Influences of different definitions of the winter NAO index on NAO action centers and its relationship with SST

JING Yujie, LI Yngchun, XU Yongfu nd FAN Gungzhou

aSchool of Atmospheric Sciences, Chengdu University of Information Technology, Chengdu, China; bState Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China;cLaboratory for Regional Oceanography and Numerical Modeling, Qingdao National Laboratory for Marine Science and Technology,Qingdao, China; dDepartment of Atmospheric Chemistry and Environmental Sciences, College of Earth Science, University of Chinese Academy of Sciences, Beijing, China

ABSTRACT Winter North Atlantic Oscillation (NAO) indexes from observations based on various winter durations are compared. Results show that there are significant differences in the interannual and decadal variations of these NAO indexes. For the same data source, a different definition of winter duration can lead to different signs of NAO index in some years, which mainly appear to be in the period of decadal phase transition. The different winter durations induce different cycles of the observation-based NAO. The longer the winter duration, the stronger the decadal variation.The NAO defined by different winter durations also can generate different descriptions of the NAO action centers,including the position and movement.The longer the winter duration,the more southerly action centers appear to be. The movement of the action centers affects not only site-based NAO indexes but also those defined by other methods, such as empirical orthogonal function(EOF)analysis.The length of time used in EOF analysis has a great influence on the spatial pattern of the NAO mode, which results in a considerable difference between the corresponding NAO indexes. Regardless of which NAO index is used, the NAO-related SST anomalies show the same tripole pattern. The longer the winter duration, the more significant the relationship between the NAO and SST affected by the timescale of sea-air interaction.

KEYWORDS NAO index; winter duration;period; action centers; sea surface temperature

1. Introduction

There is a strong inverse relationship between the monthly mean sea level pressure (SLP) of Iceland and the Azores, defined by Walker (1923) as the North Atlantic Oscillation (NAO). Hurrell (1995) found that the NAO is a meridional ‘seesaw' or dipole pattern of atmosphere pressure, with significant remote correlation characteristics. NAO index is an important tool for studying climate change in the Northern Hemisphere(Tsanis and Tapoglou 2018; Wang et al. 2017; Gong et al. 2014; Wanner et al. 2001). Changes in the NAO lead to several changes in the physical fields of the ocean (e.g. Robertson, Mechoso, and Kim 2000; Paeth,Latif,and Hense 2003).For example,the changes of the NAO can significantly affect the sea surface temperature (SST) variability in the North Atlantic region (Chen,Wu, and Chen 2015), and the North Atlantic SST is further associated with the Eurasian surface air temperature and atmospheric circulation anomaly pattern(Chen and Wu 2017; Chen et al. 2018).

Currently, there are many NAO index definitions.Since the NAO is most prominent during winter, the NAO index is usually defined by the pressure value in this season. The winter NAO index was first defined based on the difference in surface pressure between observational stations(Rogers 1984;Jones,Osborn,and Briffa 2003). Unfortunately, some studies have shown that there is a shift in the action centers of the NAO(Jung et al. 2003; Moore, Renfrew, and Pickart 2013),and this shift is related to the phase of the NAO(Cassou et al. 2004) and the season (Portis et al. 2001). As a result, deviations in NAO index based on site-based observations can arise because of the fixed positions of observational stations.

In addition to the site-based definition method,quantification of the NAO can also be achieved by empirical orthogonal function(EOF)analysis of SLP,which can generate the spatial modes of the NAO (Hurrell and Deser 2009).Gong and Wang(2000)further proposed a method of defining the NAO using regional average results,which are used to make a different regional division of the high and low pressure in winter and summer.In addition to the different index definition methods,different winter durations are often chosen for the calculation of winter NAO index, including December-January-February (DJF)(Weisse, Von Storch, and Feser 2010), December-January-February-March(DJFM)(Lehmann,Getzlaff,and Harla? 2011), November-December-January-February-March (NDJFM) (Lozano et al. 2004), and October-November-December-January-February-March (ONDJFM)(Jia,Derome,and Lin 2007).

