Minding Our Methods: How Choice of Time Series, Reference Dates

May 30, 2012 - His research has been funded by the NSF, NEH, Department of Energy, U.S. government agencies, university grants, and European and Asian...
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Minding Our Methods: How Choice of Time Series, Reference Dates, and Statistical Approach Can Influence the Representation of Temperature Change Kalb Stevenson,†,§ Lilian Alessa,†,§ Mark Altaweel,‡,§ Andrew D. Kliskey,*,†,§ and Kacy E. Krieger†,§ †

Resilience and Adaptive Management Group, University of Alaska Anchorage, 3101 Science Circle Drive, Anchorage, Alaska 99508, United States ‡ University College London, 31-34 Gordon Square, London WC1H 0PY

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REGIONAL GEOGRAPHY, SEASONALITY, AND CLIMATE VARIABILITY Alaska is the largest state in the U.S., covering an expanse of over 1.7 million square kilometers. It possesses vastly different biomes, ecoregions, and vegetation features, including temperate rainforests on the Southeast panhandle, taiga and alpine forests in Southcentral and Interior regions, and tundra wetland and upland areas throughout western Alaska and across the Arctic coastal plain. Alaska is surrounded by three large bodies of water (Pacific Ocean, Bering Sea, Arctic Ocean) and possesses numerous expansive mountain ranges, including the tallest peak in North America. Its various microclimates are based on a range of factors, including proximities to coastlines, freshwater bodies, and mountain ranges. Alaska contains more than three million lakes and over three thousand rivers.9 Due to the high latitude, Alaska and its geographic neighbors, Siberia and Northwest Canada, possess winter and summer daylength and temperature extremes. Winters are generally characterized as long and severely cold, while summers are fairly mild. Seasonality is an important factor to note in any discussion on the effects of climate change in Arctic and Subarctic regions. There are strong implications for potentially abrupt shifts in seasonality on subsistence resources and activities, the biological processes of high latitude flora and fauna, and the existing infrastructure of Northern communities that has been designed with historic patterns of seasonality in mind. Cultures focused on subsistence have developed under these conditions, and subsistence resources are often coupled to freeze−thaw events and related seasonal processes (e.g., migration and spawning of anadromous fishes). A major question that many Northern indigenous communities have is whether future trends and patterns of seasonality will shift. A longer or shorter winter, a wetter or drier summer, or the presence of more or less sea ice will affect hunting and fishing success, strategies for the acquisition of food, and other resources and personal safety. For instance, the Bering Sea communities of Nikolskoye and Tymlat in the Russian Far East and the villages of Elim and White Mountain (Figure 1) on Alaska’s Seward Peninsula are strongly seasonally influenced, each having vastly different summer and winter climates and whose residents strongly depend on subsistence resources to survive. For these and other rural communities, it is important to understand temperature trends and shifts so as to better grasp their role in affecting or interacting with seasonal transitions.

Warming trends reported for parts of Alaska in recent history have resulted in changes in permafrost regimes that have been linked to the degradation of some freshwater resources and community infrastructure.1,2 In addition, several communities in Alaska have been affected by changes in climate, including retreating sea-ice (e.g., Gambell and Savoonga), increased fall storm events (e.g., Nome, Shishmaref, and Kivalina), and resulting coastal erosion (e.g., Shishmaref and Kivalina).3 Temperature trend estimations are likely to play a greater role in future climate reports and policy decision-making in Alaska, but building accurate estimations is no easy task since Alaska’s climate is governed by a complex set of drivers acting at various scales in time and space. While change is ultimately of greatest interest to climatologists, agencies, media outlets, policy makers, and the general public, there are different ways to assess change, including the study of temperature trends. Furthermore, media reports or summaries are often based on the latest perceived or reported trends (e.g., “Is it warming?”, “Is it cooling?”), and these outlets are often the major information source for the general public and policy makers on the issue of climate. It is important that agencies, scientists, and media outlets (television, radio, online, and print media) are cautious of the potential to introduce erroneous information and bias into reports on climate due to a lack of consideration of appropriate statistical methods or approaches. Several sources cite criticisms or provide discussion on issues relevant to this topic.4−8 © 2012 American Chemical Society

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Figure 1. Village of White Mountain in summer. Located on the southern part of Alaska’s Seward Peninsula, on the coast of the Bering Sea. Photo courtesy of A. Kliskey.

