SC/57/IA6
Alternative estimation of Antarctic minke whale abundance
taking account of possible animals in the unsurveyed large
polynya using GAM-based spatial analysis: A case study in
Area II in 1997/98 IWC/SOWERHIROTO MURASE1, HIROYUKI SHIMADA2 AND TOSHIHIDE KITAKADO3
1 The Institute of Cetacean Research, 4-5 Toyomi-cho, Chuo-ku Tokyo, 104-0055, Japan
2 National Research Institute of Far Seas Fisheries, Fisheries Research Agency, 5-7-1 Orido, Shimizu-ku Shizuoka,
424-8633, Japan
3 Tokyo University of Marine Science and Technology, 4-5-7 Konan, Minato-ku, Tokyo 108-8477 Japan.

Contact e-mail: murase@cetacean.jp
ABSTRACTAn Antarctic baleen whale management area, Area II (0o-60oW), was surveyed by the IWC/IDCR-SOWER in 1986/87 as the second
circumpolar survey (CPII) and, in 1996/97 and 1997/98 as the third circumpolar survey (CPIII). The whole area of Area II was covered in
1986/87. In CPIII, the area was separated into two at 25oW. The sector between 0o and 25oW was surveyed in 1996/97 and the rest (25oW60oW) was surveyed in 1997/98. Sea ice extent in the southeastern Weddell Sea was unusually large in the summer of 1996/97. Unusual
extensive sea ice free area, polynya, adjacent to southeastern side of Antarctic Peninsula was observed in the 1997/98. Such a large
polynya wasn’t observed during satellite observation period (1979-2002) except in 1997/98. The survey vessels could not conduct survey
in the polynya because sea ice prevented the access to there. The area of the polynya was estimated as 89,602 n.mile2 using satellite
derived data. It was 29.2% of the surveyed area in 1997/98. Abundance estimate of Antarctic minke whale in the polynya was extrapolatedusing a GAM based spatial model to assess the impact of unsurveyed polynya on the abundance estimate in CPIII. Environmental variables,
satellite derived SST and chlorophyll-a concentration, bottom depth and distance from ice edge were used in the model. It was reported
that abundance estimates using the IWC standard method in Area II in CPII and CPIII were 131,177 and 43,592 individuals, respectively.
Abundance of Antarctic minke whale in the Ronne Polynya was estimated as 63,364 individuals using the spatial model. Abundance
estimates using GAM-based spatial modeling in CPII and CPIII were 144,793 and 110,859 individuals, respectively including the estimate
in the polynya in 1997/98. The result suggested that abundance estimate in the CPIII would be underestimated because of presence of thelarge polynya.
KEYWORD: ANTARCTIC MINKE WHALE; SEA ICE; POLYNYA; ABUNDANCE ESTIMATE; ANTARCTIC

1INTRODUCTION
The International Whaling Commission (IWC) has conducted the Antarctic minke whale abundance assessment cruises
since 1978/79 in the Antarctic in austral summer (Matsuoka et al., 2003, for review). The name of the cruises werecalled as the International Decade of Cetacean Research programme (IDCR) from 1978/79 to 1995/96 and then changed
to the Southern Ocean Whale and Ecosystem Research programme (SOWER) from 1996/97to 2003/04. The cruises
covered three circumpolar surveys. Abundance estimation was made using each circumpolar data set; 1978/79-1983/84(first circumpolar, CPI), 1984/85-1990/91 (second circumpolar, CPII) and 1991/92-1997/98 (third circumpolar, CPIII).
Though the abundance estimate of the third circumpolar set has not been completed, a noticeable decline in abundance
estimates from CPII (766,000) to CPIII (268,000) (Branch and Butterworth, 2001) brought question whether the decline
is true or apparent. Several hypotheses that might affect the apparent abundance change were pointed out (IWC, 2005).
One of the factors is proportion of Antarctic minke whales population south of the ice edge where survey vessels can
not enter.
In the past, the IWC conducted the sighting survey of Antarctic minke whale between 0° and 60°W (Area II) in
1986/87 as CPII and 1996/97 and 1997/98 as CPIII. Whole Area was surveyed in CPII whereas Area was separated into
two at 25oW and surveys were conducted in two separate years (1996/97 and 1997/98) in CPIII. The 1996/97 SOWER
was conducted in eastern half (0°-25°W) of Area II. It was reported that amount of sea ice in the southeastern Weddell
Sea was unusually large (Hegseth and Von Quillfeldt, 2001). The 1997/98 SOWER was conducted in western half
(25°W-60°W) of Area II. Though the large sea ice free area, polynya, was observed adjacent to southeastern side ofAntarctic Peninsula during the cruise, the vessels could not conducted survey in the area because sea ice prevented thevessels accessing (Ensor et al., 1998). The polynya was called as the Ronne Polynya and it had largest extent in 25
years satellite observation periods (Ackley et al., 2001). In Area II, there is outstanding difference in abundance
estimates between CPII (131,177 individuals) and CPIII (43,592 individuals) (Branch and Butterworth, 2001) and theunusual large polynya could contribute the lower abundance estimates in CPIII. Murase and Shimada (2004) estimatedthe abundance of Antarctic minke whale in the Ronne Polynya assuming that the density in the polynya was same as
adjacent surveyed strata. Abundance estimates in CPIII increased to 86,264 individuals after adding estimates in thepolynya (Murase and Shimada, 2004) though the method was crude. Spatial models based on the Generalize Additive
Model (GAM) have been developed to estimate the abundance of cetaceans in unsurveyed area (e.g. Hedley et al.,2004). In this paper, abundance estimation of Antarctic minke whale in the polynya was carried out using GAM-based
spatial model. The implications of unusual sea ice conditions in CPIII for the interpretation of the abundance difference
between CPII and CPIII in Area II were discussed.