Since the method used to define NAO index differs,the description of several associated phenomena will also vary. For instance, the sensitivity of the climatic impacts of the NAO to the definition of the NAO has been studied.Jia, Derome, and Lin (2007) compared three patternbased NAO indexes in winter calculated by EOF and rotated EOF analysis of mean monthly SLP and of 500-hPa geopotential height poleward in the winter duration of ONDJFM, and found that results were very similar.Pokorná and Huth(2015)compared seven different NAO indexes,and found that the correlation between the station-based NAO index and the NAO index described by principal component analysis was low in summer.Meanwhile, it was found that the correlations between different NAO indexes and surface temperature/precipitation in Europe were different. Thus, their study implies that analysis of the relationship of climate events with the NAO should not rely only on a single NAO index.

Besides the different performances of NAO indexes defined by different methods and from different reanalysis datasets,it is unclear whether the differences between the winter durations used to define winter NAO index can lead to differences in the conclusions of research objectives,and whether the differences between the different reanalysis data affect the accuracy of the analysis results.In the above context,here,we compare and analyze the different features of the winter NAO obtained by different definitions,including different winter durations,different data sources, and different processing methods.In addition, the influences of the different NAO indexes on the North Atlantic SST are explored.

2. Data and methods

2.1. Data

Four definitions of the NAO are used in this work:(1)a sitebased NAO index from the Climate Analysis Section of the National Center for Atmospheric Research (NCAR; www.climatedataguide.ucar.edu/climate-data/hurrell-northatlantic-oscillation-nao-index-station-based), called NAONCAR-obs; (2) an NAO index produced by NOAA(National Oceanic and Atmospheric Administration),based on rotated principal component analysis of monthly mean standardized 500-mb height anomalies from NCEPNCAR reanalysis data, called NAONOAA-obs(www.cpc.ncep.noaa.gov/products/precip/CWlink/pna/nao.shtml); (3) an NAO index based on the method of Gong and Wang(2000), called NAOGong-obs; and (4) an NAO index defined as the leading EOF mode of SLP over the North Atlantic(30-80°N,100°W-40°E),called NAOPC1-obs.NAONCAR-obsand NAONOAA-obsare monthly data, and their time ranges are 1865-2017 and 1950-2017, respectively. NAOGong-obsand NAOPC1-obsare calculated based on observed SLP from the 10-member ensemble of coupled climate reanalyses of the twentieth century (CERA-20C) of the European Centre for Medium-Range Weather Forecasts (http://apps.ecmwf.int/datasets/data/cera20c/levtype= sfc/type = an/), and their time range is 1901-2010.The dataset of observed SLP from the NCEP-NCAR reanalysis dataset(https://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.pressure.html)is used to calculate the NAO index, and its time range is 1948-2018.

2.2. Methods

The index proposed by Gong and Wang (2000) is expressed as

where P* represents the normalized SLP. A three-point(10°W, 0°E, and 10°E for the high-pressure area and 10°W, 20°W, and 30°W for the low-pressure area) spatial arithmetic average of P* differences between the highand low-pressure area is used.

For EOF analysis, we use simultaneous regression analysis and equation (24) of North et al. (1982) to evaluate the eigenvalue separation. The error range of eigenvalue iswhere λ is eigenvalue, and N is the number of time steps. When adjacent eigenvalue λj+1satisfies λj+1-λj≥δλj, the spatial mode is in significant level.

Several different winter durations are used to define the winter NAO index, such as January (J), DJF, and DJFM. For the NAO index of DJF and DJFM, the January in the given year is used as the reference to obtain the winter NAO index. For example, the NAO index for DJF of 1980 is obtained based on data in December of 1979 and January and February of 1980.

For NAONCAR-obs, NAOGong, and NAOPC1-obs, when calculating the seasonal average NAO index(DJF and DJFM),the winter season average of SLP is firstly calculated,and then the NAO index is obtained; whereas, for NAONOAA-obs, because NOAA does not provide seasonal average NAO index (DJF and DJFM) directly, the winter NAO index is obtained by averaging the monthly NAO index in the given winter duration in this study, which inevitably causes some deviation.

