east-west asymmetry in coastal temperatures of hudson …...east-west asymmetry in coastal...

East-West Asymmetry in Coastal Temperatures of Hudson Bay as a Proxy for Sea Ice

by

Peter Graeme McGovern

A thesis submitted in conformity with the requirements for the degree of Masters of Science Graduate Department of Geography

University of Toronto

© Copyright by Peter Graeme McGovern (2013)

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East-West Asymmetry in Coastal Temperatures of Hudson Bay as a Proxy for Sea Ice

Peter Graeme McGovern

Masters of Science

Graduate Department of Geography

University of Toronto

2013

Abstract

The seasonal asymmetry in coastal temperatures on Hudson Bay was explored

and evaluated as a proxy to hindcast sea ice conditions prior to 1972. Various indices of

air temperature difference (∆T) between Churchill, MB and Inukjuak, QC were tested for

linear correlations with spatially averaged sea ice concentration (SIC) and ice-free season

length (IFS). A multiple regression equation employing a 31-day average of peak ∆T and

a 61-day average of temperature during freeze-up reproduced the IFS record with an

average error of 8.1 days. This equation was employed to extend the IFS record by 28

years. The resulting 68-year time series revealed a significant increasing trend most

pronounced from 1985 to 2011. Hindcast data helped eliminate low-frequency climate

oscillations of periodicity <68 years as a source of this trend, lending further evidence to

the growing consensus of a declining sea ice being the result of anthropogenic climate

forcing.

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Acknowledgments

First and foremost I would like to thank my supervisor, Dr. Bill Gough, for giving

me the opportunity to study a topic of great interest and importance to me, while offering

his expertise and mentorship along the way. I am incredibly grateful for this formative

experience, which was made all the more valuable and interesting by Bill’s unique

teaching style and infectious enthusiasm for geography and climatology.

I would like to extend my gratitude to the two other committee members, Dr.

Sharon Cowling and Dr. Tanzina Mohsin, for offering their feedback in the final stages of

my thesis, and for cultivating my interests through thought-provoking coursework.

I would also like to acknowledge the contributions of individuals who graciously

offered their time to ensure the statistical soundness of the results presented herein:

Shannon Allen for taking her time to address all my concerns relating to climate data,

Slawomir Kowal for offering his help with sea ice data, and Dr. Ken Butler for lending

his expertise on statistics and trend analysis.

I am also very grateful to the University of Toronto Geography Department for

providing the funding that made this research possible

To my family, and to my partner Danielle, thank you for your continued love and

support.

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Table of Contents Chapter 1: Introduction ....................................................................................................... 1

1.1 Relevance .................................................................................................................. 2 1.2 Research Objectives .................................................................................................. 4

Chapter 2: Literature Review .............................................................................................. 6 2.1 Sea Ice Measurement ................................................................................................ 6 2.2 Seasonal Breakup and Freeze-up Patterns on Hudson Bay ...................................... 7 2.3 Temporal Trends in Hudson Bay Sea Ice ................................................................. 8 2.4 East-West Asymmetry in Hudson Bay ................................................................... 10 2.5 Thermal Modification ............................................................................................. 11

2.5.1 Physical Properties of Sea Ice vs. Water ......................................................... 12 2.5.2 Heat Flux over Open Water ............................................................................. 14 2.5.3 Heat Flux over Ice ............................................................................................ 16

2.6 Temperature as a Proxy for Sea Ice ........................................................................ 18 2.7 Other Proxies for Sea Ice ........................................................................................ 21 2.8 Literature Summary ................................................................................................ 23

Chapter 3: Methodology ................................................................................................... 25 3.1 Site Selection and Description ................................................................................ 25

3.1.1 Hudson Bay Region ......................................................................................... 25 3.1.2 Churchill and Inukjuak: Local Climatic Factors .............................................. 26 3.1.3 Weather Stations/Climate Data ........................................................................ 28

3.2 Defining Temperature Asymmetry: ∆T .................................................................. 29 3.3 Assessing Weekly SIC-ΔTW Correlation ................................................................ 29 3.4 Assessing IFS -∆T Correlation ............................................................................... 31

3.4.1 Capturing Maximum ∆T .................................................................................. 31 3.4.2 Determining Ice-Free Season Length .............................................................. 32 3.4.3 Classification of ∆TMAX by IFS ....................................................................... 33

3.5 Wind Direction Analysis ......................................................................................... 35 3.5.1 Wind Direction Counts/Wind Rose Construction for ∆TMAX Period ............... 35 3.5.2 Re-classification of ∆TMAX for Low NE+E Years ........................................... 36

3.6 Evaluating Proxy Performance: Temperature as a Benchmark .............................. 37 3.7 Combined Approach: ∆TMAX and TF in a Multi-Proxy .......................................... 38 3.8 Hindcasting and Trend Analysis of Extended Record ............................................ 39 3.9 Notes on Data Quality ............................................................................................. 41

3.8.1 Temperature Data ............................................................................................. 41 3.8.2 Wind Direction Data ........................................................................................ 42 3.8.3 Ice-free Season Data ........................................................................................ 43

Chapter 4: Results ............................................................................................................. 44 4.1 ΔT Climate Normal ................................................................................................. 44 4.2 Weekly SIC-ΔTW Correlation ................................................................................. 45 4.3 IFS-ΔTMAX Correlation ........................................................................................... 46

4.3.1 Classification of ∆TMAX by IFS ........................................................................ 48 4.4 Wind Direction Analysis ......................................................................................... 51

4.4.1 Wind Direction Frequency Distributions ......................................................... 51

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4.4.2 Correlation of Wind Direction Components to IFS ......................................... 58 4.4.3 Classification of ∆TMAX by IFS for Low NE+E Years .................................... 58

4.5 IFS-TF Correlation .................................................................................................. 61 4.5.1 Classification of TF by IFS .............................................................................. 62

4.6 IFS-∆TMAX-TF Multiple Linear Regression ............................................................. 64 4.7 Hindcast IFS............................................................................................................ 67

Chapter 5: Discussion ....................................................................................................... 70 5.1 Interpreting ∆T Climate Normal ............................................................................. 70 5.2 SIC-∆TW Relationship ............................................................................................. 71 5.3 IFS-∆TMAX Relationship ......................................................................................... 72 5.5 Wind Direction ........................................................................................................ 75 5.5 Multiple Variable Approach ................................................................................... 79 5.6 Evaluating Proxies .................................................................................................. 79

5.6.1 Classifications .................................................................................................. 80 5.6.2 Linear Regression ............................................................................................ 81

5.7 Trend Analysis of Extended Record ....................................................................... 82 5.8 Complicating Factors in the Sea Ice-∆T Relationship ............................................ 84 5.8 Sources of Error ...................................................................................................... 87 5.9 Research Impacts .................................................................................................... 88

Chapter 6: Conclusion ....................................................................................................... 90 6.1 Research Objectives ................................................................................................ 90 6.2 Recommendations for Future Research .................................................................. 91

References ......................................................................................................................... 93 Appendix: Wind Roses ................................................................................................... 100

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List of Tables Table 1: Climate station summary. ................................................................................... 28 Table 2: Definition of classes of ice-free season length. .................................................. 33 Table 3: Ice-free season length and ∆TMAX for 1972-2011. ............................................. 47 Table 4: Classification of ∆TMAX by IFS for all years on record. ..................................... 48 Table 5: P-values obtained from interclass comparison of ∆TMAX means by

one-tailed t-test, adjusted using the Bonferroni correction. ................................ 49 Table 6: Identification of misclassified years based on ∆TMAX thresholds. ..................... 50 Table 7: Classification of ∆TMAX by IFS for years when NE+E wind count

is below average. ................................................................................................ 59 Table 8: Identification of misclassified years when NE+E winds count is

below average. .................................................................................................... 60 Table 9: Ice-free season lengths and TF for 1972-2011. .................................................. 61 Table 10: Classification of TF by IFS for all years on record. ......................................... 62 Table 11: P-values obtained from interclass comparison of TF means by

one-tailed t-test, adjusted using the Bonferroni correction. ............................. 63 Table 12: Identification of misclassified years based on TF thresholds ........................... 63 Table 13: Comparison of temperature variables in terms of coefficients

of determination, statistical significance, and percent misclassifications. ....... 64 Table 14: IFS results from Eqn. 1 (TF+∆TMAX) compared with actual IFS in

terms of absolute error for the period 1972-2011. ............................................ 65 Table 15: IFS results from Eqn. 2 (TF) compared with actual IFS in terms of

absolute error for the period of 1972-2011. ..................................................... 66 Table 16: Comparison of temperature variables in terms of the coefficients of

determination and statistical significance of linear relationships with IFS. ....... 67 Table 17: Comparison between baseline and trend in terms of τ and statistical

significance for different time series divisions. .................................................. 69

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List of Figures Figure 1: Site map of Hudson Bay indicating the location of the 36 points for which

breakup and freeze-up dates were derived. ......................................................... 33 Figure 2: Climate normal for ∆T (Churchill Daily Mean T - Inukjuak Daily Mean T)

calculated over the period 1944-2011. ................................................................ 44 Figure 3: Correlation of ∆TW with spatially averaged SIC for all weekly observations

on record 1971-2011. .......................................................................................... 45 Figure 4: Correlation of ∆TW with spatially averaged SIC for all weekly observations

during the breakup period, 1971-2011. ............................................................... 45 Figure 5: Correlation of ∆TW with spatially averaged SIC for all weekly observations

during the freeze-up period, 1971-2011. ............................................................ 46 Figure 6: Climate normal wind rose for Inukjuak over Julian days 320-350, calculated

over the period of 1981-2007. ............................................................................ 51 Figure 7: 1981 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -2.4°C,

IFS = 153 (Long). ............................................................................................... 52 Figure 8: 1982 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -10.5°C,

IFS = 133 (Medium). .......................................................................................... 52 Figure 9: 1983 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -0.2°C,

IFS = 137 (Medium). .......................................................................................... 53 Figure 10: 1985 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -8.6°C ...... 53 Figure 11: 1986 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = 0.0°C,

IFS = 130 (Medium). .......................................................................................... 54 Figure 12: 1988 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -9.7C,







IFS = 160 (Long). ............................................................................................... 58 Figure 19: Time series of IFS from 1944-2011 constructed using actual observations

and data derived by proxy from ∆TMAX and TF [Eqn. 2]. ................................... 68 Figure 20: Time series for actual and hindcast IFS smoothed by use of a 5-year

moving average. .................................................................................................. 68 Figure 21: 1984 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -5.1°C,

IFS = 132 (Medium). ........................................................................................ 100 Figure 22: 1987 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -2.8°C,

IFS = 128 (Short). ............................................................................................. 101

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Figure 23: 1989 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -7.6°C, IFS = 141 (Medium). ........................................................................................ 102

Figure 24: 1995 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -5.3°C, IFS = 147 (Medium). ........................................................................................ 102

Figure 25: 1996 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -9.0°C, IFS = 151 (Long). ............................................................................................. 103





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Chapter 1: Introduction

Northeastern Canada’s Hudson Bay, through its unique geographical

characteristics, presents a compelling case study for climatologists and geographers alike.

As the second largest bay in the world, occupying 1,300,000 km2, it exerts a powerful

influence over the regional climate (Martini, 1986). Hudson Bay (HB, the Bay) is also the

largest water body in the world to undergo an annual cycle between total sea ice coverage

and complete open water. This annual cryogenic cycle adds another layer of complexity

to the regional climate, as the interaction between the Bay and the boundary layer

atmosphere fluctuates considerably on a seasonal basis.

Open water bodies have a significant impact on local and regional climate through

exchanges of heat, moisture and momentum with the air above them. The effects of this

are manifest in coastal regions, where temperatures are moderated by open water and

meteorological phenomena such as lake-effect snow and land-sea breezes are common

(Oke, 1978). Sea ice acts to limit this exchange of energy and mass between atmosphere

and water, thus reducing or eliminating these effects (Gerbush et al., 2008; McPhee,

2008; Niziol, 1987). Differences in physical properties between water and sea ice, most

importantly their ability to reflect shortwave radiation, means an even greater contrast in

the energy budgets of an ice-covered vs. an ice-free water body (McPhee, 2008). On

Hudson Bay, the seasonal variation of sea ice, combined with the prevailing westerly

winds, creates an interesting seasonal asymmetry in coastal temperatures. During the ice-

free season, winds arriving on the east coast have been thermally modified through

advection over the Bay, leading to generally warmer conditions than on the west coast.

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This asymmetric temperature signal is very evident following annual extremes of sea ice

cover. The aim of this study is to determine if unique temperature signals exist not only at

these extremes, but also for varying degrees of sea ice cover, with a view to

reconstructing the sea ice record using coastal temperatures as a proxy.

1.1 Relevance

The current consensus that sea ice in Hudson Bay is in decline is based largely on

observations of an approximately 40-year sea ice record (Gagnon & Gough 2005; Gough

et al., 2004a; Hochheim & Barber, 2010; Hochheim et al., 2011). This record, made

available by Environment Canada’s Canadian Ice Service (CIS), relies heavily upon

satellite imagery to maintain accurate, high-resolution coverage of Canada’s northern

regions (CIS, 2013). Prior to the advent of satellite imagery, sea ice data for this area is

sparse and unreliable, constrained to observations from coastal stations, sea vessels, and

airplanes. Trend analysis for any climate variable is sensitive to the length of its record,

as short-term changes sometimes prove less significant in the context of long-term

variability (Hodgkins, 2013). Lengthening the sea ice record could serve to strengthen

the conclusion that a decline has indeed been forced by anthropogenic climate change, as

is the current hypothesis. Alternatively, a longer record might prove recent changes to be

part of some natural low frequency climate oscillation (W. Gough, pers. comm., 2012).

Either way, a more accurate characterization of the trend in Hudson Bay sea ice would be

highly valuable to researchers and policy makers from local to global levels.

The observed negative trend in sea ice on Hudson Bay has social, economic, and

environmental implications at all geographic scales. A thorough understanding of these

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historical trends is essential to establishing linkages to current impacts as well as

projecting future impacts. A longer ice-free season on the Bay has potential positive

economic impacts as it opens up the opportunity for improved navigation of sea vessels

to the Port of Churchill on the Bay’s western coast (Ho, 2010; Stewart et al., 2010).

While this is one example of an impact of sea ice decline that could be construed as

positive, it must nevertheless be weighed against the many negative impacts. Traditional

ways of life for communities along the Bay may cease to be viable as seasonal sea ice

patterns continue to change. Coastal communities practicing subsistence hunting, which

often rely on the presence of sea ice floes as hunting platforms, may be forced to adapt in

response to changes in sea ice (Laidler et al., 2009). The ecological impacts of a negative

sea ice trend have also been studied extensively and shown to be significantly deleterious

to local fauna (Kovacs et al., 2011; Moore & Huntington, 2008). Perhaps the most

notable species to be affected by these changes is the polar bear, whose reliance on sea

ice as a transportation corridor and primary hunting platform leaves them particularly

vulnerable to changes in its patterns (Kovacs et al., 2011; Stirling et al., 1999). The most

significant impact of declining sea ice on a global scale is the potential amplification of

global warming through the ice-albedo feedback loop (Curry et al., 1994). This feedback

mechanism relies on the significantly lower albedo of water compared to sea ice or snow.

Declining sea ice results in a concomitant decline in the sea ice: open water ratio and

hence the overall albedo of Hudson Bay, and the Arctic Ocean in general. A lower albedo

means greater absorption of incoming shortwave radiation, leading to further

amplification of atmospheric warming.

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The impacts described above are all associated with a decline in sea ice or

changes in sea ice patterns that have been correlated with anthropogenic climate change.

Improvements to the sea ice record in terms of continuity and length might serve to

strengthen the basis for the observed trends and their associated impacts. Any new

information garnered in the process would be a boon to researchers and stakeholders in

climate change mitigation and adaptation.

1.2 Research Objectives The two primary research objectives for this thesis are:

1. To investigate the relationship between the east-west coastal asymmetry in temperature of Hudson Bay and sea ice concentration (or other metric of sea ice), identifying and accounting for any other climatic variables obscuring this relationship.

2. To develop a proxy using this temperature asymmetry for the purpose of

reconstructing the sea ice record for Hudson Bay prior to 1972 and conducting a temporal trend analysis.

The basis for this study is the observation of a seasonal change in the temperature

difference between coasts. Objective 1 aims to further explore that asymmetry as it

relates to sea ice, testing the correlation between temperature difference and sea ice

concentration. I hypothesize that though there will be a correlation, it will be limited by

inherent climatic variability, such that the relationship will only be significant at coarser

temporal resolutions. As part of objective 1, it is presumed that wind direction will be an

important climatic variable in need of consideration to effectively characterize the

relationship. I hypothesize that the strength of the temperature asymmetry, while largely

driven by sea ice conditions, will also be highly dependent on, and proportional to, the

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frequency of westerly winds.

In the process of pursuing objective 1, the groundwork is being laid for completing

objective 2. Having characterized the sea ice-temperature asymmetry relationship, a

realistic, simple proxy method will be developed. This proxy will be evaluated by its

ability to reconstruct the existing record. Should it be deemed a useful proxy by this

measure, it will be used to reconstruct sea ice conditions prior to 1972, producing a

lengthened time series upon which temporal trend analyses may be conducted.

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Chapter 2: Literature Review

The following literature review serves to identify the most significant

contributions to the current body of knowledge on sea ice in Hudson Bay. The theoretical

basis for the relationship between sea ice and coastal temperatures will be established

along with the gaps in the knowledge this study aims to address by investigating this

relationship.

