Optimal multiparameter analysis of source water distributions

Author’s Accepted Manuscript
Optimal multiparameter analysis of source water
distributions in the southern drake passage
Marina Frants, Sarah T. Gille, Christopher D. Hewes,
Osmund Holm-Hansen, Mati Kahru, Aaron Lombrozo, Chris I. Measures, B. Greg Mitchell, Haili Wang,
Meng Zhou
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http://dx.doi.org/10.1016/j.dsr2.2012.06.002
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Deep-Sea Research II
Cite this article as: Marina Frants, Sarah T. Gille, Christopher D. Hewes, Osmund HolmHansen, Mati Kahru, Aaron Lombrozo, Chris I. Measures, B. Greg Mitchell, Haili Wang
and Meng Zhou, Optimal multiparameter analysis of source water distributions in the
southern drake passage, Deep-Sea Research II, http://dx.doi.org/10.1016/
j.dsr2.2012.06.002
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Optimal Multiparameter Analysis of Source Water
Distributions in the Southern Drake Passage
Marina Frantsa,∗, Sarah T. Gillea , Christopher D. Hewesa , Osmund
Holm-Hansena , Mati Kahrua , Aaron Lombrozoa , Chris I. Measuresc , B.
Greg Mitchella , Haili Wange , Meng Zhoud
a
Scripps Institution of Oceanography, University of California, San Diego, La Jolla,
California 92093-0202
b
University of Washington, Seattle, Washington 98195
c
University of Hawaii, Honolulu, Hawaii 96822
d
University of Massachusetts Boston, Massachusetts 02125
e
Xiamen University, Fujian Province,China
Abstract
In order to evaluate the effects of horizontal advection on iron supply in
the vicinity of the Shackleton Transverse Ridge (STR) in the southern Drake
Passage, the water composition in the region is estimated along the isopycnal
containing the subsurface iron peak. Optimal Multiparameter (OMP) analysis of temperature, salinity, oxygen and nutrient data is used to estimate
the water composition at CTD stations sampled in summer 2004 and winter
2006. The highest iron concentrations in the Ona Basin are found below the
mixed layer, both in summer and in winter. The water composition derived
from the OMP analysis is consistent with a scenario in which iron-rich shelf
waters from the South Shetland Islands and the Antarctic Peninsula are advected northward on the eastern side of the STR, where they interact with
∗
Corresponding author
Email address: [email protected] (Marina Frants)
Preprint submitted to Deep-Sea Research I
June 14, 2012
the low-iron waters of the Antarctic Circumpolar Current (ACC) in the Ona
Basin. The shelf waters and the ACC waters appear to interact through a
stirring process without fully mixing, resulting in a filamented distribution
that has also been inferred from the satellite data. To the west of the STR,
the shelf waters are primarily confined to the continental shelf, and do not
extend northwards. This source water distribution is consistent with the idea
that iron enters the Ona Basin from the continental shelf through advection
along an isopycnal, resulting in an iron concentration peak occurring below
the winter mixed layer in the Ona Basin.
Keywords: Southern Ocean, Drake Passage, Iron, OMP analysis, Ona
Basin
1
1. Introduction
2
Satellite-based and in situ measurements of phytoplankton abundance
3
in the Southern Ocean show a heterogeneous distribution, with regions of
4
high phytoplankton biomass occurring primarily in shallow waters near is-
5
lands and continental margins and in deeper waters located downwind and
6
downstream from land features that interrupt the flow field of the Antarc-
7
tic Circumpolar Current (ACC) between 45◦ and 60◦ S (Blain et al., 2001;
8
Sullivan et al., 1993). Since biological productivity in the pelagic Southern
9
Ocean is primarily iron-limited (Martin et al., 1990; Chisholm and Morel,
10
1991; de Baar et al., 1995; Boyd, 2002), these observations suggest that phy-
11
toplankton biomass in the open ocean is increased by the redistribution of
12
iron from shelf waters into pelagic waters in regions where mixing between
13
waters from different sources is enhanced by topographic features (Holm-
2
14
Hansen et al., 1997, 2004). However, the physical processes that drive the
15
regional differences in iron distribution are not yet well understood (de Baar
16
and de Jong, 2001). A number of possible mechanisms have been examined.
17
Whitehouse et al. (2008) found evidence of nutrient upwelling resulting from
18
diverging flow of the ACC over the shelf near South Georgia Island. Sokolov
19
and Rintoul (2007) have found that similar upwelling occurs wherever the
20
ACC interacts with topography. Hewes et al. (2009) observed that shallow
21
mixed-layer depths contribute to increased Chl-a levels near the South Shet-
22
land Islands. In situ observations near the Kerguelen Plateau (Blain et al.,
23
2001) and the Crozet Plateau (Venables et al., 2007) suggest that sediment
24
mixing in shallow waters near islands and continental shelves, followed by
25
downstream advection, can supply iron to facilitate blooms in off-shore wa-
26
ters.
27
In this study, we examine the water properties in the vicinity of the
28
Shackleton Transverse Ridge (STR) in Southern Drake Passage near the
29
Antarctic Peninsula (Figure 1a). The STR runs diagonally across our study
30
region, extending northwest into Drake Passage from Elephant Island (see
31
Figure 1b). The shallowest depth over the ridge is approximately 800 m,
32
while the basins on either side reach depths of over 4000 m; the gap between
33
the ridge and Elephant Island has a depth of over 3000 m. The flow of
34
the ACC around the topography creates a region of high mixing, as the
35
meridional meandering of the Southern ACC Front (SACCF) brings the ACC
36
waters into close proximity with the shelf waters off the Antarctic Peninsula
37
and the South Shetland Islands (Orsi et al., 1995), as well as with the Weddell
38
Sea waters flowing north toward the Scotia Sea (Barré et al., 2008; Brandon
3
39
et al., 2004; von Gyldenfeldt et al., 2002; Whitworth et al., 1994).
40
Satellite-derived Chlorophyll-a (Chl-a) images in this region (Kahru et al.,
41
2007) show a sharp gradient in surface chlorophyll levels in the vicinity of the
42
STR (Figure 1b). Low Chl-a water is located to the west of the ridge, and
43
high Chl-a water is found to the east in the Ona Basin and continues down-
44
stream into the southern Scotia Sea. Shipboard iron incubations conducted
45
across the gradient have shown that phytoplankton biomass in the western
46
Drake Passage is iron-limited, except in the shallow waters on the continental
47
shelf (Helbling et al., 1991; Hopkinson et al., 2007). The incubation results,
48
together with the low iron levels measured in the ACC west of the STR by
49
Martin et al. (1990), the iron distributions reported by Ardelan et al. (2010),
50
and the Chl-a distributions shown by Kahru et al. (2007), suggest that the
51
Ona Basin consistently has higher levels of iron than the surrounding waters.
52
Previous studies of hydrographic data in the vicinity of the STR and the
53
Antarctic Peninsula show the presence of Circumpolar Deep Water (CDW),
54
Bransfield Strait Water (BW) and Weddell Sea Deep Water (WSDW) (Zhou
55
et al., 2010b; Hofmann et al., 1996; Whitworth et al., 1994). The water col-
56
umn of the ACC is characterized primarily by CDW, overlaid by Antarctic
57
Surface Water (ASW) during the summer. On the continental shelf, interac-
58
tion between these water masses, combined with the effects of local cooling,
59
ice melt and precipitation effects, form the shelf waters (Hofmann et al., 1996;
60
Zhou et al., 2002, 2010b). Shelf waters flowing northward from the Weddell
61
Sea branch at the northern tip of the peninsula, with some of the waters
62
flowing eastward into the Weddell-Scotia Confluence and some flowing west-
63
ward and contributing to the formation of the BW (Hofmann et al., 1996;
4
64
Zhou et al., 2002). The BW, in turn, combines with the CDW from the ACC
65
to form the shelf waters around the South Shetland Islands (Hofmann et al.,
66
1996; Zhou et al., 2002). Since the shelf waters are iron-rich compared to
67
the ACC waters (Hopkinson et al., 2007), their distribution affects biological
68
productivity throughout the region.
