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Origins and Levels of Seasonal Forecast Skill for Sea Ice in Hudson Bay Using Canonical Correlation Analysis

ADRIENNE TIVY Foothills Climate Analysis Facility, Centre for Alpine and Arctic Climate Research, Department of Geography, University of Calgary, Calgary, Alberta, Canada, and International Arctic Research Center, University of Alaska Fairbanks, Fairbanks, Alaska

STEPHEN E. L. HOWELL Climate Processes Section, Atmospheric Science and Technology Directorate, Environment Canada, Toronto, Ontario, Canada

BEA ALT Balanced Environmental Associates, Ottawa, Ontario, Canada

JOHN J. YACKEL Foothills Climate Analysis Facility, Centre for Alpine and Arctic Climate Research, Department of Geography, University of Calgary, Calgary, Alberta, Canada

THOMAS CARRIERES Canadian Ice Service, Meteorological Service of Canada, Environment Canada, Ottawa, Ontario, Canada

(Manuscript received 16 November 2009, in ﬁnal form 3 August 2010)

ABSTRACT

Canonical correlation analysis (CCA) is used to estimate the levels and sources of seasonal forecast skill for July ice concentration in Hudson Bay over the 1971–2005 period. July is an important transition month in the seasonal cycle of sea ice in Hudson Bay because it is the month when the sea ice clears enough to allow the ﬁrst passage of ships to the Port of Churchill. Sea surface temperature (quasi global, North Atlantic, and North

Paciﬁc), Northern Hemisphere 500-mb geopotential height (z500), sea level pressure (SLP), and regional surface air temperature (SAT) are tested as predictors at 3-, 6-, and 9-month lead times. The model with the

highest skill has three predictors—fall North Atlantic SST, fall z500, and fall SAT—and significant tercile forecast skill covering 61% of the Hudson Bay region. The highest skill for a single-predictor model is from fall North Atlantic SST (6-month lead). Fall SST explains 69% of the variance in July ice concentration in Hudson Bay and a possible atmospheric link that accounts for the lagged relationship is presented. CCA diagnostics suggest that changes in the subpolar North Atlantic gyre and the Atlantic multidecadal oscillation (AMO), reflected in sea surface temperature, precedes a deepening/ weakening of the winter upper-air ridge northwest of Hudson Bay. Changes in the height of the ridge are reflected in the strength of the winter northwesterly winds over Hudson Bay that have a direct impact on the winter ice thickness distribution; anomalies in winter ice severity are later reflected in the pattern and timing of spring breakup. July ice concentration in Hudson Bay has declined by approximately 20% per decade between 1979 and 2007, and the hypothesized link to the AMO may help explain this significant loss of ice.

1. Introduction Corresponding author address: Adrienne Tivy, International Arctic Research Center, University of Alaska Fairbanks, Fair- September ice extent in the Arctic has declined by ap- 21 banks, AK 99775. proximately 10% decade between 1979 and 2007 (e.g., E-mail: [email protected] Comiso et al. 2008). This dramatic loss of ice has fueled

DOI: 10.1175/2010JCLI3527.1

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FIG. 1. (a) July mean ice concentration in tenths ice coverage and (b) standard deviation in July mean ice concentration in tenths ice coverage. The mean opening date for the shipping route to Churchill, 1972–2004, is 25 Jul, and the four choke points where ice clears last along the route are outlined in black. interest in the seasonal predictability of sea ice, both re- than the heavily deformed ice in the center of the bay gionally and Arctic wide, as a means to isolate the main (Markham 1986). internal and external climate forcings. Regionally, with Factors that influence the timing and pattern of spring the exception of the Bering Sea, the greatest reductions breakup in Hudson Bay include local wind forcing, tides, have occurred in Hudson Bay (Parkinson and Cavalieri river runoff, air temperature, snow depth on the ice, and 2008). Over the same period, looking at July, which is the the ocean heat flux. The importance of the local wind month before the region becomes essentially ice free and forcing on spring sea ice variability has been identified the shipping season begins, sea ice declined by approxi- in both observations (Wang et al. 1994b) and modeling mately 20% decade21 (Stewart et al. 2010). July is an studies (Wang et al. 1994a; Saucier and Dionne 1998), important month in the Hudson Bay region since it is the where strengthened northerly winds are associated with month before the region becomes essentially ice free and heavy ice conditions. A positive correlation between river the shipping season begins. Exacerbating the need for sea runoff and sea ice extent at a 1-yr lag is identified in Wang ice forecasts in this region is the potential of the Arctic Sea et al. (1994a) and is supported by the modeling study of Bridge (Murmansk, Russia, to Churchill, Canada) becom- Saucier and Dionne (1998), who show an increase in ing a major commercial shipping route. modeled ice thickness in southeast Hudson Bay due to a Spring breakup in Hudson Bay starts in May when leads, freshening of the mixed layer caused by increased river areas of open water within the ice pack, form in the north- runoff. Saucier and Dionne also show a decrease in the western part of the bay. Dynamic- and thermodynamic- winter ice volume by more than 20% in response to a driven melt proceeds from the northwest and the east temperature increase of 28C. Using the same model, Joly with the ice along the southwest coast clearing last. In et al. (2011) show a decrease in the winter ice season by Hudson Strait, breakup is also initiated by the presence of 7–9 weeks with a mean warming of approximately 48C. open water as leads form along the northern coast, causing The sensitivity of sea ice cover to temperature is sup- the ice to clear from northwest to southeast, with Ungava ported by observations where Etkin (1991) find a signifi- Bay clearing last (CIS 2002; Fig. 1a). In a still-relevant cant negative correlation between the timing of breakup review of the ice regime in Hudson Bay, Markham (1986) and cumulative melting degree days. The importance of attributes the first clearing of ice in northwestern Hudson snow depth on the sea ice is highlighted in Gough et al. Bay to the mean northerly winds throughout the winter, (2004). In their study of ice thickness at coastal stations which keep the ice thin and drifting offshore and which around Hudson Bay, Gough et al. found that snow depth continue into spring, widening the leads and initiating on the ice contributed more to the interannual variability melt. The clearing in western Hudson Strait is also attrib- in ice thickness than air temperature. The influence of uted to the winter and spring wind forcing of leads but is the ocean heat flux on ice severity is explored indirectly combined with tides that ultimately flush the ice out into in Gough and Houser (2005), where a link is identified the Labrador Sea. Clearing in eastern Hudson Bay is between the length of the ice-free season and summer initiated by spring runoff and proceeds relatively quickly air temperature to the timing of freeze up in Hudson since this is an area of fast ice that is generally thinner Strait.