3. Results and discussion

3.1. Differences in basic state

3.1.1. Temporal series

Three different NAO indexes, obtained from CERA-20C,NOAA, and NCAR, are shown in Figure 1(a), which are named NAOGong-obs, NAONOAA-obs, and NAONCAR-obs,respectively. To investigate the differences arising from these different NAO indexes,the time span is chosen to be the same, from 1950 to 2010. Variations of the NAO indexes obtained from these three observed datasets in terms of different methods of calculating the NAO index are generally consistent.The NAO indexes are dominated by negative values before 1973,but positive values from 1980 to 2010. The correlation coefficients between NAONOAA-obsand NAONCAR-obscan exceed 0.9 regardless of the winter duration. Similarly, the correlation coefficients between NAOGong-obsand NAONOAA-obsor NAONCAR-obsare greater than 0.84 and 0.88, respectively.All correlations are significant at the 0.01 level.In addition,the correlation coefficient between NAOGong-obsand NAONCAR-obsincreases with the increase in winter duration. When the winter duration is DJFM, the correlation coefficient can be as high as 0.97.The correlation results of these three sets of NAO indexes calculated by the different methods based on different reanalysis datasets demonstrate that they are comparable with each other.

The main difference between NAOGong-obs,NAONOAA-obs,and NAONCAR-obsis that the NAO signs are not the same in some specific years. For example, during 1950-55, when the winter duration is J,the NAO indexes in NAOGong-obsare all negative,but all positive in NAONOAA-obs.This difference may be caused by the different calculation methods or the different reanalysis datasets. In order to compare the difference in the NAO indexes caused by different datasets,two different reanalysis datasets (NCEP-NCAR and CERA-20C)and the Gong method are used to calculate the NAO index. Results are shown in Figure 1(a). The correlation coefficient of these two sets of NAO indexes based on different reanalysis datasets is 0.98, which is statistically significant at the 0.01 level,regardless of winter duration.No different signs for these two NAO indexes are found.Therefore, the difference in the NAO signs between NAOGong-obsand NAONOAA-obs, as mentioned above, can be attributed to the difference in the calculation methods.For the same data source, when the winter duration is different, there is also a case where the NAO phase is inconsistent. For NAONCAR-obsin around 1980, when the winter duration becomes longer, the weak NAO negative phase becomes a positive phase. This situation also appears in other time periods, as well as the other two NAO indexes.

From the results of the decadal variation obtained after calculating the 15-yr running average of the NAO index (Figure 1(b)), it can be seen that the positive and negative phases of three sets of the NAO indexes from different data sources coincide roughly. As shown in Figure 1(b), the periods of 1950-55 and around 1980 are the periods of phase transition, and these periods are also the time when the different signs of NAO indexes defined with different winter durations occur(Figure 1(a)). When the winter duration is different, the variations of NAONCAR-obsare quite different, especially among 1861-1900, 1930-35, and 1995-2010, and the variations of NAOGong-obsare also quite different during the last two periods.

3.1.2. Temporal period

Analysis of the power spectrum of the NAO indexes shows that most of the indexes can reveal a significant period from 2.3 to 2.7 years characterized by an interannual signal,except for the DJFM NAONOAA-obs(Table 1, Figure S1).Moreover,when the winter duration is longer,the significant period is longer. When the winter duration is DJF or DJFM, both NAONCAR-obsand NAOGong-obsshow a significant period of 8.3 years, while NAONCAR-obseven has a significant period of 25 years or more,characterized by a decadal signal.The significant periods of NAONOAA-obsare shorter, because of the short time span of the data(1971-2017). It can be confirmed by NAOGong-obsand NAONCAR-obsthat if the time span of 1971-2017 in both NAOGong-obsand NAONCAR-obsis used to analyze their power spectra,some significant long periods also become nonsignificant.

3.2. Representation of the shift of winter action centers

NAONOAA-obs, NAOGong-obs, and NAONCAR-obscan only reflect the variation of characteristics of the NAO index over time, but cannot reflect either the spatial mode of the NAO or the shift of the NAO centers of action. Therefore, we analyze the SLP of CERA-20C in the different NAO phases.