69
To understand the iron sources associated with the water masses in our
70
study region and the horizontal transport and mixing mechanisms, we will
71
use Optimal Multiparameter Analysis (OMP) (Tomczak and Large, 1989) to
72
estimate the relative contributions of these waters for a region comprising
73
the deep basins to the east and west of the STR, the gap to the south of
74
the STR, and the continental shelf along the South Shetland Islands. Our
75
analysis is based on the assumption that advection moves water primarily
76
along isopycnals; therefore we examine source water distributions for the
77
isopycnal layer where the iron concentrations are highest in both summer
78
and winter. We also perform the analysis for the density range below the iron
79
peak, where water properties are more uniform and source water definitions
80
are more distinct. Use of the OMP method allows us to assess quantitatively
81
the horizontal propagation of iron-rich shelf waters within our study region.
82
2. Data and methods
83
Two cruises were conducted in the vicinity of the STR to study oceano-
84
graphic transport and its possible influence on biological activity in the On-
85
a Basin. In February and March 2004, the A.S.R.V. Laurence M. Gould
86
(LMG0402) collected hydrographic, chemical and biological data in the vicin-
87
ity of the STR. In July and August 2006, the I.B.R.V. Nathaniel B. Palmer
5
88
(NBP0606) revisited the area to collect similar measurements. In addition,
89
a survey by the U.S. Antarctic Marine Living Resources (AMLR) Program
90
was conducted in January and February of 2004, overlapping with LMG0402.
91
The locations of all the hydrographic stations are shown in Figure 2.
92
A total of 121 casts were made during LMG0402, and 192 casts were
93
made during NBP0606, all to 1000 m or 10 m above the bottom, whichever
94
was shallower. Each station included a rosette-CTD cast using a rosette
95
from the Raytheon Polar Service Company (RPSC) and/or a Trace Metal
96
Clean (TMC) rosette-CTD cast using a rosette from the University of Hawaii
97
(Measures et al., 2008). Temperature, salinity and oxygen measurements
98
were sampled during each RPSC and TMC cast using a SBE911 CTD and a
99
SBE42 oxygen sensor. In addition, samples for measuring phosphate, nitrate
100
and silicate concentrations were taken from bottles mounted on each rosette,
101
with 12 bottles per cast.
102
The 2004 NOAA-AMLR survey performed 91 CTD casts during Leg 1
103
(January-February) and 98 casts during Leg 2 (February-March), using a Sea-
104
Bird CTD mounted on a rosette equipped with 11 Niskin bottles. Nutrients
105
were sampled only during Leg 1. Lipsky (2004) provides a full description of
106
the instruments and methods used by the survey.
107
Two sets of CTD sensors were mounted on the RPSC rosettes and com-
108
pared against each other at the beginning and end of the cruise in order
109
to check for sensor drift. One set of sensors was used on the TMC rosette
110
during LMG0402 and compared against the RPSC sensors. Because the ther-
111
mocline waters in the study region are subject to high temporal variability,
112
comparisons of RPSC vs. TMC sensors were done only for the 24 stations
6
113
for which RPSC and TMC casts were performed within four hours of each
114
other, and where the casts reached a depth of at least 1000 m. All sensor
115
pair comparisons showed temperature differences within 0.01◦ C and salinity
116
differences within 0.01 ppt. (Zhou et al., 2010a). In addition to the CTD
117
casts, 36 expendable CTDs (XCTDs) were dropped during NBP0606 but
118
were not included in the analysis due to possible instrument bias.
119
Dissolved iron concentrations were determined from water samples taken
120
with the TMC rosette at locations indicated by the shaded circles in Figure 2.
121
The concentrations were originally determined on board ship using the flow
122
injection analysis method and subsequently reprocessed using inductively
123
coupled plasma mass spectrometry (ICP-MS) (?). Only a limited amount
124
of data was obtained in the ACC waters with the lowest iron concentrations
125
during LMG0402. Furthermore, iron was not measured during the 2004
126
NOAA-AMLR survey. In this study, we use the iron profiles to identify a
127
density range corresponding to the subsurface iron peak but, since the iron
128
data are sparse, we do not use iron as a parameter in the OMP analysis.
129
However, other water properties, such as temperature, salinity, oxygen and
130
nutrients, can be used to analyze the distribution of waters originating on
131
the Antarctic shelf, (Hewes et al., 2008), which are known to be high in iron
132
throughout the region (Hewes et al., 2008; Ardelan et al., 2010).
133
The oxygen concentrations measured by the RPSC sensors during LMG0402
134
and NBP0606 were calibrated by using Winkler titration oxygens from se-
135
lected rosette bottles. Potential density for each titration was calculated
136
from the CTD data at the depth of the bottle closures, and oxygen values
137
from the titrations were compared against the sensor readings at matching
7
138
densities during the downcasts. Oxygen samples were not drawn from the
139
bottles mounted on the TMC rosette, so the TMC oxygens were calibrated
140
using only the stations where titrations from an RPSC cast were available
141
for the same location. The AMLR oxygen concentrations were not calibrated
142
on board ship, since no titrations were conducted during the survey.
143
2.1. Iron distribution and selection of the density range for OMP analysis
144
Profiles of iron versus density for the stations sampled in the Ona Basin
145
during LMG0402 and NBP0606 are shown in Figure 3. While the LMG0402
146
concentrations throughout the water column are significantly lower than the
147
NBP0606 values, the highest iron concentrations for both cruises were ob-
148
served below the mixed layer, in the depth range from 100 to 200 m. For
149
the Ona Basin profiles, the iron maximum for most stations is located at a
150
potential density surface in the range 27.5≤ σθ ≤27.6, which is the range we
151
selected as the focus for our analysis. The thickness and median depth of
152
this density layer are shown in the top rows of Figure 4 for LMG0402 and
153
Figure 5 for NBP0606.
154
The 27.5≤ σθ ≤27.6 density range was chosen to be wide enough to
155
include at least one nutrient bottle sample for all stations included in the
156
analysis. However, the nutrient profiles in this range show high gradients that
157
may affect the OMP results once the nutrient values are vertically averaged
158
to compute the OMP inputs. To reduce this effect and better evaluate the
159
vertical consistency of our results, we also examine the density layer below
160
the iron maximum, defined as 27.6≤ σθ ≤27.7, where the nutrient gradients
161
are small. The thickness and median depth for this deeper layer are shown
162
in the bottom rows of Figure 4 for LMG0402 and Figure 5 for NBP0606.
8
163
For both cruises, the two density layers are thicker in the deep waters to
164
the west of the STR than the deep waters to the east. For LMG0402, both
165
layers are thinnest over the continental shelf on both sides of the ridge, and
166
become thicker away from the shelf. For NBP0606, the layers are thinnest
167
for shelf transects A and C (Figure 2 b), where the end point stations for the
168
shelf waters used in our OMP analysis are defined.
169
2.2. Selecting source water for OMP analysis
170
Optimal Multiparameter analysis, as developed by Tomczak and Large
171
(1989) and described in detail in Appendix A, is based on the assumption that
172
observed water properties at a hydrographic station are the result of mixing
173
among two or more “source waters”. Usually the source waters are assumed
174
to be linear combinations of two or more sea water types (SWTs), whose
175
physical and chemical properties are known (Tomczak and Large, 1989).
