identify anomalous wintertime temperatures in the U.S.

Transcription

1 1 1 2 The pattern of sea level pressure to effectively identify anomalous wintertime temperatures in the U.S. 3 4 Huikyo Lee 1, Wenxuan Zhong 2, Seth Olsen 3, Daeok Youn 4 and Donald J. Wuebbles Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 2 Department of Statistics, University of Illinois, Champaign, IL 3 Department of Atmospheric Sciences, University of Illinois, Urbana, IL 4 Department of Earth Science Education, Chungbuk National University, Cheongju, South Korea October 16, Corresponding author:

2 Abstract We found key spatial patterns of pressure, wind and sea surface temperature patterns explaining variation of the January temperatures averaged over the contiguous United States (U.S.) during the last 34 years ( ). In this study, we examine the use of linear discriminant analysis (LDA) as a tool to compensate for weaknesses in principal component analysis (PCA) and composite analysis. PCA has been widely used to find the dominant spatial patterns or modes explaning climate variablity and the relationship of the patterns to particular weather events. However, sometimes the relationship is weak because PCA aims at the best description of a single climate variable not taking into account other climate anomalies. Overall, the projection of sea level pressure (SLP) anomalies on the LDA eigenvector based on the grouped U.S. wintertime temperatures explained the cold and warm extremes including the warm winter in more effectively than the PCA derived eigenvector using the same SLP data (aka Arctic Oscillation). LDA analysis clearly suggests that the warmer sea surface temperature and higher sea level pressure over the North Pacific and Atlantic occur with the warmer temperature in the U.S. With the increased sea level pressure over the ocean, high pressure system over the land weakens and warm advection enhances near the surface

3 Introduction The United States (U.S.) experienced its fourth warmest winter on record in ( The relationships between global-scale climate variability and winter temperatures in the U.S. are getting a great deal of attention in the mass media as well as the scientific community. One aspect of this is determining the link between the Arctic Oscillation (AO) and winter weather in the U.S. For example, Griffiths and Bradley [2007] found that the AO index is related to nighttime temperatures and daytime humidity in the Northeast U.S. For the Southeast U.S., Lim and Schubert [2011] found that the positive AO phase can cause more 56 frequent warm winter temperatures. AO is defined as the 1 st eigenvector from the Principal Component Analysis (PCA) of the sea level pressure (SLP) poleward of 20 N [Thompson and Wallace, 1998]. The studies mentioned above commonly investigated the link between a leading mode of PCA with anomalous temperature or precipitation events in the wintertime U.S. Because key meteorological variables representing weather events and climate have spatially correlated patterns, PCA has been widely used to study climate variability. Although a leading mode of PCA is useful to explain variability of a single climate variable, sometimes there is no statistically significant relationship between a temporally varying principal component (PC) and other variables of our interest, such as extreme weather events in the U.S. In this case, the composite analysis, which categorizes the entire data based on values of PC and compared averages of the two subgroups, has been popularly applied and the difference between two groups has been

4 interpreted as impacts of the PCA mode. However, it is always questionable that the difference between two extreme cases, for example, temperature differences between high positive AO and low negative AO phases, can really represent the impact of AO on temperatures as only small subgroup of data is used to calculate the temperature difference pattern through composite analysis. The composite difference is also highly dependent on the definition of extreme phases used for grouping data. The linear discriminant analysis (LDA) is one of the most popular algorithms to reduce dimensions [Wilks, 1995] and an alternative statistical tool for the combination of PCA and composite analysis. This is because LDA extracts a spatial pattern of a single variable as PCA does, but the spatial pattern is optimized to explain the difference of other variables of our interest. LDA has not been as frequently used to investigate climate variability as PCA. Schneider and Held [2001] and Swanson et al. [2009] applied LDA to separate natural variability and anthropogenic forcing in the time series of surface temperature. Recently, Tung and Camp [2008] classified the greater than 40 years of temperature data into two groups according to solar activity, and analyzed the spatial pattern of temperature fields that effectively discriminate difference between the low and high solar activity groups. The purpose of this study is to investigate unusually cold and warm winter temperatures averaged over the US by applying LDA to sea level pressure anomalies. This study demonstrates that LDA provides a useful and insightful time series to scrutinize climate variability Data and methodology

