“Not to be cited without prior reference to the author”
ICES C.M. 2012/ R:02
Mapping plankton biomass in the deep-ocean: an ecological provinces
approach
A. Bode, J.L. Acuña, J. Bueno, M.L. Fernández de Puelles, J.I. González Gordillo, S. HernándezLeón, X. Irigoien, C. Mompeán and M.P. Olivar
The distribution of epipelagic plankton biomass by size-fractions was studied during Malaspina-2010
expedition across the Indian, Pacific and Atlantic oceans. The objective was to characterize plankton
biomass structure at large spatial scales in poorly explored areas of the ocean. Samples from 95
stations, representative of 3 of major ocean biomes and 12 ecological provinces, were fractionated in 5
size-classes (40 to 5000 µm) and biomass determined as dry weight. Mean plankton biomass was
similar for all oceans and major biomes but varied significantly between provinces, being particularly
high in the N Pacific Equatorial Countercurrent and in the Caribbean provinces. The differences were
mainly due to increases in medium-sized plankton, while for most provinces the biomass was
uniformly distributed across logarithmic size-classes. Total and size-class plankton biomass was
negatively and non-linearly correlated with the mixing layer depth and with the depth of the
chlorophyll maximum across provinces. In contrast only the biomass of the smaller plankton was
positively and linearly correlated with sea surface temperature, while the biomass of other size-classes
was positively affected by the thermal stratification gradient in the upper layer. The obtained
relationships will improve our ability to monitor and model the ocean response to global change.
Keywords: plankton, biomass, deep-ocean, size-fractions, ecological provinces, Atlantic, Pacific,
Indian
Contact author: Antonio Bode. Instituto Español de Oceanografía (IEO). Centro Oceanográfico de A
Coruña, Apdo. 130, E15080 A Coruña (Spain). e-mail: antonio.bode@co.ieo.es
50
NASE
NPTG
NATR
0
PNEC
PEQD
CARB
SPSG
ISSG
EAFR
-50
AUSW
SSTC
-150
-100
-50
0
TASM
50
100
150
Figure 1. Location of plankton sampling stations (red dots) in the biogeochemical
ocean provinces defined in Longhurst (2007).
1
Introduction
Despite the importance of the ocean in the response and regulation of global changes (HoeghGuldberg and Bruno, 2010), large regions of the deep ocean remain unexplored. Only the surface is
regularly accessed by satellites, thus providing data on primary production and phytoplankton biomass
(e.g. Behrenfeld et al., 2006). Information on most of the components of the food web is thus restricted
to a few and sparse observations by cruises covering a small part of the unexplored regions, while
most repeated cruises concentrate along established navigation routes (Reid et al., 2003; Isla et al.,
2004; San Martin et al., 2006).
Information on the marine ecosystems for large regions may be provided by models. Ecosystem
models allow to estimate biomass and abundance along the food web but for practical reasons the
estimations are generally limited to a few components (Shin et al., 2010). Alternatively, models based
on macroecological functions and body-size of organisms allow for biomass estimations on practically
any organism (Lopez-Urrutia et al., 2006; Jennings et al., 2008). However, the implementation and
testing of models require observations acquired in the ocean.
One way to overcome the impossibility of having observations on oceanic ecosystem components at
all spatial and temporal scales relies in the common properties of ocean biomes and biogeochemical
provinces (Longhurst, 2007). These large portions of the ocean are defined over the main geographic
and hydrodynamic boundaries and allow for a synthesis of the main biological and biogeochemical
processes of production and loss of organic matter and elements in a relatively small number of units.
In this way, average values of productivity, biomass and seasonal changes are available for all regions
of the ocean, including the deep ocean (Longhurst, 2007).
The objectives of this study are to characterize plankton biomass structure in deep ocean provinces
and to determine empirical relationships predicting plankton biomass in the deep ocean.
Materials and methods
Plankton samples were collected during Malaspina-2010 expedition (Fig. 1). In this study only
samples from 95 stations visited during legs 4 (February 2010) to 7 (July 2010) were employed.