2.1 Sea Ice Measurement There are many different metrics employed to track the seasonal patterns of sea

ice formation/melt as well as its long-term trends. Thickness has been used as a measure

of sea ice to track its decline in both the Hudson Bay region (Gagnon & Gough, 2006;

Gough et al., 2004b) and the broader Arctic Ocean (Kwok & Rothrock, 2009; Rothrock

et al., 1999). A thinning trend naturally translates into a decline in sea ice volume,

another unit of measurement for sea ice with precedent in the literature (Kwok et al.,

2009; Rothrock & Zhang, 2005). The most commonly used metrics, however, are sea ice

extent (SIE) and sea ice concentration (SIC). SIE is usually defined as the area that

contains sea ice above a certain concentration threshold, and is widely used in the

literature to monitor climate-induced changes to sea ice (Comiso et al., 2008; Vinnikov et

al., 1999; Parkinson et al., 1999). SIC, on the other hand, is defined as the relative

proportion of sea ice to open water for a given area, usually reported in tenths. SIC has

been a particularly popular metric for examining sea ice patterns and trends in the

Hudson Bay region (Hochheim et al., 2011; Hochheim & Barber, 2010; Wang et al.,

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1994). The advantage of SIC over SIE is that it gives the user specific information on the

ice cover for a particular point or area of interest. SIE can be derived from a map of SIC,

but not vice versa, so SIC inherently contains more information. Breakup and freeze-up

dates, important variables for areas undergoing annual freeze/thaw cycles, have been

defined using the SIC threshold of 5/10. With this methodology, first proposed by Etkin

(1991), breakup is defined as the earliest date when SIC equals 5/10 or less, while freeze-

up is defined as the earliest date when SIC equals 5/10 or more. Though somewhat

arbitrary, this 50% threshold also carries some significance to nautical navigators

(Gagnon & Gough, 2005). This methodology for determining breakup/freeze-up dates

has been adapted and used by Stirling et al. (1999), Gough et al., (2004a), and Gagnon &

Gough (2005).

2.2 Seasonal Breakup and Freeze-up Patterns on Hudson Bay

The progression of sea ice freeze-up and breakup on the Bay is influenced by

regional variations in wind, temperature and water circulation. James Bay is the first

region to undergo breakup in late June due to the relatively warm winds arriving from

northern Ontario (Gagnon & Gough, 2005). Eastern Hudson Bay also undergoes

relatively early breakup due to spring freshwater inputs (Markham, 1986). Shortly

thereafter, offshore SICs in northwestern Hudson Bay also surpass the 5/10 threshold,

likely due to sea ice advection by northwesterly winds (Saucier et al., 2004). Landfast ice

on the northwestern and northeastern shores persists for another 3-4 weeks. The last

region of the Bay to break up is the southwestern shore, typically around the third week

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of July, though remnants of ice may still be present as late as mid-August (Gagnon &

Gough, 2005; Hochheim et al, 2011).

The ice-free period for Hudson Bay is quite short (<3 months), as ice formation in

the northern region begins in late October, starting along the northwestern coast and

along the shores of South Hampton Island (Hochheim & Barber, 2010). In mid-

November, northern Hudson Bay is the first region to reach the 5/10 freeze-up threshold

(Gagnon & Gough, 2005). From there, freeze-up progresses southward and eastward

(Maxwell, 1986) with the southeast portion of the Bay freezing last (Hochheim & Barber,

2010). The Bay as a whole is usually consolidated (SIC≥80%) by late December to early

January. Hence, the ice-covered period is significantly longer than the ice-free period,

lasting on average almost 6 months. These general patterns of breakup and freeze-up

persist from year to year, however the specific dates exhibit a strong interannual

variability and have undergone long-term changes in response to climate forcing (Gough

et al., 2004a; Gagnon & Gough, 2005; Wang et al., 1994).

2.3 Temporal Trends in Hudson Bay Sea Ice

In light of the observed decline in sea ice for the Arctic as a whole (Comiso et al.,

2008: Parkinson et al., 1999; Stroeve et al., 2007; Vinnikov et al., 1999), many recent

studies have attempted to assess what trends might emerge on a more regional scale, with

a particular focus on the Hudson Bay region. Gagnon and Gough (2005) identified trends

in the sea ice freeze-up and breakup dates for the Bay over the period of 1971-2002.

Their findings suggest an overall trend toward later freeze-up and earlier breakup, with

regional variation in the magnitude and statistical significance of these trends. James Bay,

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southern Hudson Bay, and western Hudson Bay all exhibited statistically significant

trends toward earlier breakup, while the northern and northeastern regions of the Bay

exhibited a trend toward later freeze-up. Hochheim et al. (2011) investigated the

atmospheric forces behind the observed trends in sea ice concentration and sea ice extent

in Hudson Bay from 1980 to 2005 during the spring period and Hochheim & Barber

(2010) during the fall period. Many of their findings corroborate previous descriptions of

SIC patterns and trends on the Bay. During the fall, statistically significant trends in SIC

anomalies averaged across the Bay ranged from -23.3% to -26.9% per decade. These

trends were in turn highly correlated with surface air temperature (SAT) anomalies

(Hochheim & Barber, 2010). The spring break-up exhibited similar trends of -15.1% to -

20.4% per decade, also concomitant with increased SATs (Hochheim et al., 2011).

Negative SIC trends in the breakup and freeze-up periods would be expected to

translate into a lengthening trend of the ice-free season. Gough et al. (2004a) found such

a trend in a regional assessment of southwestern Hudson Bay. This study showed a

statistically significant increase in the duration of the ice-free season for the area from

1971 to 2003, driven primarily by a decreasing trend in the breakup date of 0.3 days/year.

Passage of years was used as an implicit measure of warming temperatures, which is

justified by the fact that statistically significant positive trends in spring temperatures

have been observed in nearby northern Ontario locations (Gagnon & Gough, 2002).

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2.4 East-West Asymmetry in Hudson Bay

The basis for the proposed study lies in the seasonally varying differences in

temperature between the east and west coasts of Hudson Bay. This east/west asymmetry

has emerged as a common theme in much of the relevant literature. As described above,

the progression of sea ice breakup and freeze-up on the Bay is non-uniform and

regionally variable such that sea ice may be present on one side of the Bay and absent on

the other depending on the time of year. Hence, we see coastal asymmetry in sea ice

concentrations owing to regional climatic variations. These east-west variations in SIC

are further explored by Hochheim et al. (2011) who examine the role of dynamic and

thermodynamic forcing. Hochheim et al. (2011) compare SIC anomalies in east and west

regions of the Bay during the early spring period in relation to both surface air

temperature and wind. One of their most significant observations was that asymmetries in

SIC were correlated with westerly winds. For example, years with positive sea ice

anomalies in the eastern region and negative sea ice anomalies in the western region

(strong asymmetry) were correlated with strong westerly winds. On the other hand, years

with positive sea ice anomalies on both sides of the bay tended to be associated with

weaker westerly winds. A similar correlation between winds and ice thickness is

observed on an annual basis. Again as the result of eastward dynamic forcing, ice piles up

on the eastern side of Hudson Bay leading to a disparity in thickness when compared

with the upwind west coast (Gagnon & Gough, 2006). These results highlight the role of

dynamic advection on asymmetry of sea ice conditions.

The examples above demonstrate east/west asymmetry that can be observed in a

single year. When considering the long-term trends of sea ice, coastal asymmetry can

11

also arise. In a study investigating the long-term trends of landfast ice thickness in

Hudson Bay, Gagnon and Gough (2006) found very different results for either coast. A

statistically significant thickening trend on the west coast was contrasted with a

statistically insignificant thinning trend on the east coast. The contrasting trends on the

west and east coasts were associated with negative temperature trends and the lack of a

negative temperature trend, respectively, albeit with many exceptions for specific sites.

The lack of correlation between temperature trends and ice thickness for these sites

suggested another important variable, which was identified as snow cover. The results of

this study provide an example of asymmetry in the long-term trends of sea ice on the

Bay.

These observed coastal asymmetries on the Bay in both annual sea ice patterns

and long-term trends in sea ice are an interesting by-product of the unique geography of

Hudson Bay. With the exception of the long-term trend in thickness, the unifying element

seems to be the prevailing westerly/northwesterly winds. This, combined with the vast

distances over which the winds can exert their influence, leads to some interesting east-

west contrasts.

2.5 Thermal Modification

The underlying mechanism leading to the temperature asymmetry on the Bay is

the thermal modification of overlying air through sensible and latent heat transfer. The

seasonality of this temperature asymmetry is brought about by the seasonality of sea ice,

which interacts with the boundary layer in a manner very different from water. The

contrasting roles of ice and water in terms of their ability to modify overlying air arise

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from two fundamental differences (1) the physical properties that dictate how each gains

heat, and (2) the way each exchanges heat with overlying air.

2.5.1 Physical Properties of Sea Ice vs. Water

The contrasting physical properties of land and water are a major driver of

weather and climate from local to global scales. The properties of sea ice are in many

ways analogous to those of snow-covered land or permafrost, though as we will see it can

also behave quite differently. One of the most important distinctions between water and

sea ice is in their albedo (α), or reflecting power of their surface. The albedo of open

water, though very high for solar altitudes of <30°, remains consistently between 0.03 to

0.10 for the majority of the day when the sun is at least 30° above the horizon (Oke,

1978). Averaged over a cloudless day, α for water is approximately 0.06, meaning only

6% of incoming shortwave radiation is reflected (Dieckmann & Hellmer, 2009). The

remaining 94% of that energy is transmitted throughout the water column and absorbed,

increasing the temperature of the water (more on that below).

Obtaining a generalized value for sea ice albedo is much more complicated, as it

can exhibit significant spatial, temporal, and spectral variability (Perovich et al., 1998). If

one were considering a uniform chunk of first-year, snow-covered sea ice, the albedo

would likely be in the range of 0.8-0.9 (Brandt et al., 2005; Grenfell & Perovich, 1984).

Bare ice albedo is significantly lower than snow covered, usually in the range of 0.5-0.7

(Perovich, 1996). For snow-covered ice, the age of the snow is also important as it

becomes more compacted and soiled with time, decreasing its albedo (Oke, 1978).

However, the most dramatic change to sea ice albedo happens when its coverage is

13

interrupted by water. This interruption can be caused by leads (large fractures) or

polynyas (circular opening in the ice caused by oceanic heat flux), in which case the

lower albedo of water can reduce the overall albedo for a given area. Melt ponds, or pools

of open water on top of sea ice resulting from surficial melting in the thawing season, can

also reduce overall albedo. Melt ponds only a few cm deep can reduce albedo down to

~0.5, but this value decreases exponentially with depth until it reaches that of open water

(Morassutti & Ledrew, 1996). Hence, sea ice albedo will decrease as the melt season

progresses, but so long as ice remains in a given area, its α will be greater than that of

water, and less energy will be absorbed than if that area were completely ice-free. As

Hudson Bay undergoes a complete annual cryogenic cycle, its overall albedo will

undergo this change on an annual basis. Furthermore, since all sea ice on the Bay would

be considered first-year ice, there should be no variability in albedo owing to multi-year

ice and average albedo during the period of complete ice cover should be >0.8.

The implication of the large difference in albedo between sea ice and open water

is that open water absorbs a much greater proportion of incident shortwave radiation. For

sea ice, the resulting shortwave flux during the winter months is insufficient to produce

enough heat to initiate a phase change to water, so its temperature rarely surpasses 0°C.

The much larger shortwave flux into open water leaves the potential for a much greater

change in its temperature. However, it is at this point that the other important physical

properties of water present a paradox. Despite being an excellent absorber of radiation,

the thermal response of water to this energy flux is very slow due to its ability to transmit

shortwave radiation to considerable depths, ability to dissipate energy through

convection, and high thermal capacity (Oke, 1978). The resulting thermal inertia of large

14

water bodies is the reason they play such a significant role in weather and climate

through systems such as land-sea breezes and lake-effect snow. Despite this lag between

energy flux and thermal response, large bodies will continue to warm up so long as

incident shortwave radiation is maintained or increasing. In the case of Hudson Bay, the

spatially averaged sea surface temperature (SST) reaches its maximum in August and is

typically ~7.5°C but has been as high as 9.9°C (Galbraith & Larouche, 2011). The

contrast between the higher temperatures of open water and the temperature of the sea ice

surface (0°C or less) is key to understanding the east-west asymmetry.

2.5.2 Heat Flux over Open Water

Sensible and latent heat flux are driven by the differences in temperature and

moisture, respectively, between a surface and the boundary layer. If the air and water

differ in terms of temperature, then there exists a gradient that will eventually be

eliminated by a flux of sensible heat (QH). The formula for sensible heat illustrates how

its flux is proportional to this gradient:

QH=ρACpCH|V|(TA-TSfc)

where, ρA = air density, V= velocity, Cp = specific heat capacity of air at ground,

CH = turbulent exchange coefficient, TA= air temperature, and TSfc= surface temperature

(Friehe & Schmitt, 1976). Say, for example, the overlying air temperature is TA=2°C,

while the temperature of the water at the surface is Tsfc= 7°C, then QH will be directed

upward into the air until a new temperature equilibrium is reached when TA=TSfc.

For latent heat flux, in the case of air advecting over open water, there will always

be a difference in moisture between the two mediums, as air saturated near the surface is

15

diffused by the turbulent atmosphere. This creates a sustained gradient in vapour

concentration, along which evaporation transfers energy (Oke, 1978). Similarly to QH,

latent heat transfer is proportional to that gradient, as well as the turbulent exchange

coefficient. Energy is drawn from the water itself and transferred into the overlying air as

a vertical flux of latent heat (QE). Simply put, the greater the magnitude of the difference

in conditions between surface and air, the stronger the gradient and hence the larger the

heat flux (Oke, 1978). Hence, the higher the SSTs on the Bay, and the more area of

exposed water, the greater potential that exists for upward fluxes in sensible and latent

heat respectively.

When an air mass transitions between surfaces of contrasting temperature (in this

case from permafrost to warmer open water), a thermal internal boundary layer (TIBL)

develops above the new surface within the larger atmospheric boundary layer (Stull,

1988). As the distance travelled by the air mass increases, the TIBL deepens as the now-

unstable warm air rises, driving further convection. By definition, the entire TIBL has

been influenced to some degree by the surface below, but it is usually only the bottom

10% that is considered to be in equilibrium with that surface (Kaimal & Finnigan, 1994).

The distance covered by this air mass travelling over a water body is termed “fetch”.

Initially, the greater the fetch, the longer time an air mass has in contact with open water

and hence the greater the transfer of heat. However, as the TIBL deepens, the differences

in temperature and humidity at the air-water interface are in turn diminishing. Therefore,

there is an upper limit to a fetch distance beyond which equilibrium between air and

water is reached and heat flux ceases to have a warming effect on advecting air (Stull,

1988). Depth of the TIBL grows as a function of fetch to a certain power that is

16

dependent on atmospheric stability, in the range of 0.2 to 0.8. (Stull, 1988). Unstable

conditions promote development of the TIBL, so the power is inversely proportional to

stability. Fetch distances for air masses arriving on the east coast of Hudson Bay may

vary depending on the direction of the wind, but a geodesic line drawn from Churchill

(west coast) to Inukjuak (east coast) yields a distance of 928 km. Studies aiming to

quantify fetch distances required for full adjustment of the boundary layer to new

surfaces are usually concerned with distances far smaller than this, ranging from 10s of

metres to a few hundred km (Garratt, 1990). For fetch distances on the scale of those in

Hudson Bay, it is safe to say that even under stable conditions the TIBL will be fully

developed and hence modulate air temperature downstream.

2.5.3 Heat Flux over Ice

The exchange of heat at an interface between air and ice, while adhering to the

same physical principles outlined above, is very different than that which is seen in the

case of an air-water interface. The latent heat flux from ice is lower than that of water

because in order to release that heat the ice must undergo two phase changes. Hence,

energy that would be expended on transitioning water to vapour (releasing latent heat in

the process) must first be used to facilitate the transition from ice to water (Oke, 1978).

Likewise, sensible heat flux from ice will also be lower than that from water owing to the

fact that its temperature is always <0°C. At the onset of spring melt, when the ice/snow

approach 0°C these energy fluxes become more complicated, but in general upward heat

flux will increase as the surface becomes water-dominated.

17

One of the complicating factors that distinguish sea ice from snow-covered land is

that of ice thickness. While sea ice often acts as a barrier to energy flux between water

and the atmosphere, its insulating power is highly dependent on its thickness (Dieckmann

& Hellmer, 2009). Systems such as Hudson Bay that undergo complete annual cryogenic

cycles experience a continuum of ice thicknesses during the breakup and freeze-up

seasons. Furthermore, even when peak thickness is reached, there will be considerable

spatial variability latitudinally as well as longitudinally owing to the prevailing NW

winds (Gagnon & Gough, 2006; Gough et al., 2004b). It is important to account for these

variations as they can have a dramatic influence over the heat exchange between air and

water, especially when the ice is thin (Maykut, 1982). From the equation:

hQ*=k(TS-TW)

where, h=ice thickness, Q*=net heat flux, k=thermal conductivity of ice, TS=temperature

of ice surface, and TW=water temperature; we can see that heat flux through ice is

proportional to the temperature gradient between water and the ice surface, and inversely

proportional to ice thickness. To further complicate matters, the layer of snow often

found on sea ice has its own insulating properties that are depth-dependent, and act to

reduce heat losses from ice (Maykut, 1986). The heterogeneities in heat flux imparted by

melt ponds, variable ice thickness, and leads/polynyas suggest that: i) even under total ice

cover the energy budget of a water body may differ from that of snow-covered land,

hence ii) a TIBL will likely develop over the water body, but iii) said TIBL will also be

very spatially heterogeneous and complex, comprised of “IBLs within IBLs” (Stull,

1988). The last point is particularly applicable for freeze-up and breakup periods when

sea ice cover is highly variable.

18

Evidently, there are several complex interrelated variables that combine to dictate

energy exchange between air and water in a sea-ice system at any given time. What is

clear is that heat flux from water to the boundary layer is much greater for an ice-free

water surface than an ice-covered one. Studies aiming to quantify this disparity have

revealed a difference of two orders of magnitude. While heat flux over multi-year ice has

been shown to be less than 5 Wm-2 (Maykut, 1982), open water-air heat flux can be as

high as 600 Wm-2 (Maykut, 1986; Andreas & Murphy, 1986). Given that the balance of

this energy will go towards heating the boundary layer, it is evident that sea ice will

modulate regional temperatures to some degree. In areas that undergo seasonal growth

and retreat of sea ice such as Hudson Bay, this influence will be most evident between

annual extremes. In between these extremes, heterogeneities in sea ice concentration and

thickness conspire to make quantifying heat flux over the entire Bay, and hence effects

on temperature, very difficult.