176
The input values for the OMP computation are then determined by linear
177
regression of all parameters against temperature. By limiting our analysis to
178
a vertically narrow isopycnal layer, we were able to define each of our source
179
waters as a single SWT. This approach allowed us to determine the input
180
values directly from observations by taking measurements of each parameter
181
at selected end point stations and averaging them vertically within the layer
182
where the analysis would be performed.
183
Appropriate definition of source water properties is crucial to achieving
184
physically meaningful results from OMP. To identify the stations that best
185
represent the source waters for our region, we compared the temperature-
186
salinity (TS) profiles from the CTD casts in our data set against the charac-
187
teristic TS properties of the water masses in Drake Passage (Whitworth et al.,
9
188
1994; Hofmann et al., 1996; Zhou et al., 2010b). We considered potential end
189
points in the ACC, the Bransfield Strait, and on the continental shelf, with
190
additional consideration given to differences between the shelf waters to the
191
east and west of the STR.
192
Figure 6 shows the TS profiles for stations used to select potential OMP
193
end points for summer (Figure 6a) and winter (Figure 6b). Profiles plotted
194
in red represent stations located north of the SACCF and east of the STR,
195
where the ACC flow can be expected to dominate. All stations in both
196
years show the typical CDW profile, with Upper Circumpolar Deep Water
197
(UCDW) profile below the 27.2 isopycnal, consistent with previous sections
198
across Drake Passage (Brandon et al., 2004). Above the 27.2 isopycnal, the
199
LMG0402 stations show the warmer and slightly fresher Antarctic Surface
200
Water (ASW) layer that is not present during NBP0606, as is consistent with
201
surface warming during the summer months.
202
The shelf water profiles in Figure 6 are plotted in green for stations west
203
of the STR, and blue for stations to the east. During LMG0402, the western
204
stations fall into two distinct clusters. One cluster shows the characteris-
205
tic CDW profile, closely overlapping with the ACC profiles above the 27.2
206
isopycnal, but becoming consistently colder than the ACC for σθ >27.2, con-
207
sistent with local cooling of the CDW. The other cluster shows colder, saltier
208
shelf waters consistent with the intrusion of BW into the shelf waters around
209
the South Shetland Islands. However, the TS profiles in the second cluster
210
could not be easily distinguished from the profiles east of the STR. For the
211
NBP0606 profiles, the differences between the two clusters of the western
212
shelf stations are less distinct, and the coldest of the western shelf stations
10
213
once again show significant overlap in water properties with the eastern shelf
214
stations.
215
Profiles from the Bransfield Strait are plotted in magenta in Figure 6.
216
For LMG0402, the BW profiles are similar to the SW profiles sampled east
217
of the STR, but with temperatures up to 0.5◦ C colder than SW in our chosen
218
density range. During NBP0606, when the Bransfield Strait stations were
219
sampled in a high-resolution transect across the entire strait, the TS profiles
220
overlap with the SW profiles both east and west of the STR, reflecting the
221
difference in water properties between the northeastward flow of the Brans-
222
field Current along the southern shelf of the South Shetland Islands and the
223
southwestward countercurrent in the southern part of the strait (Hofmann
224
et al., 1996; Zhou et al., 2002, 2006).
225
Temperature and salinity alone suggest two potential source waters for
226
OMP analysis, one representing the ACC and one representing all shelf wa-
227
ters (SW) in the study region. However, circulation studies based on drifter
228
tracks and ADCP measurements (Zhou et al., 2002; Thompson et al., 2007,
229
2009; Niiler et al., 1991; Whitworth et al., 1994) suggest that the shelf wa-
230
ters upstream of the STR are modified by Bransfield Water, while the shelf
231
waters downstream are influenced by outflow from the Weddell Sea. There-
232
fore, the upstream and downstream shelf waters can potentially represent
233
two separate source waters, with ACC as the third source. OMP analysis
234
allows for the inclusion of other parameters, such as nutrients, oxygen and
235
potential vorticity, which may help distinguish waters that have similar TS
236
properties but originate from different sources. While nutrient concentra-
237
tions are affected by biogeochemical processes and cannot be assumed to be
11
238
conserved during mixing, Karstensen and Tomczak’s (1998) extension of the
239
original OMP method accounts for these changes through the use of Redfield
240
ratios, further explained in Appendix A. The nutrient data allow us to make
241
further distinction between the shelf waters to the east and west of the STR.
242
We will refer to the SW on the western side of the STR as SW1, and to the
243
SW on the eastern side as SW2. The additional parameters also allow us to
244
test the suitability of BW as an additional source water, both as a potential
245
fourth source and as a replacement for either SW1 or SW2 in a three-source
246
scenario.
247
The potential vorticity (PV) for our analysis was computed as
N 2f
PV =
,
g
(1)
248
where N is the buoyancy frequency, f is the Coriolis frequency, and g is the
249
gravitational acceleration. As seen in Figures 4 and 5, the density layers
250
covered in our analysis are thickest in the northwest portion of our sampling
251
region, where the CDW TS properties dominate, and thinnest on the shelf.
252
The resulting difference in potential vorticity helps us to further distinguish
253
the ACC waters from the shelf waters.
254
To select appropriate stations for defining our source waters, we defined
255
a parameter space of seven dimensions: temperature, salinity, oxygen, phos-
256
phate, nitrate, silicate and PV. At each station, a seven-element vector of
257
these parameters was computed by vertically averaging the values of each
258
parameter over the 27.5≤ σθ ≤27.6 density layer. Each vector was then nor-
259
malized following Karstensen and Tomczak’s (2005) method as described in
260
Equation A.2 in Appendix A. To ensure that the results of the OMP analy12
261
sis most fully describe the water composition in our region, it is desirable to
262
select stations whose property vectors most fully span our parameter space
263
to represent our source waters. If using two source waters, this criterion can
264
be satisfied by choosing two stations whose coordinate vectors place them
265
farthest apart in the parameter space. To select three source waters, we can
266
view them as points defining a triangle in the parameter space, and select
267
the three stations whose coordinate vectors span the largest triangle area.
268
By extension, an ideal four-source scenario would use four points defining a
269
solid with maximum volume in the parameter space. However, preliminary
270
tests with a four-source scenario showed that it did not represent the mixing
271
in the region as well as a three-source scenario, and the possibility of a fourth
272
source water was not explored in greater detail.
273
The locations and averaged water properties of the source water stations
274
selected for the two-source and three-source scenarios are shown in Tables 1
275
and 2. The profiles for these stations are plotted as solid and dashed lines in
276
Figure 6.
277
2.3. Sensitivity analysis
278
To obtain a quantitative measure of the robustness of our computed
279
source water distributions, we examined the sensitivity of our results to ran-
280
dom variations in the source water definitions. A total of 100 iterations of
281
a Monte Carlo simulation were performed. For each iteration, random per-
282
turbations for each parameter – temperature, salinity, oxygen and nutrients
283
– were generated from a zero-mean Gaussian distribution with the same s-
284
tandard deviation as the measured parameter within each source water. A
285
standard deviation of the difference between the simulated scenarios and the
13
286
unperturbed scenario was computed for the fractional contribution from each
287
source water at every station, as well as a mean standard deviation for the
288
entire region. Standard deviations for the mass residuals at each station were
289
also computed.