2

MATERIALS AND METHODS

Cetacean survey data
IWC divided southern ocean into six areas for the management of baleen whales (Donovan, 1991). Area II is set
between 0o and 60oW (Fig. 1). Sighting survey for the abundance estimation of Antarctic minke whale was conducted in
austral summer. CPII survey was conducted from December 28, 1986 to February 4, 1987. Full longitudinal coverage
was made in 1986/87 cruise. In CPIII, Area II was divided into two at 25°W. Eastern half (0o-25oW) was surveyed in
1996/97 cruise (January 16-February 14, 1997) whereas western half (25oW-60oW) was survey in 1997/98 cruise(January 18-February 14, 1998). Latitudinal coverage was basically south of 60oS to ice edge except 0o-20oW of CPII
where the northern limit was set at 61oS-63oS. In addition, the northern limit of latitudinal coverage was extended up to
58°S in western portion of Area II because sea ice was extended far north. Sighting effort data, sighting data of
Antarctic minke whales, boundary lines of strata, waypoint and ice edge data stored in the IWC Database-Estimation
Software System (DESS) version 3.4 (Strindberg and Burt, 2004) were used. Three sighting vessels, Kyo Maru 27(K27), Shonan Maru (SM1) and Shonan Maru 2 (SM2) conducted the survey in CPII whereas two vessels, SM1 andSM2 engaged in the survey in CPIII. The sighting surveys were conducted in two mode: closing and IO. Both closing
and IO mode data were used in the analysis. In closing mode, two observers were stationed in top barrel while noobserver was stationed in independent observation platform (IOP). Once a sighting was made, the ship approached tothe sighting to confirm species and school size. In the IO mode, two observers were stationed in top barrel while anobserver was stationed in IOP. No approach was made to sightings. Detailed explanation of survey modes is given in
Branch and Butterworth (2001). Sightings with estimated perpendicular distance more than 1.5 n.miles were excludedin the analysis. The ice edge is defined by a level of ice cover that prevents the survey from being conducted at normal
survey speed (11.5 knots) (IWC, 2003). The ice edge was obtained by the dedicated ice edge survey vessel in CPII
whereas it was estimated using the sea ice chart published by the National Ice Center (US) except around the waypoints.
Because the sea ice chart was published weekly, the estimated ice edge using it lacked precision of CPII though the data
were comparable (Ensor et al., 1997; Ensor et al., 1998).

Satellite sea ice data
Satellite derived daily sea ice data, Bootstrap Sea Ice Concentrations from Nimbus-7 SMMR and DMSP SSM/I(Comiso, 1999) from 1978 to 2002 was used to map the see ice concentration and extent south of the ice edge. Sea ice
observation using the satellite passive microwave sensors was started with the launch of Scanning Multichannel
Microwave Radiometer (SMMR) on Nimbus-7 in 1978. The sensor was changed to Special Sensor Microwave/Imager(SSM/I) in 1987 and the data collection is still on going. The data were collected every other day for the SMMR

3

whereas those were collected every day for the SSM/I. The daily satellite data corresponding to midday of the surveyed
period in each 5-10 latitudinal and longitudinal degree sectors were integrated into a map using geographic information
system (GIS), Marine Explorer (Environmental Simulation Laboratory Co. LTD, Japan). Because the most of the iceedge was estimated using the weekly charts in CPIII, they were referred to determine the appropriate date of the satellite
data. The area of the polnya was calculated using the map. The polynya was defined as 0% sea ice concentration area
south of the ice edge in this paper. Monthly mean sea ice satellite data in January from 1979 to 2002 were used toinvestigate long term sea ice configuration change in Area II.