5 The monthly averaged surface temperature and sea level pressure (SLP) anomalies for LDA are from the National Centers for Environmental Prediction and National Center for Atmospheric Research/National Center for Atmospheric Research (NCEP/NCAR) reanalysis [Kalnay et al., 1996]. The anomaly of SLP from its climatological mean value over the last 34 years between 1979 and 2012 well follows the normal distribution with zero mean and standard deviation of about 4 mb. The confidence levels for the normality are higher than 95% according to Shapiro-Francia test and Pearson chi-square test. As a representative month with the coldest temperature of a year, only January data were used. While the eigenvectors from PCA best explain variance of data, LDA eigenvectors maximize the difference between the predefined classes of targeted response variable [Wilks, 1995]. More detailed description about LDA can be found in Schneider and Held [2001] or Camp and Tung [2007]. In this study, a response variable is temperature and a predictor variable is SLP. Similar to PCA, LDA extracts eigenvectors that are linear combinations of SLP anomalies, X = [ ur x1, uur x2,..., uur x n ], in n grid points. Therefore, the vectors from LDA are linear classifiers that separate X into predefined temperature groups. However, the vectors from LDA are not orthogonal to each other as those in PCA. So our analysis focused on the LDA eigenvector ( ur β ) with the largest ratio of variance between groups to variance within groups. Geopotential height, zonal and meridional winds from NCEP/NCAR reanalysis and National Oceanic and Atmospheric Administration s reconstructed sea surface temperatures were used to obtain the spatial patterns of each field related to the LDA eigenvector. 114

6 Results Figure 1 (a) shows a histogram for 34 years of January surface temperatures averaged over the contiguous U.S. The contiguous U.S. average is taken as the area mean within the longitude range of W and latitude range of N. The overall mean and standard deviation of 34 temperatures are K and 1.67 K respectively. Based on the mean and standard deviation of its distribution and spatial pattern of temperature anomaly, the January mean temperatures were classified into four groups. These are a group of extremely cold winter (blue: 1979, 1982 and 1985), another group of extremely warm winter (red: 1990, 2006 and 2012), while the others belong to the moderately cold (green: 13 Januaries) and moderately warm (orange: 15 Januaries) groups. The temperature difference from the mean temperature is greater than one standard deviation in extreme cold and warm Januaries. Figure 1 (b) and (c) display that nationwide cooling or warming characterizes spatial patterns of temperature anomalies for the two extreme groups. The fourth coldest January in 1994 was classified as slightly cold January because its cold temperature anomalies are shown only in the eastern half of the contiguous U.S. whereas warm anomalies are dominant in the western half. ur Figure 2 (a) shows how well the projection of SLP anomalies ( βx ) on the 1st LDA eigenvector (LDA1 hereafter) explains the changing January temperatures. The corresponding ratio of the between group variance to the within group variance is There are distinctive differences in the projected values between moderate (green and orange) and anomalous (blue and red) winters. Large positive and negative values of LDA1 are related to extreme warm and cold anomalies respectively. Although it is

7 possible for results from LDA1 to depend on the data grouping, it turned out that LDA1 is useful to explain even continuous variations of the temperature, not just for discriminating the four groups. The almost linear relationship between LDA1 and the average temperature in Figure 2 (a) indicates that LDA1 from SLP anomalies is a simple but good predictor to explain even the continuous variation of winter temperatures in the contiguous U.S. In contrast, Figure 2 (b) shows that the AO index defined as normalized projection of SLP anomaly on the 1st eigenvector of PCA is not an as good predictor as LDA1. The four temperature groups do not show noticeable differences in terms of their AO indices. In Figure 2 (c), normalized LDA1 and AO index are compared with normalized time series of the mean U.S. temperatures with corresponding linear correlation coefficient (r 2 ) and its 95 % confidence interval. LDA1 explains 80% of temporal variation of the averaged U.S. temperatures while AO index does not have statistically significant correlation with the temperature. Thus the composite analysis comparing the difference between two extreme AO phases can mislead the impacts of AO on the temperature anomalies in the U.S. regardless of statistical significance of the difference between two composite groups. Although using PCA to analyze SLP highlights the meaningful oscillation pattern near the North Pole, the meaningful SLP anomalies related to the U.S. winter temperature found from LDA1 is different from AO. To find the relationship between LDA1 and ten PCs from PCA, we tested a multiple linear regression model as below. LDA1(t) = b 0 +b 1 *AO+b 2 *PC2+.+b 10 *PC10