2.6 Temperature as a Proxy for Sea Ice

The relationship between sea ice and the east-west coastal temperature asymmetry

on the Bay is a site-specific one. Since the relationship is dependent on the unique

geography of the area, its use as a tool for predicting or hindcasting cannot be reapplied

to other locations. There is currently no literature that explores this asymmetry, nor any

other metric of temperature as a potential proxy for sea ice on the Bay. Despite the

unique nature of the Bay, studies focusing on similar sites and their accompanying sea

ice-temperature relationships might prove valuable in developing a proxy hindcasting

tool. The fundamental difference between these studies and what is being undertaken by

19

this study must first be stressed. In most cases where temperature acts as proxy for sea

ice, it is the temperature that is driving the resulting sea ice concentration by creating

conditions leading to either its formation or degeneration. In the case of Hudson Bay,

while clearly this is also happening, it is presumed that the sea ice (or lack thereof) is

driving the temperature on the east coast and hence the asymmetric temperature signal.

Despite this important distinction, any use of temperature as a proxy for sea ice would

help evaluate the performance of a new method. Unfortunately, studies on the use of

temperature records as a proxy for Arctic sea ice are scant. More often, broad estimates

on sea ice conditions are inferred indirectly from temperatures which themselves have

been derived via other proxies (Macias-Fauria, 2010; Isaksson et al., 2005; Polyak et al.,

2010) This is perhaps due to the fact that temperatures only serve as a very coarse stand-

in for sea ice, and are therefore only useful when there are no superior alternatives.

Though there is little precedent in the literature for temperature proxies for sea

ice, studies on lake ice may be relevant given Hudson Bay’s morphology. The shallow

channels north of Hudson Bay limits water exchange and thermal influences from the

Atlantic Ocean while advection of sea ice into and out of the Bay is negligible,

characteristics befitting of lakes (Etkin, 1991; Saucier & Dionne, 1998). In a

comprehensive analysis of lake ice records for all Canadian lakes, Williams (1971) found

that the breakup date (defined in this case as the date at which the lake is 100% ice-free)

was predicted within a standard error of 1.6-4.3 days if the date of the start of breakup

was known along with temperatures for the duration of the melting period.

In certain cases, the predictor and predictand in the sea ice-temperature coupling

might be reversed such that sea ice conditions serve as a proxy for air temperature. This

20

approach has shown some success in reconstructing local air temperatures for areas with

extensive ice records. For example, the timing of ice-breakup on a high-altitude lake in

the Swiss Alps was shown to have a shared variance of 64% with local air temperatures

(Livingstone, 1997). In this case, where the ice records predate those of temperature,

breakup dates may be used as part of a multi-proxy approach to hindcast local air

temperature. However, other factors such as local weather, lake morphometry, and

sheltering prevent a more direct relationship between the two variables, and hence limit

accuracy of such predictions. In a similar study based on lakes in Finland, Palecki &

Barry (1986) suggested that freeze-up and breakup dates derived from satellite

observations could be used as a proxy for air temperature in mid-to-high latitudes that

lacked data coverage. This conclusion was drawn from the fact that they could correlate

changes in dates of freeze-up/breakup to a certain change in mean monthly temperature

leading up to that date. However, the regression coefficients varied across the country,

and were only suitable for hindcasting temperature for an area a few hundred km in

diameter.

The dearth of studies aimed at using temperature as a proxy for sea/lake ice, or

vice-versa, may be indicative of the inadequacies of such an approach. Indeed, of the few

studies found that do show some predictive value in certain sea ice-temperature

correlation models for a specific area, the authors admit such predictions are improved

upon or made redundant by complementary or alternative approaches employing other

proxies. The limited spatial scale of the studies that demonstrate some predictive value

also points toward the limitations of this approach. As scale increases, the

21

temperature/ice signal may be increasingly overridden by the effects of synoptic scale

systems.

2.7 Other Proxies for Sea Ice

Reconstruction of sea ice records need not necessarily rely on meteorological

proxies, the disadvantages of which have been noted. There is an abundance of evidence

in the paleorecord for decadal to millennial-scale changes in sea ice using marine

sediments, coastal depositions, driftwood and skeletons of microscopic organisms

(Polyak et al., 2010). Of primary interest to this study however are those proxies that can

resolve sea ice conditions at a sub-annual time scale.

Recent advances in ice core analysis have led to reconstructions of sea ice records

in Antarctica using chemical tracers preserved in the ice. One such advance involves the

analysis of methane sulfonic acid (MSA), produced through oxidation of the biogenic

dimethylsufide (DMS) from the ocean and subsequently aerially transported and

deposited in the continental Antarctic ice sheet (Abram et al., 2013). Since productivity

of DMS (and oxidation of MSA) increases with the area of ocean exposed to sunlight, a

positive relationship between Antarctic ice core MSA records and sea ice variability

should exist (Welch et al. 1993; Curran & Jones, 2000). This seems to be the case,

although the results are mixed and site-specific as the MSA production signal is

complicated by variability in its concentration resulting from its transport. Nevertheless,

researchers have found statistically significant relationships between SIE and MSA

production for various regions in the Antarctic that may be applied to reconstruct sea ice

22

records as far back as 160 years (Foster et al, 2006; Curran et al, 2003; Abram et al.,

2010; Abram et al, 2013; Becagli et al, 2009).

Another method employing ice core chemistry as a proxy for sea ice involves sea

salt aerosols generated through atmospheric interaction with open water. As with MSA,

the sea salt particles are transported to the Antarctic continental ice sheet where they are

deposited and preserved in the ice strata. Measurements of sodium in the ice core are

most representative of sea salt aerosols, and should in theory be negatively correlated

with sea ice extent (Abram et al., 2013). This was shown to be the case in the Canadian

Arctic, where sea salt sodium from an ice core on the Penny Ice Cap was negatively

correlated with spring SIE in Baffin Bay over the 20th century (Grumet et al., 2001). This

correlation was weak however, such that only 7% of the variability in sea salt was

accounted for by changes in SIE. Attempts to find a similar correlation in the Antarctic

have been complicated by the fact that sea ice itself seems to be a major source of

fractionated sea salt aerosols in the winter at coastal regions (Rankin et al, 2002; Douglas

et al, 2012; Abram et al, 2013). These findings have led researchers to believe that this

approach is best suited to areas that are dominated by open water such as the Arctic

Ocean (Abram et al, 2013).

Although ice core records contain a wealth of information of past climate

conditions, their application to sea ice conditions is still in its infancy. Both the MSA and

sodium methods have their limitations in their respective locales, and their applicability

to the broader Arctic is even more uncertain. Furthermore, as both methods rely on

atmospheric transport of chemical compounds, their accuracy diminishes with increasing

distances from source to deposition. This makes them particularly unsuitable for

23

reconstructing sea ice conditions on Hudson Bay as the distance between the Bay and the

nearest viable ice cores is on the order of 1000s of km.

2.8 Literature Summary

There is a clear consensus on the decline in Arctic sea ice (Comiso et al., 2008:

Parkinson et al., 1999; Stroeve et al., 2007; Vinnikov et al., 1999). Despite having

comparatively fewer studies on the subject, consensus appears to be growing for a similar

trend in Hudson Bay (Gagnon & Gough, 2005; Gough et al., 2004b; Hochheim et al.,

2011; Hochheim & Barber, 2010). A longer sea ice record would undoubtedly aid in

further characterizing this trend, but a review of the literature revealed no proxies for sea

ice on Hudson Bay. A few select studies on lake ice have had some success with proxies

exploiting its relationship to local temperatures, though limitations of scale suggest the

same approach for Hudson Bay might not yield the same results (Livingstone, 1997;

Williams, 1971; Palecki & Barry, 1986).

One of the defining characteristics of sea ice on Hudson Bay is the tremendous

spatial and temporal variability it exhibits throughout the cryogenic cycle (Hochheim &

Barber, 2010; Hochheim et al., 2011; Gagnon & Gough. 2005; Markham et al., 1986).

Often this variability manifests itself into a relatively well-defined east-west coastal

asymmetry. The prevailing westerly winds have been shown to have a strong role in these

asymmetries, through dynamic advection of sea ice eastward (Hochheim et al., 2011;

Gagnon & Gough, 2006; Saucier et al., 2004).

The theoretical basis for thermal modification of advecting air on the Bay has

been established by illustrating the contrast between open water and sea ice in terms of

24

their energy fluxes with the boundary layer atmosphere, which can vary by orders of

magnitude (Andreas & Murphy, 1986; Maykut, 1982; Maykut, 1986). Since these fluxes

vary with ice thickness, melt-pond coverage, snow depth, and other factors;

heterogeneous sea ice cover will likely have a much less predictable effect on advecting

air (Dieckmann & Hellmer, 2009, Maykut, 1986; Maykut, 1982). In summary, the

literature strongly supports the theory of sea ice leading to a temperature asymmetry on

Hudson Bay, but it remains unclear how this asymmetry will respond to the various states

of coverage seen throughout the cryogenic cycle.

25

Chapter 3: Methodology

3.1 Site Selection and Description

3.1.1 Hudson Bay Region

Hudson Bay covers an area of 1,300,000 km2 and has a drainage basin

encompassing 3,861,400 km2 (Martini, 1986; NRCAN, 1985). While connected to both

the Atlantic Ocean via Hudson Strait, and the Arctic Ocean via Foxe Basin, its waters

flow predominantly into the Atlantic (Lewis et al., 2000). Due to the large extent of the

Bay, its shores occupy various terrestrial ecozones, each exhibiting slight variations in

landform characteristics and regional climate (EFC, 2013). The Hudson Plains ecozone

covers much of the southern and western coasts of the Bay, including James Bay.

Roughly coincident with this ecozone is the Hudson Bay Lowlands, the largest wetland in

North America, characterized by vast stretches of peat bog and marsh. This region marks

a transition between temperate and arctic in terms of climate and biogeography. North of

the plains, the Taiga Shield ecozone covers much of the east coast of the Bay, and some

of the west coast. Here the peatlands give way to drier, flat terrain with rolling hills. The

northern half of the Bay is dominated by the Southern Arctic ecozone on both coasts. The

landscape of rolling plains is barren of trees due to harsh winters. Permafrost, defined as

ground that remains at or below 0°C for a minimum period of two years, is a prevalent

feature for all coastal areas of the Bay (NRCAN, 2009). All western coastal regions of

HB, as well as the northeastern coast, contain continuous permafrost (90-100%). James

Bay and the southeastern coast of HB experience isolated patches (0-10%) to extensive

discontinuous permafrost (50-90%), increasing in prevalence with latitude (NRCAN,

2009).

26

It is clear that the size of the Bay and resulting variability in climate factors

should be acknowledged when attempting to isolate for the influence of sea ice. Hence,

this study requires at least two sites with sufficiently lengthy climate records that also

fulfill the following criteria: (1) located on western and eastern coasts of the Bay (one of

each), (2) at latitudes comparable enough as to eliminate that as a source of climatic

variability, and (3) sharing other geographical characteristics that may contribute to

climatic differences such as terrain and altitude. Given the relative scarcity of climate

stations in the HB area, there are only two sites with climate records that fulfill criteria 1

and 2: Churchill, Manitoba and Inukjuak, Quebec. The suitability of these sites based on

criterion 3 is discussed below.

3.1.2 Churchill and Inukjuak: Local Climatic Factors

The town of Churchill, MB is located in the Northern region of Manitoba, on the

west coast of the Bay, at 58°46’09” N, 094°10’09” W. Inukjuak is a village and Inuit

community located in the Nord-du-Québec region of northern Quebec, on the east coast

of the Bay, at 58°27’00” N, 78°06’00” W. The fact that both sites are within less than

half a degree of latitude from each other means it is within reason to assume negligible

climatic variability owing to latitudinal differences. As temperatures typically decrease

with height, differences in elevation above sea level (m.a.s.l.) should be considered.

Orographic features that might obstruct or funnel wind, induce precipitation, or otherwise

influence climate should also be identified. As it turns out, the topography of Churchill

and Inukjuak are similar enough to discount these potential sources of climate variability.

Churchill being located at the intersection of the aforementioned Hudson Plain, Southern

27

Arctic and Taiga Plains ecozones, and Inukjuak being in the Taiga Plains ecozone,

topographic features for both sites are limited to rolling hills and plains. The elevations

of the weather stations used in this study are 29 and 25 m.a.s.l. for Churchill and

Inukjuak, respectively. Since both sites are located in regions classified as continuous

permafrost, energy and moisture flux at the land-atmosphere interface would be similar in

both cases and hence not account for differences in climate.

Both Churchill and Inukjuak are coastal communities, and as such we would

expect temperature and winds at both locations to be moderated to a certain degree by the

open water during the ice-free season. These effects play out on seasonal timescales (the

basis of this study), as well as diurnal time scales. For example, diurnal changes in

land/water temperature differences leads to a land and sea breeze circulation that can in

turn influence local air temperatures (Oke, 1978). This same mechanism accounts for

diurnal fluctuations in wind direction (e.g. an afternoon onshore breeze may change wind

direction). However, the design of this study assumes that these localized effects are

overridden by larger scale atmospheric circulation. In other words, it is assumed that over

the long term temperatures on both coasts are largely being driven by the westerlies – the

winds blowing from west to east that dominate in the middle latitudes. Monthly climate

normals show the most frequent wind direction for Churchill to be either W or NW in

every month except June (when it is NE). In Inukjuak, the westerlies appear to dominate

most months; however there are some months when the most frequent wind directions are

NE (March, April May) and N (June and November). Despite mostly prevailing

westerlies at both sites, wind frequency distributions show some variability month-to-

28

month and between coasts. Such differences will be taken into account as necessary (see

3.5 Wind Direction Analysis).

With the exception of wind direction, major climatological factors are very

similar between the proposed study sites. Therefore, most of the asymmetrical

temperature signal can confidently be attributed to the thermal influence of the Bay

combined with the prevailing westerlies.

3.1.3 Weather Stations/Climate Data

The weather stations used to represent climate in Churchill, MB and Inukjuak, QC

are listed below.

Table 1: Climate station summary.

Name Latitude Longitude Climate ID WMO ID Elevation Churchill (A) 58°44'21.0” N

94°03'59.0” W

5060600 N/A 29.30 m

Inukjuak (A) 58°28'00.0” N

78°05'00.0” W

7103283

N/A 25.30 m

Inukjuak (UA) 58°28'00.0” N

78°05'00.0” W

7103282

71907

24.40 m

While data for Churchill was sourced from a single climate station, it was

necessary to combine data from two Inukjuak stations to produce a record of comparable

length. Despite the change in station ID, the coordinates and elevation are nearly identical

so it is assumed there are no implications for data quality and continuity (See 3.9 Notes

on Data Quality).

29

3.2 Defining Temperature Asymmetry: ∆T

Since it is not the values of coastal temperatures themselves that are of primary

interest to this study, but rather the difference between those values, a new variable was

defined. The variable ΔT, with units of °C, is defined as the temperature at Inukjuak

subtracted from the temperature at Churchill for the same time interval (ΔT = TCHURCH –

TINUK). By this definition, a positive ΔT indicates that Churchill was warmer than

Inukjuak for that time interval, while a negative ΔT indicates that Inukjuak was warmer

than Churchill. Since the main period of interest for this study is the time between the

start of ice melt and when it is completely frozen, one would expect the thermal effect of

open water would result in warmer temperatures in Inukjuak most of the time (assuming

prevailing westerlies). Thus, it is expected that ΔT during this period of interest will most

often be negative. Ultimately the sign of ∆T is arbitrary, as long as it is clear which of the

two coasts is warmer, so it is the magnitude of this value that is of greatest importance.

The resulting database of ∆T values was used to construct a high-resolution

climate normal for this new variable. A single value was obtained for each Julian day (1-

366 including leap year days) by averaging ∆T values for that day from all years on

record. The resulting plot showed the average progression of ∆T throughout the year and

helped define another index of coastal temperature difference (See Figure 2).

3.3 Assessing Weekly SIC-ΔTW Correlation

The first approach taken to characterize the relationship between sea ice

concentration (SIC) and ΔT was to examine the correlation at a weekly time scale. The

assumption is that in the 1-week period between SIC observations, the SIC at the start of

30

that period is driving ΔT such that each SIC value might have a unique ΔT signal

associated with it. To assess that relationship, each SIC observation was paired with a 7-

day average ΔT (ΔTW) that spanned the day the SIC observation was made to the day

prior to that when the next SIC observation was made. In cases when more than 7 days

elapsed between observations, or when observations ceased at the end of the freeze-up

season, the same 7-day average was calculated to maintain consistency. Having

calculated a ΔTW for each unique SIC observation, the two variables were tested for

correlation using simple linear regression.

In addition to the analysis of all SIC observations, two further analyses were

conducted that separated the observations into those that occurred during breakup and

those that occurred during freeze-up. As shown in the Literature Review, the warming

effect of the Bay, and hence ΔT, is largely dependent on the temperature of the water

itself. Since water temperature will be increasing throughout the summer, it is likely that

the amount of temperature modulation for any given SIC will be different depending on

whether that observation is made during breakup or during freeze-up. Hence, another

simple linear regression analysis was performed only for those observations prior to the

first observation of SIC=0 in a year. Likewise, another analysis was performed only for

those observations following the last observation of SIC=0 in a given year. This provided

two sets of data, the former representing the breakup period and latter representing the

freeze-up period, in an attempt to eliminate the variability imparted by the seasonal

difference in water temperature.

31

3.4 Assessing IFS -∆T Correlation

In the event that the sea ice-∆T relationship could not be resolved at finer

spatial/temporal scales, it was hypothesized that the cumulative effects of open water

might produce a signal in ∆T towards the end of the season. In other words, the relative

length of time when the Bay is predominantly open water might be knowable based on

the maximum ∆T (averaged over a certain period to eliminate variability), which is

presumably reached towards the end of the season when the water itself is at its warmest.