290
As an alternative sensitivity estimate, we also examined the standard
291
deviations of each source water distribution within the isopycnal layer prior
292
to averaging. The resulting sensitivity values (not shown) were smaller than
293
the values given by the Monte Carlo method for 85% of all stations. Since
294
this estimate does not account for measurement bias or for the high degree of
295
correlation likely to exist for vertically adjacent points within an isopycnal, we
296
chose the Monte Carlo method as a more complete measure of the sensitivity
297
of our results.
298
3. Results and discussion
299
We performed the OMP analysis for all CTD stations, using as inputs
300
the averaged temperature, salinity, nutrient and PV values for the density
301
range illustrated in the top row panels of Figures 4 and 5. The source water
302
distributions were computed twice, once for the two-source and once for the
303
three-source scenario. Changing the number of source waters in the analysis
304
affects the residuals computed by OMP. Therefore the two-source and three-
305
source scenarios cannot be meaningfully compared based on the residuals.
306
Instead, we compared the scenarios by calculating a chi-square (χ2 ) estimator
307
(Press et al., 1986) for the standard deviation of individual parameters at all
308
stations, and computed the probability of exceeding a given χ2 value with
309
random data. The details of the method are given in Appendix B.
14
310
The resulting source water distributions are illustrated by the pie charts
311
in Figure 7, and the spatially averaged results of the Monte Carlo sensitivity
312
analysis for the entire study region are summarized in Table 4. The distri-
313
butions for individual LMG0402 and AMLR stations are shown in Figure 7a
314
for the three-source scenario and Figure 7b for the two-source scenario. The
315
same scenarios for NBP0606 are illustrated in Figure 7c and d. Stars indi-
316
cate the locations of the stations used to define the source waters for each
317
scenario. The different criteria for two-source and three-source selections, as
318
described in Section 2.2, resulted in different stations representing the ACC
319
source water in the two scenarios. For comparison, we also performed the
320
analysis using the same ACC definition for both scenarios. The results for
321
individual stations (not shown) did not differ from the results in Figure 7
322
by more than the standard deviation computed from the sensitivity analysis
323
described in Section 2.3.
324
Upstream of the STR, where the density layer is thickest, the distributions
325
for both summer and winter show the ACC water as the dominant water mass
326
in the region, with little or no shelf water present in the stations north of
327
the 2500 m bathymetry contour. This part of the region is also characterized
328
by low iron (Martin et al., 1990; Hewes et al., 2008; Ardelan et al., 2010)
329
and low Chl-a (Figure 1b). Downstream of the STR, where the Chl-a levels
330
are elevated, The three-source scenario shows the shelf waters dominating
331
the water composition, with 60% of LMG0402 stations and 67% of NBP0606
332
CTD stations in the 3-source scenario showing ACC contributions of less than
333
5% (Figure 7a and 7c). This distribution is consistent with Zhou et al.’s
334
(2010a) conclusion that the ACC flow east of the STR is redirected to the
15
335
northeast by conservation of potential vorticity.
336
One unexpected result of the analysis was the inconsistency between the
337
two-source and three-source scenarios for NBP0606, as seen in Figure 7c and
338
d. The two-source scenario shows ACC water present throughout the region,
339
including the shelf stations on both sides of the STR. A possible reason for
340
the inconsistency between the two and three-source scenarios for NBP0606
341
comes as a result of the averaging of the input parameters within a density
342
layer. For NBP0606, the nutrient profiles for the selected source waters show
343
high gradients in the 27.5≤ σθ ≤27.6 density layer, with overlapping values
344
between the ACC and shelf water profiles. Averaging over the density layer
345
produces values for ACC, SW and SW1 that cannot be easily distinguished.
346
The similarities in the source waters are reflected in the higher uncertainties
347
produced by the Monte Carlo analysis for the NBP0606 data (Table 4).
348
A clearer distinction between the ACC and shelf waters can be seen on the
349
27.6≤ σθ ≤27.7 isopycnal (Figure 8 c and d), where the source water nutrient
350
profiles do not overlap, and the gradients are smaller.
351
The three-source scenarios for both summer and winter show both SW1
352
and SW2 present upstream and downstream of the STR, with SW1 proper-
353
ties dominating. However, our sensitivity analysis indicates that the stations
354
dominated by mixing between SW1 and SW2 show the highest sensitivity to
355
small perturbations in the source water definitions, suggesting that the prop-
356
erties of SW1 and SW2 are not sufficiently different to be well-distinguished
357
by the OMP analysis. The χ2 estimator test indicates a probability difference
358
of less than 0.5% between the two-source and three-source scenarios, and the
359
ACC contributions between the two scenarios showed no statistically signifi-
16
360
cant changes, with differences at all stations being smaller than the standard
361
deviations computed in our sensitivity analysis. The similarity between the
362
two scenarios suggests intermixing among shelf waters in the sampling re-
363
gion, with Weddell Sea waters influencing the hydrographic properties at all
364
shelf stations. Such mixing is consistent with past hydrographic (Niiler et al.,
365
1991; von Gyldenfeldt et al., 2002) and drifter (Zhou et al., 2002) studies,
366
which indicate that some northward-flowing Weddell Sea waters turn south-
367
westward at the tip of the Antarctic Peninsula and intrude into the Bransfield
368
Strait and the shelf break around the South Shetland Islands.
369
The distributions for the three-source scenarios that included BW as a
370
source point (not shown) were similar to the three-source distribution shown
371
in Figure 7, with a mixture of BW and SW dominating the circulation east of
372
the STR. However, both the sensitivity analysis described in Section 2.3 and
373
the χ2 estimator computed following the method in Appendix B indicate that
374
the waters in the Ona Basin are more accurately represented as a combination
375
of ACC and shelf waters only, with BW affecting the circulation primarily
376
through its influence on the shelf waters west of the STR.
377
Distribution of water properties in the ocean is affected by stirring, which
378
redistributes properties through advection while maintaining the presence of
379
gradients, and by mixing, which decreases the gradients through diffusion
380
(Eckart, 1948). Abraham et al. (2000) have demonstrated the importance of
381
horizontal stirring in the development and sustainment of an iron-fertilized
382
bloom. The OMP-derived distributions in Figure 7 show that within the
383
Ona Basin, in the central part of our study region, the water composition
384
varies from station to station. Adjacent stations are frequently dominated by
17
385
different source waters. Using Argo data, Barré et al. (2008) found similar
386
patchiness of potential temperature, salinity and σθ distributions in the same
387
region. Such variable distribution near the ridge is consistent with a filament-
388
ed structure that could be caused by advective stirring. Farther downstream,
389
the easternmost LMG0402 stations show a more uniformly mixed water com-
390
position dominated by shelf waters, suggesting that the waters are retained
391
within the basin long enough for the stirring to lead to mixing, homogenizing
392
the water properties as the water advects downstream. Such a scenario is
393
consistent with Argo floats becoming trapped in the basin for periods rang-
394
ing from 6 to 20 months between 2002 and 2006 (Barré et al., 2008). For
395
NBP0606, the stations at the eastern edge of the study region are too few
396
and too closely spaced to determine if homogenized mixing has taken place.