but may overlook long-term climatic patterns. Conversely, long time series show trends over a greater duration of time but may overgeneralize patterns or obscure important events. An appropriate selection of time series for the analysis and discussion of climate is necessary for a correct understanding of actual trends, cycles, and patterns. It is important to consider both the start and end dates of a time series, as this will consequently determine the length of the period analyzed. Physical scientists have been dealing with issues surrounding time series for some time. For example, Marvin (1923) explored very different trends in precipitation over long time series that resulted from choosing variable reference dates.28 Generally, time scales that are too short do not provide a broad enough scope for detection of influences or trends. Previous work focusing on signal-to-noise ratios (S/N) has shown that trends of greater than 17 years are required for identifying some specific influences on tropospheric temperature.29 Additionally, trends in global mean temperature have been assessed at 25, 50, 100, and 150 years to determine rates of change at different time scales.22 Logically, longer time periods help to improve the identification of anomalies, natural cycles, and actual trends or changes. To demonstrate the effect of different time series on climate change analysis, we show the change in mean annual temperature throughout Alaska for three different spans: 1949−2009, 1949− 1976, and 1977−2009 (Figure 2a) These three time spans show the effect of the 1976 PDO on Alaska’s climate.30 To map the effect, we used existing temperature data sets from the Alaska Climate Research Center31 and NASA Goddard Institute for Space Studies for the 19 first-order National Weather Service stations in Alaska, three stations from the Yukon Territory, Canada, and three stations from the Russian Far East. Temperature change at each of the 25 sites is the result of a simple linear regression through each time span. The change was then interpolated using a tensioned spline, a spatial analysis tool that is a generalization of a cubic spline and has a tension factor that approaches a linear interpolation for large values, between each data point − this does not account for elevation, vegetation, or urbanization within the extent of the analysis. This spatial analysis helps to clarify the complex climate data making it easily discernible and generalizes the trend across a region where data sets are spatially

The effects of multiple pressure systems, such as the Siberian High, the Arctic High, or the Aleutian Low Pressure Systems affect local climates.10−14 Additionally, the Circumpolar Vortex, a persistent, large-scale cyclonic circulation in the middle and upper troposphere, is centered over the Polar region of the Northern Hemisphere, where it surrounds the Polar Highs and exists as part of the Polar Front. Furthermore, oscillating sea surface temperatures, climatic cycles or climatic events can influence temperatures in Alaska or other parts of the Pacific, as has been documented with the 20−30-year Pacific Decadal Oscillation (PDO) cycle, the 5-year El Niño-Southern Oscillation (ENSO) cycle, and the 1−2-year El Niño and La Niña events.15−21 In 1976, the PDO dramatically shifted from a cool phase to a warm phase, elevating temperatures of eastern pacific waters that subsequently resulted in increasing surface temperatures across Alaska (additional information on the PDO, including Pacific decadal variability, is available22). El Niño winters, in particular, tend to lead to warmer winters across most of the state.23,24 Ocean currents are also involved in regulating atmospheric temperature through the physical exchange of heat, water, and momentum.25,26 Long-term climatic data sets from dozens of weather stations in and around Alaska are available to the general public and are useful for studying short- and long-term trends in climate. Climatic cycles and patterns, as well as the interplay between them, can be identified and interpreted either graphically or through statistical analyses. However, several cautions must be taken in analyzing long-term climatic data in order to avoid misleading or erroneous conclusions. An examination of recent research from the Resilience and Adaptive Management (RAM) group at the University of Alaska Anchorage show the importance of referencing correct time scales and applying appropriate starting and ending reference dates and statistical approaches in the analysis and interpretation of climate data.27,2

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TIME SERIES Climate is incredibly complex, especially in a place as expansive and geographically diverse as Alaska. The use of different time series can have a strong impact on climate change reports, thereby influencing our understanding of the magnitude and duration of change. Short time series can isolate specific events, 7436