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Interannual variability in spring ice conditions has also prediction models are starting to be realized (e.g., Pellerin been linked to large-scale climate variability. Mysak et al. et al. 2004) and while this is an area of active research, the (1996) and Wang et al. (1994b) show greater than normal focus to date has been on short-term forecasting. Climate spring ice extent in Hudson Bay in response to coincident models that include atmosphere–sea ice–ocean coupling positive North Atlantic Oscillation and El Ninõ events. A are also starting to be used for seasonal predictions, but deepening of the Icelandic low (positive NAO) during their skill for sea ice forecasting is quite limited to date. winter is associated with negative winter temperature Statistical models have been developed for seasonal sea ice anomalies and enhanced northerly winds over eastern forecasting, but they have focused solely on the prediction Canada, including Hudson Bay (Agnew 1993; Wang et al. of scalar sea ice parameters: seasonal and regional ice 1994b). The Pacific–North America (PNA) teleconnec- extent (Barnett 1980; Johnson et al. 1985; Chapman and tion pattern (Wallace and Gutzler 1981), which is often Walsh 1991; Drobot et al. 2006, Drobot 2007; Lindsay well developed during strong El Ninõ episodes, has an et al. 2008), the Beaufort severity index (Drobot and intensified center of high pressure over western Canada, Maslanik 2002; Drobot 2003), the opening date of the resulting in enhanced northerly winds over Hudson Bay shipping season in Hudson Bay (Tivy et al. 2007), and the (Wang et al. 1994b). Colder than normal air temperatures length of the ice-free and ice-covered seasons in Hudson and stronger than normal northerly winds promote ice Strait (Gough and Houser 2005). These models all rely thermodynamic and dynamic ice growth in Hudson Bay. on multiple linear regression techniques that relate sea Tivy et al. (2007) link variability in the opening date of the ice severity to antecedent climate, and the skill of the shipping route to Churchill with low frequency vari- models is most sensitive to lead time and whether the ability in the North Atlantic. Evidence of both decadal long-term trend is removed from the data prior to model and multidecadal variability in ice anomalies are shown development. in Mysak and Venegas (1998) and Venegas and Mysak With a focus on Hudson Bay, this study expands on (2000), although Hudson Bay is not discussed directly previous work by assessing the empirical predictability of in these studies. both spatial and interannual variability in early-summer Canonical correlation analysis (CCA) is a multivariate sea ice concentration at 3-, 6-, and 9-month lead times. statistical technique that measures the linear relationship CCA is used both as a forecasting tool and a diagnostic between two or more multidimensional variables. The tool to explore potential dynamic pathways in the climate technique is slightly different from the more commonly system that link variability in atmospheric and oceanic used singular value decomposition (SVD) since, instead predictors to variability in sea ice. It is hoped that results of maximizing covariance, cross-correlation is maximized from this analysis will offer insight into the recent dra- (Von Storch and Zwiers 1999). In climate research, CCA matic decline in early summer sea ice concentration in is used to identify coupled patterns in climate data (e.g., Hudson Bay. In the next two sections the datasets used Bretherton et al. 1992), and a variant of CCA developed in this study are presented, the rationale for the pre- by Barnett and Preisendorfer (1987, hereafter BP) is the dictors chosen for the experiment are discussed, and most reliable and most commonly used statistical seasonal the CCA methodology is described. Results from each forecasting technique (Zwiers and Von Storch 2004). predictor experiment are presented and discussed in Operationally, CCA models based on the BP methodol- section 4, followed by a summary of the main findings in ogy are used for generating seasonal precipitation and section 5. temperature forecasts in North America (Barnston 1994; Shabbar and Barnston 1996) and other parts of the 2. Data world—Africa (Thiaw et al. 1999; Landman and Mason 1999), Korea (Hwang et al. 2001), Europe (Johansson Sea ice data on a 0.258 grid is obtained from the Ca- et al. 1998), the tropical Pacific Islands (He and Barnston nadian Ice Service Digital Archive (CISDA) regional 1996)—and worldwide (Barnston and Smith 1996). In all charts database (CIS 2007a,b). The dataset spans from of these studies predictability stems from low frequency 1969 to present and is a compilation of the weekly regional variability in the ocean. While dynamic models are state of ice charts that are an integration of ice information from the art for short- and medium-range predictions of the state various satellite sensors, aerial reconnaissance, ship ob- of the atmosphere, at lead times greater than 3 months, servations, and other in situ measurements. This dataset statistical models generally outperform dynamic models is selected over the passive-microwave-derived record (Zwiers and Von Storch 2004). since, as Agnew and Howell (2002) have shown, passive- Compared to the atmosphere, seasonal sea ice fore- microwave-derived ice concentration can underestimate casting is in its infancy. While the benefits of coupling sea ice area by approximately 30% during spring melt in ice and ocean models to operational numerical weather marginal sea ice regions such as Hudson Bay.

