
profiles).
Profile analysis
From each profile we derived (1) the depth and (2) the potential density
anomaly σθ where oxygen concentration went below 20 µM
and (3) the oxygen inventory, integrated above this limit
(Fig. ). The threshold value of 20 µM used to define
the upper interface of the suboxic layer was suggested to compare oxygen
observations issued from sensors with different detection limits
. To evaluate how a 10 µM underestimation by
Argo profilers would affect the main conclusions, oxygen penetration depths
an density levels for Argo were also computed using a threshold of
10 µM.
The CIL cold content (Fig. ) was diagnosed from corresponding
salinity and temperature profiles following . It
indicates on the intensity of CIL formation smoothed over 4–5 years, i.e,.
the residence time of cold intermediate waters
:
CILcoldcontent=cρ∫CILT(z)-TCILdz,
where ρ is the density and c the heat capacity and
TCIL=8.35∘C .
DIVA analysis
Climatologies for the whole period and interannual trends were identified for
the three oxygen diagnostics by applying the DIVA detrending algorithm on the
ship-based data set (see details in Appendix ).
In short, the DIVA interpolation software
(http://modb.oce.ulg.ac.be/mediawiki/index.php/DIVA;
) computes a gridded climatology obtained by minimizing
a cost function which penalizes gradients and misfits with observations. The
DIVA detrending algorithm computes trends for each
year, i.e., the average difference between data pertaining to this year and
the spatial analysis at these data locations. This procedure allows one to
account for the sampling error associated with spatial/temporal variability.
ResultsSpatial variability
The spatial distribution of the oxygen penetration depth
(Fig. a) reflects the general curvature of the Black Sea
vertical structure. A range of approximately 70 m was observed
between oxygen penetration depth in the periphery (150 m) and in the
central part (80 m).
Annual climatologies of (a) oxygen penetration depth (where
[O2] = 20 µM), (b) potential anomaly at oxygen
penetration depth and (c) oxygen inventory. These spatial
climatologies were constructed from the ship-based data set (1955–2005),
accounting for the temporal variability of these diagnostics and the uneven
distribution of data (see Sect. ).
A significant spatial variability remains when expressing oxygen penetration
in terms of potential density anomaly σθ
(Fig. b). While the central part bears typical values of
15.75 kgm-3, a deeper anomaly (in terms of density) can be seen
in the area of the Bosporus plume (16.1 kgm-3), which then
decreases along the southern (15.85–15.9 kgm-3) and eastern
periphery (15.85 kgm-3). These result in a range of spatial
variability of 0.35 kgm-3.
(a) Oxygen penetration depth, (b) oxygen
penetration density levels and (c) oxygen inventory derived from
Argo profiles. The color legend gives the unique Argo identification number
of the floats. Colored lines and color-filled areas indicate smoothed time
series for each float (second-degree LOESS smoother, span = 0.5, 0.95
confidence intervals). The black line and gray shaded area are the smoothed
time series obtained when considering all floats (reported in
Fig. ).
The spatial distribution of the oxygen inventory (Fig. c)
follows that of the oxygen penetration depth. The range of spatial
variability reaches 12 molO m-2, i.e., between
17 molO m-2 in the central part and
29 molO m-2 in the periphery.
The ranges of spatial variability derived from these spatial analyses agreed
with those depicted by the Argo profilers (Fig. ), bearing
in mind the different timescales under consideration.
Temporal variability
Between 1955 and 2005, the oxygen penetration depth rose by an average rate of
7.9 m per decade (Fig. a). The basin average was of 140 m in
1955 (ship-based), 100 m in 2005 (ship-based) and 90 m in 2015 (Argo).
Considering a systematic underestimation by 10 µM in the Argo data
would result in an oxygen penetration depth around 95 m for 2015 (Argo).
This shoaling was also observed on the potential density scale
(-0.074 kgm-3 per decade, Fig. b). The basin
average was of 16.05 kg m-3 in 1955 (ship-based), 15.6 kg m-3
in 2005 (ship-based) and around 15.3 kg m-3 in 2015 (Argo).