Samples were collected by vertical hauls of a bongo-type net (30 cm diameter, 40 µm mesh size)
between 200 m depth and the surface
Table 1. Biogeochemical ocean provinces and biomes, as
during early morning hours. Plankton
defined in Longhurst (2007), sampled in this study.
was size-fractionated using sieves of
200, 500, 1000, 2000 and 5000 µm,
Code
Province
Biome
collected on pre-weighted glass-fiber
EAFR E. Africa Coastal Province
Coastal
filters and oven dried (60°C, 24 h) on
ISSG
Indian S. Subtropical Gyre Province
Trades
board. Biomass was later determined AUSW Australia‐Indonesia Coastal Province
Coastal
in the laboratory as dry weight (±0.01 SSTC S. Subtropical Convergence Province
Westerlies
Westerlies
mg). Hydrographic information was TASM Tasman Sea Province
SPSG
S.
Pacific
Subtropical
Gyre
Province
Trades
obtained from CTD-rosette casts at
PEQD Pacific Equatorial Divergence Province
Trades
the same stations and chlorophyll-a
PNEC N. Pacific Equatorial Countercurrent Province
Trades
was determined from acetonic NPTG N. Pacific Tropical Gyre Province
Trades
extracts of phytoplankton collected at CARB Caribbean Province
Trades
Trades
up to 8 discrete depths in the photic NATR N. Atlantic Tropical Gyral Province
Westerlies
layer
(>0.1%
of
surface NASE N. Atlantic Subtropical Gyral Province (East)
2
photosynthetically active irradiance). Details of the sampling and analytical methods employed can be
found in Moreno-Ostos (2012). The difference in temperature between the surface and 50 m depth was
used as an index of stratification of the upper ocean.
In addition to in situ measurements, mean values of primary production, surface chlorophyll, mixing
layer and euphotic depth, and stratification for each sampled biogeochemical province were obtained
from Longhurst (2007).
Results and discussion
Mean biomass distribution
DW (mg m-3)
Our study covered 12
Pacific
Atlantic
provinces in 3 ocean
35
basins
and
were
DW
*
30
distributed
over
all
Indian
biomes, except the polar
25
biome (Table 1). A
20
* *
preliminary
analysis
15
*
indicated no significant
10
differences between mean
5
values of total plankton
18
5
3
9
2
6
9
5
15
2
6
15
0
biomass (i.e. the sum of
biomass in all sizefractions) between biomes
or
oceans
(ANOVA,
Figure 2. Mean (±se) plankton biomass (mg DW m-3) in the
P>0.05). Mean plankton
biogeochemical ocean provinces defined in Longhurst (2007) and
biomass was also very
major oceans. The numbers at each bar indicate the number of
similar among provinces
(Fig. 2) but in this case some differences appeared due to the values found in the North Pacific
Equatorial Countercurrent Province (PNEC, Dunnett-C test, P<0.05). Although temporal variability
(e.g. seasonality) may explain some of these differences, the similarity in mean biomass of plankton in
the upper ocean, particularly in the central regions, is consistent with an steady state of the
ecosystems, with primary production inputs balanced by consumer and export losses (Platt and
Denman, 1977; Rodriguez and Mullin, 1986).
Biomass by size classes
There was an even distribution of biomass by the chosen size classes in most provinces (Fig. 3). This
implies an approximately equal amount of biomass in logarithmic individual body carbon classes, as
predicted by pelagic size spectrum theory (Platt and Denman, 1977; Kerr and Dickie, 2001), and
reported for most of the oligotrophic deep ocean (e.g. Rodriguez and Mullin, 1986; Piontkovski et al.,
2003; San Martín et al., 2005). Only in some provinces there are an excess of biomass in some classes,
as in the Caribbean that showed maximum biomass in large mesozooplankton (500-1000 µm),
suggesting temporal deviations from the steady state. The use of a single net to capture a relatively
large range of plankton sizes in this study may have negatively affected the collection of
macrozooplankton (>1000 µm) that may have avoided the net. This may be the case of samples
collected in the Atlantic where biomass decreased with increasing sizes (Fig. 3). However, most
samples from the other basins did not show such decrease, suggesting that there were increases of
small plankton in the Atlantic instead. Similarly there may have been losses of large zooplankton
3
because the sampling was performed during daylight when some macrozooplankton is expected to be
in deep water layers (Gallienne et al., 2001), but other detailed vertical studies in the deep ocean have
found a remarkably constant and low biomass of large zooplankton in the upper 400 m (Koppelmann,
and Weikert, 1992).