Environmental covariates in the model
Following environmental variables as well as distance from ice, latitude and longitude were used as covariates in the
GAM-based spatial model. Because data used in the analysis had different map projections, they were converted tosame projections. To get equidistance grid, geological reference data were converted to the equidistant cylindricalprojection assuming that the equator was at 65oS and 30oW. In addition, because original resolutions of the data werealso different from data to data, all data were converted to 30 n.miles by 30 n.miles grid (900 n.mile2) data based on
Kriging method using software, Surfer (Golden Software Inc., 1997).
Satellite chlorophyll-a concentration data
To see the chlorophyll-a concentration in Area II in winter of 1998, The SeaWiFS (Sea-viewing Wide Field-of-view
Sensor) Level-3 winter averaged chlorophyll-a concentration 9km mapped data (Feldman and McClain, 2005) was used.
Because the SeaWiFS image is available after September, 1997, there is no satellite chlorophyll-a concentration image
for the 1986/87 and 1996/97 cruise.
Satellite sea surface temperature data
Satellite derived sea surface temperature (SST) data, AVHRR Oceans Pathfinder global 4km equal-angle all SST v5(NOAA,NASA) (Kearns et al., 2004), were used in the analysis. January monthly mean data in 1987, 1997 and 1998
were used as the representative SST in each survey years. Accuracy of the data was ±0.3-0.5oC.
Digitized bottom depth data
Digitized bottom depth data, 2-Minute Gridded Global Relief Data (ETOPO2) published by National Geophysical Data
Center, NOAA/NGDC were used.

Spatial abundance estimation modelling
Essentially, a GAM-based spatial model, the count model, developed by Hedley et al. (1999) was used but several
points were different. In the GAM-based spatial model, shorter sighting effort distance in a segment is problematic for4the model fitting because it could result in higher abundance estimates in the segment. In this analysis, each transects
was divided into 30n.mile equidistance segments and the sighting effort data were pooled in each segment. By this way,closing mode data could be used in analysis instead of using only IO mode data because it could avoid above mentioned
problem. Segments with zero sighting effort distance were omitted in the analysis. In some cases in closing mode,sightings with no sighting effort distance were recorded. Individual density of Antarctic minke whale in each segment
was estimated as;Di =mi E[ S ],2ws Liwhere
Di= the whale individual density of the ith segment (individuals/n.mile2)
mi= the number of whale schools in the ith segment
E[S] = the estimated mean school size
ws = the effective search half-width for schools (n.miles)
Li = the length of the ith segment (n.miles).
Estimated mean school size and effective search half width for schools reported in Branch and Butterwroth (2001) wereused in the analysis and they were summarized in Table 1. Ideally, survey area should be gridded as same resolution of
the segmented area (i.e. Li times ws) to estimate the abundance in each segment but because it was technically difficult,the survey areas were divided into 30 n.miles by 30 n.miles grids as approximately same size of segmented areas.
Abudance in each 30 n.miles by 30 n.miles grid (Ni) was estimated using the Di.
To model the response as a function of spatial environmental covariates, we use a GAM with spatiallyreferenced environmental covariates, with the following general formulation:⎡⎤
E [N i ] = exp ⎢ β 0 + ∑ s j ( zij )⎥ ,
j =1
⎣⎢
⎦⎥

where
Ni = the abuandace in the ith grid (Di*900n.mile2, individuals)

β0 =an intercept
sj = nonparametric smooths of explanatory variables
zij = the value of the jth covariates in the ith grid.
A GAM with a logarithmic link function and overdispersed Poison error distribution was used. Environmental
covariates, original latitude, longitude (Original.Long, Original.Lat), distance from ice edge (Ice.Dist), SST
5

(SST.degree.Celsius.), chlorophyll-a concentration (Ch.a.mg.m.3.), water bottom depth (Depth.m.) were used for the
initial model. Terms in the parentheses were names used in the model. Each grid had unique values of theenvironmental variables. Details of environmental covariates were descried in the previous section. Models wereselected using mgcv package (version 1.2-4) (Wood, 2001) of R software (R Development Core Team, 2005). At first,
models were fitted within survey area then extrapolated to the polynya to estimate the abundance in there.