Figure 1.(a)Four observation-based NAO indexes(two NAO indexes calculated by the Gong method and based on NCAR reanalysis data and CERA-20C reanalysis data, respectively (rows 1 and 2), NAONOAA-obs (row 3), and NAONCAR-obs (row 4)), and (b) the 15-yr running averages of three observation-based NAO indexes(NAONOAA-obs(left),NAONCAR-obs(middle),and NAOGong-obs(right),based on CERA-20C reanalysis data),for the three winter durations of J(green),DJF(red),and DJFM(black).All data in(a)are from 1950 to 2010, and the time spans for NAONOAA-obs, NAONCAR-obs, and NAOGong-obs in (b) are 1950-2017, 1865-2017, and 1902-2010,respectively.

Table 1. The specific periods of observation-based NAO indexes calculated by the power spectrum. The time spans for NAOGong-obs, NAONOAA-obs, and NAONCAR-obs are 1901-2010, 1950-2017 and 1865-2017,respectively.

According to the NAO index results after calculating the 15-yr running average (Figure 1(b)), we define 1950-1972 as the negative phase period of the NAO and 1973-2010 as the positive phase period.The defined negative phase period is consistent with that of Cassou et al. (2004), in which the NAO negative phase period is from the 1950s to 1960s. Johnston et al. (2012) defined the NAO positive phase period as the years 1973-2006,which is included in our defined positive phase period.The EOF analysis of SLP from CERA-20C (NAOPC1-obs) is performed in different phase periods. The NAO spatial pattern for the first EOF of the SLP from CERA-20C is shown in Figure 2. The movement of action centers of the NAO can be clearly seen during the different NAO phases, regardless of the winter duration.The high- and low-pressure action centers are at about 30°W in the negative NAO phase and move to other positions in the positive NAO phase. This is consistent with the cluster analysis results reported by Cassou et al.(2004), who argued that compared with the negative phase of the NAO, the range of action centers was expanded to Europe in the positive phase of the NAO. When the time span includes the two phases, the NAO centers of action are also different. In particular, when the winter duration is defined as DJFM, the low-pressure action center is even split into two parts.

A significant correlation(coefficients greater than 0.74)between NAOPC1-obsand other NAO indexes is obtained in the negative phase of the NAO(Table 2).When the time span covers the positive phase, the correlation coeffi-cients decrease with increasing degrees of freedom. In particular, when the winter time duration is DJFM, the correlation coefficients are even smaller than those with the time range taking the whole period(1950-2010)and larger degrees of freedom. In addition, the correlation coefficients between NAOPC1-obsand other NAO indexes are much smaller than those between NAOGong-obs,NAONOAA-obsand NAONCAR-obs. The weak correlation between NAOPC1-obsand other NAO indexes over long periods was also found by Pokorná and Huth(2015).

The comparison of NAOPC1-obsand NAOGong-obsbased on the same reanalysis dataset (CERA-20C) shows that during the negative decadal phase(1950-72)the obvious difference between these two indexes mainly occurs during the first five years, and during the positive decadal phase these two indexes are different from each other after 1995, which decreases the correlation between NAOPC1-obsand NAOGong-obs(Figure 3).It should be noted that the PC1 gained with the SLP during the positive decadal phase(Figure 3(d2,d3))is also very different from that gained during the whole period(Figure 3(f2,f3))after 1995.Considering the difference in the EOF1 between the positive period and the whole period, it indicates that the definition of the action center position is important to the NAO index. Unfortunately, it seems counterintuitive that the correlation between NAOPC1-obsand NAOGong-obsin the positive NAO period is weak,because the centers of positive and negative SLP anomalies during the positive NAO period (1973-2010) seem closer to the grid points used in Equation(1)compared to those during the nega-tive NAO period(Figure 2),which should suggest that the variability of SLP at these grid points should contribute more to‘NAO'in the positive NAO period.It is speculated that the signal extracted by the PC1 after 1995 in the EOF analysis for the positive period is weak and probably not the NAO signal.