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Figure 2. (a) Interpolated surfaces showing the change in mean annual temperature across Alaska for three time series: 1949−2009, 1949−1976, and 1977−2009. Red colors represent a temperature increase, blue indicates a decrease, and beige indicates no change. Data are from temperature records for 25 weather stations across Alaska, Canada, and Russia, made available by the Alaska Research Center (ACRC, 2011) and the Goddard Institute for Space Studies. (b) Chart showing mean annual air temperature (fine black line) for Nome, Alaska. Linear trendlines show temperature trends from 1949−1976 and 1977−2009 (blue dashed), and 1949−2009 (red dashed), and loess regression line (bold black line) from 1949−2009. The figure illustrates the effect of the PDO in affecting trend patterns (see Hartman and Wendler,30). It also helps to demonstrate how cooling can occur over two time periods but warming is shown when time series are grouped together. The application of different reference start dates and statistical approaches to multidecade climate data can result in drastically different temperature trend estimations.

and temporally limited. In addition, the array of diverse bioclimatic zones across Alaska32 is reflected within the pattern. Temperature change patterns over the different time scales reveal some interesting aspects of climate change in Alaska. Figure 2a shows a general increase in temperatures from 1949 to 2009 throughout Alaska. However, when the time scale is divided into two time spans bridging the 1976 PDO shift, we

see that from 1949 to 1976 much of the state was cooling, while from 1977 to 2009 there were several areas that were cooling, and others that were stable or warming slightly. This analysis presents an interesting pattern. Several stations record cooling temperature trends from both 1949 to 1976 and 1977 to 2009. However, from 1949 to 2009 many of these locations show a warming trend. How can temperatures cool for both halves of a 7437

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STATISTICAL APPROACH The choice of statistical approach to analyze data sets and generate temperature trend estimations can also allow for biases in trend estimations and misleading information to be reported due to the window of values used in estimation and how these values are treated. Some methods, such as running means that are implemented for smoothing data, are referred to as “local statistics” and estimate average temperatures by sampling relatively few sequential observations. However, smoothed time series data are inherently subject to boundary conditions, which has prompted the development of methods for dealing with such constraints,33,34 although these methods have been deemed subjective and not necessarily accurate regarding temperature trends.35 An alternative to local statistics is the use of global statistics, which can be employed to utilize all values in a time series. For example, a linear-fit model based on least-squares regression has previously been employed to estimate temperature trends in Alaska,30,36 including in this paper to map the change across the state (Figure 2). Bone et al.27 have noted that while the method avoided the issue of selecting window size (i.e., the number of values used to estimate the mean) in their analyses, the use of a linear best-fit line minimized localized variation. Based upon complete temperature records for ten climate stations across Alaska, they analyzed temperature data sets with start dates ranging from 1958 to 1993, a single reference end date of 2003, and with five different statistical approaches for quantifying temperature trends: (1) a 5-year running average, (2) a 10-year running average, (3) a 5-year Hamming filter, (4) a 10-year Hamming filter, and (5) a linear best-fit model. Each of these five methods was an accepted method of estimating temperature change, and each was specifically chosen based on the need to compare local and global methods, to determine the influence of different window sizes for smoothing data sets, and to evaluate how filters impact smoothing procedures. The Hamming filter is described as

data set but warm along the whole? From 1976 to 1977 there was a large jump in the mean annual temperature as a result of a shift in the PDO. After a period of warm years, temperatures began to cool again (Figure 2b). In over 30 years since the shift in the PDO, the cooling has not reached temperatures as low as were experienced in the region before the 1976 to 1977 PDO shift. The effects of the PDO become apparent when observing temperature changes at varying time scales across a large region such as Alaska. These observations are important to consider in the context of climate change. Mean annual temperature is changing throughout Alaska. It has both increased and decreased over the past 60 years. However, the trend over the shorter scales is generally cooling, while the trend over the longer scale has generally been one of increasing temperature (Figure 2b). Large-scale climate shifts, such as the PDO, should be addressed when climate change is reported by media outlets or through agency or international reports; start and end dates should also be referenced when discussing temperature change trends. Time periods used for analyzing changes should account for these oscillations, with differences in scale acknowledged. In addition, climate reports should follow the World Meteorological Organization (WMO) guidelines to include the use of 30-year time periods ending in a year evenly divisible by 10 rather than arbitrary start and end dates. While we have not focused on this in our examples, it is important for climate reports coming from various countries and regions.