If so, one would expect an anomalously lengthy ice-free season to correspond with an

anomalously high |∆T| (more negative by our definition of ∆T).

3.4.1 Capturing Maximum ∆T

Having created a high-resolution ∆T climate normal (Figure 2), it was possible to

identify the period(s) of greatest temperature asymmetry. From this visualization, the

time of year when the maximum |ΔT|s are most likely to occur seems to lie in the range

of Julian days 320-350 (November 16th to December 16th for normal years, November

15th to December 15th for leap years). Hence, a 31-day average of ∆T covering this period

was identified as ∆TMAX and calculated for all available years. The averaging of ∆T over

this specific period was done in hopes of i) capturing the time of year when |∆T| is at its

highest, and ii) eliminating some of the noise in the data.

32

3.4.2 Determining Ice-Free Season Length

As discussed in the Literature Review, breakup and freeze-up dates are defined as

the date when SIC passes the 5/10 threshold. Using these dates, a new variable was

identified as “ice-free season length” (IFS). This variable was defined as the number of

days between the breakup date and the freeze-up date. Note that, while by definition it is

the number of days when SIC<5, here it is serving as a general measure of the relative

lengths of the season where the Bay is predominantly open water. Gagnon & Gough

(2005) determined breakup and freeze-up dates from 1971-2003 for 36 point coordinates

evenly distributed throughout the Bay (See Figure 1). This database has since been

updated by S. Kowal (pers. comm., 2012) to include the years 2004-2011. Although

breakup and freeze-up dates vary significantly throughout the Bay according to sea ice

advance and retreat patterns, these data had to be homogenized into a single annual value

in order to capture the influence of season length on the Bay as a whole. To that end, a

single breakup date and a single freeze-up date were produced for each year in the record

by simply averaging the dates of the 36 points. The difference between the breakup and

freeze-up date was then calculated to provide a single value indicative of ice-free season

length for each year.

33

Figure 1: Site map of Hudson Bay indicating the location of the 36 points for which breakup and freeze-up dates were derived (Gagnon & Gough, 2005; reprinted with permission from the Arctic Institute of North America).

3.4.3 Classification of ∆TMAX by IFS

In the interest of ultimately developing a proxy tool that could approximate IFS

based on ∆TMAX alone, a simple classification scheme was devised consisting of three

categories:

Table 2: Definition of classes of ice-free season length.

Class Ice-Free Season Length (days) Short < 129

Medium 130-149 Long >150

This content downloaded on Wed, 16 Jan 2013 20:53:52 PMAll use subject to JSTOR Terms and Conditions

34

The range of these categories reflects the IFSs for the available 40-year sea ice

record, which ranges from 111-180. With exception to the outlier year when IFS=180,

values range from 111-170, meaning three equidistant categories with a range of roughly

20 days can be defined. Using this scheme, ∆TMAX values for each available year were

classified based on the IFS for that same year. This allows for a comparison of the ∆TMAX

values that arise in three generalized scenarios of IFS, as well as a measure of how likely

it is that a given year might be misclassified based on its ∆TMAX. A comparison of the

means of each category was conducted using the one-tailed homoscedastic Student’s t-

test. The resulting p-values were then adjusted using the Bonferroni correction. This

correction is a simple method by which we can counter the greater familywise error rate

associated with performing a multiple-hypothesis statistical test (Dunn, 1961). In this

case, the null hypothesis that all classes are not different in terms of their populations’

∆TMAX values is actually three null hypotheses that there are no differences between i)

short and long classes, ii) short and medium classes, and iii) medium and long classes.

Increasing the number of hypotheses applied to a dataset also increases the likelihood of

encountering anomalous events, and hence the likelihood of making a Type I error. To

mitigate this effect, p-values are multiplied by the number of hypotheses (three in this

case), and hence held to a higher standard of statistical significance.

Based on the results of this classification and comparison of means, thresholds of

∆TMAX were defined on the basis of minimizing overlap between categories. For

example, the threshold between the short and medium categories was selected by its

ability to maximize the actual short years captured while minimizing long or medium

35

years captured that simply had a ∆TMAX more indicative of short years. It is these ∆TMAX

thresholds that would eventually serve as the basis for classifying years as having a short,

medium or long IFS. To determine how well ∆TMAX predicts IFS, years with ∆TMAX s

outside of the defined threshold for their category were tallied. The count of these years

expressed as a percentage of n=33 provides the fraction of misclassified years using this

particular method. The closer this percentage value is to zero, the more successful the

method predicts the record, and hence the better it is expected to perform as a hindcasting

tool.

3.5 Wind Direction Analysis

3.5.1 Wind Direction Counts/Wind Rose Construction for ∆TMAX Period

As noted in 3.1.2, there are discrepancies in the climate normal between Churchill

and Inukjuak that prevent us from simply assuming prevailing westerlies during the

∆TMAX period. Inukjuak in particular seems to deviate from this pattern more frequently,

including during November when the most frequent direction is from the north. An

analysis of the wind directions in Inukjuak during the period of maximum ∆T might help

clarify why certain years do not exhibit the ∆TMAX signal expected given the length of the

ice-free season.

Wind direction data for the area was available in the form of hourly observations

in units of 10s of degrees on a 36-point wind rose. To simplify the data into more

meaningful directions, observations were reclassified on an eight-point rose in

accordance with Environment Canada’s guidelines (EC, 2013a). The frequency count for

each of these eight classes was then summed over the same 31-day period used for

36

calculating ∆TMAX (Julian Days 320-350). From these values, a single wind frequency

distribution chart (wind rose) was constructed for each year on record that is specific to

the period during which the Bay is exerting its greatest influence on advecting air. The

wind rose analysis focused on those years when ∆TMAX did not conform to the

established thresholds based on IFS (i.e. all misclassified years) in search of some pattern

explaining these anomalies.

Having qualified the relationship of anomalous ∆TMAX values to the distribution

of wind directions, the correlation between ∆TMAX and specific combinations of

directions was quantified by linear regression. The W and NW components of the

constructed wind roses were summed into a single value, NW+W, meant to be an

indicator of the relative frequency of winds arriving in Inukjuak that have been thermally

modified by the Bay. As a complementary approach, the summed components of NE+E

were calculated to serve as an indicator of the relative frequency of winds arriving in

Inukjuak over land and hence not subject to the same thermal modification. The northerly

component of the wind roses was omitted from this analysis as these winds have travelled

over both land and water and hence are not likely to contain as clear a signal of sea ice

conditions. Both NW+W and NE+E were correlated with IFS by linear regression and

tested for statistical significance.

3.5.2 Re-classification of ∆TMAX for Low NE+E Years

Having shown the correlation between IFS and NE+E to be the most statistically

significant, the classification of ∆TMAX values by IFS was done again. This time, only

years when NE+E counts were below average were included. The resulting percentage of

37

misclassifications was then compared to the original analysis to determine if this

approach eliminates weak ∆T signals on account of predominant easterly and

northeasterly winds.

3.6 Evaluating Proxy Performance: Temperature as a Benchmark

In order to evaluate ∆TMAX as a proxy for IFS, a benchmark using another proxy

method was established against which the rate of misclassification could be compared.

As discussed in 2.7, there has been some success in using temperature as a stand-in for

sea/lake ice conditions (Livingstone, 1997; Palecki & Barry, 1986; Williams, 1971).

These studies stress the limitations of such an approach, making temperature a very

coarse approximator of sea ice. This provides a suitable benchmark, as any method

outperforming it can be identified as a superior alternative to the worst-case scenario

proxy method.

There are a number of different indices of temperature one can use to correlate to

sea ice by focusing on different areas of the Bay and periods of the cryogenic cycle. For

simplicity and consistency, the same temperature records for Churchill and Inukjuak used

to calculate ∆T were used to calculate a new index of temperature that is representative of

the whole Bay. The two temperature records were combined into a single average

temperature record ([TCHURCH + TINUK]/2). The period over which this spatially averaged

temperature was temporally averaged was optimized to capture a period when

temperature is likely to be exerting an influence on IFS. This period was chosen to be the

61 days spanning Julian days 260-320 (Sept. 17th to Nov. 16th for regular years; Sept. 16th

to Nov. 15th for leap years). This period was chosen because it encompasses the vast

38

majority of the freeze-up process, during which air temperatures play a role in either

promoting or delaying ice formation, thereby lengthening of shortening IFS. Having

defined this index of temperature as TF, another classification scheme was developed in

the same fashion as that of ∆TMAX, using new thresholds of TF. All three classification

methods were then compared in terms of their performance in classifying the existing

record.

3.7 Combined Approach: ∆TMAX and TF in a Multi-Proxy Results from the evaluative process described above led to the consideration of TF

as either an alternative or a complementary proxy. The relationships that both ∆TMAX and

TF exhibit with IFS suggest that both variables each contain some unique information

regarding ice-free season length. Despite both variables being indices of mean air

temperature, they are different in terms of: i) the temporal period over which they are

calculated and, ii) the underlying mechanisms that relate them to IFS. In the case of

∆TMAX, it is the sea ice (or lack thereof) that is acting upon advecting air that leads to the

temperature difference signal. In the case of TF however, it is TF that is acting upon sea

ice (or open water), hence playing a role in determining IFS. Furthermore, despite being

the most highly correlated to IFS, TF by definition contains only information regarding

freeze-up conditions. By contrast, ∆TMAX is theoretically determined by the cumulative

effects of open water, and hence should inherently contain some information regarding

break-up conditions. Therefore, the information contained in TF and ∆TMAX with respect

to IFS should not be redundant, and it should be expected that a multiple regression

between both temperature variables and IFS would yield a more significant relationship

39

than either temperature variable alone. If so, the use of the regression equation to hindcast

IFS in lieu of the classification scheme might produce higher resolution results within an

acceptable range of error. To test this hypothesis, a multiple linear regression was

conducted on the 33-year record with IFS as the dependent variable and both ∆TMAX and

TF as independent variables. The resulting equation was assessed as a proxy by its ability

to recreate the historical IFS record. The difference between actual IFS values and those

produced from the equation was calculated as absolute error. As with the classification

approach, TF was used as a benchmark of comparison, to assess if the ∆TMAX + TF multi-

proxy results offer a significant improvement. Thus another comparison of actual IFS vs.

IFS derived from a linear equation was conducted, this time using a simple linear

regression equation derived from just TF and IFS. A comparison of the errors produced

from either approach informed the final decision of what proxy method is best suited to

hindcast IFS.

3.8 Hindcasting and Trend Analysis of Extended Record

Given the success the multiple regression equation had with recreating the

historical record, it was determined that this method could confidently hindcast IFS prior

to 1972 (See Tables 14 & 15). Hence, IFS values were calculated for all years prior to

1972 with available temperature data for both Churchill and Inukjuak. The resulting

hindcast time series was appended to the actual IFS time series for comparison. To

highlight the long-term trend in IFS, a five-year moving average time series was also

produced by producing new values for each year that are an average of the two preceding

values, the value itself, and the two following values. For example, the new IFS value for

1990 would be the average of values from 1988, 1989, 1990, 1991, and 1992. The

40

application of this method eliminates four years from the data set, as the first and last two

years of the data set are lacking the two preceding/following years respectively.

To determine if there are any trends in the data set, the Mann-Kendall statistical

test was employed to produce Kendall’s tau coefficients (τ) for various portions of the

original time series (not the data smoothed by moving average). This non-parametric test

provides a measure of rank correlation, or probability that two variables are ranked in the

same order (Kendall, 1938). The test yields a τ value between -1 and 1, with the sign and

magnitude of τ indicating the direction and probability of a correlation between two

variables, and a value of 0 indicating no correlation. In the case where the independent

variable is time, that correlation corresponds to a temporal trend in the dependent

variable. The test was run using the XLSTAT add-on for Microsoft Excel 2011. The

hypotheses for these tests were as follows:

H0= There is no trend in the time series. HA=There is a trend in the time series.

In order to contextualize any trends in IFS, τ values were obtained for various

periods of the extended time series. Firstly, the hindcast time series was considered on its

own as a baseline period for IFS and compared to the actual time series in terms of τ. In

order to identify the period where it is most probably that a trend is occurring, additional

analyses were done using different division points in the dataset at five-year intervals

from 1980 to 1990.

41

3.9 Notes on Data Quality

All climate data obtained from Environment Canada has been reviewed and

undergone the appropriate procedures to ensure it conforms to their own data quality

standards (EC, 2013b). Some issues may arise in this study as new variables are

constructed as a combination of other variables (e.g. 31-day temperature averages). To

ensure the validity of the conclusions drawn from this data, certain guidelines were

followed to omit variables for certain years if their constituent values were sufficiently

lacking.

3.8.1 Temperature Data

The mean daily temperature record for Churchill, which extends back to 1943, is

continuous and uninterrupted with the exception of three missing months in the period of

1944-1946. There are no missing values for the period of 1972-2011. Inukjuak’s

temperature record is more fractured, as it is split between two climate stations and

contains periods with intermittent gaps in the daily records. The records for both Inukjuak

stations were combined into a single record on the assumption that their nearly identical

geographic coordinates and elevation obviated any need for data homogenization. The

transition between stations occurs in 1994, and as a result that year is severely lacking in

data and thus omitted from the analysis.

Environment Canada’s “3 and 5” rule allows for the calculation of an average

monthly temperature if the month has no more than 3 consecutive missing daily values

and no more than 5 total missing daily values (S. Allen, pers. comm., 2013). This quality

standard serves as a useful benchmark in the calculation of ∆TMAX, as it is a 31-day

average. In this case, a slightly less stringent “4 and 7” rule was followed in calculating

42

31-day averages. This is to allow for the inclusion of the year 2001 in the analysis, when

the 320-350 period contains 4 consecutive missing days and a total of 7 out of 31 missing

days. Note that all other years adhere to the “3 and 5” rule.

The distribution of data for all temperature indices was tested for normality using

the Anderson-Darling test, with the null hypothesis that the input data come from a

normal population (Stephens, 1986). The test on ∆TMAX produced p-value of 0.1465,

meaning the null hypothesis cannot be rejected. The test on TF produced a p-value of

0.5456, meaning the null hypothesis cannot be rejected. The test was not run on the raw

∆T database as the population was extremely large and these values were not used for

any trend analysis, eliminating the need to demonstrate normality.

3.8.2 Wind Direction Data

The availability of wind data for Inukjuak is limited to the period of 1981 to 2007.

This record contains 24 hourly observations available for most days in the 320-350

period, with the exception of certain years when hourly observations may be as low as

12. In order to eliminate the influence of diurnal fluctuations in wind (e.g.

onshore/offshore breeze), it is important to use only those days whose hourly

observations number at or near 24. To that end, wind direction analysis was only

conducted for years when the 320-350 period met the following criteria: i) no more than

10 days when # of observations < 22, ii) no more than 2 days when # of observations <

20, and iii) 0 days when # of observations < 14. The application of these quality

standards resulted in the omission of years 1992 and 1993. The test for normality was

done only on the wind direction components used in the linear regression with IFS

43

(NE+E). The resulting p-value of 0.0016 indicates that the null hypothesis may be

rejected at the 99% confidence interval. This lack of normality means that any trend

analysis of IFS values obtained by a proxy that includes wind data would require the use

of non-parametric tests.

3.8.3 Ice-free Season Data

There are 36 geographical points used to derive the spatially averaged breakup

and freeze-up dates, and most years all of them are accounted for. However, there are a

few years when dates are unavailable for certain points, usually because freeze-up/break-

up had already occurred before observations were made (Gagnon & Gough, 2005). In

these cases, years were included only if n≥20. If either a breakup date or a freeze-up date

was deemed unusable, then the ice-free season length for that year was not calculated.

This resulted in the omission of years 1973, 1997, 1998, 1999, and 2002. The test for

normality on the IFS dataset yielded a p-value of 0.9489. Hence, there is insufficient

evidence to warrant the rejection of the null hypothesis that the data comes from a normal

population.

44

Chapter 4: Results

4.1 ΔT Climate Normal

The calculation of ΔT using Churchill and Inukjuak temperature data produced a

dataset 68 years in length spanning from 1944 to 2011. The only years missing enough

data to be omitted were 1994, when the moving of the Inukjuak station left a gap in its

record, and 2008 when the latter half of the year’s data is missing for Churchill. The

following graph depicts the daily fluctuations in ΔT for a year as an average of the entire

record.

Figure 2: Climate normal for ∆T (Churchill Daily Mean T - Inukjuak Daily Mean T) calculated over the period 1944-2011.

-‐10

-‐8

-‐6

-‐4

-‐2

0

2

4

6

40 80 120 160 200 240 280 320 360

∆T (°C )

Julian Date

45

4.2 Weekly SIC-ΔTW Correlation

The correlation of weekly SIC observations to average weekly ΔT was conducted

in three parts: one containing all observations, one covering the breakup period and one

covering the freeze-up period (Figs. 3, 4 & 5 respectively).

Figure 3: Correlation of ∆TW with spatially averaged SIC for all weekly observations on record 1971-2011.

Figure 4: Correlation of ∆TW with spatially averaged SIC for all weekly observations during the breakup period, 1971-2011.

-‐20

-‐15

-‐10

-‐5

0

5

10

15

20

0 2 4 6 8 10 ∆TW (° C)

Sea Ice Concentration (tenths)

-‐15

-‐10

-‐5

0

5

10

15

20

0 1 2 3 4 5 6 7 8 9 10 ∆TW (° C)


46

Figure 5: Correlation of ∆TW with spatially averaged SIC for all weekly observations during the freeze-up period, 1971-2011.

The above plots effectively demonstrate the lack of any correlation between SIC

and ΔT at a weekly temporal resolution. There is clearly no correlation when considering

all observations on record (R2= 0.0053, p= 0.287). Dividing the observations by season

fared no better, as a linear regression for the break-up period yielded an imperceptible

slope and an extremely low R2 of 0.003 (p = 0.42356). Likewise, linear regression on the

freeze-up period yielded no significant trends and an equally low R2 value (R2= 0.00227,

p= 0.7477).