Considering a systematic underestimation by 10 µM in the Argo data
would result in values of 15.5 m for 2015 (Argo).
The oxygen inventory, integrated from the surface down to the suboxic upper
interface, decreased by 44 % during the last 60 years
(Fig. c), considering the ship-based estimate for 1955
(27 molOm-2) and the Argo estimate for 2015
(15 molOm-2). The few ship-based profiles available after the
mid-1990s revealed the lowest oxygen inventories recorded during the time frame
covered by the present study.
The temporal signals departed from these linear trends between 1988 and 1996,
during which deeper oxygen penetration (both in terms of depth and density)
and higher oxygen content were observed.
Oxygen inventory and CIL cold content
Positive relationships between oxygen inventory and CIL cold content were
obtained for all periods (Fig. ). Considering a given level of
CIL cold content, the corresponding oxygen inventory decreased significantly
from period 1955–1975 to period 1986–1998 (Fig. b).
The relationship between oxygen inventory and CIL cold content for the period
1999–2015 does not differ significantly from that obtained for the period
1986–1998 (Fig. b). This comparison should be considered with
caution, however, as oxygen profiles for the period 1999–2015 originate
mainly from Argo floats whose sampling rate is much higher than ship-based
casts.
High CIL cold content is much more frequent during the period 1986–1998,
while low CIL cold content is more frequent during 1999–2013.
Discussion
The spatial analysis of oxygen penetration depth showed that the use of
density coordinates does not eliminate the sampling error associated with
uneven spatial coverage (Fig. ). Deeper oxygen
penetration (on a density scale) in the Bosporus area were expected, in relation with the
intermediate lateral injections associated with the Bosporus plume. In
addition, deeper oxygen penetration (on a density scale) in the southern and eastern
periphery suggests the occurrence of diapycnal ventilation along the steep
bathymetry . The aggregation of the most recent
ship-based profiles in the Bosporus area and in the southeastern region
(Fig. ), might have led to an overestimation of the
basin-average oxygen penetration depth in the last decade, hence to an
underestimation of the shoaling trend of the Black Sea oxic layer.
Trends of (a) oxygen penetration depth, (b) oxygen
penetration density level (σθ) and (c) oxygen inventory
deduced from (dots) DIVA analysis of ship-based casts and (blue) ARGO floats.
In (a) and (b), the diagnostics from ARGO are also shown
for the lower threshold of 10 µM to acknowledge a potential bias
between Winkler and Argo data. Red lines: the linear trends assessed from the
ship-based data set are -7.9 m decades-1,
-0.074 kg m-3 decades-1 and
-1.44 mol O m-2 decades-1 for (a), (b) and
(c), respectively. Error bars on DIVA estimated trends indicate the
standard error associated with the estimation of the mean misfit for each
year (see Appendix ).
Considering spatial variability revealed a clear shoaling trend for oxygen
penetration depth. This shoaling can be seen on both depth and density scales
(Fig. a, b). This confirms the hypothesis that the shoaling of
oxygen penetration depth is not due to a general shoaling of the main
halocline, but is associated with a shifted biogeochemical balance in the
oxygen budget .
Using σθ coordinates depicts clearer temporal variations
(Figs. and ). The shoaling rate varies in time
and was more intense during 1970–1985 and from 1996 onwards. Argo
diagnostics using different oxygen threshold show a larger discrepancy in the
case of pycnal coordinates. The co-occurrence of density and oxygen gradients
(Fig. ) results in a higher sensitivity to the sensor accuracy
for the σθ diagnostic for oxygen penetration. However, even a
systematic underestimation by 10 µM of oxygen concentration by Argo
profilers does not invalidate our results.