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b. Choice of predictors Four climate variables are tested as potential pre-

dictors: 3-month-averaged SST, z500, SAT, and SLP. SST is chosen because it varies over time much more slowly than the atmosphere and is the main source of predictability in seasonal forecast models for the atmosphere (e.g., Barnston 1994; Shabbar and Barnston 1996) and sea ice (Lindsay et al. 2008). North Atlantic (SST-NA; 208–708N, 758W–108E), North Pacific (SST-NP; 208–708N, 1058E– 1208W), and quasi-global (SST-LG; 508S–708N, 3608 azi- muth) SST are all tested as potential predictors. The SST predictor domain is restricted to the North Atlantic and North Pacific to ensure that, after prefiltering (see section 3c), variability in tropical Pacific SST does not mask the main modes of low frequency variability in the North Atlantic (e.g., North Atlantic tripole) and North Pacific FIG. 2. Seasonal cycle in ice cover for Hudson Bay and Hudson (e.g., Pacific decadal oscillation), which may influence Strait expressed as monthly averaged (1971–2007) percent ice weather patterns over the Hudson Bay region. Northern coverage over the combined area. The error bars represent one standard deviation from the mean. Hemisphere SLP and z500 are included since they are the variables for which preferred modes of low-frequency atmospheric variability and teleconnection patterns are Monthly sea surface temperature (SST) data are from identified (e.g., Wallace and Gutzler 1981) and monitored the Met Office Hadley Centre Sea Ice and Sea Surface (e.g., available online at http://www.cpc.noaa.gov/data/ Temperature version 1.1 (HadISST1.1) dataset (Rayner teledoc/telecontents.shtml). Local SAT over Hudson Bay et al. 2003) on a 18 grid for the period 1870 to present. (508–608N, 2658–2958E) is included since it is an important Monthly 500-mb geopotential height (z ), surface air 500 factor controlling sea ice thickness. Other variables temperature (SAT), sea level pressure (SLP), and surface that likely influence interannual variability—such as local vectors winds all on a 2.58 grid are from the National wind forcing, snow depth on the ice, and the ocean heat Centers for Environmental Prediction–National Center flux—are not included owing to the lack of comprehen- for Atmospheric Research (NCEP–NCAR) reanalysis sive datasets. dataset (Kalnay et al. 1996). Monthly sea level fields on a 18 grid for the period 1993–2007 are combined Ocean To- c. CCA methodology pography Experiment (TOPEX)/Poseidon and Jason-1 data with the inverse barometric effect removed. CCA is a variant of a multiple linear regression analysis that is used in climate research to determine the linear 3. Methods relationship between variables that vary in space as well as in time. The objective of CCA analysis is to find correlated a. Choice of predictand patterns and lead–lag relationships between the predictor The predictand is July average ice concentration from and predictand fields. The end result of CCA is a series of 1971 to 2005 in Hudson Bay and Hudson Strait (Fig. 1). modes for which each mode is a pair of predictor and July is the main transition month between complete ice predictand patterns (canonical component vectors), each coverage in winter and open water in summer (Fig. 2), with a time series (canonical component time series) that and ice conditions in July largely determine the start of describes how each pattern varies in time. The mathemat- the shipping season. The mean opening date for the ics is similar to singular value decomposition (SVD) shipping route to Churchill is 25 July (Tivy et al. 2007), analysis with the exception that, instead of maximizing and an approximation of the shipping route through the covariance between the two variables, the correlation Hudson Strait and Hudson Bay is shown (Fig. 1a) along is maximized. The correlation between the two canonical withthefourregionswhereiceclearslastalongtheroute component time series decreases with each successive (Tivy et al. 2007). The mean pattern in July ice concen- mode and like SVD or EOF analysis, the modes are un- tration (Fig. 1a) shows that the ice clears first in north- correlated. Because CCA is a regression technique, the western Hudson Bay, east Hudson Bay, and Hudson standard assumptions of linear regression, that is, inde- Strait; the largest variability (Fig. 1b) is along the seaward pendence and constant variance of the errors, normality margin. of the distribution of errors, and linearity, all apply.