4.3 IFS-ΔTMAX Correlation

The values of IFS and ΔTMAX for the period of 1972-2011 are presented in Table

3. Linear regression between these two variables yields a statistically significant negative

correlation (R2=0.25353, p=0.00331). Note that, by our definition of ∆T, a negative

correlation means that longer IFS are more likely to be associated with higher |∆TMAX|

-‐20

-‐15

-‐10

-‐5

0

5

10

15

0 2 4 6 8 10

∆TW (° C )


47

Table 3: Ice-free season length and ∆TMAX for 1972-2011.

*(Note that years when either variable was missing were omitted entirely)

Year IFS ΔTMAX

1972 111 -4.1 1974 124 -1.7 1975 143 -13.4 1976 137 -5.5 1977 149 -6.9 1978 122 -1.9 1979 143 -2.3 1980 146 -7.3 1981 153 -2.4 1982 133 -10.5 1983 137 -0.2 1984 132 -5.1 1985 131 -8.6 1986 130 0.0 1987 128 -2.8 1988 147 -9.7 1989 141 -7.6 1990 144 -10.3 1991 141 -12.7 1992 120 -1.9 1993 135 -6.6 1995 147 -5.3 1996 151 -9.0 2000 144 -8.4 2001 164 -9.2 2003 158 -9.6 2004 134 -8.4 2005 160 -7.6 2006 170 -9.7 2007 162 -8.0 2009 159 -6.2 2010 181 -10.9 2011 165 -8.4

48

4.3.1 Classification of ∆TMAX by IFS

The results of the classification of ΔTMAXs by IFS are presented in Table 4.

Table 4: Classification of ∆TMAX by IFS for all years on record.

Short Medium Long -1.7 0.0 -2.4 -1.9 -0.2 -6.2 -1.9 -2.3 -7.6 -2.8 -5.1 -8.0 -4.1 -5.3 -8.4 -5.5 -9.0 -6.6 -9.2 -6.9 -9.6 -7.3 -9.7 -7.6 -10.9 -8.4 -8.4 -8.6 -9.7 -10.3 -10.5 -12.7 -13.4 Mean -2.5 -7.2 -8.1 Std. Dev. 1.0 3.5 2.4

Since the data is normal, the medium category contains the largest sample size

(n=17), with the short and long categories being less populated (n=5 and 10 respectively).

The summary statistics for each category show their associated means appear to be

distinct, so a t-test was conducted to test for statistical significance (Table 5).

49

Table 5: P-values obtained from interclass comparison of ∆TMAX means by one-tailed t-test, adjusted using the Bonferroni correction.

Short Medium Short - 0.01833 Long 0.00036 0.70734

The t-test results show that the means for the short and long categories are very

distinct, with statistical significance at the 99% confidence interval. Of greater interest is

the level of differentiation of the medium category. The high p-value in the case of

medium vs. long means there is no statistically significant difference in their means.

However, in the case of medium vs. short, means are significantly different at the 99%

confidence interval.

Based on the distributions of ∆TMAX for each category, thresholds were defined

such that the chance of misclassification is minimized. When these thresholds are applied

to the same 33 years from which they were derived, the proportion of misclassified years

to correctly classified years serves as an indicator of the success of ∆TMAX as a proxy.

50

Table 6: Identification of misclassified years based on ∆TMAX thresholds.

Short Medium Long -1.7 0.0 -2.4 -1.9 -0.2 -6.2 -1.9 -2.3 -7.6 -2.8 -5.1 -8.0 -4.1 -5.3 -8.4 -5.5 -9.0 -6.6 -9.2 -6.9 -9.6 -7.3 -9.7 -7.6 -10.9 -8.4 -8.4 -8.6 -9.7 -10.3 -10.5 -12.7 -13.4 Threshold > -4.5 -4.5>∆TMAX> -8.0 < -8.0 Misclassified 0 11 3 Total % Mis 42 *Note: values in red indicate a misclassification by one category, values in red and italics misclassified by two categories.

51

4.4 Wind Direction Analysis

4.4.1 Wind Direction Frequency Distributions

Wind roses showing the distribution of direction frequencies over the period of

Julian days 320-350 were produced for every year from 1981-2007. Presented below are

the wind roses for all years that were misclassified based on ∆TMAX (those in red in Table

6). Anomalous distribution of wind direction frequencies are made clear by comparing a

year’s wind rose with the climate normal wind rose (Figure 7).

Figure 6: Climate normal wind rose for Inukjuak over Julian days 320-350, calculated over the period of 1981-2007.

The climate normal for wind direction frequencies in Inukjuak over the period of

interest show that the NE and W components dominate most often with average counts of

127 and 124 respectively.

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

52

Figure 7: 1981 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -2.4°C, IFS = 153 (Long).

The 1981 wind rose shows the second highest count for frequency of NE, and the

absolute lowest for W.

Figure 8: 1982 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -10.5°C, IFS = 133 (Medium).

The 1982 wind rose had the second highest frequency of W winds.

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

53


The 1983 wind rose shows the 3rd highest on record count of NE winds.

Figure 10: 1985 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -8.6°C

While NE winds were above average in 1985, so were both NW and W, hence

NW+W>NE+E.

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

54

Figure 11: 1986 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = 0.0°C, IFS = 130 (Medium).

1986 had the 4th highest NE count on record, but also had an above average

westerly component.

Figure 12: 1988 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -9.7C, IFS = 147 (Medium).

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

55

The largest component in the 1988 wind rose is the N wind, with below average

W, NW, NE, and E components.


As with the previous example, the distribution of wind frequencies for 1990 is

roughly equal among all 8 components, with a strong northerly component.

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

56


1991 saw above average W and SW winds, and below average NE and E winds.


2000 saw above average W and NW components, as well as below average NE

components. E winds were above average but to a lesser degree than W and NW.

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

57


2002 had average NE and above average E frequencies.


2004 year saw no major anomalies in wind direction frequency.

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

58


2005 saw the second highest on record SW count, but also NE and E counts well

above average.

4.4.2 Correlation of Wind Direction Components to IFS

Since the assumption that westerly winds have a strong influence on ∆T has been

shown to have some merit, ∆TMAX was tested for correlation with both NW+W and

NE+E. While NW+W showed a slight positive relationship (R2=0.28972, p=0.08761),

the negative relationship with NE+E proved stronger and statistically significant at the

99% confidence interval (R2=0.37594, p=0.00241).

4.4.3 Classification of ∆TMAX by IFS for Low NE+E Years

The classification of ∆TMAX by IFS was conducted again, this time only including

those years when the NE+E wind component was below average.

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

59

Table 7: Classification of ∆TMAX by IFS for years when NE+E wind count is below average.

Short Medium Long -5.1 -8.0 -7.6 -9.2 -8.4 -9.6 -8.4 -9.7 -8.6 -9.7 -10.3 -10.5 -12.7 Mean N/A -9.0 -9.1 Std. Dev. N/A 2.1 2.4 Since the years when NE+E are above average are eliminated from this data set, it

is expected that the overall averages for each category be higher than in the previous

analysis. This is indeed the case for the medium and long categories, but the exclusion of

all short years prevents the determination of a new mean for this category. Furthermore, a

comparison of means by t-test between long and medium categories reveals a p-value of

0.3784, suggesting that the elimination of high NE+E years has not helped in

significantly distinguishing ∆TMAX values between these categories. Due to this shift in

means, new thresholds of ∆TMAX can be identified that minimize misclassification for this

new data set.

60

Table 8: Identification of misclassified years when NE+E winds count is below average.

Short Medium Long -5.1 -8.0 -7.6 -9.2 -8.4 -9.6 -8.4 -9.7 -8.6 -9.7 -10.3 -10.5 -12.7 Threshold N/A -4.5>∆TMAX> -9.0 < -9.0 Misclassified N/A 4 1 Total % Mis 39 The relative proportion of misclassifications has been reduced from 42% to 39%

by eliminating above average NE+E years. However, this slight improvement comes at

the expense of a loss of confidence in the results due to the drastic reduction in the

population of the classification table.

61

4.5 IFS-TF Correlation

Table 9 shows the values calculated for TF, the freeze-up temperatures calculated

over Julian days 260-320 and spatially averaged over Inukjuak and Churchill.

Table 9: Ice-free season lengths and TF for 1972-2011.

Year IFS TF

1972 111 -5.0 1974 124 -3.0 1975 143 -0.2 1976 137 -1.9 1977 149 1.5 1978 122 -3.1 1979 143 -3.1 1980 146 -2.6 1981 153 -0.1 1982 133 -1.6 1983 137 0.1 1984 132 -1.8 1985 131 -1.0 1986 130 -4.2 1987 128 -1.3 1988 147 -0.2 1989 141 -2.3 1990 144 -2.6 1991 141 -2.6 1992 120 -3.2 1993 135 -2.9 1995 147 -2.1 1996 151 -0.6 2000 144 -0.2 2001 164 0.9 2003 158 -1.0 2004 134 -0.4 2005 160 0.9 2006 170 0.1 2007 162 -0.4 2009 159 -0.5 2010 181 2.0 2011 165 1.9

*Note: years when either variable was missing were omitted entirely

62

Linear regression between IFS and TF reveals a statistically significant negative

relationship (R2 = 0.59051, p = <0.0001)

4.5.1 Classification of TF by IFS

The classification of TF values by IFS can be found in Table 10. Populations for

each category are the same as those in the ∆TMAX – IFS classification, since both are

based on IFS and derived from the same temperature records.

Table 10: Classification of TF by IFS for all years on record.

Short Medium Long -5.0 -4.2 -1.0 -3.2 -3.1 -0.6 -3.1 -2.9 -0.5 -3.0 -2.6 -0.4 -1.3 -2.6 -0.1 -2.6 0.1 -2.3 0.9 -2.1 0.9 -1.9 1.9 -1.8 2.0 -1.6 -1.0 -0.4 -0.2 -0.2 -0.2 0.1 1.5 Mean -3.1 -1.6 0.3 Std. Dev. 1.3 1.4 1.1

The summary statistics show that the means for each category appear to be

distinct and increasing in magnitude with increasing ice-free season length, as should be

63

expected. A comparison of means by t-test revealed significant differences between all 3

categories (Table 11).

Table 11: P-values obtained from interclass comparison of TF means by one-tailed t-test, adjusted using the Bonferroni correction.

Short Medium Short - 0.05028 Long <0.0001 0.00168

Thresholds of TF were established in the same way as ∆TMAX thresholds by

minimizing overlap between categories.

Table 12: Identification of misclassified years based on TF thresholds (misclassifications in red).

Short Medium Long -5.0 -4.2 -1.0 -3.2 -3.1 -0.6 -3.1 -2.9 -0.5 -3.0 -2.6 -0.4 -1.3 -2.6 -0.1 -2.6 0.1 -2.3 0.9 -2.1 0.9 -1.9 1.9 -1.8 2.0 -1.6 -1.0 -0.4 -0.2 -0.2 -0.2 0.1 1.5 Threshold ≤ -3.0 -3.0<∆TMAX≤ -1.0 > -1.0 Misclassified 1 8 1 Total % Mis 30

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Table 13 puts the performance of the TF approach in the context of the two ∆TMAX

methods.

Table 13: Comparison of temperature variables in terms of coefficients of determination, statistical significance, and percent misclassifications.

R2 p-value % Misclassified ∆TMAX 0.25353 0.00331 42 ∆TMAX (NE+E)* 0.54356 0.00622 39 TF 0.59051 <0.0001 30 *Note: The R2 and p-value listed here are for the linear regression of ∆TMAX and IFS only for those years when NE+E wind count was below average.

4.6 IFS-∆TMAX-TF Multiple Linear Regression

The equation obtained by running a multiple linear regression with IFS as a

dependent variable and both ∆TMAX and TF as independent variables is:

[Eqn. 1] IFS = 144.6224 - 0.9602�∆TMAX + 6.0560�TF

When all ∆TMAX and TF values on record from the period of 1972-2011 are used

as inputs into this equation, predicted values of IFS are produced (Table 14). The

absolute difference between predicted IFS and actual IFS is shown in the |Error| column.

The same process was conducted using the following equation acquired by simple

linear regression with IFS as dependent variable and TF as independent variable:

[Eqn. 2] IFS =152.1479 + 6.9146 � TF

The resulting IFS values and |Error| values are found in Table 15.

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Table 14: IFS results from Eqn. 1 (TF+∆TMAX) compared with actual IFS in terms of absolute error for the period 1972-2011.

Year IFS (Actual) IFS (Eqn.) |Error| 1972 111 118 7 1974 124 128 4 1975 143 156 14 1976 137 138 1 1977 149 161 11 1978 122 128 6 1979 143 128 15 1980 146 136 10 1981 153 146 7 1982 133 145 12 1983 137 145 9 1984 132 138 6 1985 131 147 16 1986 130 119 11 1987 128 140 12 1988 147 152 6 1989 141 138 3 1990 144 139 5 1991 141 141 0 1992 120 127 7 1993 135 134 1 1995 147 137 10 1996 151 150 2 2000 144 152 7 2001 164 159 5 2003 158 148 10 2004 134 150 16 2005 160 157 3 2006 170 155 15 2007 162 150 12 2009 159 148 11 2010 181 167 13 2011 165 164 1

Average 8.1 Std. Dev. 4.7

66

Table 15: IFS results from Eqn. 2 (TF) compared with actual IFS in terms of absolute error for the period of 1972-2011.

Year IFS (Actual)

IFS (Eqn.) |Error|

1972 111 117 6 1974 124 131 7 1975 143 151 8 1976 137 139 2 1977 149 163 14 1978 122 131 9 1979 143 131 12 1980 146 134 12 1981 153 151 2 1982 133 141 8 1983 137 153 16 1984 132 139 7 1985 131 145 14 1986 130 123 7 1987 128 143 15 1988 147 150 4 1989 141 136 5 1990 144 134 10 1991 141 134 7 1992 120 130 10 1993 135 132 2 1995 147 137 10 1996 151 148 3 2000 144 151 7 2001 164 158 6 2003 158 145 13 2004 134 149 15 2005 160 158 2 2006 170 153 17 2007 162 150 13 2009 159 149 10 2010 181 166 14 2011 165 165 0

Average 8.7 Std. Dev 4.7

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Comparing Tables 14 and 15 shows that the multiple regression equation

improves error on average by 0.6 days (1 day when rounded). An updated comparison of

the various temperature indices and their correlation to IFS in terms of R2 and p-value can

be found in Table 16.

Table 16: Comparison of temperature variables in terms of the coefficients of determination and statistical significance of their linear relationships with IFS.

R2 p-value ∆TMAX 0.25353 0.00331 ∆TMAX (NE+E)* 0.54356 0.00622 TF 0.59051 <0.0001 TF + ∆TMAX 0.62863 <0.0001 *Note: The R2 and p-value listed here are for the linear regression of ∆TMAX and IFS only for those years when NE+E wind count was below average.

4.7 Hindcast IFS

By applying Eqn. 1 to the temperature record for all available years prior to 1972,

a hindcast record of IFS values 28 years in length was obtained. The time series for this

new dataset was appended to the time series for actual IFS values, producing a record 68

years in length with 5 missing values (all from the actual dataset).

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Figure 19: Time series of IFS from 1944-2011 constructed using actual observations and data derived by proxy from ∆TMAX and TF [Eqn. 2].

Application of a 5-year moving average resulted in the smoothed curve seen in

Fig. 20. Note that the smoothed data is shown here only for visual interpretation, and that

all trend analyses were done using the original data presented in Fig. 19.

Figure 20: Time series for actual and hindcast IFS smoothed by use of a 5-year moving average.

0

20

40

60

80

100

120

140

160

180

200 Ice-‐free Season Length (days)

Year

Hindcast

Actual

0

20

40

60

80

100

120

140

160

180

Ice-‐free Season Length (days)

Year

Actual

Hindcast

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The Mann-Kendall test conducted on the entire time series (1944-2011) from Fig.

19 showed a weak positive association between time and IFS that is statistically

significant at the 95% confidence interval (τ = 0.208, p = 0.017). Since it is assumed that

this positive trend is being driven by a recent increase in IFS, the test was run for four

different pairs of baseline/trend time series, defined by a division year (Table 17). The

first entry (1972) uses the entire hindcast record as a baseline and the entire actual record

as a trend. The other three entries were arbitrarily selected as intervals of 5 years starting

in 1980 in an effort to isolate the period where there is most likely a trend. As another

example, the second entry in Table 17 (1980) has a baseline τ and p-value that

correspond to the period 1944-1980. That same entry has a trend τ and p-value that

correspond to 1980-2011, and so on.

Of the four pairs of baseline and trend time series presented in Table 17, those

with the division year of 1985 have the greatest contrast. For the period of 1944-1985,

there is no statistically significant trend occurring, while the τ value of 0.607 for the

period of 1986-2011 strongly suggests a statistically significant positive trend in IFS with

time (p<0.0001).

Table 17: Comparison between baseline and trend in terms of τ and statistical significance for different time series divisions.