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REFERENCE DATES Climatic events or temperature anomalies can skew statistical means or cause a disproportionate influence when estimating trend lines. Hence, a poor choice of reference dates could introduce bias into temperature trend estimations. For example, observed temperature increases over a 50-year period in Alaska from 1951 to 2001 can be viewed as temperature declines when estimating trends within the period of 1951−1975 and within the period of 1977−2001 to account for the 1976 PDO event.30 The 1976 PDO event led to higher than average temperatures recorded at most weather stations starting in 1976 and continuing for a varying number of years after, depending on the station. Data from all climate stations in Alaska studied by Bone et al.27 demonstrated a trend of increasing temperature from data beginning in 1958, regardless of the method employed. They reported that temperature trend estimates were highly sensitive to reference start dates, varying by as much as 4 °C when using differing start dates with some statistical methods. This variation was highest when a given reference start date was defined by an extreme temperature. This was particularly evident in estimations for eight of the ten sites using the 5-year Hamming filter, a method for estimating global temperature trends that weights observations based on their location within a window. The Hamming filter is similar to a running mean where a set of observations is used to estimate average temperature at a specific date, but observations further from the estimated date have less influence. Bone et al.27 have reported that temperature trend estimates are highly dependent on the reference start date selected. The authors state that discrepancies in estimates for Alaska are expected over decades due to observed warming temperatures. However, these discrepancies should exhibit a pattern of gradually declining temperature change estimates. That is, temperature change estimates should be higher when using 1958 for a reference start date, then gradually decline until the reference start date of 1993, in their given example.

W (i) = 0.54 − 0.46cos(2πi(n − 1))

(1)

with n equaling window size (e.g., 10), while the running average, or mean (MA), is described as n

MA =

∑ j = 1 yi n

(2)

with n being the time window. Hamming filters are essentially low pass filters that estimate trends using a neighborhood function that weights observations based on locations within the window used. The running mean essentially allows a series of averages of subsets for the full data set. All weather stations, regardless of the method employed, demonstrated a trend of increasing temperatures between 1958 and 2003. However, of all the methods the linear best-fit was determined to typically estimate the greatest temperature change when employing relatively early reference start dates. When using local methods (i.e., methods which account for short spans such as 5-year running mean), the highest estimates of temperature change often occur when reference start dates just prior to the PDO shift have been selected27 ( see Figure 3). The linear best-fit method is often not as sensitive to cooler temperatures prior to the PDO because it takes all observations in the time series into account. The cool and warm temperatures occurring immediately before and after the PDO shift, respectively, lead to a moderate temperature change at most 7438

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Figure 3. Nome, Alaska temperature 1950−2010 and 10-year running mean compared to mean annual temperature from two different years.

long-term temperature trends. A cautious approach should be taken when comparing temperature trends from multiple studies that do not use identical methods or when considering the selection of reference start date from a year exhibiting a temperature extreme. Furthermore, different types of climatic patterns and anomalies are captured when using various local and global methods, suggesting that caution is needed when comparing estimates from these different classes of methods. The chosen method should be able to capture trends in a data set without being overly sensitive to variation. A subfield of robust statistics has been developed to handle this.37 The ability to adequately describe temperature change may, at some point, be compromised given the increase in temperature extremes in contemporary climate change.38 Therefore, an essential part of future estimations of multidecadal temperature trends in Alaska and elsewhere should be the implementation of a comprehensive and comparative analysis of time series and sensitivities to start dates and statistical methods. Applying multiple methods with different start and end dates, along with varying window size and filters used, should be considered and outputs tested using sensitivity analysis in order to determine how sensitive results are to extreme variations. Methods that overemphasize extreme variations are likely to be less useful to climate scientists and policy makers interested in long-term temperature trends. Furthermore, comparisons of studies carried out by different groups would be best served by using standardized time periods along WMO guidelines (see above). This is especially important when different methods are used to analyze data. There are a number of complex drivers underpinning arctic and subarctic climate, and therefore caution should be used against making large, broad-scale, or sweeping statements about climate and climate change. In the recent past, some regions of Alaska have been warming while others appear to have been cooling. However, the summarized or reported direction and degree of change depends heavily upon the choice of time scale, reference date, and statistical approach. For Alaska, greater variation in microclimates could lead to temperature trend estimates being more sensitive to reference start dates, and thus greater discrepancy between temperature changes reported by different statistical methods. This has implications for management practices that rely either on historical trend estimates or