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Prior to CCA a linear trend is removed at each grid interannual covariability in the predictor and predictand point in the predictand and predictor data. This is done and a persistent long-term trend in the predictand. to reduce the likelihood that the CCA-modeled predictor– All models are trained on the 35-year record from predictand relationship is due to a common external forc- 1971 to 2005. Models are generated for each predictor at ing, namely, the change in radiative forcing due to increased lead times of 3, 6, and 9 months; seasonal averages for each greenhouse gases in the atmosphere. It is acknowledged predictor are January–March (JFM), October–December that there may be some leakage, as the true global warming (OND), and July–September (JAS). To determine signal is nonlinear (Solomon et al. 2007) and this is not whether sources of skill identified in the single predictor addressed. experiments are unique to a specific predictor field or com- After detrending, the general CCA methodology fol- mon to two or more predictor fields, mixed-predictor lows BP; the mathematics of the methodology is presented experiments are run. It is assumed that, if the skill of in the appendix of BP. The predictor and predictand data the mixed predictor experiment is higher than the skill are standardized and prefiltered using principal compo- of the individual predictor experiment, then the signals nent (PC) analysis. The PCs are truncated to reduce the are unique. amount of noise in the predictor and predictand datasets d. Evaluation of skill prior to CCA. The number of PC and CCA modes retained in the final model is chosen by maximizing the The field-averaged (global) cross-validated correlation field-averaged ‘‘leave one out’’ cross-validated correla- between the observed and modeled data is used to eval- tion coefficient between the observed and modeled data. uate model skill; it is the standard metric used in the lit- A leave-one-out cross-validation scheme is commonly erature to evaluate the skill of CCA-based forecasting used to prevent overfitting (Michaelson 1987; Elsner and models (e.g., Barnston 1994; Barnston and He 1996; Schmertmann 1994) and, as in BP, the use of the tech- Shabbar and Barnston 1996; Johansson et al. 1998; Hwang nique is justified since after detrending only 3% of the et al. 2001; Mo and Thiaw 2002; Cannon and Hsieh 2008). grid points have significant autocorrelations at 1-yr lag. The significance of local skill (skill at a single grid point) is The PC modes are truncated to reduce the amount of determined using a one-tailed t test of the null hypothesis noise in the predictor and predictand datasets prior to r 5 0withp 5 0.05; correlations greater than 0.28 are CCA. The choice of PC truncation points in this study significant at 95%. The significance of global skill (num- differs from BP and other studies (e.g., Barnston 1994; ber of grid points with r . 0.28) is evaluated at the 95% Johansson et al. 1998) in which the delineation between confidence level using the Monte Carlo–based (1000 tri- signal and noise was determined using Monte Carlo tech- als) field significance test outlined in Livezey and Chen niques. Livezey and Smith (1999) caution that the choice of (1983). For detrended July ice concentration the 95% PC truncation in the BP methodology can have a profound threshold determined from the Monte Carlo run is 5.4%. impact on the CCA results and that often sample sizes are As a final check, significance of experiments that pass field too small to determine the optimum truncation technique significance are tested using a Monte Carlo simulation for a priori. Results from their sensitivity study of the BP which the predictand field is randomly shuffled 100 times methodology to different PC truncation rules suggests that and the percent of grid points with significant local skill the optimal number of predictor modes is much larger, and recorded to determine a 95% confidence level. Although the optimal number of predictand modes is much smaller the field-averaged correlation coefficient is used to deter- than the result in BP. As a result, two simple methods for mine PC and CCA truncation points, it is a measure that is determining PC truncation points are used in this study. less intuitive than the percentage of grid points with sig- For the predictand, where Livezey and Smith (1999) found nificant local correlation. In the discussion, the percentage that the BP methodology retained too many modes, the of grid points with significant local correlation is used to very conservative North et al. (1982) criterion is used. For compare models. the predictor fields that Livezey and Smith (1999) found Forecasts will be expressed categorically as above nor- the BP methodology retained too few modes, a more lib- mal, near normal, and below normal. This is the standard in eral approach that uses screen plots to separate signal from seasonal forecasting since there is an appreciable amount noise is used (O’Lenic and Livezey 1988). of uncertainty. Instead of ranking the data to determine To generate the final model the linear trend that was the tercile boundaries (BP), the threshold is set at 60.43 removed is added back. For simplicity, CCA 1 trend standard deviations from the mean, which is the con- refers to the detrended CCA result with the linear trend vention used at the Canadian Meteorological Centre added back at each grid point. Skill is evaluated for both (Servranckx et al. 1999). In theory, both methods the detrended CCA result and the CCA 1 trend result so would yield the same limits for a normally distributed as to isolate the relative contribution to predictive skill of population.

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TABLE 1. Forecast skill for the three benchmark models. TABLE 2. Forecast skill for 6-month lead (OND).

Global cross-validated Global cross-validated correlation; correlation;percentage Global tercile percentage grid points r . 0.28 . Benchmark grid points r 0.28 skill score (%) Predictor CCA CCA 1 trend Model Detrended Raw Raw z500 0.012; 15.6 0.228; 41.4 Persistence Not significant 0.100; 16.3 28 SLP Not significant N/A —July SAT 20.026; 9.4 0.200; 34.9 Persistence 0.051; 5.9 0.092; 12.7 31 SST-GL Not significant N/A —November SST-NA 0.105; 21.6 0.280; 50.55 Climatology N/A N/A 33 SST-NP Not significant N/A

Mixed predictor Climatology and persistence are used as benchmark SST-NA; z500 0.228; 38.3 0.344; 68.5 SST-NA; SAT 0.196; 28.7 0.307; 56.2 models. Persistence is the monthly averaged ice concen- z500, SAT 0.050; 14.8 0.231; 41.0 tration anomaly at each grid from both the preceding July SST-NA, z500, SAT 0.251; 44.6 0.346; 69.0 and the preceding November added to the mean July ice concentration. Complete ice coverage in winter prevents CCA models with a cross-validated correlation skill that the use of anomaly persistence at the time of the forecast. passed the field significance test. For all models, the percentage of grid points with a significant correlation be- 4. Results tween the observed and modeled data was less than 5.4%.

Depending on the variable and lead time, initial PC 3) SIX-MONTH LEAD TIME (OND) truncation for the climate variables ranged between 2 and 14 and represented between 69% and 86% of the total The results from the single predictor experiments run variability in the original data. The climate truncation at a 6-month lead time, predicting detrended July ice points are conservative compared to the results of the concentration from the preceding fall (OND), are sum- sensitivity analysis in Livezey and Smith (1999). PC trun- marized in Table 2. The fall forecasts had significant skill cation for July sea ice concentration was chosen at four covering 9.4%, 15.6%, and 21.6% of the total area for modes, representing 60% of the original variance in the SAT, z500, and North Atlantic SST, respectively. Forecast data. Tables 1–4 summarize the skills scores for the skill for SLP, global SST, and North Pacific SST is not benchmark models and all predictor experiments at 3-, 6-, significant. Figure 3 shows the geographic distribution of and 9-month lead times. skill for each predictor with significant forecast skill. All three predictors, particularly SST-NA, show some skill in a. Forecast skill Hudson Strait. In Hudson Bay, the skill for SST-NA and 1) PERSISTENCE AND CLIMATOLOGY z500 is in eastern Hudson Bay whereas the skill for SAT is in northwestern Hudson Bay. SST-NA has the greatest Table 1 shows skill results for the three benchmark models. Persistence skill scores were calculated using both raw and detrended monthly ice concentration data. TABLE 3. Forecast skill for 3-month lead (JFM). With the long-term trend removed, there was no signifi- Global cross-validated correlation; cant skill in forecasts made from July anomaly persistence, % grid points r . 0.28 and the skill from November anomaly persistence is Predictor CCA CCA 1 trend barely significant (5.9%). For global tercile skill (Table 1, column 3), persistence did not outperform climatology. z500 Not significant N/A SLP Not significant N/A The skill for persistence was not calculated in a cross- SAT 0.056; 14.3 0.226; 45.7 validated framework and is likely inflated. As a result, the SST-GL Not significant N/A low skill for November persistence is not considered signif- SST-NA 20.020; 5.9 0.193; 28.1 icant, so the only benchmark model available is climatology SST-NP Not significant N/A (long-term mean), which has a tercile skill score of 33%. Mixed predictor 2) NINE-MONTH LEAD TIME (JAS) SAT, SST-NA 0.118; 20.3 0.268; 45.0 SAT, SST-NA (OND) 0.133; 24.9 0.278; 49.5 The results from the single predictor experiments run at SAT, z500 (OND) 0.164; 23.4 0.300; 55.8 a 9-month lead time, predicting detrended July ice con- SAT, SST-NA (OND), 0.232; 39.0 0.335; 62.1 centration from the preceding summer (JAS), yielded no z500 (OND)