Division Baseline τ Trend τ Baseline p Trend p 1972 0.177 0.490 0.198 < 0.0001 1980 -0.024 0.484 0.848 0.0004 1985 -0.033 0.607 0.770 < 0.0001 1990 -0.088 0.578 0.399 0.001

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Chapter 5: Discussion

5.1 Interpreting ∆T Climate Normal

The climate normal constructed for ∆T (Figure 2) shows a clear annual cycle,

with daily values spanning from ~+5°C to -8°C. Beginning on day 1, ΔT is in the

negative phase of this cycle, indicating that TINUK>TCHURCH, and that despite being well

into the ice-covered season, there is perhaps some residual heat flux through the ice that

has not yet reached maximum thickness. However, ΔT continues to approach zero and

enters the positive phase between days 30 and 50. From 30-150, temperatures in

Churchill and Inukjuak are similar enough that ∆T is for the most part close to 0°C, as

would be expected under complete ice cover. Following this period, ∆T actually starts to

climb, becoming more positive and ultimately reaching its peak around day 200 at about

5°C. At this point the graph exhibits an interesting feature, whereby ΔT seems to drop

precipitously before climbing back to what appears to be a second peak of ~4°C around

day 230. It is interesting that ∆T appears to undergo this positive phase, reaching as high

as it does, when one might expect the near-0°C values of the previous period to persist

until reverting to the negative phase following breakup. One can speculate that this

represents a period when warmer spring winds arriving in Churchill are subsequently

cooled down upon advecting over the ice that persists on the Bay. Following the

secondary peak, ΔT undergoes a steady decline, surpassing 0°C around days 270 to 280

and re-entering the negative phase. This reversal in ∆T lags by roughly 80-100 days

behind both the average breakup date and average ice-free date for the Bay (~180 and

200 respectively). ∆T continues to trend downwards throughout the ice-free season and

well into the freeze-up season. Maximum |ΔT| is observed late in the year in the range of

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days 330-340 and reaches an average magnitude of approximately 7.5°C. Note that this

maximum temperature difference is occurring in the vicinity of, or shortly after, the

average freeze-up date for the Bay (~330). Again, this demonstrates the degree to which

upward heat flux persists despite growing ice cover. The apex of the ∆T curve marks

some point at which this heat flux is overtaken by the insulating power of the ice,

following some critical threshold in its cover and thickness. Following this point, another

sharp reversal and subsequent positive trend persists until the positive phase is reached

once again around day 40.

The most important conclusions derived from this graph come from placing the

fluctuations in ∆T in the context of seasonal changes in ice cover. As shown above, the

major changes in ∆T lag significantly behind every major milestone in ice cover. Peak

|∆T|, which is theoretically associated with open water conditions, lags so far that it is

actually most likely to occur when the bay is more than 50% ice-covered. Lag owing to

thermal inertia was expected, but the significant length of time between changes in sea

ice and a corresponding asymmetry signal imposes some severe limitations on the

temporal resolution of a proxy based on this relationship.

5.2 SIC-∆TW Relationship

No correlation could be found between the weekly SIC observations and

subsequent weekly ∆T averages. Comparing Figures 4 and 5, it is clear that on average

∆Tw values are lower for SIC observations during freeze-up than breakup, with the vast

majority being above 0°C for breakup and below 0°C for freeze-up. However, despite

accounting for this expected difference, the resulting correlations between ∆TW and SIC

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in both cases reveal no statistically significant trends. In light of the aforementioned lag

between a change in sea ice conditions and resulting ∆T signal, it is not surprising that a

weekly average of ∆T is not necessarily representative of recent SIC. It is clear from

these three graphs that the ∆T-SIC relationship is not strong enough to be of any

predictive value at this fine a resolution.

5.3 IFS-∆TMAX Relationship

The statistically significant negative correlation between IFS and ∆TMAX

(R2=0.25353, p=0.00331) suggests that the length of time the Bay is ice-free has some

effect on the temperature asymmetry following the end of the IFS. More specifically,

shorter IFSs tends to be associated with smaller |∆TMAX| (closer to 0), while the longer

IFSs tend to be associated with greater |∆TMAX| values (Note the use of || bars to avoid

confusion regarding signs – this way a ∆TMAX of -13 for example can be referred to as a

large temperature difference). However, this relationship exhibits a great degree of

variability, such that years with an average or below average IFS can also have a

significantly large |∆TMAX| signal. Indeed, the top 2 years in terms of magnitude of

∆TMAX (-13.4, -12.7) were not coincident with long IFS, but rather from rather average

years (IFS=143 and 141, respectively). The converse of this problem occurs as well, as

there are years with lengthy IFS but very little temperature asymmetry. For example, the

∆TMAX value of -2.4 occurs during a year with an IFS=153. Such examples are less

common however, and in general it seems as though ∆TMAX values closer to 0 are more

reliably associated with shorter IFS, while the larger |∆TMAX| values are not as

consistently associated with the longer IFS. Consider that of the top 10 years in terms of

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|∆TMAX|, only 5 are also top 10 years in terms of IFS. However, of the bottom 10 years in

terms of |∆TMAX| (i.e. closest to 0), 7 are also bottom 10 in terms of IFS. This suggests

that large temperature differences between coasts may arise under a slightly wider range

of IFS, whereas smaller temperature differences are more often constrained to years when

IFS was below average. The classification of ∆TMAX values by IFS aids to highlight how

the inconsistencies in this relationship would affect the results of the proposed proxy

methodology.

When ∆TMAX values are classified into three categories of IFS (Table 4), many of

the characteristics and anomalies of the relationship noted above become more evident.

The fact that ∆TMAX values for the medium class range from 0.0 to -13.4°C reinforces the

above observation that there is considerable variability in ∆TMAX independent of IFS,

particularly in years when the ice-free season is average. The observation of -2.4°C sticks

out among the predominantly higher values of the long class, demonstrating that despite

the tendency towards higher temperature differences following long IFSs, anomalously

lower values may occur. The observation that shorter IFSs are more consistently

associated with ∆TMAXs closer to 0 gets further credence here from the fact that the range

of ∆TMAX for short years is the smallest of all classes, spanning less than 3°C. The range

of ∆TMAX values for the long class is also smaller than that of the medium class

(considerably so if the -2.4 outlier is omitted) suggesting that longer IFS years also

produce a more consistent signal in ∆TMAX. Though both short and long classes have a

smaller range of values, they differ in terms of the degree to which their respective ranges

overlap that of the medium class. While the ranges of the short and medium classes

overlap by only three values (i.e. observations of 0.0, -0.2 and -2.3 in the medium class),

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the entire range of long values is contained within the range of the medium class. Hence,

it is difficult to distinguish between medium/long classes, but easier to distinguish

between short/medium, and short/long. Table 5 provides a quantitative measure of this

distinction between classes via interclass comparison of means. A p-value of 0.70734 for

the medium/long comparison confirms that these populations are not very distinct. The

short-medium comparison yields a p-value of 0.01833, indicating the two classes are

significantly different at the 95% confidence interval. As expected, the most significantly

different classes are short/long, at a 99% confidence interval (p=0.00036). From these

results, we would expect that any proxy method employing ∆TMAX to discriminate

between IFS lengths would be most successful at identifying short years. Conversely,

such a method would be of little use in distinguishing between medium and long years,

owing to the substantial overlap of the actual ∆TMAX values for these two populations.

Despite the substantial interclass overlap, thresholds of ∆TMAX were established

for each class such that they would maximize inclusion of records with corresponding

IFSs (Table 6). These thresholds, when applied to the existing record, provide an

indicator of the expected confidence such a proxy would carry when hindcasting IFS.

When these thresholds were applied to the 33-year record, it resulted in 14

misclassifications (42%). These thresholds were able to successfully identify all actual

short years, albeit while misclassifying three actual mediums and one actual long as

short. The medium year, with its significant overlap and wide range of values, had eleven

misclassifications out of 18. The long category, while only having three of ten

misclassified, contained a year misclassified by two categories (1981, ∆TMAX=-2.4). The

rather dismal misclassification rate (nearly half) reveals the inadequacies of this

75

approach, though the fact that all actual short years can be identified may be of some

value in the absence of any preferable method.

5.4 Wind Direction

As hypothesized, wind direction appears to play an important role in determining

the magnitude of the temperature asymmetry on the Bay. A non-significant, positive

relationship exists between westerlies (NW+W) and ∆TMAX (R2=0.28972, p=0.08761).

This is consistent with the assertion that the temperature asymmetry relies upon Inukjuak

winds having advected over the Bay itself, and hints that to some degree ∆TMAX may

actually be proportional to the frequency of such winds over the 320-350 period. In a

complementary approach, the combined count of NE and E wind direction components

(NE+E) was found to be negatively correlated with ∆TMAX (R2=0.37594, p=0.00241). In

this case, the greater the count of winds arriving from the east (having predominantly

advected over land), the smaller the magnitude of the ∆TMAX signal was generally seen.

The strength of these relationships suggests that wind direction may influence ∆TMAX as

much, or perhaps even more so, than does the length of the ice-free season. With that in

mind, two approaches were taken to explain, and isolate for, the effects of wind

frequency: interpreting wind roses from misclassified years, and reclassifying ∆TMAX

values for years when NE+E was below average.

Of the 33 years on record, 14 do not conform to the established thresholds of

∆TMAX (Table 6). A case-by-case interpretation of the wind roses for those 14 years

reveals that at least seven may be partially explained by an anomalous distribution of

wind direction frequencies when compared to the climate normal for the period of 320-

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350 (Fig. 7). These years include 1981, 1982, 1983, 1985, 1991, 2000, and 2002 (See

Figs. 8-11, 15-16). In general, a year where ∆TMAX is higher than expected based on IFS

tends to also be a year when the W, NW, or SW components are above average (often

with concomitantly lower E/NE components). Presumably, this leads to an amplified ∆T

signal as a greater proportion of winds arriving in Inukjuak have been thermally modified

by the Bay. For example, 1982 saw a ∆TMAX of -10.5°C, despite having an IFS of only

133 days. The wind rose for this year clearly shows a prevailing W component, the

second highest on record. In 1991, both W and SW components are above average, which

again may have contributed to the anomalously high |∆TMAX| of 12.7°C when IFS =141.

Similarly, above average W and NW components in 2000 may explain its

misclassification, though that may also be attributed to the fact that its ∆TMAX of -8.4°C is

simply too close to the medium/long threshold of -8.0°C. In the case of the 1985 wind

rose it can be argued that, despite having an above average NE component, the

combination of above average W and NW components and a very small E component

resulted in the westerlies having a dominant effect on the temperature asymmetry.

Furthermore, as with the latter example, this year’s misclassification may have simply

been a result of its ∆TMAX’s proximity to the medium/long threshold.

In the case of years when |∆TMAX| is lower than expected given IFS, E/NE

components tend to be above average (often with concomitantly lower NW/W

components). This may dampen the ∆T signal, as a lesser proportion of winds arriving in

Inukjuak have been thermally modified by the Bay. Such is likely the case in 1981, when

the distribution of wind directions is dominated by the NE component (second highest on

record) and conspicuously devoid of W observations (lowest on record), with a resulting

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temperature difference closer to 0 than would be expected given IFS (∆TMAX = -2.4°C,

IFS =153). The wind rose for 1983 exhibits a similar distribution with an anomalously

high NE component (3rd highest on record), and below average W component (∆TMAX = -

0.2°C, IFS = 137). In the case of 2002 (∆TMAX = -4.0°C, IFS = 146), the W component is

actually above average, but it might be argued that the combined effect of slightly above

average SE, E, and NE components may have tempered the temperature asymmetry this

year as well. Alternatively, or complementary to that observation, one can also point to

the fact that the ∆TMAX in this case is simply too close to the short/medium threshold of -

4.5°C.

Having demonstrated the nullifying effects of easterly winds on temperature

asymmetry, the classification of ∆TMAX for years when NE+E is below average was done

in hopes of clarifying the ∆TMAX-IFS relationship (Table 7). If isolating for wind effects

results in IFS classes more distinct in terms of ∆TMAX, then a multi-proxy hindcasting

method may be theoretically feasible. Unfortunately, the omission of years when NE+E is

above average, combined with the limitations imposed by the wind record (which only

covers 1981-2007), results in a much less populated dataset from which we can draw

conclusions. Hence, any improvement in the results comes at the expense of a loss in

confidence in said results. Regardless, this approach does not seem to have improved

inter-class differentiation, since the means of medium and long classes are not

significantly different (p=0.3784), and the lack of any short entries precludes further

inter-class comparison. It is worth noting that eliminating above average NE+E years also

eliminated many of the outliers whose ∆TMAX was closer to 0 than expected given IFS

(most notably ∆TMAX= 0.0. -0,2, and -2.3°C from the medium class; and ∆TMAX = -2.4, -

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6.2, and -7.6°C from the long class). However, some of these observations were

eliminated due to absence of wind data for that year rather than due to above average

NE+E winds (∆TMAX = -2.3 and -6.2°C). As a result of the elimination of these

observations, the ∆TMAX means have increased relative to the initial classification, both in

the medium class (from -7.2 to -9.0) and in the long class (from -8.1 to -9.1). This again

demonstrates the tendency of strong easterly winds to dampen (or strong westerly winds

to enhance) the ∆T signal.

As a result of the shift in ∆TMAX values, a new threshold was defined between

medium and long classes that would minimize misclassifications when applied to the

existing record (Table 8). The slightly lower percentage of misclassifications suggests a

slight improvement over the method that includes all years of data. Furthermore, the

elimination of outlier low ∆TMAX years noted above has mitigated misclassification of

actual medium/long years as short. However, the marginal improvements afforded by

eliminating anomalous wind years are rendered less meaningful when one considers the

much smaller dataset.

The relative frequency of westerly and easterly wind components in Inukjuak is

likely an important factor in the sea ice/temperature asymmetry relationship. The true

nature of wind’s role in defining the asymmetry may be more complex than represented

here, but the general rule that westerlies amplify ∆TMAX independent of IFS seems to be

supported by the data. Thus, it is fair to say that any potential proxy for sea ice on

Hudson Bay looking to exploit the temperature asymmetry would suffer in terms of

accuracy without the consideration of wind direction in some form. Unfortunately, the

lack of wind data prior to 1982 precludes the possibility of any such multi-proxy.

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5.5 Multiple Variable Approach

The equation produced by multiple regression [Eqn. 1] is revealing of the physical

relationships between each temperature variable and ice-free season length. The

regression coefficient for the explanatory variable TF is approximately 6 times that of the

variable ∆TMAX. This reiterates what was discovered in the classification approach, that

TF is a stronger indicator of IFS. However, the R2 value of 0.62863 obtained in the

multiple variable regression is higher than those obtained using either variable considered

alone. The improvement over the TF-IFS relationship (R2=0.59051) is marginal, though it

again demonstrates that ∆TMAX does add some unique information regarding IFS. As a

sort of “thermal memory” term, whose magnitude is determined by conditions throughout

the entire ice-free season, ∆TMAX inherently contains some information regarding breakup

conditions that cannot be conveyed by TF. Since TF is the stronger explanatory variable,

this approach can be thought of as a tweaked version of the TF regression, where the

addition of the ∆TMAX explanatory variable further hones the prediction. The actual value

added by adopting a multi-variable proxy approach is further quantified below.

5.6 Evaluating Proxies

The temperature variable TF serves here as a benchmark for evaluating the

performance of ∆TMAX as a proxy in two ways. Firstly, TF values are classified by IFS to

assess the performance of ∆TMAX in classifying IFS as short, medium and long. Secondly,

the IFS values produced by the equation obtained by linear regression between TF and

IFS are compared to those produced by the multiple regression equation to again assess

the value of ∆TMAX in such a proxy.

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5.6.1 Classifications

To obtain the TF variable, temperature was averaged over Churchill and Inukjuak,

as well as being averaged over a longer period of time (61 days, compared to 31 for

∆TMAX). As a result, the range of values of TF is much smaller than that of ∆TMAX,

spanning only from -5.0 to 2.0 °C. With this smaller range, it is even more important that

the populations of the three classes be distinct with little overlap in order for this method

to be useful as a predictor for sea ice. When classified (Table 10), the means of each class

increase along with length in IFS. This is to be expected, since colder temperatures

during the 260-320 freeze-up period would tend to expedite sea ice formation leading to a

shorter IFS (with warmer temperatures tending to delay freeze-up for the opposite effect).

A comparison of means reveals that all three classes are significantly different from each

other at the 95% confidence interval (Table 11). More importantly, a comparison of

these p-values to those found in the ∆TMAX –IFS approach (Table 5) shows a marked

improvement in the TF approach in terms of inter-class distinction, particularly between

the medium and long categories. This means that despite the smaller range of TF values,

the differentiation between classes is greater than in either of the two previous methods

using ∆TMAX.

Having established thresholds of TF for each class, applying them to the existing

record provides a measure of how reliably these thresholds can be expected to hindcast

IFS. The misclassification rate for this method was the lowest yet at 30%, though there

are also some important differences in terms of what was misclassified. Most

importantly, there are no misclassifications by two classes, as was the case in the first

∆TMAX method. The one misclassified short year here indicates that this method cannot

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capture all actual short years, the singular advantage of the ∆TMAX method. However, this

method nearly captures all actual long years, with the only misclassification in that

category having a TF straddling the medium-long threshold.

A side-by-side comparison of the three classification proxy methods investigated

makes it clear that the ∆TMAX proxy method does not outperform the TF method in

recreating the existing IFS record (Table 13). As evidenced by the higher R2 value, TF is

much more useful at explaining variability in IFS, and as a result can be used to classify

IFSs more reliably.

5.6.2 Linear Regression

By including both explanatory variables in a multiple regression with IFS, both R2

and p-value were greater than either of the single-variable correlations with IFS (Table

16). This marked improvement presents the opportunity for the use of the multiple

regression equation to predict IFS in lieu of the classification approach. A comparison of

Tables 14 & 15 reveals how much the multiple regression approach improves error in

reproducing the IFS record. The average error using the TF equation is 8.7 days, while the

TF-∆TMAX equation average error is 8.1 days. Thus, including the temperature difference

variable can be expected to improve results on average by 1 day (rounded up). The

multiple regression errors have a standard deviation of 4.7, meaning that 68% of the

predictions for IFS will be accurate to within 4.7 days of actual IFS. This is a fair level of

accuracy when one considers that the breakup and freeze-up dates used to determine IFS

themselves are only measured every 7 days (Gagnon & Gough, 2005). Therefore, for the

purposes of hindcasting IFS to a degree of accuracy that is comparable to the actual

record, the multi-proxy approach employing both TF and ∆TMAX is superior to the TF

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proxy alone. Furthermore, the advantages of the multiple regression equation results over

the classification results in terms of temporal resolution make the TF-∆TMAX multi-proxy

the best candidate to produce a hindcast time series of IFS.