sites when averaged. In a comparison of all methods, the linear best-fit has been reported as least correlated with the others,27 a result that was expected given the distinction between local versus global methods. In the study by Bone et al., the 5-year Hamming filter provided the least amount of smoothing of the four local methods because it diminished the influence of data points that are closer to the window boundary.27 It previously generated the greatest variation for all dates between 1958 and 1993 and generated the greatest amount of variation between consecutive dates. The trend estimation was, therefore, more susceptible to year-to-year variations in temperature, especially when temperature extremes were involved. The 5-year running mean also displayed notable variation among all estimations and between consecutive year estimations, but the lack of declining weights made it less significant than the Hamming filter. The 10-year running mean and 10-year Hamming filter produced a less variable set of estimates, which were presumably due to enhanced smoothing produced by the inclusion of additional values in calculating the means (Figure 3). Bone et al. also showed that the 10-year running mean, a local method, smoothed the data over the given period.27 The 10-year Hamming filter allowed variations in data to have a stronger effect on estimates, resulting in greater volatility (Figure 3). Using coefficients of correlation to compare methods demonstrated that the 10-year hamming filter was least different among methods. It maintained relatively constant standard deviation values, produced moderate estimates, and was able to capture some local variation in time series while not being overly sensitive toward year-to-year temperature differences.

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FUTURE RECOMMENDATIONS

Choice of time scale, reference dates, and statistical approach can severely impact the representation of climate change. In particular, special consideration must be given to major climatic events, such as the 1976 PDO shift, which has the potential to interact with nearby reference start dates and introduce erroneous information into reports. Having a time range that covered well before and after the 1976 PDO would help to minimize the effects of this event; a method that de-emphasized extremes, such as a running mean, could be used to estimate 7439

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on anticipated temperature trajectories. It also has strong implications for Northern cultures that either directly or indirectly depend on a certain level of predictability in seasons and seasonal events (e.g., freeze−thaw events, cold snaps, first snowfall, spring melt, density of the snowpack, storm frequency, sea ice availability or thickness, river ice thickness) for their acquisition of food and fuel, their socio-cultural identity, and their safety while traveling for subsistence purposes. If scientists are able to utilize the methods and approaches described above appropriately, there is likely to be better representation of changes in climate, shifts in seasonality, and any resulting influence on subsistence fish and game species or existing infrastructure. As policy makers contend with developing responses to climate change and its impacts in Alaska and beyond, it is imperative that the use and interpretation of scientific studies to support policy development minimizes any potential for bias by giving due consideration to the methods used to estimate temperature change.

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Management Group at the University of Alaska Anchorage. Kacy has a background in geomorphology. His previous work explored the distribution, change, and morphology of thermal erosion features and thermokarst in northern Alaska. He has a strong background in GIS, remote sensing, and LiDAR, and he currently studies human−landscape interactions.

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ACKNOWLEDGMENTS We are grateful to the National Science Foundation (EPSCoR grants EPS-0701898 and EPS-0919608; AON grant OPP0856305; and Arctic Social Science grant OPP-0755966) for funding this research. The views expressed here do not necessarily reflect those of the National Science Foundation. We thank Holly McQuinn for her design skills to improve the graphics, Drew Cason for his help in developing some of the figures, and Chris Bone for his earlier work in the RAM Group that contributed to this paper.