Pacific
10
Indian
TASM
DW (mg m-3)
8
10
EAFR
2
6
0
40-200
4
10
CARB
200-500 500-1000 1000-2000
>2000
ISSG
8
8
DW (mg m-3)
40-200
DW (mg m-3)
8
10
6
4
2
6
4
0
40-200
4
6
2
0
200-500 500-1000 1000-2000
10
>2000
40-200
200-500 500-1000 1000-2000
>2000
10
PEQD
NATR
2
0
40-200
200-500 500-1000 1000-2000
>2000
10
AUSW
DW (mg m-3)
8
8
8
DW (mg m-3)
DW (mg m-3)
>2000
SPSG
0
DW (mg m-3)
200-500 500-1000 1000-2000
10
2
6
4
2
6
200-500 500-1000 1000-2000
>2000
40-200
200-500 500-1000 1000-2000
>2000
SSTC
DW (mg m-3)
40-200
PNEC
NASE
4
2
6
0
4
10
2
8
>2000
8
6
8
200-500 500-1000 1000-2000
10
8
10
4
0
40-200
10
0
6
2
0
4
2
6
4
2
0
40-200
200-500 500-1000 1000-2000
>2000
40-200
200-500 500-1000 1000-2000
>2000
NPTG
0
40-200
200-500 500-1000 1000-2000
>2000
DW (mg m-3)
DW (mg m-3)
4
DW (mg m-3)
DW (mg m-3)
8
Atlantic
6
6
4
2
0
40-200
0.1
200-500 500-1000 1000-2000
1.0
5.9
27.9
>2000
167.9 µg C
Figure 3. Mean (±se) plankton biomass (mg DW m-3) by size-classes (µm) in the
biogeochemical ocean provinces defined in Longhurst (2007) and major oceans. The median
value of individual carbon biomass for each class is indicated in the yellow box.
4
Empirical relationships between biomass and oceanographic variables
Notwithstanding they were mostly located in deep waters, the sampled provinces were characterized
by a large range of vertical oceanographic structure and consequently primary production and biomass
(Table 2). These values allowed for exploring their relationships with plankton biomass and producing
empirical predictive functions.
Table 2. Mean values of oceanographic variables characterising the biogeochemical
provinces, as defined in Longhurst (2007) and those measured in this study. PP: primary
production (mg C m-2 d-1), Chla0: surface chlorophyll-a from satellite (mg Chla m-2), Chlai:
photic depth integrated chlorophyll-a from in situ samples (mg Chla m-2), ze: photic zone
depth (m), MLD: mixing layer depth (m), DCM: depth of chlorophyll maximum (m), SST:
sea surface temperature (⁰C), T50: temperature at 50 m (⁰C), T0_200: mean temperature of the
layer 0-200 m (⁰C), T0-50: temperature difference between 0 and 50 m (⁰C).
Province
EAFR
ISSG
AUSW
SSTC
TASM
SPSG
PEQD
PNEC
NPTG
CARB
NATR
NASE
PP
0.52
0.19
0.55
0.37
0.45
0.24
0.31
0.29
0.16
0.52
0.29
0.33
Chla0
Mean values (Longhurst, 2007)
ze
MLD
SST
2.92
2.08
5.42
8.67
9.92
3.21
6.13
4.29
1.38
6.58
3.63
3.88
49.5
63.3
46.8
50.0
40.0
62.9
55.8
53.3
68.8
44.2
55.2
55.0
34.7
41.7
43.0
87.9
67.9
49.2
32.9
22.5
43.8
23.0
36.2
61.3
24.04
23.03
23.45
13.96
17.82
22.83
26.01
27.56
23.71
26.94
25.56
19.62
T50
22.78
22.10
22.63
13.34
17.09
22.10
24.37
24.25
22.72
25.84
24.56
18.45
T0‐50
1.26
0.93
0.81
0.62
0.73
0.72
1.63
3.31
0.99
1.10
1.00
1.17
Chlai
32.19
13.24
15.72
16.72
25.63
17.06
18.35
23.33
21.38
17.89
15.77
12.96
Mean values in situ
DCM
SST
121.00
71.33
24.80
169.59 111.78
23.63
145.20
85.20
22.31
133.00
58.50
16.96
129.00
65.00
21.45
156.25
92.00
27.22
134.75
59.60
27.96
133.93
41.67
28.03
171.83 119.00
23.72
135.00
78.00
28.96
186.25 131.89
27.15
162.00 120.50
22.59
ze
T0_200
18.80
18.83
18.16
13.90
18.35
24.69
25.24
17.98
20.58
25.40
23.89
20.37
T0‐50
1.96
1.69
1.48
0.07
0.19
0.12
0.07
5.89
0.35
0.71
1.38
0.86
Mean values of biomass by province were not significantly correlated with either mean reported
primary production or surface chlorophyll (Table 3). However there was a positive correlation
between biomass in the 40-200 µm size class and temperature which can be described by a linear
function (Fig. 4) implying enhanced biomass of small plankton at high temperatures. This relationship
is consistent with the prediction of smaller body sizes with warming by macroecological theories
(Lopez-Urrutia et al., 2006). The strongest negative correlations were found between mean biomass in
several
size
classes and the
Table 3. Correlations (Pearson’s r) between mean values of plankton biomass
depth of the
(mg DW m-3) by size classes and oceanographic variables characterising the
mixing
layer
biogeochemical provinces. province: mean values from Longhurst (2007), in
(Table 3). In the
situ: mean values measured in this study. Yellow shading indicate signficant
case of total
values (P<0.05). Variable names as in Table 2.