5.7 Trend Analysis of Extended Record

The appended time series shown in Figure 19 provides a longer period of time

over which baseline conditions for IFS can be assessed. In doing so, it also provides a

means of eliminating low frequency climate oscillations as an explanation for the recent

increase in IFS. The high interannual variability of IFS throughout this record is a quality

that should be expected given the inherent variability of sea ice and driving climate

factors. Even considering this variability however, the tendency towards higher IFS in the

latter decades appears to be unprecedented from 1944-1995. Values in this earlier period

generally range from 120-160 days ice-free, with a few exceptions in 1947, 1948, 1968

and 1972. Following 1995, short IFSs appear to be less frequent, with only one year

having an IFS<140 (2004). Conversely, long IFS appear to become more frequent, with 7

years having IFS>160. Applying a five-year moving average leads to a smoothed curve in

which this increasing trend is made more apparent (Figure 20). This graph shows

averages oscillating with a periodicity of approximately 5 years, but maintaining a

relatively steady state over the long term up until about 1995, when an increasing trend

begins to develop.

The observed trends were assessed over different time periods using the Mann-

Kendall test (Table 17). The τ value of 0.208 for the entire time series (1944-2011) hints

at a trend, but this value is likely being diluted by the lengthy period when there is no

trend. When considering only the latter decades of the time series, the trend becomes

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more apparent and statistically significant. Of the four arbitrarily selected “trend” time

periods, all produce τ values indicative of positive trends that are statistically significant

at the 99% confidence interval. By contrast, none of the accompanying baseline periods

exhibit any significant trends. The period with the greatest evidence for a positive trend

in IFS is that of 1985-2011 (τ = 0.607, p<0.0001).

Appending the hindcast record to the historical record provides context for the

increasing trend in IFS observed in the last few decades. The actual IFS time series on its

own does present compelling evidence for an increase in the duration of the ice-free

season, but the hindcast time series provides greater confidence in that trend by showing

that such long IFS are unprecedented in a 68-year record. Taking temperature as the most

significant source of variability, one can point to many non-anthropogenic oscillations on

various temporal and spatial scales that might account for fluctuations in IFS. Any such

oscillations with a sub-decadal periodicity, such as the El Nino Southern Oscillation

(ENSO) or the North Atlantic Oscillation (NAO), would be resolved by the actual IFS

time series. When considering the extended time series, many of the interdecadal

oscillations, such as the Interdecadal Pacific Oscillation (IPO), would be reflected by a

periodicity in IFS if they were in fact driving the recent increasing trend. However, even

the 68-year record cannot conclusively eliminate all sources of climatic variability in this

manner, as there exist low frequency climate oscillations on larger time scales that this

time series cannot capture (Mahasenan et al., 1997). Thus, the extended time series

provides conclusive evidence that the recent increasing trend in ice-free season on

Hudson Bay is not attributable to low-frequency climate oscillations of a periodicity <68

years.

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5.8 Complicating Factors in the Sea Ice-∆T Relationship

Despite the fact that sea ice is most certainly influencing ∆T on an annual time

scale, and that interannual variations in ∆TMAX seem at least partially related to variations

in IFS, this study has shown that this relationship on its own is not strong enough to

exploit as a useful proxy. The climate system and its interrelationships with sea ice are

inherently complex with a multitude of interacting variables. Wind direction is one such

variable that was accounted for in this study, though its role may be more nuanced than

presented here. For example, wind velocity, though not taken into consideration here, has

been shown to be an important variable in the exchange of latent heat at the air-water

interface (Sousonis, 1992; Raymond, 1986; DeMaria, 1985). Hence, upward heat flux on

the Bay, and by extension the asymmetrical temperature signal, may differ between two

days that have an identical wind direction distribution but vary in terms of the relative

strength (velocity) of those winds. Furthermore, the binary characterization of wind

direction as strong westerly /strong easterly, though appropriate towards the objective of

developing a simple proxy, ignores the effects of other direction components (particularly

N/S). Wind analysis by vector summation would account for both these issues (Coffin,

1964). Such an approach might help in better explaining years with anomalous ∆TMAX

signals, further elucidating the role of wind in the sea ice-temperature asymmetry

relationship. Beyond wind effects unaccounted for in this study, there remain further

complicating factors that warrant some discussion; namely ice thickness, water

temperature, and spatial scale.

The insulating properties of sea ice have been shown to be highly dependent on

thickness (Dieckman & Hellmer, 2009). This is highlighted by the ∆T climate normal

85

(Figure 2), when the greatest temperature difference seems to be occurring well into the

freeze-up season, and the negative phase persists even after the entire Bay is frozen. This

suggests that the upward flux of heat allowed by immature, thin ice is sufficient to

produce an asymmetric temperature signal. This complicates efforts to accurately

characterize the SIC-∆T relationship, as observations of SIC do not discriminate between

areas of similar concentration but differing thicknesses. This complicating factor may

explain some of the variability in weekly ∆T values, but is not expected to affect the IFS-

∆TMAX analysis, as IFS is serving only as a general indicator of sea ice conditions in a

given year.

As outlined in section 2.6, the temperature asymmetry arises in response to

upward fluxes of sensible and latent heat from open water. Sensible heat flux is in turn a

function of the difference, or gradient, in temperature between the water and the

overlying air. Sea surface temperatures (SST) are continually increasing throughout the

IFS, reaching an average maximum of ~7.5°C in August (Galbraith & Larouche, 2011).

This peak in SST does not coincide with the peak in ∆T. This is likely because as air

temperatures start to drop in the fall, the gradient at the air-water interface will sharply

increase as the heat capacity of the water slows its temperature decrease relative to the

air. Along with this stronger gradient comes a greater upward heat flux, and hence greater

∆T, that persists until the water temperature begins to decline in turn. This relationship

between SST and air temperature is the driving force behind the temperature asymmetry,

but these variables are not used directly in this study. An analysis of how SST and the

temperature in Churchill (the last upwind air temperature observation for westerlies)

86

track throughout the IFS might help clarify the role of sea ice in defining the temperature

asymmetry.

Hudson Bay is a vast body of water exhibiting considerable spatial and temporal

heterogeneity in its sea ice cover. Those few studies demonstrating some success in using

a temperature-lake ice correlation as a predictive tool were done on much smaller scales,

generally lake systems spanning <100 km (Livingstone, 1997; Palecki & Barry, 1986;

Williams, 1971). Unlike with these past studies, the temperature asymmetry in this study

is being shaped by local, regional, and synoptic scale atmospheric forces that conspire to

make a clear signal of sea ice conditions very difficult to detect. Therefore, it is highly

likely that there are limitations to the spatiotemporal resolution of any proxy that attempts

to make generalized predictions on sea ice across the entire Bay. The issue of scale may

also be affecting the temperature signal in a more direct way, by placing an upper limit

on upward heat flux. Lake effect phenomena are often said to be “fetch-limited”, that is

to say that their occurrence or severity is a function of the upwind distance over which

advecting air has the opportunity to be moistened and destabilized (Andreas & Cash,

1999). Once an air mass responding to a new surface has fully developed a thermal

internal boundary layer (TIBL), it is at equilibrium with the new surface and energy flux

ceases until conditions change. Since this typically occurs in the range of 10s of km to a

few 100 km, it is safe to say that the Bay is not fetch-limited (Garratt, 1990). This means

that there may sometimes be an upper limit to the thermal modification of an overlying

air mass, beyond which there ceases to be any energy input and hence any additional

information in the temperature signal. This is particularly important given the spatial

heterogeneities inherent to sea ice on the Bay, as it might be difficult, for example, to

87

distinguish between a ∆T signal for completely open water, and a ∆T signal when all but

the southwestern coast is open water (as is the case toward the end of the breakup

season). This problem would have more of an effect on finer resolution proxies such as

the abandoned weekly ∆T approach, but probably does not present any issues for the IFS

approach.

The preceding are but a few complicating factors that are likely influencing the

sea ice-temperature difference relationship, but there are likely other variables

unaccounted for that may be just as important. Some of these might theoretically be

incorporated into a more complex, multi-variable proxy for sea ice, though only if the

extent of their records allow for it. Regardless, if the aim were to develop a simple proxy

based only on air temperature data, these complicating factors would tend to hinder such

an approach.

5.8 Sources of Error

Since all of the data used in this study was originally obtained from Environment

Canada, and hence subject to their own scrutiny before being made available, it is

unlikely to be the source of any errors (See 3.9 Notes on Data Quality). It is possible that

the variables derived from the source data (IFS, ∆TMAX, TF) were not optimized. For

example, since the ∆TMAX window of 320-350 was informed by the ∆T climate normal,

combined with empirical trial-and-error of alternative windows, it is likely that most

years it does in fact capture the strongest ∆T signal of the year in question. However,

there also may be certain outlier years in IFS when the period of maximum asymmetry is

shifted. If so, there may be some other window that would provide a more representative

88

∆TMAX. Though accounting for this error might help further characterize the IFS-∆TMAX

relationship, it is inconsequential for the purpose of developing a proxy, since a fine-

tuned ∆TMAX window would not be possible in the absence of ice data.

Another source of error likely comes from the simplification of the data set

necessitated by this methodological approach. Reducing 36 spatial points of data into a

single value ignores the heterogeneity of breakup and freeze-up dates on the Bay. This

results in a useful general indicator of sea ice conditions, but perhaps at the expense of a

stronger relationship between predictor and predictand. Likewise, while averaging

temperature data over 31 or 61-day periods reduces noise and ensures the desired signal

is captured, it also may result in a dampening of the signal. While these concessions are

necessary given the nature of the study, their shortcomings should be noted. Additionally,

refining the definition of these variables in light of new information could yield

improvements to the relationship and by extension a proxy method.

5.9 Research Impacts

While this study has elucidated the unique phenomena of seasonal temperature

asymmetry on Hudson Bay, the most tangible impacts of its findings come from: 1)

advancing the knowledge on site-specific sea ice proxies, and in so doing 2) producing a

hindcast time series that allows for a more robust trend analysis of ice-free season.

Although the temperature asymmetry alone was shown to be a weak proxy for sea ice,

combining it with a measure of absolute temperature created a multi-proxy that allowed

the Hudson Bay sea ice record to be extended by 28 years. This extended time series in

turn allows for a superior trend analysis, whereby the recent increase in IFS can more

89

confidently be attributed to anthropogenic climate forcing. These findings contribute to

the existing body of knowledge on climate change, specifically as it relates to sea ice in

Hudson Bay. What it reveals is not new, but rather further evidence that corroborates past

studies showing a decline in various metrics of sea ice on Hudson Bay and the broader

Arctic Ocean (Comiso et al., 2008; Gagnon & Gough, 2005; Gough et al., 2004;

Hochheim et al., 2011; Hochheim & Barber, 2010; Parkinson et al., 1999; Stroeve et al.,

2007; Vinnikov et al., 1999). The implications of a continuing and accelerated decline in

sea ice; economically, socially, and ecologically, would be profound. The sensitivity of

Arctic mammals such as polar bears to declining sea ice has been well documented, and

further declines would most certainly prove detrimental to their population ecology

(Derocher et al., 2004; Stirling et al., 1999; Stirling & Parkinson, 2006). Inuit populations

along the coasts of the Bay may also have to further adapt their subsistence hunting and

travel practices as sea ice patterns continue to change (Tristan et al., 2010). The local

economy will be affected, for better or worse, as the shipping season for routes through

the Hudson Strait to the Port of Churchill depend upon breakup and freeze-up dates

(Prowse et al., 2009; Tivy et al, 2007). The stakeholders in these three issues would all

benefit from a stronger trend analysis that allows for an accurate impact assessment of

future sea ice conditions, while hopefully informing public policy and decision-making

with regard to mitigation and adaptation to these changes

90

Chapter 6: Conclusion

6.1 Research Objectives

In fulfilling Objective 1, the nature of the temperature asymmetry’s response to

changes in sea ice was characterized at both weekly and seasonal time scales. Based on

the results of the weekly SIC-∆TW correlation, it can be concluded that the average SIC

of the Bay does not produce a consistent weekly average temperature difference signal.

The lack of any relationship between these two variables can be attributed in part to

inherent climatic variability at finer temporal scales, but is also likely due to the

significant lag time between a change in sea ice conditions and a thermal response from

the Bay’s water. This lag means that peak temperature differences, the driving agent of

which was open water, are not seen until well into the freeze-up season. This fact makes

the determination of any cause-effect relationship at a weekly temporal resolution wholly

unfeasible.

Based on the IFS-∆TMAX analysis, it can only be concluded that, over the ∆TMAX

period, there is a general tendency toward greater coastal temperature differences in

years when the ice-free season is above average. It can be stated with greater confidence

that during years with anomalously short ice-free seasons (IFS<129), coastal temperature

differences are more likely to be close to zero (∆TMAX >-4.5°C). The hypothesis that wind

direction was a major contributor to the temperature asymmetry proved to have some

merit, with strong westerlies (and/or weak easterlies) tending to be associated with

greater temperature differences.

With regard to Objective 2, this study did propose a proxy method employing the

temperature asymmetry alone, but its utility was determined to be negligible for lack of a

91

strong enough relationship with IFS. Based on the results of applying ∆TMAX thresholds

to the existing record, it can be expected that hindcasting IFS into three classes using this

method would carry with it a 42% error rate. This method can be used to greater effect in

capturing all actual short years, but there would still me misclassifications owing to the

expected inclusion of medium and long years. A multi-proxy method that classifies IFS

based on ∆TMAX only for those years when easterly winds are below average produced

marginally better results. However, the lack of wind data prior to 1982 precludes the use

of such a method to hindcast IFS. Therefore, it can be concluded that the seasonal

temperature asymmetry on Hudson Bay should not be used in isolation as a proxy for sea

ice conditions. In arriving at that conclusion however, the use of absolute temperature as

a benchmark for evaluating proxies demonstrated some potential itself as a tool for

hindcasting ice-free season. A multiple linear regression equation using both TF and

∆TMAX was able to reproduce the existing IFS record with an average error of 8.1 days,

an approximately 1 day improvement over a linear regression equation using TF alone.

This multi-proxy was used to hindcast 28 years of IFS, producing a time series that

totaled 68 years in length. From this lengthened time series, it can be concluded that the

recent increase in IFS is unprecedented during the period of 1944-2011, and hence

unlikely to be a result of climate variability.

6.2 Recommendations for Future Research

Since the sea ice-temperature asymmetry relationship is fundamentally lacking

sufficient strength to allow for a fine-resolution proxy, further research into this particular

approach is not recommended. However, given that the combination of ∆TMAX with TF

92

was able to predict IFS within 8.1 days, further research into this multi-proxy for sea ice

on the Bay is definitely warranted. Experimentation with the TF variable that makes use

of other climate stations, or a focus on different periods of the cryogenic cycle might

yield even better results. In addition, further inquiry into altogether different approaches

than those investigated here is highly advisable. For example, the same contrasts in

energy budgets between land and sea exploited in this study also lead to local circulations

in coastal regions. These local circulations are very different depending on the ice state of

the adjacent sea. The resulting diurnal variability of temperature contains a signal that, if

strong enough, could be predictive of sea ice cover for that location (W. Gough, pers.

comm., 2012). Such local-scale approaches acknowledge the spatial limitations imposed

by the complexity of sea ice-atmosphere interaction and the heterogeneity of sea ice on

the Bay. Furthermore, results from an alternative proxy for Hudson Bay sea ice could be

used to corroborate the conclusions arrived at in this study. With further research, it is

likely that the proposed method for hindcasting sea ice conditions based on temperature

can be honed to provide more accurate results, lending further confidence to the trend

analysis.

93

References

Abram, N.J., Thomas, E.R., McConnell, J.R., Mulvaney, R., Bracegirdle, T.J., Sime,

L.C., & A.J. Aristarain. 2010. Ice core evidence for a 20th century decline of sea ice in the Bellingshausen Sea, Antarctica. Journal of Geophysical Research: Atmospheres 115(D23101).

Abram, N.J., Wolff, E.W., & M.A.J. Curran. 2013. A review of sea ice proxy information

from polar ice cores. Quaternary Science Reviews, In press. Andreas, E. & B.A. Cash. 1999. Convective heat transfer over wintertime leads and

polynyas. Journal of Geophysical Research 104(C11), 25,721-25,734. Andreas, E.L. & B. Murphy. 1986. Bulk transfer coefficients for heat and momentum

over leads and polynyas. Journal of Physical Oceanography 16, 1875–1883. Becagli, S., Castellano, E., Cerri, O., Curran, M., Frezzotti, M., Marino, F., Morganti, A.,

Proposito, M., Severi, M., Traversi, R., & R. Udisti. 2009. Methanesulphonic acid (MSA) stratigraphy from a Talos Dome ice core as a tool in depicting sea ice changes and southern atmospheric circulation over the previous 140 years. Atmospheric Environment 43 (5), 1051-1058.

Brandt, R.E., S.G. Warren, A.P. Worby, & T.C. Grenfell. 2005. Surface Albedo of the

Antarctic Sea-ice Zone. Journal of Climate 18(17), 3606-3622. CIS (Canadian Ice Service. 2013. Canadian Ice Service. Retrieved on July 15th, 2013

from: http://www.ec.gc.ca/glaces-ice/ Coffin, H.C. 1964. Wind analysis by vector summation. The Professional Geographer

16(4), 13-14. Comiso, J.C., Parkinson, C.L., Gersten, R., & L. Stock. 2008. Accelerated decline in the

Arctic sea ice cover. Geophysical Research Letters 35(1). Curran, M.A.J. & G.B. Jones. 2000. Dimethyl sulfide in the Southern Ocean:

Seasonality and flux. Journal of Geophysical Research 105(D16), 20,451- 20,459.

Curran, M.A.J., van Ommen, T.D., Morgan, V.I., Phillips, K.L., & A.S. Palmer. 2003. Ice

core evidence for Antarctic sea ice decline since the 1950s. Science 302(5648), 1203-1206.

Curry, J.A., Schramm, J.L., & E.E. Ebert. 1994. Sea Ice-Albedo Climate Feedback

Mechanism. Journal of Climate 8(2), 240-247.

94

DeMaria, M. 1985. Linear Response of a Stratified Tropical Atmosphere to Convective Forcing. Journal of Atmospheric Science 42, 1944-1959.

Derocher, A.E., Lunn, N.J., & I. Stirling. 2004. Polar bears in a warming climate.