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TABLE 4. Principal component (PC) and CCA truncation points for each experiment. The percentage of the original variance in the predictand and predictor retained after PC truncation and the percentage of the original variance in the predictand explained by each CCA mode are shown in parentheses.

Truncation points (% var. expl.) Canonical correlation2 (% predictand var. expl.) PC—July ice concentration PC—predictor CCA CCA1 CCA2 CCA3 CCA4 SAT (OND) 4 (60) 2 (88) 2 0.47 (38) 0.28 (22) n/a n/a SAT (JFM) 4 (60) 2 (88) 2 0.36 (39) 0.19 (21) n/a n/a SST-NA (OND) 4 (60) 7 (73) 2 0.67 (31) 0.48 (22) 0.12 0.02 z500 (OND) 4 (60) 6 (74) 3 0.58 (39) 0.18 (12) 0.11 (8) 0.01 regional coverage of significant skill and the highest model (Fig. 3d) compared to the single predictor models global cross-validated correlation, r 5 0.105. Although highlights the fact that each predictor provides unique there is significant regional overlap in skill between the predictive information and that the best model is the three predictors, skill in northwestern Hudson Bay is combination of all three predictors. unique to SAT and skill in southeastern Hudson Bay is 4) THREE-MONTH LEAD TIME (JFM) unique to z500. Mixed predictor experiment results are listed at the bottom of Table 2. The addition of z500 and The results from the single predictor experiments run at SAT to SST-NA forecasts raises the coverage of skill from a 3-month lead time—predicting detrended July ice con- 21.6% to 38.3% and 28.7%, respectively. Although the centration from the preceding winter—are summarized in addition of SAT to z500 forecasts did not raise the percent Table 3. No significant skill was found in forecasts from coverage, 15.6% to 14.8%, the cross-validated correlation z500, SLP, near-global SST, and North Pacific SST. The skill increased from 0.012 to 0.05. The highest skill, 44.6% skill from North Atlantic SST, which was the highest (0.251), is achieved by combining all three predictors. The skill for a single predictor in fall, is barely significant geographic distribution of skill for the three predictor (5.9%) and is the only significant model that does not

FIG. 3. Geographic distribution of CCA skill (cross-validated correlation) for fall forecasts from (a) SST-NA,

(b) local surface air temperature, (c) Northern Hemisphere z500, and (d) mixed: SST-NA, z500, and SAT.

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FIG. 4. Geographic distribution of CCA skill (cross-validated correlation) for winter forecasts from (a) SST-NA surface air temperature, (b) temperature surface air temperature, and

outperform November persistence. The skill for SAT not change, however, and all of the model skill scores forecasts increased slightly from 9.4% (20.026) to 14.3% outperform the persistence benchmark models. (0.056). The geographic distribution of skill (Fig. 4b) for The model proposed to be used operationally is the fall SAT differs from fall (Fig. 3b). There is almost no skill in three-predictor model. With the addition of the long-term Hudson Strait, and in Hudson Bay the skill shifts from trend forecast skill increases from 44.6% (0.251) to 69% northwestern Hudson Bay to central Hudson Bay. For (0.346). Figure 5 is a comparison of the geographical dis- SST some skill remains in Hudson Strait, but there is no tribution of skill for CCA and CCA 1 trend. The regions skill in Hudson Bay (Fig. 4a). An increase in skill from with greatest skill coincide with the regions with the most combining both predictors (Table 3) suggests each pre- variability (Fig. 1b). The main operational consideration is dictor adds unique predictive information. the shipping route to Churchill, and the model has sig- To determine whether there is value in including winter niﬁcant skill covering most choke point areas along the information in the fall model, the winter values of SST-NA route (Fig. 1a). The geographic distribution of tercile skill and z500 are replaced with the fall values. The geographic (not shown) is similar to the correlation skill shown in distribution of skill for the new three predictor model— Fig. 5b. The model outperforms climatology (Table 1),

SST-NA (OND), z500 (OND), and SAT (JFM)—is shown there is significant tercile skill covering 61% of the in Fig. 4c. Compared to the original fall model, skill cov- Hudson Bay region, and the tercile skill at a given lo- erage is reduced in northwestern Hudson Bay and eastern cation ranges from 40% to 80%. Hudson Bay. Also, forecast skill (Table 3) for the new b. Source of predictability: Interannual variability model, 39% (0.234), is less than the original fall model, 44.6% (0.251). It is concluded that there is little value in The final forecast model was a combination of three replacing fall SAT with winter SAT. predictors: SST-NA (OND), SAT (OND or JFM), and z (OND). Canonical correlation maps and time series 5) CCA 1 TREND:OPERATIONAL MODEL 500 are used to explore sources of predictive skill for each To generate the final forecast, the long-term trend is predictor. Table 4 summarizes final PC and CCA trun- added to the CCA prediction. Skill in all models improves cation points for each predictor. The squared canonical dramatically with the addition of the long-term trend correlations are also listed for each CCA mode in each ex- (Tables 2 and 3). The relative ranking of the models does periment along with the percentage of the original variance