397
The source water distributions along the 27.6≤ σθ ≤27.7 density layer,
398
shown in Figure 8, indicate that the source water distributions for LMG0402
399
are vertically consistent over different density ranges, while the distributions
400
for NBP0606 show a clearer distinction between ACC and shelf waters, with
401
ACC waters present only in the northernmost stations. These distributions
402
were calculated using the same end point station locations as the iron peak
403
layer. For the three-source scenario, the distributions for NBP0606 (panel c)
404
are largely the same as in the iron maximum layer, with a slightly greater
405
presence of SW1 in the Ona Basin, and ACC water still dominant west of
406
the STR. The LMG0402 distribution (panel a) shows a smaller presence of
407
ACC water throughout the region, but retains the filamented distribution in
408
the Ona Basin with homogenized mixing in the east. Distributions computed
409
with endpoints optimized for the 27.6≤ σθ ≤27.7 layer (not shown) slightly
18
410
increase the ACC concentrations west of the STR, but do not significantly af-
411
fect the results for the Ona Basin. The two-source distribution for LMG0402
412
(panel b) is similar to the distribution for the 27.5≤ σθ ≤27.6 density lay-
413
er, while the two-source distribution for NBP0606 (panel d) shows a higher
414
proportion of ACC waters, especially for stations where SW1 is dominant in
415
the three-source scenario, suggesting a stronger winter influence of CDW in
416
this density range on the shelf waters west of the STR.
417
The extended OMP analysis for the two-source scenario on the 27.5≤
418
σθ ≤27.6 isopycnal produced ∆P values of 0.014 ± 0.004 µmol/kg for LMG0402
419
and 0.20 ± 0.014 µmol/kg for NBP0606. The higher value for NBP0606 runs
420
counter to the expectation that nutrient changes should be small in winter,
421
when phytoplankton growth is low. However, physical processes such as
422
winter upwelling and deep-penetrating air-sea interactions may also affec-
423
t wintertime nutrient concentrations. In addition, the higher uncertainties
424
in the NBP0606 source water distributions suggest that the ACC and SW
425
properties are less distinct in winter than in summer. Since temperature
426
and salinity are weighted higher than nutrients in our wintertime analysis,
427
computational inconsistencies in the OMP analysis may be reflected more
428
strongly in the ∆P values.
429
While the winter distributions shown in Figures 7 and 8 are consistent
430
with the summer distribution in showing the increased presence of shelf wa-
431
ters in the Ona Basin compared to the ACC-dominated waters to the west
432
of the STR, the CTD casts during NBP0606 did not sample far enough off-
433
shore to determine if the filamented distribution seen in the summer months
434
is still present in winter.
19
435
4. Summary
436
In this study, we have used CTD data from multiple surveys to perform an
437
OMP analysis of the source water distribution in the southern Drake Passage
438
during the summer of 2004 and the winter of 2006. The extended version of
439
the OMP analysis was used, incorporating Redfield ratios to partially account
440
for the biogeochemical changes. The results give us the means to assess the
441
horizontal distribution of iron-rich shelf waters in our study region.
442
Adjacent stations near the STR in the Ona Basin show very different
443
source water compositions, consistent with a filamented distribution created
444
by advective stirring. Farther downstream, the source water distribution be-
445
comes more uniform, suggesting that the waters in the basin are retained long
446
enough for the stirring to eventually lead to homogeneous mixing. Satellite-
447
derived Chl-a images (Kahru et al., 2007) also demonstrate filamentation,
448
with adjacent strands of high and low Chl-a found in eddies and frontal
449
zones.
450
While the shelf waters near the South Shetland Islands are geographically
451
separated from the shelf waters near the Weddell Sea (Hofmann et al., 1996;
452
Zhou et al., 2010b), treating the two as separate shelf water sources did
453
not produce statistically significant improvements in either the χ2 estimator
454
or the sensitivities computed from the Monte Carlo simulation described in
455
Section 2.3. The similarities between the results of the two-source and three-
456
source scenarios for both density ranges analyzed during LMG0402 and for
457
the 27.6≤ σθ ≤27.7 range during NBP0606 suggest that the shelf waters are
458
not sufficiently distinct in their TS and nutrient properties to justify treating
459
them as separate source waters for the purposes of our analysis. By contrast,
20
460
the χ2 and sensitivity results for scenarios that include the Bransfield Strait
461
indicate that BW does not directly contribute to the mixing in the Ona
462
Basin but instead influences the source water distributions in the basin only
463
indirectly, thorough its influence on the shelf waters.
464
The distributions shown in Figures 7 and 8 indicate that in the density
465
range where iron concentration is highest, shelf waters from both east and
466
west of the STR flow into the Ona Basin. Previous studies of circulation in
467
the region (Brandon et al., 2004; Barré et al., 2008) indicate the presence
468
of persistent deep mesoscale eddies that trap water in the basin. In Barré
469
et al.’s (2008) study, Argo floats released in March 2002 and December 2003
470
remained in the basin for periods ranging from six months to two and a half
471
years. Such long retention times, combined with the offshore advection of
472
shelf waters suggested by our analysis, would allow for a build up of high
473
iron concentrations below the mixed layer in the Ona Basin. A companion
474
paper, Frants et al. (2012), explores some of the physical mechanisms that
475
may enable the iron from the subsurface maximum to reach the euphotic
476
zone.
477
Acknowledgments
478
The authors thank James Swift of Scripps Institution of Oceanography,
479
Christian Reiss of Southwest Fisheries Science Center, William T. Hiscock of
480
the Universität Bern, Switzerland, the crews of the R/V Laurence M. Gould
481
and the R/V Nathaniel B. Palmer, the members of the AMLR survey, and
482
the employees of the Raytheon Polar Services Company.
483
The funding for this research was provided by the National Science Foun21
484
dation, grants # ANT0444134, ANT0948338, OCE0957342 and OCE0622740.
22
485
Figure Captions
486
Figure 1: (a) Drake Passage bathymetry with study region indicated
487
by the red rectangle. Front definitions are taken from Orsi et al. (1995).
488
The abbreviations are: Shackleton Transverse Ridge (STR), Elephant Island
489
(EI), Polar Front (PF), Southern ACC Front (SACCF), Antarctic Peninsula
490
(AP), Powell Basin (PB) and Weddell Sea (WS). (b) A composite of Chl-a
491
distribution in the study region from January 1 to March 31 2004, computed
492
from SeaWiFS and MODIS-Aqua satellite data.
493
Figure 2: Station locations and source water points for (a) the LMG0402
494
and AMLR and (b) NBP0606 cruises. In (a), circles represent LMG0402 CT-
495
D stations, triangles represent TMC stations and diamonds represent AMLR
496
CTD stations. In (b), circles represent CTD stations and squares represent
497
XCTD casts. In both panels, stars identify the stations used as source points
498
for the three-source scenario in the OMP analysis and pentagons mark the
499
source points for the two-source scenario. Grey circles mark stations where
500
iron was sampled.
501
Figure 3: Profiles of iron concentration vs. density in the Ona Basin for
502
(a) March 2004 (LMG0402) and (b) August 2006 (NBP0606). The 27.5≤
503
σθ ≤27.6 density layer is indicated by the gray horizontal lines. Diamonds
504
indicate the iron maximum at each individual station.
505
Figure 4: Top row: median depth (a) and thickness (b) of the 27.5≤
506
σθ ≤27.6 density range containing the iron peak for LMG0402. Bottom row:
507
median depth (c) and thickness (d) of the density range 27.6≤ σθ ≤27.7.
508
Figure 5: Top row: median depth (a) and thickness (b) of the 27.5≤
509
σθ ≤27.6 density range containing the iron peak during NBP0606. Bottom
23
510
row: median depth (c) and thickness (d) of the density range 27.6≤ σθ ≤27.7.
511
Figure 6: Temperature and salinity profiles for stations used to determine
512
source water properties for OMP analysis. For the three-source scenario,
513
solid red lines represent the stations chosen to represent the source waters
514
for (a) LMG0402 and (b) NBP0606. Solid green lines represent the SW1
515
source water stations, and solid blue lines represent the SW2 stations. For
516
the two-source scenarios, dashed lines represent the stations chosen for ACC
517
and SW. During NB060, the same station was selected to represent SW2 and
518
SW in both scenarios. Dotted lines in each color represent the other stations
519
sampled within the same source water.