Table 2.Correlation coefficients between NAOPC1-obs and other three observation-based NAO indexes in both the negative and positive phase periods, and the full period. The negative and positive phase periods are 1950-72 and 1973-2010, and the full period is 1950-2010. When the winter duration is defined as J, the spatial mode of the NAO is nonsignificant, so the correlation coefficient of NAOPC1-obs is not analyzed.

Figure 2. The NAO modes of observation-based SLP with three winter durations (J, DJF, and DJFM) in the negative phase period(J-N, DJF-N, and DJFM-N), the positive phase period (J-P, DJF-P, and DJFM-P) and the full period (J-A, DJF-A, and DJFM-A). The negative phase period is 1950-72. The positive phase period is 1973-2010. The full period is 1950-2010.

Figure 3.Two observation-based NAO indexes((a,c,e)NAOGong-obs and(b,d,f)NAOPC1-obs)with three winter durations(J(1),DJF(2), and DJFM (3)) in the negative phase period (negative_Gong and negative_PC1), the positive phase period (positive_Gong and positive_PC1) and the full period (all_Gong and all_PC1). The negative phase period is 1950-1972. The positive phase period is 1973-2010.The full period is 1950-2010.When the winter duration is defined as J,the spatial mode of the NAO is nonsignificant in the full period, so the value of NAOPC1-obs is not analyzed in the full period.

From the spatial modes of two specific positive and negative phase of the NAO, it can be seen that the action centers also vary with latitude in the different phases. In order to more intuitively demonstrate this change, the time-varying positions of high- and lowpressure centers are illustrated in Figure 4, which were selected by finding the largest negative correlation of SLP at different latitudes of 20° to 80°N (Wang et al.2017).As shown in Figure 4,when the winter durations are different, the latitude of the NAO centers of action also has a certain difference: the longer the winter duration, the more southerly action centers appear to be. When the winter durations are DJF and DJFM, the north-south movement of the high- and low-pressure action centers is generally closer to each other, but the difference is still obvious during 1970-2000.This means that the movement of action centers of the NAO,which is related to the phase transformation of the NAO, is described differently because of the different winter durations of the NAO index. Therefore, the movements of the action centers of the NAO and the differences between the NAO indexes with different winter durations bring about a limitation to NAONCAR-obs,calculated by fixed sites,which is one of the two important defects of this kind of NAO index mentioned by the website that publishes the Hurrell NAO index (https://climateda taguide.ucar.edu/climate-data/hurrell-north-atlantic-oscillation-nao-index-station-based).In fact,in addition to the site-based NAONCAR-obs, other methods have a similar limitation, such as the EOF analysis method mentioned above, and the Gong method considering the zonal movement of action centers, as shown in Figure 4. For these methods, the north-south movement of the action centers is also not negligible.In spite of this, NAONCAR-obsalso has the advantage of a long length of time and long periodic signals(Table 1,Figure S1), which can be used to analyze interdecadal or even multidecadal climate variation. The advantage of NAOGong-obsis the use of the zonal average, which overcomes the zonal movement of the action centers of the NAO to a certain degree.

Figure 4.Variations of the latitudinal positions of the high-and low-pressure centers and the NAO indexes with time for the three winter durations (J, DJF, and DJFM). The gray and black lines represent the changes of the high and low latitudes. The blue and red lines denote the changes of high and low latitudes after applying a 15-yr running average. The pink line indicates the interannual change of NAOGong-obs, and the yellow line represents the change of NAOGong-obs after applying a15-yr running average.

As shown in Figure 4,during the period of a significant decadal NAO positive phase (e.g. 1980-2005), and the period of the decadal phase transition of the NAO (e.g.around 1920 and 1973-80),the latitudes of action centers(both high- and low-pressure) reveal significant cyclical changes, and are inconsistent with the fluctuation of the NAO index;whereas,in decadal NAO negative phases,the fluctuation of both the NAOGong-obsindex and the positions of action centers is coincident.This difference between the fluctuation of the NAO index and the fluctuation of the positions of action centers is probably a reason for weak signals extracted by the EOF method after 1995,which may induce the poor correlation between NAOGong-obsand NAOPC1-obsin the decadal NAO positive phase, because the temporal sequence of principal components is closely related to the spatial mode.