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FIG. 5. Geographic distribution of CCA skill (cross-validated correlation) for (a) mixed fall forecast (as in Fig. 3d) and (b) CCA 1 trend.

in the predictand explained by each CCA mode. The ca- and ice concentration are for the most part restricted to nonical correlation is the correlation between the predictor Hudson Bay. and predictand canonical correlation time series for a given Results for fall are similar to winter. CCA truncation CCA mode. Because the squared canonical correlations was at two modes; CCA1 and CCA2 explain 38% and are the eigenvalues of the cross-correlation matrix, they 22%, respectively, of the original variance in the pre- can be used to calculate the percentage of the original dictand. Canonical correlation maps and correlation time variance in the predictand that is explained by each CCA series are similar to winter, as is their interpretation. mode. For example, the first CCA mode (CCA1) from 2) FALL Z EXPERIMENTS the fall SAT predictor experiment explains 38% of the 500 original variance in the predictand [60% 3 0.47 / (0.47 1 For the fall z500 predictor CCA truncation was at three 0.28)], and CCA1 from the fall SST predictor experiment modes; CCA1, CCA2, and CCA3 explain 39%, 12%, explains 31% of the original variance in the predictand and 8%, respectively, of the original variance in the pre- [60% 3 0.67 / (0.67 1 0.48 1 0.12 1 0.02)]. Recall that dictand. CCA2 and CCA3 are omitted from the discus- only 60% of the original variance in the July ice con- sion; because they explain so little of the original variance centration data was used in the CCA analysis since 40% in July ice concentration, it is assumed that their contri- was removed when the number of principal components bution to forecast skill is minimal compared to CCA1. retained for the analysis was truncated at four. The CCA1 predictor and predictand patterns are shown in Fig. 8. The pattern in z resembles the Pacific–North 1) FALL AND WINTER SAT EXPERIMENTS 500 American teleconnection pattern. The PNA along with In the winter SAT experiment CCA truncation was at the NAO (or Arctic Oscillation) are the dominant modes two modes. CCA1 and CCA2 explain 39% and 21%, of low frequency variability in the extratropical Northern respectively, of the original variance in the predictand. Hemisphere, and both have been linked to extreme ice The canonical correlation maps and time series for conditions in Hudson Bay (Wang et al.1994b; Mysak et al. each mode are shown in Figs. 6 and 7. Correlations are 1996). The region of significant positive correlation over significant throughout the SAT and ice concentration Hudson Bay is accompanied by a second region of sig- fields for CCA1; the signs are opposite between the two nificant positive correlation over the tropical Pacific and fields, suggesting a simple thermodynamic link. Warmer two regions of significant negative correlation over the air temperatures in winter will slow ice growth, result- North Pacific and the tropical Atlantic. The centers of ing in a thinner ice cover. In spring, less energy will be action are shifted compared to the fall and winter PNA required to transition to open water. CCA2 is similar— patterns. To test the relationship, the z500 canonical cor- correlations are opposite between the two fields, sug- relation time series is correlated with the fall PNA index. gesting a thermodynamic link. The canonical correlation The correlation between the two time series was not sig- time series (Fig. 7c) exhibits strong interannual variability nificant at 95%. The z500 predictor pattern has six regions whereas the time series for CCA1 is much smoother, of significant correlation; to test if there is any relation- suggesting that a decadal or multidecadal component to ship to large-scale climate, the canonical correlation time the variability may be present. Significance in both SAT series is correlated with fall indices of the NAO, the east

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FIG. 6. CCA mode 1 winter SAT predictor experiment: (a) SAT FIG. 7. As in Fig. 6 but for CCA mode 2. The canonical correlation canonical correlation map, (b) July ice concentration canonical r 5 0.44. correlation map, and (c) SAT (green) and July ice concentration (gray) canonical correlation time series; the canonical correlation r 5 0.60. Shaded regions depict areas of significant correlations at TNH has a strong center of action in the Hudson Bay the 95% level. region. The relative dominance of these four teleconnections changes year to year, which may explain why Atlantic pattern (EA), the east Atlantic/North Pacific there is a weak relationship to all four patterns and not pattern (EP/NP), the west Pacific pattern (WP), the east a strong relationship to one. The lack of a significant Atlantic/west Russia pattern (EA/WR), the Scandina- correlation with the PNA or NAO suggests that only in vian pattern (SCA), and the tropical/Northern Hemi- certain cases—specifically, coincident positive NAO and sphere pattern (TNH). Monthly time series for these strong El Ninõ (enhanced PNA) events as identified in teleconnection patterns are available from the National Wang et al. (1994b) and Mysak et al. (1996)—is there Oceanic and Atmospheric Administration Climate Pre- a link between the phase and strength of these two tele- diction Center (CPC) at their Web site (available at http:// connections and sea ice variability. www.cpc.noaa.gov/data/teledoc/telecontents.shtml). The The strongest correlations in the predictor pattern are patterns are calculated using rotated principle component over Hudson Bay, and it is concluded from correlation analysis (RPCA); therefore, the times series associated analysis that the relationship to large-scale teleconnection with the patterns in any given month are independent of patterns is mixed. Because there was no predictive skill in each other. Significant correlations were found with the forecasts made from winter z500 and because persistence WP (r 520.45), the EP/NP (r 5 0.36), the EA/WR (r 5 in the atmosphere is low, it is assumed that the relation- 0.58), and the TNH (r 5 0.43). Of the four modes, only the ship between height anomalies and sea ice is coincident in

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FIG. 9. Mean OND averaged 500-mb geopotential height ﬁeld (m) for 1970–2004.

canonical correlation time series, 1982, is characterized by high heights over Hudson Bay and less (more) ice concentration in eastern (northwestern) Hudson Bay. Anomalously high heights over Hudson Bay will reduce the gradient of the ridge and weaken the northwesterly winds. The result is more ice in northwestern Hudson Bay because the shore leads will not be maintained by the winds and less ice in eastern Hudson Bay because of reduced advection of cold air.