RESULTS
Comparisons of survey area, survey distance and number of schools used in Branch and Butterworth (2001) and thisstudy were summarized in Table 2. Differences in survey area and distance between surveys could be caused by theconversion of the map projections. It should be noted that because values of 1996/97 in Branch and Butterworth (2001)
were longitudinal coverage between 0o and 30oW whereas those in present study were between 0o and 25oW, directcomparison could not be made. Also, smearing was applied to the number of schools in Branch and Butterworth (2001)
whereas no smearing was applied to data used in this study. January monthly averaged sea ice extent image in the Area
II in January from 1979 to 2002 was shown in Fig. 2. No large polynya was observed during the satellite observation
period except 1998. Sighting survey trackline, sighting positions of Antarctic minke whale, ice edge line defined by thesurvey vessels and satellite derived sea ice concentration data in CPII and CPIII were overlaid in Fig. 3. Positions of iceedge defined by the satellite and the vessel had good agreement though there was some discrepancy between them,especially in 1986/87. The reason of discrepancy in 1986/87 was due to the data recoding interval (every other day) of
the satellite. The sea ice extent in the southern part of the 1996/97 cruise was larger than that in the 1986/87 cruise. In
1997/98 cruise there was a large polynya which were not observed in the 1986/87 cruise. The area of the polynya wasestimated as 89,602 n.mile2. The total surveyed area in the 1997/98 was 306,981 n.mile2. The area of the polynya was
29.2% of the surveyed area.
Selected GAM-based spatial model and their GCV score in each survey year was shown in Table 3. Selectedcovariates were different among each year. Shapes of the functional forms for covariates used in the models wereshown in Figs. 4-6. Those figures suggested that the habitat choice of Antarctic minke whales in Area II would be quite
complex manner because there was neither constant decreasing nor increasing trend along the environmental covariates.
Chlorophyll-a concentration was not selected in the any model. Comparison of abundance estimates between standard
methods reported in Table 3 of Branch and Butterworth (2001) and spatial modelling methods in this study weresummarized in Table 4. Though no CV estimate was provided in this study, abundance estimates within survey area
showed quiet good agreement between the standard method and the GAM-based spatial modelling. The abundance ofAntarctic minke whale in the Ronne Polynya was estimated as 63,394 individuals using the GAM-based spatial model6

in 1997/98. Difference of abundance estimates between CPII and CPIII were reduced from 97,297 to 33,933 individuals
once the abundance in the polynya was included.

DISCUSSION
Southern portion of the 1996/97 survey area (0o-25oW) had a larger amount of sea ice than the 1986/87 survey. Because
the heavy sea ice condition in this area shortened the growth season of the phytoplankton, biomass of the phytoplankton
was low in this area in the summer of 1997 (Hegseth and Von Quillfeldt, 2001). Antarctic krill (Euphausia superba),
the dominant prey species of Antarctic minke whale (Ichiii and Kato, 1991), fed predominantly on the phytoplankton(Miller and Hampton, 1989). If the biomass of the phytoplankton was low, growth and sexual development ofAnarchistic krill was negatively affected. In the case of the food scarcity, Antarctic minke whales could change thefeeding area in response to it. The western Weddell Sea was also covered with high concentration of sea ice in the
1996/97 survey. Because Antarctic minke whales were move across the IWC baleen whale management area boundary(Wada, 1984), some proportion of the population in Area II could move to adjacent areas, such as Area III. Migration
behavior in response to the food availability could affect the change in apparent abundance estimation between CPII
and CPIII.
In contrast, there was a large polynya in the 1997/98 survey. SeeWiFS satellite image suggested that thechlorophyll-a concentrations in the polynya was high. The size of the polynya increased from November and reachedmaximum about on 1 March (Ackley et al., 2001). The prolonged open water period in the polynya could enhance theprimary production. It was reported that the Ross Sea and the Prydz Bay showed high chlorophyll-a concentrations insummer (Arrigo and van Dijken, 2003). Those two regions were reported as high Antarctic minke whale density areas
around the Antarctica (Kasamatsu et al., 1996; Kasamatsu et al. 1998b). Given the information, high density of
Antarctic minke whales could be expected in the polynya. Though the chlorophyll-a concentrations was not selected in
1997/98 model in this study, this was due to low chlorophyll-a concentrations within the survey area. Because thedifference of the chlorophyll-a concentrations between inside and outside of the polynya was remarkably large, itappeared that the chlorophyll-a was not appropriate environmental covariates in this case. This was the limitation ofusing GAM-based spatial modeling to extrapolate the abundance estimate to the unsurveyed region.
Abundance estimates of Antarctic minke whales using GAM-based spatial model were conducted in Area I(60oW-120oW) (Stahl and Borchers, 2001) and Area III (0o-70oE) (Hedley et al., 1999). Those studies indicated that
school densities of Antarctic minke whales showed a relatively consistent trend along distance from ice edge in bothstudies. In contrast, distribution pattern of Antarctic minke whales in this study showed quite complex and inconsistent
trends along the environment covariates. Kasamatsu et al. (1998a) postulated that the oceanographic conditions