biomass
this
DW40‐200
DW200‐500
DW500‐1000
DW1000‐2000 DW2000‐5000 DWtotal
PP
0.337
0.267
0.406
0.283
0.180
0.359
relationship can province
0.175
0.238
0.224
0.226
0.005
0.213
Chla0
be described by a
ze
‐0.328
‐0.308
‐0.378
‐0.244
‐0.144
‐0.343
negative power
MLD
‐0.655
‐0.584
‐0.517
‐0.588
‐0.329
‐0.607
SST
0.623
0.562
0.469
0.563
0.268
0.562
function
0.581
0.490
0.459
0.533
0.162
0.509
T50
indicating a rapid
T0‐50
0.515
0.633
0.280
0.425
0.659
0.538
decrease
of in situ
SST
0.664
0.518
0.480
0.544
0.088
0.522
DCM
‐0.483
‐0.587
‐0.366
‐0.580
‐0.729
‐0.595
biomass as the
0.442
0.217
0.323
0.368
‐0.432
0.227
T0_200
mixing
layer
0.302
0.440
0.190
0.171
0.722
0.388
T0‐50
Int. Chla
0.134
0.083
0.033
0.114
0.442
0.160
deepens but a
ze
‐0.439
‐0.446
‐0.373
‐0.503
‐0.582
‐0.518
stabilization of
5
this decrease at depths larger than 50 m (Fig. 4). Other studies have also reported the inverse
relationship between mesozooplankton biomass and the depth of the thermocline (Isla et al., 2004; San
Martín et al., 2006). In addition, positive correlations were found between thermal stratification in the
upper 50 m and biomass of some classes, particularly of macrozooplankton. However, this relationship
is caused by the large biomass and stratification found at PNEC, while there was no significant
correlation when values for this province were removed (Fig. 4). Similar correlations and relationships
were found when using mean values of environmental variables measured in situ during the Malaspina
cruises (Table 3).
30
6
DW40-200 (mg m-3)
DWtotal (mg m-3)
5
20
10
y = 98.98x-0.52
R² = 0.533
4
3
2
y = 0.154x - 0.656
R² = 0.441
1
0
0
0
20
40
60
80
100
10
20
MLD (m)
PNEC
4
3
2
y = 0.869x + 2.098
R² = 0.400
1
40
6
PNEC
5
DW2000-5000 (mg m-3)
DW200-500 (mg m-3)
6
30
SST (⁰C)
5
4
3
y = 0.783x + 1.673
R² = 0.434
2
1
0
0
0
1
2
3
4
T0-50 (⁰C)
0
1
2
3
4
A larger number of
significant
correlations
were found when using
concurrent measurements
of
environmental
variables and plankton
biomass (Table 4). The
detailed analysis of these
relationships,
however,
revealed that generally
non
linear
functions
provided the best fits and
that samples obtained at
PNEC provided most of
the variability (Fig. 5).