3) FALL NORTH ATLANTIC SST EXPERIMENTS In the fall North Atlantic SST experiment PC truncation is at two modes: CCA1 represents 31% of the original

FIG. 8. CCA mode 1 fall z500 predictor experiment: (a) z500 ca- variance in the sea ice data and CCA2 represents 22%. nonical correlation map, (b) July ice concentration canonical cor- The discussion focuses on CCA1, which is responsible for relation map, and (c) z500 (green) and July ice concentration (gray) the most predictive skill. canonical correlation time series; the canonical correlation r 5 The leading CCA mode is shown in Fig. 10. The ca- 0.76. Shaded regions depict areas of significant correlations at the 95% level. nonical correlation pattern in SST is characterized by a strong center south of Greenland over the subpolar gyre and a weaker center of opposite sign along the path of the fall and that the fall-to-summer memory is in the ice. In Gulf Stream. This pattern strongly resembles the first EOF general, positive height anomalies are associated with a of monthly North Atlantic sea surface height (SSH) warmer atmospheric column. The opposite sign in corre- (Ha¨kkinen and Rhines 2004) that is used as an index to lation over Hudson Bay between the predictor and pre- represent the strength of the subpolar gyre (Ha¨kkinen dictand could be a thermodynamic response of the ice to a and Rhines 2004; Ha¨tun et al. 2005). The EOF analysis warmer or colder atmosphere. However, the greater pre- in Ha¨kkinen and Rhines is repeated using combined dictive skill of z over SAT in fall and the dipole in the 500 TOPEX/Poseidon and Jason-1 data. The first EOF (not predictand correlation pattern between northwestern shown) is similar to Ha¨kkinen and Rhines over the period Hudson Bay and eastern Hudson Bay (Fig. 8) both sug- in common, 1993–2004, and the correlation coefficient gest a dynamic component to the forcing. A dominant between PC1 and CCA1 SST is 0.621 (more information feature in fall Northern Hemisphere 500-mb geopotential heights (Fig. 9) is a ridge west of Hudson Bay. This ridge is the cause of the climatologically dominant northwesterly 1 No significant correlation was found between CCA1 and the an- winds over Hudson Bay. The most extreme year in both nual or seasonal index of the Atlantic tripole (e.g., Deser et al. 1997).

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FIG. 11. Correlation between seasonal surface air temperature and the CCA mode 1 predictor time series.

FIG. 10. As in Fig. 8 but for the SST-NA predictor experiment; the series is correlated with fall, winter, and spring SAT, z500, canonical correlation r 5 0.79. 850-mb geopotential height (z850), and SLP. A summary of the results is shown in Figs. 11 and 12. Moderate cor- available online at www.cdc.noaa.gov/Correlation/atltri. relations (0.3 , r , 0.5) with SAT over Hudson Bay and data). This suggests that positive (negative) SST anoma- to the northwest of the bay (Fig. 11) in fall and winter lies south of Greenland in CCA1 may be related to a suggest a potential thermodynamic forcing that could be weakening (strengthening) of the subpolar gyre. The sea enhanced by advection due to the dominant northwest- ice pattern is dominated by a dipole between northwesterly winds. No signiﬁcant correlations were found with ern Hudson Bay/Hudson Strait and eastern Hudson Bay. SLP in any season, and the only signiﬁcant correlations

Is there a physical link that might explain these patterns with z500 and z850 were in winter. The apparent atmo- of covariability? The potential of a coincident atmospheric spheric response in winter is worth exploring further since forcing, direct ocean forcing, or teleconnection through the pattern in z500 (Fig. 12), season, and lead time are all the atmosphere is addressed. Because of the low skill in consistent with a series of empirical (e.g., Wen et al. 2005) the November anomaly persistence, it is suspected that the and modeling (e.g., Kushnir et al. 2002) studies that sug- contribution of a coincident atmospheric or oceanic forc- gest an early winter NAO-like atmospheric response to a ing to the overall skill is small. This is supported by the late summer horseshoelike pattern of SST anomalies in lower skill of fall z500 and SAT predictor models (Table 2). the North Atlantic. The question addressed here is how The potential for a delayed ocean forcing in winter and this winter atmospheric response could impact ice con- spring is difficult to explore owing to the lack of obser- centration in Hudson Bay. In Fig. 12 where the contoured vations of ocean temperature below the ice, but its in- mean winter pattern in z850 is superimposed on the cor- fluence is also suspected to be small. relation map, a region of significant correlations north- To explore the potential of a teleconnection through west of Hudson Bay sits directly underneath a ridge. A the atmosphere, the predictor canonical correlation time positive (negative) anomaly in the ridge height would

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FIG. 12. Correlation between CCA1 SST and (a) winter 500-mb geopotential height and (b) winter 850-mb geopotential height.

strengthen (weaken) the predominant northerly flow c. Source of predictability: Multidecadal variability over Hudson Bay. This is supported by composites of meridional surface wind anomalies during winter In light of a potential physical mechanism explaining (Fig. 13) for extreme negative and positive years in the the skill of the fall North Atlantic SST model, CCA is predictor time series. The composites clearly show rerun without removing the long-term trend to explore a anomalous southerly and northerly flows. In the con- potential decadal or multidecadal link to the North At- text of the main winter and spring processes in Hudson lantic SST. Principal component truncation and the num- Bay, enhanced (weakened) northerlies would keep ice ber of PC and CCA modes retained in the final model to the north thin by maintaining the flaw lead and the were the same as for the detrended experiment. The increased advection of cold air would thicken the fast global cross-validated correlation is similar to the ice in eastern Hudson Bay. In spring thinner ice to the detrended experiment (r 5 0.263), and the first two CCA north (thicker ice to the southeast) would promote early modes explain 39% and 21%, respectively, of the original (later) clearing (Fig. 10). variance. The first canonical correlation pattern in sea ice