7

associated with the Weddell Gyre might influence the distribution pattern of Antarctic minke whales instead of sea
surface temperature and sea ice extent alone. The presence of Weddell Gyre could results in complex and inconsistent
relationship between distribution of Antarctic minke whales and environmental covariates. Because oceanographic
conditions other than SST could not be obtained from satellite in the high latitude region of Area II, it is difficult toassess the influence of the Weddell Gyre. In such a region, direct measurement of oceanographic conditions such as
CTD cast must be conducted in future survey to clarify the relationship between the distribution pattern of Antarctic
minke whales and the oceanographic conditions.
The results of this study suggested again that the abundance estimate in the 1997/98 reported in Branch andButterworth (2001) would be underestimated because of presence of the large polynya. The effect of the polynya on the
CPIII abundance estimates in Area II must be taken account though it is difficult to estimate Antarctic minke whale inthe south of the ice edge where the sighting vessels can not conduct the survey (IWC, 2002). Without considering theeffect of the large polynya, the direct comparison of abundance estimates between CPII and CPIII is invalid. Field
studies, such as sighting survey within pack ice using ice breaker (e.g. Shimada and Kato, 2005) and biotelemetry
survey to monitor the movement of Antarctic minke whale within and outside of pack ice will enhance theunderstanding of distribution patterns of Antarctic minke whales in polynya and they should be conducted in the future
survey.

ACNOWLEGEMENT
Comments from Hiroshi Hatanaka and Hidehiro Kato greatly improve the manuscripts. We also thank Shigetoshi
Nishiwaki and Koji Matsuoka for their encouragement on the course of developing the idea of the analysis. We thankAtsushi Wada for the sea ice data management. We also thank Kiyoshi Ito, Naomi Takezoe, Yoshinobu Odaira andtheir colleagues at Environmental Simulation Laboratory Co. LTD for the development of the data preparation program.
We are grateful to the researchers, captains and crews of IDCR-SWOER for their dedication collecting cetaceansighting data under hash environmental conditions in the Antarctic.

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observations of air-ice-ocean interaction. Ann. Glaciol. 33:425-429.
Arrigo, K. R. and van Dijken, G. L. 2003. Phytoplankton dynamics within 37 Antarctic coastal polynya systems. J.
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Table 1. Summary of the estimated mean school size (E[S]) and the effective search half-width for schools (ws, n.miles)
used in this study. Values were reported in the Branch and Butterworth (2001).

Year
1986/87
1996/97
1997/98

Closing modews
E [S ]
0.369
2.82
0.551
2.23
0.526
1.92
0.835
1.72
0.306
2.06
0.612
1.79
0.881
1.81

Vessel
K27
SM1
SM2
SM1
SM2
SM1
SM2

IO modews
E [S ]
0.367
2.82
0.663
2.23
0.571
1.92
0.637
1.72
0.468
2.06
0.878
1.79
0.672
1.81

Table 2. Comparisons of survey area, survey distance and number of schools used in Branch and Butterworth (2001,
B&B) and this study (M&S&K). It should be noted that because values of 1996/97 in B&B were longitudinal coverage
between 0o and 30oW whereas those in M&S&K were between 0o and 25oW direct comparison could not be made. Also,smearing was applied to the number of schools in B&B whereas no smearing was applied to M&S&K.