These results suggest that
T0-50 (⁰C)
the sampling of PNEC
included a larger range of
ecosystem states than for
the other provinces, as it
included stations located at
both geographic limits of
the
province,
thus
producing
relationships
between biomass and environmental variables similar to those observed at scales of the whole ocean
including all provinces. For instance, the increase of biomass with temperature and thermal
stratification or the negative relationship between biomass and the depth of the euphotic zone (Fig. 5)
mimic those found using mean
Table 4. Correlations (Pearson’s r) between values of plankton
provincial values (Fig. 4). In
biomass (mg DW m-3) by size classes and oceanographic
any case, the correlation
variables measured concurrently. Yellow shading indicate
coefficients were generally
signficant values (P<0.05). Variable names as in Table 2.
larger when using mean values
Figure 4. Example of significant relationships between mean values
of plankton biomass and oceanographic variables averaged by
biogeochemical province. The red lines and the equations indicate a
significant regression function (P<0.05). R2: determination
coefficient. Blue circles indicate the value for PNEC province.
Variable names as in Table 2.
than when using in situ values
at each station, despite the
lower number of data points in
the former.
While the decrease in plankton
biomass with the deepening of
SST
T50
T0‐50
DCM
T0_200
Int. Chla
ze
DW40‐200
DW200‐500
DW500‐1000
DW1000‐2000 DW2000‐5000 DWtotal
0.327
0.255
0.289
0.246
0.113
0.277
0.140
‐0.001
‐0.059
0.086
‐0.321
‐0.085
0.196
0.283
0.412
0.175
0.542
0.426
‐0.471
‐0.505
‐0.491
‐0.535
‐0.495
‐0.608
0.099
‐0.082
‐0.081
0.007
‐0.286
‐0.124
0.217
0.238
0.170
0.226
0.181
0.247
‐0.311
‐0.341
‐0.327
‐0.354
‐0.317
‐0.399
6
the mixing layer is consistent with the decrease in primary production in regions with low supply of
nutrients from deep layers, the increase in plankton biomass with temperature and thermal
stratification is contrary to the expected decrease in plankton with global warming (e.g. Behrenfeld et
al., 2006). These findings imply a low dependence between trophic transfer along the size spectrum
and primary production, suggesting that oligotrophic ecosystems of the tropical and subtropical ocean
are very efficient in the transfer of biomass up the food web despite their low primary production
values (San Martin et al., 2005). This interpretation is supported by the equivalence of biomass values
along the size classes (implying flat slopes of the biomass size spectrum) in most provinces and the
absence of significant correlations with primary production or chlorophyll values.
50
50
PNEC
40
DWtotal (mg m-3)
DWtotal (mg m-3)
40
30
20
10
PNEC
y = 0.895x + 12.55
R² = 0.181
30
20
10
R² = 0.161
0
0
10
20
30
40
0
5
SST (⁰C)
15
50
50
PNEC
30
20
PNEC
40
DWtotal (mg m-3)
40
DWtotal (mg m-3)
10
T0-50 (⁰C)
30
y = -0.098x + 29.45
R² = 0.161
20
10
10
R² = 0.130
0
0
0
10
20
30
integrated Chla (mg m-2)
40
0
100
200
300
ze (m)
Figure 5. Example of significant relationships between values of plankton biomass
and oceanographic variables measured concurrently. The red lines and the
equations indicate a significant regression function (P<0.05). R2: determination
coefficient. Blue circles and orange dots indicate samples from PNEC province.
Variable names as in Table 2.
Conclusions
Low plankton biomass (10-15 mg DW m-3) was found in most deep ocean subtropical and tropical
provinces (except PNEC). This biomass was almost constant along logarithmic classes of individual
body size in most provinces, suggesting steady state in the plankton.
Mean plankton biomass by province was not directly correlated with mean values of primary
production or surface chlorophyll. Instead, a negative correlation was found between biomass and the
depth of the upper mixing layer or the depth of the chlorophyll maximum, which resulted the best
predictors of biomass. Also at province level, small plankton biomass increased with SST and biomass
of other classes increased with stratification.
7
Local plankton biomass was correlated with integrated chlorophyll for some classes but all classes
were negatively correlated with the depth of the chlorophyll maximum or the depth of the euphotic
zone, best predictors of biomass. At local scale the biomass increases with SST and stratification were
due to the variability observed at PNEC.