Integrative and Comparative Biology 44, 163-176. Dieckmann, G.S. & H.H. Hellmer. 2009. The Importance of Sea Ice: An Overview. In:

Thomas, D.N. & G.S. Dieckmann. Ed. Sea Ice. John Wiley & Sons, 1-110. Douglas, T.A., Domine, F., Barret, M., Anastasio, C., Beine, H.J., Bottenheim, J.,

Grannas, A., Houdier, S., Netcheva, S., Rowland, G., Staebler, R., & A. Steffen. 2012. Frost flowers growing in the Arctic ocean-atmosphere-sea ice-snow interface: 1. Chemical composition. Journal of Geophysical Research: Atmospheres 117(D00r09).

Dunn, O. J. 1961. Multiple Comparisons Among Means. Journal of the American

Statistical Association 56 (293), 52–64 EC (Environment Canada). 2013a. Documentation for the Digital Archive of Canadian

Climatological Data (Surface) Identified by Element. Retrieved on August 24th, 2013 from: http://climate.weather.gc.ca/prods_servs/documentation_index_e.html#note17

EC (Environment Canada). 2013b. Quality of Historical Climate Data. Retrieved on

August 24th, 2013 from: http://climate.weather.gc.ca/climateData/dataQuality_e.html

EFC (Ecological Framework of Canada). 2013. Ecozone and Ecoregion Descriptions.

Retrieved June 5th, 2013 from: http://ecozones.ca/english/zone/ Etkin, D.A. 1991. Break-up in Hudson Bay: Its sensitivity to air temperatures and

implications for climate warming. Climatological Bulletin 25 (1), 21-34. Foster, A.F.M., Curran, M.A.J., Smith, B.T., van Ommen, T.D., & V.I. Morgan. 2006.

Covariation of sea ice and methanesulphonic acid in Wilhelm II Lnad, East Antarctica. Annals of Glaciology 44, 429-432.

Friehe, C.A. & K.F. Schmitt. 1976. Parameterization of Air-Sea Interface Fluxes of

Sensible Heat and Moisture by the Bulk Aerodynamic Formulas. Journal of Physical Oceanography 6, 801-809.

Gagnon, A.S. & W.A. Gough. 2002 Hydro-climatic trends in the Hudson Bay region,

Canada. Canadian Water Resources Journal 27, 245-262. Gagnon, A.S. & W.A. Gough. 2005. Trends in the Dates of Ice Freeze-up over Hudson

Bay, Canada. Arctic 58(4), 370-382.

95

Gagnon, A.S. & W.A. Gough. 2006. East-west asymmetry in long-term trends of landfast ice thickness in the Hudson Bay region, Canada. Climate Research 32, 177-186.

Galbraith, P.S. & P. Larouche. 2011. Sea-surface temperature in Hudson Bay and

Hudson Strait in relation to air temperature and ice cover breakup, 1985-2009. Journal of Marine Systems 87, 66-78.

Garratt, J.R. 1990. The Internal Boundary Layer – A Review. Boundary-Layer

Meteorology 50(1-4), 171-203. Gerbush, M.R., Kristovich, D.A.R., & N.F. Laird. 2008. Mesoscale Boundary Layer and

Heat Flux Variations over Pack Ice-covered Lake Erie. Journal of Applied Meteorology and Climatology 47, 668-682.

Gough, W.A., Cornwell, A.R., & L.J.S. Tsuji. 2004a. Trends in Seasonal Sea Ice

Duration in Southwestern Hudson Bay. Arctic 57(3), 299-305. Gough, W.A., Gagnon, A.S., & H.P. Lau. 2004b. Interannual variability of Hudson Bay

ice thickness. Polar Geography 28(3), 222-238.

Grenfell, T.C. & D.K. Perovich. 1984. Spectral albedos and incident spectral irradiance over Arctic sea ice. Journal of Geophysical Research 89, 3573-3580.

Grumet, N.S., Wake, C.P., Mayewski, P.A., Zielinski, G.A., Whitlow, S.I., Koerner,

R.M., Fisher, D.A., Woollett, J.M., 2001. Variability of sea-ice extent in Baffin Bay over the last millennium. Climatic Change 49(12), 129-145.

Ho, J. 2010. The implications of Arctic sea ice decline on shipping. Marine Policy 34(3),

713-715. Hochheim, K.P. & D.G. Barber. 2010 Atmospheric forcing of sea ice in Hudson Bay

during the fall period, 1980-2005. Journal of Geophysical Research 115, C05009. Hochheim, K.P., Lukovich, J.V., & D.G. Barber. 2011. Atmospheric forcing of sea ice in

Hudson Bay during the spring period, 1980-2005. Journal of Marine Systems 88, 476-487.

Hodgkins, G.A. 2013. The importance of record length in estimating the magnitude of climatic changes: an example using 175 years of lake ice-out dates in New England. Climatic Change DOI 10.1007/s10584-013-0766-8.

Isaksson, E., Kohler, J., Pohjola, V., Moore, J., Igarashi, M., Karlo ̈f, L., Martma, T.,

Meijer, H.A.J., Motoyama, H., Vaikma ̈e, R., & R.S.W. van de Wal. 2005. Two ice- core δ18O records from Svalbard illustrating climate and sea-ice variability over the last 400 years. The Holocene 15, 501–509.

96

Kaimal, J. C. and Finnigan, J. J. 1994. Atmospheric boundary layer flows, their structure and management. Oxford University press. 289pp.

Kendall, M. 1938. A New Measure of Rank Correlation. Biometrika 30(1–2), 81–89 Kovacs, K.M., Lydersen, C., Overland, J.E., & S.E. Moore. 2011. Impacts of changing

sea-ice conditions on Arctic marine mammals. Marine Biodiversity 41(1), 181- 194.

Kwok, R., Cunningham, G.F., Wensnahan, M., Rigor, I., Zwally, H.J., & D. Yi. 2009.

Thinning and volume loss of the Arctic Ocean sea ice cover: 2003-2008. Journal of Geophysical Research 114(C7).

Kwok, R. & D.A. Rothrock. 2009. Decline in Arctic sea ice thickness from submarine

and ICESat records: 1958-2008. Geophysical Research Letters 36, L15501. Laidler, G., Ford, J., Gough, W., Ikummaq, T., Gagnon, A., Kowal, S., Qrunnut, K., & C

Irngaut. 2009. Traveling and hunting in a changing Arctic: assessing Inuit vulnerability to sea ice change in Igoolik, Nunavut. Climatic Change 94(3-4), 363-397.

Lewis, E.L., Jones, E.P., Lemke, P., Prowse, T.D., & P. Wadhams. 2000. The Freshwater

Budget of the Arctic Ocean. Springer, NATO Scientific Affairs Division. Livingstone, D.M. 1997. Break-up dates of alpine lakes as proxy data for local and

regional mean surface air temperatures. Climatic Change 37, 407-439. Macias-Fauria, M., Grinsted, A., Helama, S., Moore, J., Timonen, M., Martma, T.,

Isaksson, E., & M. Eronen. 2010. Unprecedented low twentieth century winter sea ice extent in the Western Nordic Seas since A.D. 1200. Climate Dynamics 34(6), 781-795.

Mahasenan, N., Watts, R.G., & H. Dowlatabadi. 1997. Low-frequency oscillations in

temperature proxy records and implications for recent climate change. Geophysical Research Letters 24(5), 563-566.

Markham, W.E. 1986. The ice cover. In: Martini, I.P. ed. Canadian inland seas.

Amsterdam. Elsevier, 101-116

Martini, I.P. 1986. Coastal features of Canadian inland seas. In: Martini, I.P., ed. Canadian inland seas. Amsterdam: Elsevier. 117 – 142.

Maxwell, J.B. 1986. A climate overview of the Canadian inland seas. In: Martini, I.P. ed. Canadian inland seas. Amsterdam. Elsevier, 101-116.

97

Maykut, G. 1982. Large-Scale Heat Exchange and Ice Production in the Central Arctic. Journal of Geophysical Research 87, 7971–7984

Maykut, G. 1986. The surface heat and mass balance, in: The Geophysics of Sea Ice, NATO ASI Series B Phys. Vol 146. Edited by: Untersteiner, N. 395–463. Plenum Press.

McPhee, M. 2008. Air-Ice-Ocean Interaction: Turbulent Ocean Boundary Layer

Exchange Processes. Springer, New York, NY. Moore, S.E. & H.P. Huntington. 2008. Arctic Marine Mammals and Climate Change:

Impacts and Resilience. Ecological Applications 18(12), S157-S165. Morassutti, M.P. & E.F. Ledrew. 1996. Albedo and depth of melt-ponds on sea ice.

Internationsal Journal of Climatology 16, 817-838. NRCAN (Natural Resources Canada). 1985. Canada Drainage Basins. The National Atlas

of Canada, 5th edition. 1985. NRCAN (Natural Resources Canada). 2009. Permafrost. The National Atlas of Canada,

6th edition (archival version). 2009. Niziol, T.A. 1987. Operational Forecasting of Lake Effect Snowfall in Western and

Central New York. Weather Forecasting 2, 310-321. Oke, T.R. 1978. Boundary Layer Climates. Routledge, 435 pp. Palecki, M.A. & R.G. Barry. 1986. Freeze-up and Break-up of Lakes as an Index of

Temperature Changes during the Transition Seasons: A Case Study for Finland. Journal of Climate and Applied Meteorology 25(7), 893-903.

Parkinson, C.L., Cavalieri, D.J., Gloerson, P., Zwally, H.J., & J.C. Comiso. 1999. Arctic

sea ice extents, areas, and trends, 1978-1996. Journalof Geophysical Research 104(C9), 20837-20856.

Perovich, D.K. 1996. The optical properties of sea ice. Cold Regions Research and

Engineering Laboratory. Hanover, N.H. Monogram 96-1, 25 pp. Perovich, D.K., Roesler, C.S., & W.S. Pegau. 1998. Variability in Arctic sea ice optical

properties. Journal of Geophysical Research 103, 1193-1208. Polyak, L., Alley, R.B., Andrews, J.T., Brigham-Grette, J., Cronin, T.M., Darby, D.A.,

Dyke, A.S., Fitzpatrick, J.J., Funder, S., Holland, M., Jennings, A.E., Miller, G.H., O’Regan, M., Savelle, J., Serreze, M., St John, K., White, J.W.C., & E. Wolff. 2010. History of sea ice in the Arctic. Quaternary Science Reviews 29, 1757-1778.

98

Prowse, T.D., Furgal, C., Chouinard, R., Melling, H., Milburn, D. & S.L. Smith. 2009. Implications of Climate Change for Economic Development in Northern Canada: Energy, Resource, and Transportation Sectors. Ambio 38(5), 272-281.

Rankin, A.M., Wolff, E.W., & S. Martin. 2002. Frost flowers: Implications for tropo-

spheric chemistry and ice core interpretation. Journal of Geophysical Research: Atmospheres 107 (D23).

Raymond, D.J. 1986. Prescribed Heating of a Stratified Atmosphere as a Model for Moist

Convection. Journal of Atmospheric Science 43, 1101-1111. Rothrock, D.A., Yu, Y., & G.A. Maykut. 1999. Thinning of the Arctic sea-ice cover.

Geophysical Research Letters 26, 3469-3472. Rothrock, D.A. & J. Zhang. 2005. Arctic Ocean sea ice volume: What explains it’s

recent depletion? Journal of Geophysical Research 110, C01002. Saucier, F.J. & J. Dionne. 1998. A 3-D coupled ice-ocean model applied to Hudson

Bay, Canada: The seasonal cycle and time-dependent climate response to atmospheric forcing and runoff. Journal of Geophysical Research 103(C12), 27,689-27,705.

Saucier, F.J., Senneville, S., Prinsenberg, S., Roy, F., Smith, G., Gachon, P., Caya, D., & R. Laprise. 2004. Modelling the sea ice-ocean seasonal cycle in Hudson Bay, Foxe Basin and Hudson Strait, Canada. Climate Dynamics 23, 303-326.

Sousonis, P.J. 1992. A Numerical Investigation of Wind Speed Effects on Lake-effect

Storms. Boundary Layer Meteorology 64, 261-290. Stephens, M.A. 1986. Tests Based on EDF Statistics, In D'Agostino, R.B. and Stephens,

M.A. Goodness-of-Fit Techniques. New York: Marcel Dekker. Stewart, E.J., Tivy, A., Howell, S.E.L., Dawson, J., & D. Draper. 2010. Cruise Tourism

and Sea Ice in Canada’s Hudson Bay Region. Arctic 63(1), 57-66. Stirling, I., & C.L. Parkinson. 2006. Possible effects of climate warming on selected

populations of polar bears (Ursus maritimus) in the Canadian Arctic. Arctic 59(3), 261-275.

Stirling, I., Lunn, N.J., & J. Iacozza. 1999. Long-term trends in the population ecology

of polar bears in western Hudson Bay in relation to climatic change. Arctic 52(3), 294-306.

Stroeve, J.M., Holland, M.M., Meier, W., Scambos, T., & M. Serreze. 2007. Arctic sea I ce decline: Faster than forecast. Geophysical Research Letters 34, L09501.

99

Stull, R.B. 1988. An introduction to boundary layer meteorology. Kluwer Academic Publishers, 666 p.p.

Tivy, A., Alt, B., Howell, S., Wilson, K., & J. Yackel. 2007. Long-Range Prediction of

the Shipping Season in Hudson Bay: A Statistical Approach. Weather and Forecasting 22.5, 1063-1075.

Tristan, P., Smit, B., Duerden, F., Ford, J.D., Goose, A., & Kataoyak, F. 2010. Inuit

vulnerability and adaptive capacity to climate change in Ulukhaktok, Northwest Territories, Canada. Polar Record 46(237), 157-177.

Vinnikov, K.Y., Robock, A., Stouffer, R.J., Walsh, J.E., Parkinson, C.L., Cavalieri, D.J.,

Mitchell, J.F.B., Garrett, D., & V.F. Zakharov. 1999. Global Warming and Northern Hemisphere Sea Ice Extent. Science 286(5446), 1934-1937.

Wang, J., Mysak, L.A., & R.G. Ingram. 1994. Interannual variability of sea-ice cover in

Hudson Bay, Baffin Bay and the Labrador Sea. Atmosphere-Ocean 32(2), 421-447.

Welch, K.A., Mayewski, P.A., & S.I. Whitlow. 1993. Methanesulphonic acid in coastal

Antarctic snow related to sea-ice extent. Geophysical Research Letters 20 (6), 443-446.

Williams, G.P. 1971. Predicting the Date of Lake Ice Breakup. Water Resources

Research 7 (2), 323-333.

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Appendix: Wind Roses

Below are the wind roses for those years when the actual IFS were concordant

with the established thresholds of ∆TMAX. Note the omission of years 1992,1993 and

2008-2011for lack of wind direction data, as well as the omission of 1994 for lack of

temperature data, and 1997-1999 for lack of sea ice data.


The wind rose for 1984 shows the most frequent wind direction as N, and the

frequency count for the N wind is the highest on record. With relatively fewer, W, NW,

NE and E component counts, it is likely that wind direction did not play a role in

accentuating or nullifying IFS effects on ∆TMAX.

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

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Figure 22: 1987 wind rose for Inukjuak over Julian days 320-350: ∆TMAX = -2.8°C, IFS = 128 (Short).

The 1987 wind rose is dominated by largest frequency count of NE winds on

record. If the IFS had been classified as long this year, it might be expected that this

strong NE component would have had a nullifying effect on the ∆TMAX signal, but since

this year actually had a short IFS the temperature difference could be attributed to sea ice

conditions, strong NE winds, or some combination of both. It might be argued that with

such a lack of westerly winds and a short IFS one would expect the temperature

difference to be even closer to zero, but a difference of 2.8°C could just as easily be

attributed to climatic variability.

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

102


The 1989 wind rose shows that W, NW and NE components were all close to

average. The lack of an E component may have allowed for the development of a

medium ∆TMAX signal that is representative of actual IFS conditions.


0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

103

The wind rose for 1995 shows that NE and E components were significantly

stronger than W and NW components. Despite the fact that ∆TMAX falls within the

defined thresholds for medium IFS, dominant E and NE winds could have dampened the

∆TMAX signal such that it would have been closer to the medium-long threshold under

normal wind conditions. If so, the ∆TMAX would have more strongly correlated with the

IFS, as it too is on near the medium-long threshold at 147 days.


The 1996 wind rose is dominated by an anomalously large E component (largest

on record). Despite this strong E component and relatively weak W/NW components, the

temperature difference signal is one that would be expected given the long IFS. Hence,

this year does not conform to the hypothesis of easterlies dampening temperature

differences, and there may be other climatic variables at work.

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

104


The wind rose for 2001 shows a slightly above-average NW component but an

equally strong N component. The effect of the N component is not known, though it is

presumed to have negligible amplifying or dampening effects on ∆TMAX. Hence, it is

likely that the strong NW component allowed the development of a strong temperature

asymmetry. Again, one can speculate that if the W component were stronger than the N

component that ∆TMAX might be even more significant, given the very lengthy IFS.

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

105


The wind rose for 2003 shows a roughly equal distribution of all components.

Hence, it is likely that the W/NW components was sufficient to produce an asymmetric

temperature signal in line with the long IFS, while no components were dominating

leading to amplification or dampening of that signal.


0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

106

The wind rose for 2006 shows above average W and NW components, average E

component, and below average NE component. There are no major anomalies in the

distribution of direction frequencies that would significantly alter the temperature

asymmetry, while the westerly components are allowing for its development. Hence, the

∆TMAX value alone is representative of the IFS in this case.


The wind rose for 2007 shows a significant W component (3rd largest on record)

which, combined with an average NW component, dominates over easterly wind

components. Given this year is definitively classified as long in terms of IFS, and the

relative strength of W winds, one might expect the temperature difference signal to be

greater. Despite this perceived anomaly, ∆TMAX still successfully classifies this year as a

long IFS.

0 50 100 150 200 250 300

N

NE

E

SE

S

SW

W

NW

east-west asymmetry in coastal temperatures of hudson …...east-west asymmetry in coastal...

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