Year

B&B(2001)

M&S&K

Diff.
B&B and
M&S&K
(%)

2

Survey area (n.mile )1986/97495,208
462,600
1996/97445,715
321,300
1997/98
306,981295,200
Survey distance (Closing, n.mile)
1986/97
3,329.6
3,493.3
1996/97
1,568.6
1,491.7
1997/98
1,377.2
1,400.9
Survey distance (IO, n.mile)
1986/973,650.7
3,684.0
1996/97*
1,769.4
1,631.1
1997/98
1,688.1
1,690.6
Number of schools (Closing)
1986/97257.3
261.0
1996/9754.4
51.0
1997/98
82.9
83.0
Number of schools (IO)
1986/97412.8
420.0
1996/97
77.7
74.0
1997/98
70.2
70.0

12

7%
28%
4%
5%
5%
2%
1%
8%
0%
1%
6%
0%
2%
5%
0%

Table 3. Selected GAM based model in Area II in CPII (1986/87) and CPIII(1996/97 and 1997/98).
CP
CPII
CPIII
CPIII

Year
Model
1986/87 Ind.Abun~s(Original.Long,Original.Lat)+s(DistIce.n.mile.)+s(Depth.m.)
1996/97 Ind.Abun~s(Original.Long, Original.Lat)+ s(DistIce.n.mile.)
1997/98 Ind.Abun~s(Original.Long, Original.Lat)+s(SST.degree.Celsius.)

GCV score434.84250.68110.65

Table 4. Comparison of abundance estimates between Branch and Butterworth (2001) and this study.
Standard methods (B&B, Table 3)

CPII
CPIII
Total of CPIII

Spatial modelingYear

Closing

IO

Pseudo-Passing

Invese-Varianceweighted

1986/87
1996/97
1997/98
1996/97+
1997/98

110,984
29,22821,291

128,680
26,913
12,939134,363
35,38525,776

131,177
28,15815,434

144,793
30,386
17,11080,473

CPIICPII-CPIII
Abundance
CPIII
differenceindifference(without
polynya(including
polynya)polynya)
63,364 -50,51939,852

61,161

43,59247,496

110,859

63,364

Cloising+IO(without polynya)

Cloising+IO(including polynya)

13

97,29733,933

Fig. 1. Schematic map of survey area, Area II.

14

Fig. 2. January monthly mean sea ice concentration images in Area II from 1979 to 2002.

15

Fig. 2. (Continued)

16

1986/87 (CPII)

1996/97 (CPIII)

1997/98 (CPIII)

Fig. 3. Maps of sighting survey trackline, boundary lines of strata (black line), sighting positions of Antarctic minke
whale (pink open circle), and satellite derived sea ice concentration in 1986/87 (above), 1996/97 (middle) and 1997/98(bottom) in Area II. Pink hatched area in 1997/98 was defined as the Ronne Polynya in this study.

17s(O ri
ginal.
Long
at, 2
inal.L
,Orig
Or ig
i

nal.

Lat

4.33)
Or
ig

i na

l.Lo

ng

-2
-6

-4

s(DistIce.n.mile.,3.38)

0

2

(a)

0

50

100

150

200

250

300

350

DistIce.n.mile.

-2
-6

-4

s(Depth.m.,7.67)

0

2

(b)

1000

2000

3000
Depth.m.

4000

5000

(c)

Fig. 4. Shapes of the functional forms for covariates selected for 1986/87 data: (a) 2 dimensional perspective plot of
longitude and latitude, (b) distance from ice edge and (c) water bottom depth.
18s(O ri
ginal.
Long
at, 2
inal.L
,Orig
i na

l.Lo

Or ig
ina
l. La
t

5.45)
Or
ig

ng

0
-5
-15

-10

s(DistIce.n.mile.,6.84)

5

10

(a)

0

100

200

300

DistIce.n.mile.

400

500

(b)

Fig. 5. Shapes of the functional forms for covariates selected for 1996/97 data: (a) 2 dimensional perspective plot of
longitude and latitude and (b) distance from ice edge.

19s(O ri
ginal.
Long
at, 1
inal.L
,Orig
Or ig
in

al. L
at

8.44)
Or
ig

i na

l.Lo

ng

4
2
-2

0

s(SST.degree.Celsius.,2.78)

6

(a)

-2

-1

0

1

SST.degree.Celsius.

2

3

(b)

Fig. 6. Shapes of the functional forms for covariates selected for 1997/98 data: (a) 2 dimensional perspective plot of
longitude and latitude and (b) SST.

20