8 All of the time series are normalized so that values of linear coefficients can represent the relative contribution of each PC to build LDA1. The ten PCs can explain 89% variation of LDA1 (r 2 =0.89) and only b 1 =4.84, b 2 =6.18 and b 5 =6.19 are statistically significant at 99% confidence level. Therefore, LDA1 is close to a linear combination of AO, PC2 and PC5 and this explains why AO index should not be solely used to explain the wintertime temperature variation in the contiguous U.S. We examined the spatial patterns of key atmospheric variables related to LDA1. Figure 3 (a) shows the anomaly patterns of sea surface temperature (SST, shaded) and SLP (contoured) that are regressed by LDA1. Considering that monthly averaged anomalies are regressed, Figure 3 (a) can be interpreted as stationary perturbations of SST and SLP related to interannual variation of the average surface temperature in the U.S. The dotted black contours contain statistically significant SST patterns at 90% confidence level. The pattern is featured by strong cooling of SST near Alaska, that seems to be associated with a northerly from the Arctic. Warm SST anomalies occur in west Atlantic including Gulf of Mexico and between the two cooling anomalies in the Pacific. These warm SST anomalies over the both oceanic sides of the contiguous U.S are related to the increased SLP. This positive correlation of SST and SLP anomalies is also shown in the regressions with the Pacific Decadal Oscillation [Zhang et al., 1997] and North Pacific Gyre Oscillation (NPGO) [Lorenzo et al., 2010]. Especially the warm anomaly in Figure 3 (a) which spans in a northeast-southwest direction in the Pacific is similar to the SST regression in Figure 3 (b) using NPGO index in January for the same 34 years of period between 1979 and 2012 (from However,

9 despite the similar SST pattern in the North Pacific, there is no overall agreement between LDA1 and NPGO with any statistical significance. In Figure 4 (a)-(c), geopotential height (GPH) and wind fields on 1000, 850 and 700 hpa isobaric surfaces are regressed using LDA1. Above 700 hpa, the regressed structure is almost equivalent barotropic. Below 700 hpa, the negative GPH anomaly over the land is shown between the two positive anomalies over ocean. The center of negative anomaly moves westward with height. In winter, development of high pressure system near the surface causes a cold outbreak in the U.S. [e.g., see Chapter 14 in Rauber et al., 2008]. Therefore, positive phases of LDA1 are connected to weakening of the cold outbreak. Figure 4 (d) shows the difference of regressed wind directions between 1000 and 850 hpa. Wind veering with height and accompanying warm advection is dominant over the U.S. when LDA1 values are positive. (I think this paragraph could be used to emphasize that the pattern from LDA1 show a characteristic of a physical mode Conclusion Compared to the PCA based AO, LDA finds spatial patterns of SLP to better match the temporal variation of winter temperatures in the U.S. including the warmer than average winter in By projecting SLP anomalies on the first LDA mode, 80% of the mean temperature variation is explained. The relationship between AO and the averaged U.S. temperature is not statistically significant so results from composite analysis do not represent impacts of AO on warm and cold extreme winters in the U.S. Our simple application of LDA to monthly averaged reanalysis data also shows the underlying physics linked to the January temperatures in the U.S. The warm anomalies in terms of

10 average January temperature are related to warmer sea surface temperature and higher pressure over the Pacific and Atlantic. The regressed wind anomalies clearly visualize the temperature advection related to the first LDA mode. Considering the performance of LDA in grouping the historical temperatures, the SLP pattern from LDA has great potential to make a seasonal prediction of wintertime weather extremes in the U.S. and to evaluate models currently used to make seasonal prediction. However, because LDA finds only linear discriminant functions, any nonlinear relationship between SLP anomalies at different grid points are missing in LDA eigenvectors. Also regressed fields using LDA eigenvectors are anomaly patterns whose signals become stronger with winter temperature extremes in the U.S. These patterns should not be interpreted as cause and effect relationships without further demonstration with models References Alexander, L. V., P. Uotila, and N. Nicholls (2009), Influence of sea surface temperature variability on global temperature and precipitation extremes, J Geophys Res-Atmos, 114, D18116, doi: /2009jd Camp, C. D., and K. K. Tung (2007), Stratospheric polar warming by ENSO in winter: A statistical study, Geophys Res Lett, 34, L04809, doi: /2006gl Di Lorenzo, E., K. M. Cobb, J. C. Furtado, N. Schneider, B. T. Anderson, A. Bracco, M. A. Alexander, and D. J. Vimont (2010), Central Pacific El Nino and decadal climate change in the North Pacific Ocean, Nat Geosci, 3(11), , doi /Ngeo984.