The positive correlations between CIL cold content and oxygen inventory
observed for all the periods illustrate the ventilation of intermediate
layers by CIL formation and advection (Fig. b). In the early 1990s,
the transient recovery of the three oxygenation diagnostics
(Figs. a, b, c, a) provided arguments supporting the
stability of the oxic interface . This
stabilization matched the convenient perception of a general recovery of the
Black Sea ecosystem after the reduction of nutrient load around 1990
. However, Fig. indicates that the oxygenation
diagnostics obtained for the period 1986–1998 were associated with much
higher ventilation rates (i.e., higher CIL cold content) than during the
previous periods. If, in response to nutrient reduction, the biogeochemical
oxygen consumption terms had been lower during the period 1986–1998 than
previously, the increased ventilation during that period would have resulted
in higher oxygen inventories. Instead, oxygen inventories observed during
1986–1998 are lower than those observed in the previous decade for similar
levels of CIL cold content. We conclude that high CIL formation rates during
this period provided enough ventilation to
mask ongoing high oxygen consumption.
Impact of convective ventilation on oxygen inventory. Frequency
distributions of (a) oxygen inventory and (c) cold intermediate layer (CIL) cold content diagnosed from ship-based and Argo
profiles for different periods (color legend). (b) LOESS regressions
(second degree polynomials, span = 0.75, ) between oxygen
inventory and CIL cold content for the different periods (confidence interval
α=0.99). The positive relationships observed during each period
illustrate the ventilating action of CIL formation as a source of oxygen to
the intermediate levels. The shift of these relationships towards lower
oxygen inventories indicates shift in the oxygen budgets (higher consumption)
that are independent of the intensity of CIL formation.
The fact that the relationship between oxygen inventories and CIL content for
the last period 1999–2015 is similar to that of 1986–1998 indicates a
stabilization in the biogeochemical oxygen consumption terms. Higher air
temperature in this last period , by
limiting winter convective ventilation events led to
the lowest oxygen inventories ever recorded for the Black Sea
(Fig. c).
Forecasted global warming, without excluding transient high ventilation
periods, will limit CIL water formation and reduce the
oxygenation of the Black Sea intermediate layers. At the same time,
uncertainties remain regarding the capacity of re-flourishing economies of
the lower Danube watershed to recover their productivity in a more
sustainable, less polluting form. Economic development in the Danube Basin
could reverse the improving situation of eutrophication if nutrients are not
managed properly . Under these conditions, there is no
reason to expect that the oxycline shoaling observed over the past 60 years
will stabilize.
There are reasons to worry about a rising oxycline in the Black Sea. First,
biological activity is distributed vertically on the whole oxygenated layer,
as indicated by zooplankton dial migration . The
reduction of the oxygenated volume described in this study could therefore
have impacted on Black Sea living stocks by reducing carrying capacity and
increasing predation encounter rates. It would be timely to estimate now
the impact that a further shoaling of the oxic interfaces would bear on the
Black Sea resources for the fishing industry.
Second, under present conditions, a massive atmospheric release of hydrogen
sulfide caused by a sudden outcropping of anoxic waters remains unlikely,
due to the stability of the Black Sea pycnal structure. Such outcropping
event of sulfidic waters would have dramatic ecological and economical
consequences . On 27 September 2005, an anomalous
quasi-tropical cyclone was observed over the western Black Sea that led, in a
few days, to the outcropping of waters initially located at 30 m depth
. Two years earlier, sulfide was measured in the same area
(western central gyre) at around 80 m . Because global
warming is expected to increase the occurrence of extreme meteorological
events , every meter of oxycline shoaling would bring the
Black Sea chemocline excursion events closer to the realm of possibility.
Conclusions
The present study evidenced the decline of the Black Sea oxygen inventory
during the second half of the 20th century and first decade of the 21st, and
highlighted the threat that further atmospheric warming casts upon the
vertical stability of the Black Sea oxygenated layer.
Further works are urgently required to assess how actual nutrient emission
policies adequately prevent, in the context of forecasted warming, the
ecological and economical damages that would arise from a further shoaling of
the oxic interface.
Spatially resolved biogeochemical models are needed to integrate explicitly
the interacting processes affecting the Black Sea oxycline.
It is also essential (1) to determine to which extent the shoaling of the
oxygen penetration depth entrains a shoaling of the sulfidic
onset depth, (2) to set up a continuous monitoring
of the Black Sea oxygen inventory and the intensity of winter convective
ventilation (through CIL cold content), and (3) to clarify and quantify the
interplay of diapycnal and isopycnal ventilation mechanisms and, in
particular, the role played by the peripheral permanent/semi-permanent
mesoscale structures and how this relates to the intensity of the Rim Current
. We propose that these objectives might be
answered by maintaining in the Black Sea a minimum population of both moored
and drifting autonomous profilers equipped with oxygen and sulfidic sensors.