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FIG. 14. CCA mode 1 fall SST-NA predictor experiment without detrending prior to CCA: (a) SST-NA canonical correlation map, (b) July ice concentration canonical correlation map, and (c) SST- NA (green) and July ice concentration (gray) canonical correlation FIG. 13. Composites of surface meridional wind anomalies for time series; the canonical correlation r 5 0.85. Shaded regions the five most positive CCA1 SST years (1975, 1976, 1978, 1981, depict areas of significant correlations at the 95% level. 2004) and the four most negative CCA1 SST years (1984, 1990, 1991, 1996). series using cutoff lengths ranging between 15 and 25 yr. A Huber’s weight parameter of two and prewhitening are (Fig. 14) is very similar to the detrended experiment selected (Rodionov 2006). A significant shift in 1995 is (Fig. 10). The pattern in SST (Fig. 14) is all one sign but detected in the SST canonical correlation time series strongest south of Greenland and in the midlatitudes, and the AMO. Depending on the cutoff length, signifi- similar to the detrended experiment (Fig. 10). The SST cant shifts in either 1993 or 1997 are detected for July ice canonical correlation time series (Fig. 14) is dominated concentration. by a ‘‘jump’’ in the mid-1990s, the timing of which co- incides with a change in phase of the Atlantic multi- 5. Discussion and conclusions decadal oscillation (AMO) (Kerr 2000) from cold to warm (e.g., Enfield et al. 2001). The AMO time series is The origins and levels of seasonal forecast skill for plotted with the July averaged ice concentration and July averaged ice concentration in Hudson Bay were SST canonical correlation time series (Fig. 15). The determined using canonical correlation analysis at lead main feature in all three time series is a jump in the mid- times of 3, 6, and 9 months. Seasonal forecasts made at 1990s. The Rodionov regime shift detector (Rodionov a 6-month lead time had the highest skill, and there was 2004), which requires no a priori assumptions about the little to no skill in 9-month, persistence, and climatology timing of a shift in a time series, is run on all three time forecasts. At a 3-month lead time, only the skill of SAT

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FIG. 15. Annual index of the unsmoothed AMO (data obtained from online at www.cdc.noaa. gov/Timeseries/AMO) plotted with the standardized time series of July ice coverage in Hudson Bay and the standardized CCA1 predictor time series from the raw data experiment. Negative values in all three time series are plotted without color to highlight the common shift in the mid-1990s. forecasts improved; the skill of all other predictors drop- thermodynamic processes in preconditioning the state of ped considerably. The best model has three predictors— the sea ice before breakup. fall surface air temperature over Hudson Bay, fall North Predictive skill could potentially improve with the ad- Atlantic sea surface temperatures, and fall Northern dition of new predictors. An estimate of the ice thickness Hemisphere 500-mb geopotential height—and explains would be the ultimate predictor. In addition to snow depth 53% of the interannual variability in July ice concentra- on the sea ice, the ocean heat flux, and river runoff, other tion. The model has significant tercile forecast skill cov- variables highlighted in modeling studies (e.g., Saucier ering 61% of the Hudson Bay region, and the tercile skill and Dionne 1998), such as fall mixed layer depth and at a given location ranges from 40% to 80%. spring cloud cover, may also influence the severity of the CCA diagnostics were used to investigate the sources of spring ice season. Unfortunately, these are all difficult predictive skill. The single predictor that yields the great- parameters to measure and monitor, even with remote est skill is fall North Atlantic SST. A new teleconnection sensing techniques, and reliable datasets are not yet pathway is identified linking variability in the fall subpolar available for CCA model development. The lead time of North Atlantic gyre and Atlantic multidecadal oscillation sea ice forecasts could potentially be extended by using reflected in sea surface temperature anomalies to fall and output from regional or climate models. This technique is winter atmospheric thermodynamic and dynamic forcing called perfect prognostic and is also commonly used in of sea ice that manifests as sea ice concentration anomalies weather forecasting. For example, model forecasts of fall in July. Specifically, fall SST anomalies are shown to pre- North Atlantic SST could increase the lead time of July ice cede a deepening or weakening of the winter upper-air concentration forecasts beyond six months. ridge to the northwest of Hudson Bay; this has an effect on An interesting implication of the link identified in this the strength of the northwesterly winds, which are known study between multidecadal variability in ice coverage to influence the ice thickness distribution (e.g., Markham in Hudson Bay and the Atlantic multidecadal oscillation 1986; Mysak et al. 1996). Similarly, the physical mecha- is that, if the AMO returns to a cool phase as predicted nism leading to predictive skill from fall z500 is a deepening in a recent modeling study (Keenlyside et al. 2008), there of the winter trough over Hudson Bay, which again could be some recovery in early summer ice concentra- enhances the northwesterly winds that keep ice thin along tion in Hudson Bay. Further exploration of the tele- the northern coast of Hudson Bay and Hudson Strait and connection pathway identified in this study, particularly advects cold air over the rest of the bay, promoting ice in the context of hypothesized large-scale ice–ocean– growth. Predictive skill from fall and winter SAT is likely atmosphere feedbacks, is an avenue for future research. due to a coincident thermodynamic forcing of sea ice: for the fall z500 and SST predictors, the forced sea ice thick- Acknowledgments. The authors are especially grateful ness anomalies in fall and winter are suspected to be to Simon Mason for providing the source code for the carried over to July in the memory of the ice. In general, climate prediction tool developed at the International the higher skill of North Atlantic SST and z500 predictors Research Institute for Climate and Society. We would compared to SAT suggests that fall and winter sea ice also thank John Walsh, Sheldon Drobot, Trudy Wohlleben, dynamic processes may be more important than sea ice and four anonymous reviewers for their very constructive

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