11 Griffiths, M. L., and R. S. Bradley (2007), Variations of twentieth-century temperature and precipitation extreme indicators in the northeast United States, Journal of Climate, 20(21), , doi: /2007JCLI Hart, R. E. (2011), An inverse relationship between aggregate northern hemisphere tropical cyclone activity and subsequent winter climate, Geophys Res Lett, 38, L01705, doi: /2010gl Higgins, R. W., A. Leetmaa, and V. E. Kousky (2002), Relationships between climate variability and winter temperature extremes in the United States, Journal of Climate, 15(13), Kalnay, E., et al. (1996), The NCEP/NCAR 40-year reanalysis project, B Am Meteorol Soc, 77(3), Lim, Y. K., and S. D. Schubert (2011), The impact of ENSO and the Arctic Oscillation on winter temperature extremes in the southeast United States, Geophys Res Lett, 38, L15706, doi: /2011gl Rauber, R. M., J. E. Walsh, D. J. Charlevoix (2008), Severe and hazardous weather : an introduction to high impact meteorology, 3rd ed., 574 pp., Kendall/Hunt Pub. Co., Dubuque, Iowa. Schneider, T., and I. M. Held (2001), Discriminants of twentieth-century changes in earth surface temperatures, Journal of Climate, 14(3), Swanson, K. L., G. Sugihara, and A. A. Tsonis (2009), Long-term natural variability and 20th century climate change, P Natl Acad Sci USA, 106(38),

12 Thompson, D. W. J., and J. M. Wallace (1998), The Arctic Oscillation signature in the wintertime geopotential height and temperature fields, Geophys Res Lett, 25(9), Tung, K. K., and C. D. Camp (2008), Solar cycle warming at the Earth's surface in NCEP and ERA-40 data: A linear discriminant analysis, J Geophys Res-Atmos, 113, D05114, doi: /2007jd Wilks, D. S. (1995), Statistical methods in the atmospheric sciences : an introduction, Academic Press, San Diego, Calif. ; London. Zhang, Y., J. M. Wallace, and D. S. Battisti (1997), ENSO-like interdecadal variability: , Journal of Climate, 10(5), Figure captions Figure 1. (a) Histogram of the January mean surface temperature averaged over the contiguous U.S. (from between 120W 75 W in longitude and N in latitude). The surface temperature data is from NCEP/NCAR reanalysis between 1979 and The temperature were divided into four groups, extreme cold (blue), moderately cold (green), moderately normal (orange) and extremely warm (red) groups. The dotted lines show ±1 standard deviation (±1.67 K) range from the overall average (271.8K). Figure 2. Scatter plots of (a) the SLP projected on the first eigenvector from LDA and (b) the SLP projected on the 1st eigenvector from PCA

13 (Arctic Oscillation) with the mean U.S. temperatures in January. The eigenvectors from LDA and PCA are normalized. The blue, green, orange and red colors represent the group information in Figure 1 (a). (c) The normalized time series of the projected SLP on the first eigenvector from LDA (LDA1, solid blue), AO index (solid red) and the mean U.S. temperatures in January (dotted black). The linear correlation coefficient 278 r 2 between the temperature time series and LDA1 or AO is given. The values in the parenthesis are 95% confidence interval of r 2. Figure 3. Anomaly structures of sea surface temperature regressed using (a) LDA1 and (b) the North Pacific Gyre Oscillation index. Inside the dotted black contours in (a), the regressed sea surface temperature is statistically significant at 90% confidence level. Solid orange contours and blue dotted contours are the regressed sea level pressure using LDA1 representing positive and negative anomalies respectively. Figure 4. Geopotential height (shaded) and wind (arrow) fields regressed upon LDA1 at (a) 1000 hpa, (b) 850 hpa and (c) 700 hpa isobaric surfaces. (d) shows the angle difference in degrees between the regressed wind directions plotted in (a) and (b). 290