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AUTHOR INFORMATION

REFERENCES

(1) White, D.; Hinzman, L.; Alessa, L.; Cassano, J.; Chambers, M.; Falkner, K.; Francis, J.; et al. The arctic freshwater system: changes and impacts. J. Geophys. Res. 2007, 112, G04S54. (2) Alessa, L.; Altaweel, M.; Bone, C.; Kliskey, A.; Schnabel, W.; Stevenson, K Alaska’s freshwater resources: Issues affecting local and international interests. J. Am. Water Resour. Assoc. 2011, 47 (1), 143− 157. (3) Arctic Climate Impact Assessment (ACIA); Cambridge University Press: New York, 2005. (4) AIM (Accuracy in Media). “AIM Report: Science for sale: The global warming scam”. 26 August 2002. http://www.aim.org/aimreport/aim-report-science-for-sale-the-global-warming-scam/ (Accessed 18 May 2012). (5) Ward, B. “A media relations mistake and inaccurate reporting about climate change”. Grantham Research Institute on Climate Change and the Environment, 15 July 2011. http://www2.lse.ac.uk/ GranthamInstitute/Media/Commentary/2011/July/inaccuratereporting-climate-change.aspx (Accessed 18 May 2012). (6) Booker, C. “Global warming? A new ice age? The only certainty is that YOU’RE paying for the hysteria of our politicians”. The Daily Mail, 06 July 2011. http://www.dailymail.co.uk/debate/article2011667/Global-warming-new-ice-age-YOURE-paying-politicianshysteria.html# (Accessed 18 May 2012). (7) Bowling, S. A. Problems with the use of climatological data to detect climatic change at high latitudes. In Proceedings of the International Conference on the Role of the Polar Regions in Global Change, June 11−15, 1990, University of Alaska Fairbanks, Fairbanks, AK, pp 206−209. http://climate.gi.alaska.edu/bowling/AKchange. html (Accessed 18 May 2012). (8) Henson, B. Going to extremes. UCAR Quart. 2005. Winter 2004−2005. http://www.ucar.edu/communications/quarterly/ winter04/extremes.html (Accessed 18 May 2012). (9) Gates, N., Ed. The Alaska Almanac: Facts About Alaska, 30th Anniversary ed.; Alaska Northwest Books: Portland, OR, 2006. (10) Benson, C. S.; Bowling, S. A.; Weller, G. Urban climates in Alaska. Environment 1983, 15 (2), 23−26. (11) Martyn, D. Climates of the World: Developments in Atmospheric Science; Elsevier: Amsterdam, Netherlands, 1992. (12) Overland, J. E.; Adams, J. M; Bond, N. A. Decadal variation of the Aleutian Low and its relation to high-latitude circulation. J. Climatol. 1999, 12 (5), 1542−1548. (13) Stafford, J. M.; Wendler, G; Curtis, J. Temperature and precipitation of Alaska: 50 year trend analysis. Theor. Appl. Climatol. 2000, 67, 33−44. (14) Polyakov, I. V.; Bekryaev, R. V.; Alekseev, G. V.; Bhatt, U. S.; Colony, R. L.; Johnson, M. A.; Maskshtas, A. P.; Walsh, D Variability and trends of air temperature and pressure in the Maritime Arctic. J. Climatol. 2003, 16, 2067−2077.

Corresponding Author

*E-mail: [email protected]. Author Contributions §

Equal contributing authors

Notes

The authors declare no competing financial interest. Biography Kalb Stevenson is a postdoctoral scientist affiliated with the Department of Biological Sciences and Resilience and Adaptive Management Group at the University of Alaska Anchorage. His experience is rooted in the disciplines of ecology and environmental science at seasonal or thermal extremes. He has studied fish and wildlife ecology, animal physiological ecology, social ecological systems, and sustainable food systems in arctic, sub-arctic, and desert environments. He has spent the last decade studying and publishing in these disciplines. Lilian Alessa is a Professor of Biological Sciences at the University of Alaska Anchorage and coleader of the Resilience and Adaptive Management Group at UAA. She conducts extensive research on human adaptation to climate change that is funded by the National Science Foundation. Her ongoing projects include the Arctic Observing Network and Dynamics of Coupled Natural Human Systems. Her other areas of expertise lie in the conceptual development and application of complex systems thinking, social ecological complexity, and development of research strategies. Mark Altaweel is a Lecturer at University College London and a visiting scientist at the University of Chicago and Argonne National Laboratory. Dr. Altaweel is interested in researching past and modern social ecological systems as they pertain to water, agriculture, and transportation issues. He has published over 40 academic papers and one book. His research has been funded by the NSF, NEH, Department of Energy, U.S. government agencies, university grants, and European and Asian research funding bodies. Andrew Kliskey is a Professor of Biological Sciences and Environmental Studies at the University of Alaska Anchorage, where he co-leads the Resilience and Adaptive Management (RAM) Group. Originally from Aotearoa/New Zealand he trained as a land surveyor, resource planner, and earned a PhD degree in geography that integrated geographic information systems, behavioral geography, and resource management. He has spent the last eight years working with people in Inupiat communities in northwestern Alaska and Denai’na communities in southcentral Alaska examining community perception and response to environmental change. Kacy Krieger is a Geospatial Scientist with the Resilience and Adaptive 7440

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NOTE ADDED AFTER ASAP PUBLICATION The caption of Figure 2 was modified in the version of this paper published June 18, 2012. The correct version published June 28, 2012.

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