520
Figure 7: Source water distributions along the 27.5≤ σθ ≤27.6 isopycnal
521
computed with OMP analysis during LMG0402 (a and b) and NBP0606 (c
522
and d). The pie charts show station locations, and stars show the locations of
523
source point stations. The source waters for the three-source scenario (a and
524
c) are ACC water (ACC), Shelf Water 1 (SW1), and Shelf Water 2 (SW2).
525
The source waters for the two-source scenario (b and d) are ACC and Shelf
526
Water (SW). Pie charts circled in black represent stations where Monte Carlo
527
analysis produced a root-mean-square difference of more than 0.05 from the
528
unperturbed case.
529
Figure 8:Source water distributions along the 27.6≤ σθ ≤27.7 isopycnal
530
computed with OMP analysis using only CTD stations during LMG0402 (a
531
and b) and NBP0606 (c and d). Symbols and colors are as in Figure 7.
24
532
25
NO3 (µmol/kg)
Pot. Vort
1.84
34.46
189
2.4
35.1
54.5
0.10
SW1
-61.20
-58.03
1.56
34.44
228
2.7
51.4
115.3
0.10
SW2
-60.51
-58.70
1.37
34.42
208
2.2
33.1
69.1
0.21
Longitude
ACC -60.52 -57.26
Latitude
Si (µmol/kg)
PO4 (µmol/kg)
02 (µmol/kg)
Salinity (psu)
Temperature (◦ C)
Source Water
Table 1: Definitions of source water end points used for the three-source OMP analysis.
27.5≤ σ ≤27.6 LMG0402+AMLR
27.6≤ σ ≤27.7, LMG0402+AMLR
ACC -60.53 -57.26
2.08
34.61
171
2.4
34.6
74.9
0.06
SW1
-61.20
-58.03
1.80
34.59
175
2.3
34.3
70.3
0.10
SW2
-60.51
-58.70
1.33
34.54
191
2.3
34.7
75.3
0.08
27.5≤ σ ≤27.6, NBP0606
ACC -60.50 -58.56
0.81
34.38
217
1.9
31.8
71.7
-0.18
SW1
-61.61
-57.73
0.49
34.36
297
1.9
33.9
75.7
-0.88
SW2
-61.25
-54.88
-0.55
34.26
288
1.7
32.6
77.2
0.06
27.6≤ σ ≤27.7, NBP0606
ACC -60.50 -58.56
2.07
34.61
173
2.2
34.6
79.2
0.07
SW1
-61.61
-57.73
0.25
34.43
264
2.0
31.2
75.4
0.08
SW2
-61.25
-54.88
-0.37
34.42
265
1.8
35.0
87.3
-0.02
26
NO3 (µmol/kg)
Si (µmol/kg)
Pot. Vort
2.2
31.9
54.5
0.10
SW
1.37
34.42
208
2.2
33.1
69.1
0.22
02 (µmol/kg)
189
Salinity (psu)
34.45
Longitude
1.80
Latitude
ACC -60.25 -58.70
Source Water
PO4 (µmol/kg)
Temperature (◦ C)
Table 2: Definitions of source water end points used for the two-source OMP analysis.
27.5≤ σ ≤27.6 LMG0402+AMLR
-60.51 -55.04
27.6≤ σ ≤27.7, LMG0402+AMLR
ACC -60.25 -58.70
2.08
34.61
171
2.4
34.6
74.9
0.06
SW
2.03
34.62
198
2.4
44.3
93.6
0.06
-60.51 -55.04
27.5≤ σ ≤27.6, NBP0606
ACC -60.75 -58.37
SW
-61.32 -54.88
1.69
34.45
189
2.2
37.7
64.8
0.11
-1.24
34.23
316
1.9
26.1
77.9
0.13
27.6≤ σ ≤27.7 , NBP0606
ACC -60.75 -58.37
SW
-61.25 -54.88
2.00
34.60
173
2.2
30.0
74.1
-0.79
-0.53
34.42
276
1.8
34.6
77.3
0.09
27
Table 3: Weights used for OMP analysis in summer 2004 (LMG0402) and winter 2006
(NBP0606).
3-source
Parameter
2-source
LMG0402
NBP0606
LMG0402
NBP0606
Temperature
10
10
9
9
Salinity
10
11
7
13
Oxygen
7
25
7
15
16
4
2
2
Nitrate
8
3
6
3
Silicate
17
4
2
1
Pot. Vorticity
11
19
19
14
Phosphate
Table 4: Spatially averaged standard deviations of source water distributions, computed
from a 100-iteration Monte Carlo simulation. The original distributions are given as
percentage contributions of each source water to the total mixing at each station, and the
percentages in the table represent absolute deviations from the unperturbed case.
LMG0402+AMLR
NBP0606
Source 27.5≤ σ ≤27.6 27.6≤ σ ≤27.7
Water
27.5≤ σ ≤27.6
27.6≤ σ ≤27.7
Isopycnal
Isopycnal
Isopycnal
Isopycnal
ACC
2.2%
1.8%
5.0%
3.9%
SW1
2.9%
5.1%
3.4%
5.0%
SW2
1.7%
4.5%
4.0%
4.8%
28
533
29
54˚S
a
58˚S
00
60˚S
60˚S
62˚S
64˚S
62˚S
00
-40
-40
00
00
-30
-1000
0
-200
0
-100
63˚S
0
64˚S
64˚W 60˚W 56˚W 52˚W 48˚W
62˚W 60˚W 58˚W 56˚W 54˚W 52˚W
mg m-3
m
-8000
-6000
-4000
-2000
0
0.05
0.10
0.60
1.00
Figure 1: (a) Drake Passage bathymetry with study region indicated by the red rectangle.
Front definitions are taken from Orsi et al. (1995). The abbreviations are: Shackleton
Transverse Ridge (STR), Elephant Island (EI), Polar Front (PF), Southern ACC Front
(SACCF), Antarctic Peninsula (AP), Powell Basin (PB) and Weddell Sea (WS). (b) A
composite of Chl-a distribution in the study region from January 1 to March 31 2004,
computed from SeaWiFS and MODIS-Aqua satellite data.
30
0
-3
-30
00
00
-40
61˚S
Ona Basin
.
S
TR
PF
ls
s
I
t
d
ai
n
r
a
F tl EI
St
CC
SA She eld
i
PB
.
AP
So nsf
a
WS
Br
00
b
-40
56˚S
59˚S
59˚S
a
-3
-400
0
00
00
0
000
-3000-2-0100
61˚S
62˚S
63˚S
0
00
-4
59˚S
60˚S
00
00
-40
-40
60˚S
-400
0
0 4
b
-3
00
0 40
00
000
-3000-2-0100
61˚S
0
00
-4
0
-100
62˚S
-100
0
0
63˚S
0
0
-100
64˚S
62˚W 60˚W 58˚W 56˚W 54˚W
0
-100
62˚W 60˚W 58˚W 56˚W 54˚W
Figure 2: Station locations and source water points for (a) the LMG0402 and AMLR and
(b) NBP0606 cruises. In (a), circles represent LMG0402 CTD stations, triangles represent
TMC stations and diamonds represent AMLR CTD stations. In (b), circles represent CTD
stations and squares represent XCTD casts. In both panels, stars identify the stations used
as source points for the three-source scenario in the OMP analysis and pentagons mark
the source points for the two-source scenario. Grey circles mark stations where iron was
sampled.