3.3. Relationship between the NAO and SST

Figure 5 shows the regression coefficients (RCs) of the North Atlantic SST anomalies against the NAO indexes.Regardless of which NAO index is used, the NAOrelated SST anomalies show a significant tripole pattern(negative and positive RCs along the meridional direction), which is consistent with Chen, Wu, and Chen(2015). The relationships between different NAO indexes and SST are different in the values of the RCs and the range of significant RCs in the midlatitude region. Compared with the three sets of the NAO indexes calculated by the different methods, the RCs of the SST against NAOGong-obsare smaller in the North Atlantic, and the significant positive RCs in the midlatitudes are only concentrated in a small western sea area.Compared with the J NAO indexes, the negative RCs of the DJF and DJFM NAO indexes in the tropics and high latitudes are larger, and the area of significant positive RCs in the midlatitudes expands eastward. The larger RCs of the SST and NAO indexes (DJF and DJFM)demonstrate that the NAO indexes defined with winter durations of three months or more have more significant influences on SST than those defined with winter durations of one month.

4. Conclusion

The differences between winter NAO indexes defined by different winter durations were studied. Three observation-based NAO indexes, including NAOGong-obs,NAONOAA-obsand NAONCAR-obs,with different winter durations, have been mutually confirmed to be reliable. The main difference between the NAO indexes defined by different data sources,or defined by the same data source with different winter durations,is that the sign of the NAO indexes is inconsistent in some years,which are the periods of decadal phase transition of the NAO indexes.After comparing the NAO indexes calculated by the same method but based on different datasets, the difference in NAO signs between NAOGong-obsand NAONOAA-obscan be attributed to the difference in the calculation methods.Different winter durations also have a certain impact on the description of the decadal signal of the NAO indexes.Only when the winter duration is DJF or DJFM is the decadal signal significant. On the decadal scale, the three NAO indexes of NCAR (NAONCAR-obs) are quite different, especially among 1861-1900, 1930-35, and 1995-2010. A possible reason is that the positions of NAO action centers defined by different winter durations are different: the longer the winter duration, the more southerly action centers appear to be. The north-south movements of the NAO action centers and the differences between these indexes with different winter durations should greatly influence not only the results based on the station data like NAONCAR-obsbut also the results based on EOF analysis and the Gong method, such as NAOPC1-obsand NAOGong-obs.

Figure 5. Distribution of regression coefficients (RCs) of the winter SST anomalies against the (a-c) NAONOAA-obs, (d-f)NAONCAR-obs and(g-i)NAOGong-obs,with three winter durations of(a,d,g)J,(b,e,h)DJF,and(c,f,i)DJFM.shaded areas indicate that RCs are statistically significant at the 0.05 level,based on the student's t-test.The time span for the data ranges from 1950 to 2010.

Furthermore, the NAO action centers move with time,and the NAO indexes defined by different winter durations have different descriptions of the movement of action centers. The movement of the action centers has an impact on the results of the EOF analysis.For the observations, when the time span is different, the signs of NAO indexes indicated by the PC1s during some special periods,like 1995-2010,will be different.As a result,the time span used in the analysis is critical.Therefore,besides the NAO indexes based on site data,a poor correlation between the NAO index based on the EOF method and other methods is induced by the movement of the NAO action centers.

The relationship between SST anomalies and various NAO indexes defined by different data sources shows the same tripole pattern,although the influences of the different NAO indexes on the SST are reflected in the magnitude of the RCs and the range of significant RCs in the midlatitudes. Under the influence of the timescale of ocean-atmosphere interaction, the NAO indexes defined with winter durations of three months or more have more significant influences on SST than those defined with a winter duration of one month.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was supported jointly by the National Key Research and Development Program of China [grant number 2016YFB0200800] and the National Natural Science Foundation of China [grant number 41530426].