These results contribute to the global database of plankton biomass and will allow for the estimation of
biomass in unexplored regions
Acknowledgements
We acknowledge the collaboration of the Commander Chief and crew of R/V Hesperides, to the Chief
Scientists and to the technicians of UTM-CSIC during the 7 legs of the cruise. Sampling of plankton
was achieved thanks to the coordinated participation of all scientists and technicians of Workpackage
7 (Zooplankton). CTD and chlorophyll data were provided by Workpackages 1 (Physical
oceanography) and 4 (Ocean optics). This research was funded by project Malaspina-2010 (CSD200800077) funded by program CONSOLIDER-INGENIO 2010 of the Ministerio de Ciencia e Innovación
(Spain), and by funds of the Instituto Español de Oceanografia (IEO). C.M. and J.B. were supported
by PFPI fellowships of IEO.
References
Behrenfeld, M.J., O’Malley, R.T., Siegel, D.A., McClain, C.L., Sarmiento, J.L., Feldman, G.C.,
Milligan, A.J., Falkowski, P.G., Letelier, R.M. and Boss, E.S., 2006. Climate-driven trends in
contemporary ocean productivity. Nature, 444: 752-755.
Gallienne, C.P., Robins, D.B. and Woodd-Walker, R.S., 2001. Abundance, distribution and size
structure of zooplankton along a 20° west meridional transect of the northeast Atlantic Ocean in
July. Deep-Sea Res. II, 48: 925-949.
Hoegh-Guldberg, O. and Bruno, J.F., 2010. The Impact of Climate Change on the World’s Marine
Ecosystems. Science, 328: 1523-1528.
Isla, J.A., Llope, M. and Anadón, R., 2004. Size-fractionated mesozooplankton biomass, metabolism
and grazing along a 50°N–30°S transect of the Atlantic Ocean. J. Plankton Res., 26: 1301-1313.
Jennings, S., Mélin, F., Blanchard, J.L., Forster, R.M., Dulvy, N.K. and Wilson, R.V., 2008. Globalscale predictions of community and ecosystem properties from simple ecological theory. Proc. R.
Soc. B., doi:10.1098/rspb.2008.0192.
Kerr, S.R. and Dickie, L.M., 2001. The biomass spectrum. Columbia University Press, New York, 320
pp.
Koppelmann, R. and Weikert, H., 1992. Full-depth zooplankton profiles over the deep bathyal of the
NE Atlantic. Mar. Ecol. Prog. Ser., 86: 263-232.
Longhurst, A.R., 2007. Ecological geography of the sea. Elsevier, Amsterdam, 542 pp.
Lopez-Urrutia, A., San Martin, E., Harris, R. and Irigoien, X., 2006. Scaling the metabolic balance of
the oceans. Proc. Natl. Acad. Sci. U.S.A. , 103: 8739-8744.
Moreno-Ostos, E. (Editor), 2012. Expedición de circunnavegación Malaspina 2010. Cambio global y
exploración de la biodiversidad del océano. Libro blanco de métodos y técnicas de trabajo
oceanográfico. Consejo Superior de Investigaciones Científicas (CSIC), Madrid.
Piontkovski, S.A., Williams, R., Ignatyev, S., Boltachev, A. and Chesalin, M., 2003. Structuralfunctional relationships in the pelagic community of the eastern tropical Atlantic Ocean. J.
Plankton Res., 25(9): 1021-1034.
Platt, T. and Denman, K., 1977. Organisation in the pelagic ecosystem. Helgoländer wiss.
Meeresunters., 30: 575-581.
8
Reid, P.C., Colebrook, J.M., Matthews, J.B.L., Aiken, J. and Team, C.P.R., 2003. The Continuous
Plankton Recorder: concepts and history, from Plankton Indicator to undulating recorders.
Progress in Oceanography 58: 117-173.
Rodriguez, J. and Mullin, M.M., 1986. Relation between biomass and body weight of plankton in a
steady state oceanic ecosystem. Limnol. Oceanogr., 31: 361-370.
San Martin, E., Harris, R.P. and Irigoien, X., 2006. Latitudinal variation in plankton size spectra in the
Atlantic Ocean. Deep Sea Res II, 53: 1560-1572.
Shin, Y.-J., Travers, M. and Maury, O., 2010. Coupling low and high trophic levels models: Towards
a pathways-orientated approach for end-to-end models. Progress in Oceanography, 84: 105-112.
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