31
64˚S
27
27
27.2
27.2
Density (kg m−3)
26.8
−3
Density (kg m )
26.8
27.4
27.6
27.4
27.6
27.8
27.8
a
28
0
b
0.5
1
Iron (nmol/l)
1.5
2
28
0
2
4
6
Iron (nmol/l)
Figure 3: Profiles of iron concentration vs. density in the Ona Basin for (a) March
2004 (LMG0402) and (b) August 2006 (NBP0606). The 27.5≤ σθ ≤27.6 density layer
is indicated by the gray horizontal lines. Diamonds indicate the iron maximum at each
individual station.
32
58˚W 56˚W 54˚W
62˚W 60˚W 58˚W 56˚W 54˚W
59˚S
00 b
0 40
0
-3
-400
-4
0
00
0
60˚S
00
-40
0
000
-3000-2-0100
000
-3000-2-0100
61˚S
0
00
-4
62˚S
0
-100
63˚S
0
0
0
-100
0
-100
m
200
300
m
0
50
100
150
200
59˚S
00 d
0 40
0
-3
-400
-4
0
00
64˚S
0
60˚S
00
-40
0
000
-3000-2-0100
000
-3000-2-0100
61˚S
0
00
-4
62˚S
0
-100
0
63˚S
0
0
-100
58˚W 56˚W 54˚W
0
-100
62˚W 60˚W 58˚W 56˚W 54˚W
m
300
400
500
600
m
0
100
200
Figure 4: Top row: median depth (a) and thickness (b) of the 27.5≤ σθ ≤27.6 density
range containing the iron peak for LMG0402. Bottom row: median depth (c) and thickness
(d) of the density range 27.6≤ σθ ≤27.7
33
300
64˚S
58˚W 56˚W 54˚W
62˚W 60˚W 58˚W 56˚W 54˚W
59˚S
00 b
0 40
0
-3
-400
-4
0
00
0
60˚S
00
-40
0
000
-3000-2-0100
000
-3000-2-0100
61˚S
0
00
-4
62˚S
0
-100
63˚S
0
0
0
-100
0
-100
m
200
300
m
0
50
100
150
200
59˚S
00 d
0 40
0
-3
-400
-4
0
00
64˚S
0
60˚S
00
-40
0
000
-3000-2-0100
000
-3000-2-0100
61˚S
0
00
-4
62˚S
0
-100
0
63˚S
0
0
-100
58˚W 56˚W 54˚W
0
-100
62˚W 60˚W 58˚W 56˚W 54˚W
m
300
400
500
600
m
0
100
200
Figure 5: Top row: median depth (a) and thickness (b) of the 27.5≤ σθ ≤27.6 density
range containing the iron peak during NBP0606. Bottom row: median depth (c) and
thickness (d) of the density range 27.6≤ σθ ≤27.7
34
300
64˚S
3.5
2.5
2.5
SW2
BW
1.5
27
SW1
27.8
27
2
27.6
27.2
3
27.4
ACC
0.5
0
27.6
0
27.8
27
27.2
27.6
0.5
27.4
1
27.2
1
27.4
27.8
1.5
−0.5
27
Temperature
o
C
2
27.8
−0.5
−1
−2
33.6
a
33.8
34
34.2
34.4
−2
33.6
34.6
Salinity
28
27.6
27.4
−1.5
28
−1.5
27.2
−1
b
33.8
34
34.2
34.4
34.6
Salinity
Figure 6: Temperature and salinity profiles for stations used to determine source water
properties for OMP analysis. For the three-source scenario, solid red lines represent the
stations chosen to represent the source waters for (a) LMG0402 and (b) NBP0606. Solid
green lines represent the SW1 source water stations, and solid blue lines represent the
SW2 stations. For the two-source scenarios, dashed lines represent the stations chosen for
ACC and SW. During NB060, the same station was selected to represent SW2 and SW in
both scenarios. Dotted lines in each color represent the other stations sampled within the
same source water.
35
60˚S
b
00
0
-340000
00
-4
00
0
a
-40
-3000-200
0
-5000
00
-10
SW1
62˚S
00
-3000-200
0
-5000
00
-10
ACC
ACC
SW
SW2
00
-40
-5000
62˚S
-3000-200
0
-40
00
-10
-5000
0
62˚W
60˚W
00
00
61˚S
d
0
-4
00
00
0
-4
c
-4
00
0
0
0
0
-4
60˚S
-40
00
0
00
-4
0
00
-4
61˚S
-340000
00
-4
59˚S
-3000-200
0
00
-10
0
58˚W
56˚W
54˚W
62˚W
60˚W
58˚W
56˚W
Figure 7: Source water distributions along the 27.5≤ σθ ≤27.6 isopycnal computed with
OMP analysis during LMG0402 (a and b) and NBP0606 (c and d). The pie charts show
station locations, and stars show the locations of source point stations. The source waters
for the three-source scenario (a and c) are ACC water (ACC), Shelf Water 1 (SW1), and
Shelf Water 2 (SW2). The source waters for the two-source scenario (b and d) are ACC
and Shelf Water (SW). Pie charts circled in black represent stations where Monte Carlo
analysis produced a root-mean-square difference of more than 0.05 from the unperturbed
case.
36
54˚W
60˚S
b
00
0
-340000
00
-4
00
0
a
-40
00
00
-10
SW1
-3000-200
0
-5000
00
-10
ACC
ACC
SW
SW2
00
-40
-5000
62˚S
-3000-200
0
-40
00
-10
-5000
0
62˚W
60˚W
00
00
61˚S
d
0
-4
00
00
0
-4
c
-4
00
0
0
0
0
-4
60˚S
00
0
-4
-3000-200
0
-5000
62˚S
-40
00
00
0
-4
61˚S
-340000
00
-4
59˚S
-3000-200
0
00
-10
0
58˚W
56˚W
54˚W
62˚W
60˚W
58˚W
56˚W
Figure 8: Source water distributions along the 27.6≤ σθ ≤27.7 isopycnal computed with
OMP analysis using only CTD stations during LMG0402 (a and b) and NBP0606 (c and
d). Symbols and colors are as in Figure 7.
37
54˚W
534
Appendix A. OMP analysis
535
Appendix A.1. The method
536
Optimal Multiparameter analysis was introduced by Tomczak and Large
537
(1989). It is an extension of the multiparameter method originally developed
538
by Tomczak (1981), which in itself is an extension of temperature-salinity
539
diagram analysis. The method allows for the use of hydrographic properties
540
other than temperature and salinity to determine quantitatively the mixing
541
ratios of n water types from a system of m linear equations. It has been
542
used to evaluate water mass properties both in the Southern Ocean (Budillon
543
et al., 2003; Tomczak and Liefrink, 2005) and in other regions, (e.g. Tomczak
544
and Large, 1989; Tomczak and Poole, 1999). This section provides a brief
545
summary of the method.
546
Consider a situation in which n source waters contribute to a mixture
547
of water observed at a hydrographic station. Assume the existence of a
548
minimum of m − 1 oceanic parameters (such as temperature, salinity or oxy-
549
gen), where m > n. The values of these parameters are measured both for
550
the source water end point stations and for the other hydrographic stations.
551
Water properties are assumed to be conserved during mixing. An additional
552
mass balance constraint is created by requiring that some mixture of the
553
source waters fully describe the water at the point of observation. The rel-
554
ative contributions of the n source waters at the observation point can then
555
be represented by the linear system of conservation equations
Gx − d = r,
556
(A.1)
where G is an m × n matrix containing the parameter values for the source
38
557
waters, d is an m-element vector containing the observed parameter values
558
for the mixed water, x is an n-element vector containing the relative contri-
559
butions of the source waters to the mixing, and r is the m-element residual
560
vector. The last line of G and the last element of d are set to 1 to repre-
561
sent the mass balance constraint. Traditionally, this final constraint is used
562
as a measure of the uncertainty of the result, with mass balance residual-
563
s of 0.05 or less considered acceptable (Budillon et al., 2003; Tomczak and
564
Large, 1989; Tomczak and Poole, 1999; Tomczak, 1981) The system is solved
565
as an overdetermined least squares problem, minimizing rT r, subject to the
566
constraint that all elements of x must be nonnegative.