The DIVA detrending algorithm
DIVA (Data-Interpolating Variational Analysis) is a method for spatial
interpolation. Its principle is to construct an analyzed field φ that
satisfies a set of constraints expressed in the form of a cost function over
a spatial domain Ω. The cost function is made up of (1) an
observation constraint, which penalizes the misfit between data and
analysis, and (2) a smoothness constraint, which penalizes the
irregularity of the analyzed field (gradients, Laplacian, etc.).
Let us assume that we work with data anomalies, i.e., a reference (or
background) field is subtracted from the data points prior the analysis. For
N data anomalies di at locations (xi,yi), the cost function reads,
in Cartesian coordinates,
J[φ]=∫Ω∇∇φ:∇∇φ+α1∇φ⋅∇φ+α0φ2dΩ+∑i=1Nμidi-φ(xi,yi)2=Jsmooth[φ]+Jobs[φ],
where μi, α0 and α1 are coefficients related to
characteristics of the data set. ∇ is the horizontal
gradient operator and ∇∇φ:∇∇φ=∑i∑j(∂2φ/∂xi∂xj)(∂2φ/∂xi∂xj), the generalization of the scalar product of two
vectors.
The first term of Eq. () measures the spatial variability
(curvature, gradient and value) of the analyzed field and is identified as
the smoothness constraint. The second term is a weighted sum of data-analysis
misfits and is identified as the observation constraint: it tends to pull the
analyzed field towards the observations. The coefficients of
Eq. () can be determined from (1) the relative weights wi
attributed to each observation di, (2) the correlation length L and
(3) the signal-to-noise ratio λ. The analyses
presented in this study were achieved with equal weights wi=1,
L=0.8∘ and λ=0.5. The minimization of Eq. ()
is solved over Ω with a finite-element technique
which excludes data influence across land points .
The detrending algorithm, presented in with synthetic
and real case studies, proceeds as follows. Input data can be classified
amongst the different classes Cj (e.g., 1990, 1991, …) of a given
group C (e.g., the year). The observation constraint of the functional
Eq. () can then be rewritten by including an unknown trend
value for each class (dC1, dC2, …):
Jobs[φ]=∑i∈C1μidi-dC1-φ(xi,yi)2+∑i∈C2μidi-dC2-φ(xi,yi)2+⋯.
If the function φ(x,y) were known, minimization with respect to each
of the unknowns dCj would yield
dC1=∑i∈C1μidi-φ(xi,yi)∑i∈C1μi
and similarly for the other classes: the trend for each class is the weighted
misfit of the class with respect to the overall analysis.
Using an analysis without detrending as a first guess for φ, trends
are computed for each classes in each group and subtracted from the original
data. Following this, a new analysis is performed, the trends are
recalculated, and the iterations continue until a specified convergence
criterion is fulfilled. The procedure can be generalized with several groups
of classes. The present study considered years and months.
The DIVA software and up-to-date related information can be found on
http://modb.oce.ulg.ac.be/mediawiki/index.php/DIVA.
Acknowledgements
This study was achieved in the context of the PERSEUS project, funded by the
EU under FP7 Theme “Oceans of Tomorrow” OCEAN.2011-3 Grant Agreement
No. 287600. A. Capet is currently cofunded by the European Union under
FP7-People-Co-funding of Regional, National and International Programmes, GA
n. 600407 and the Italian Ministry of University and Research and National
Research Council (Bandiera project RITMARE). E. V. Stanev acknowledges
support from the EC project E-AIMS (grant 312642). Argo data were collected,
checked and made freely available by the International Argo Program, part of
the Global Ocean Observing System, and the national programs that contribute
to it (http://www.argo.ucsd.edu,
http://argo.jcommops.org). This is MARE publication number 323. Edited by:
L. Stramma
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