567
Before the system of equations in A.1 can be solved, the values in G must
568
be normalized in order to make parameters of different units comparable. We
569
follow Karstensen and Tomczak’s [2005] method of computing the normalized
570
matrix G′ where
G′ij = (Gij − Gj )/σj ,
(A.2)
571
where Gij is the value of parameter j for source water i, G′ij is the normalized
572
value, Gj is the mean value of the parameter, and σj is the standard deviation.
573
In order to account for the biogeochemical changes in the source waters,
574
we followed Karstensen and Tomczak’s [1998] extension of the original OMP
575
method by adding another column rpara ∆P to the left-hand side of Equa-
576
tion A.1. The new column contains the Redfield ratios (Redfield et al., 1963)
577
for oxygen, nitrate, phosphate and silicate, multiplied by the new unknown
578
variable ∆P representing the change in phosphate (Karstensen and Tomczak,
579
2005). For temperature, salinity and mass balance, corresponding elements
39
580
in the new column are set to 0. Equation (A.1) can then be rewritten as
Gext x′ − d = r,
(A.3)
581
where Gext = [G rpara ] and x′ = [x ∆P ]T . In this new equation, Gext
582
becomes a m × n + 1 matrix, requiring m > n + 1 in order to ensure that the
583
system remains overdetermined.
584
The canonical N:P:O2 ratios suggested by Redfield et al. (1963) are 16:1:-
585
138. Hoppema and Goeyens’s [1999] analysis of N:P ratios in the western
586
Weddell Sea indicated that the canonical values apply in Antarctic surface
587
waters. Silva et al. (1995) showed similar mean values for the N:P ratio in
588
the waters around Elephant Island, but found that mean Si:P values var-
589
ied from 23:1 to 43:1, depending on depth and region of observation. Our
590
own calculations, based on averaging the ratios for stations within the Ona
591
Basin, produced Si:N:P:O2 of 29:15:1:-156 for LMG0402 and 41:18:1:-184 for
592
NBP0606. The results discussed in Section 3 are based on our calculated
593
ratios for each cruise. Replacing the O2 and N ratio with canonical Redfield
594
values produced no statistically significant differences in the source water
595
distributions or in the computed values of ∆P .
596
Due to variations in measurement accuracy and spatial and temporal
597
variability of the observed parameter values, a diagonal weight matrix W of
598
dimension m × m is introduced. The full solution of the OMP analysis is
599
then found by minimizing
(Gext x′ − d)T WT W(Gext x′ − d) = rT r.
600
(A.4)
Usually, the source waters in OMP analysis are assumed to be linear
40
601
combinations of two or more sea water types (SWTs), whose physical and
602
chemical properties are known (Tomczak and Large, 1989). The values of
603
G are then determined by linear regression of all parameters against tem-
604
perature. By limiting our analysis to a vertically narrow isopycnal layer, we
605
were able to define each of our source waters as a single SWT. This approach
606
allowed us to determine the values of G directly from observations by taking
607
measurements of each parameter at selected end point stations and averaging
608
them vertically within the layer where the analysis would be performed.
609
Appendix A.2. Determining the weights
610
In OMP analysis, the weight matrix W is usually constructed so that the
611
mass balance equation is assigned the highest weight among all the property
612
conservation equations, and the mass balance residuals provide an objective
613
indicator of the quality of the solution (Tomczak, 1981). In an ideal case,
614
in which there is no measurement error, and the source waters specified in
615
the input matrix G fully represent all of the waters that have been mixed
616
to form the water at a given station, the last element of r would be equal to
617
zero. Stations with high mass residuals may have water from other sources
618
contributing to the mixing, or may be subject to non-linear processes that
619
are not well-described by the linear model used in OMP analysis. Therefore,
620
we follow Tomczak and Poole [1999] and focus our discussion on stations
621
where the mass residuals are less than 0.05.
622
To obtain W for our analysis, we adapted the method originally described
623
by Tomczak and Large (1989), which is based on relating the variance of
624
each input parameter among the source waters to the variance of the same
625
parameter within each source water. We define σj as a measure of how well
41
626
parameter j is able to resolve the differences among n water masses:
v
u n
u1 ∑
σj = t
(Gij − Ḡj )2 ,
n i=1
(A.5)
627
where Gij represents the element of G corresponding to the value of param-
628
eter j in water mass i, and Ḡj is the mean value of parameter j at the end
629
points.
630
We then calculated the source water variances δj using the TS-diagrams
631
in Figure 6 to determine which stations were most likely sampled within the
632
same source water. We computed the mean value of each parameter for each
633
group of stations within the layer where the analysis was to be performed,
634
and computed the variance of the means. The largest of the δj values among
635
our n source waters is defined as δjmax . The weights are then calculated as
Wj = σj2 /δjmax .
(A.6)
636
The weights computed for each parameter from the resulting variances
637
are summarized in Table 3. Since OMP does not provide a straightforward
638
method for assigning weights to the mass balance equation, which is not
639
based on any measurements (Tomczak and Large, 1989; de Brauwere et al.,
640
2007), we followed the usual practice (Tomczak and Large, 1989; You and
641
Tomczak, 1993) and assigned the largest of our calculated weights to the
642
mass balance. As an alternative method, we also performed our analysis with
643
weights based on the inverse variances of individual parameter measurements,
644
as is typically done for least-squares fitting methods. While distributions
645
at individual stations were affected by the resulting changes in weights, the
42
646
resulting spatial distributions of SWT percentages and mass balance residuals
647
remained consistent with the conclusions we present in Section 3. We selected
648
Tomczak and Large’s (1989) method as being more physically meaningful,
649
since it takes into account the variability of properties among the different
650
water masses as well as the variability within each mass.
651
The high weight assigned to Si in the three-source scenario for LMG0402
652
introduces a potential source of error, since the Si:N ratio can vary spatially
653
due to varying iron availability in the study region (Takeda, 1998; Timmer-
654
mans et al., 2004). The increased error may provide an additional reason why
655
the two-source scenario produces smaller residuals and lower uncertainties in
656
the source water distribution.
657
Appendix B. Computing Chi-square estimator to assess the opti-
658
659
660
mal number of source waters
The chi-square distribution for the output of OMP analysis for a normallydistributed variable r can be defined as
χ ≡
2
)2
m (
∑
ri
i=1
σi
(B.1)
661
where m and r are defined as in Appendix A and σi is the standard deviation
662
of each parameter measured at the station (Press et al., 1986). For values
663
of σi for at each individual station, we used the standard deviation of that
664
parameter within the source water that dominated at that station, comput-
665
ed using the same method as the standard deviations used to compute the
666
weights in Appendix A.2
43
667
For a given number of degrees of freedom ν, we compute the probability
668
that the data will not exceed a given value of χ2 by chance, with higher
669
probability indicating a higher chance that the end point definitions represent
670
the source waters mixing into the region. This probability can be computed
671
as the incomplete gamma function Q(0.5 × ν, 0.5 × χ2 ). (Press et al., 1986)
672
For the distribution computed here, ν is the number of stations used in the
673
OMP analysis minus the number of columns in matrix G.
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