on multi-timescale variability of temperature in china in modulated

ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 27, NO. 5, 2010, 1169–1182

On Multi-Timescale Variability of Temperature in China

in Modulated Annual Cycle Reference Frame

QIAN Cheng∗1 (钱诚), Zhaohua WU2, FU Congbin1,3 (符淙斌), and ZHOU Tianjun4 (周天军)

1Key Laboratory of Regional Climate-Environment Research for Temperate East Asia,

Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029

2Department of Meteorology & Center for Ocean-Atmospheric Prediction Studies,

Florida State University, Tallahassee, Florida, USA

3Institute for Climate and Global Change Research, Nanjing University, Nanjing 210093

4State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics,

Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029

(Received 14 July 2009; revised 15 November 2009)

ABSTRACT

The traditional anomaly (TA) reference frame and its corresponding anomaly for a given data spanchanges with the extension of data length. In this study, the modulated annual cycle (MAC), instead ofthe widely used climatological mean annual cycle, is used as an alternative reference frame for computingclimate anomalies to study the multi-timescale variability of surface air temperature (SAT) in China basedon homogenized daily data from 1952 to 2004. The Ensemble Empirical Mode Decomposition (EEMD)method is used to separate daily SAT into a high frequency component, a MAC component, an interannualcomponent, and a decadal-to-trend component. The results show that the EEMD method can reflect his-torical events reasonably well, indicating its adaptive and temporally local characteristics. It is shown thatMAC is a temporally local reference frame and will not be altered over a particular time span by an exten-sion of data length, thereby making it easier for physical interpretation. In the MAC reference frame, thelow frequency component is found more suitable for studying the interannual to longer timescale variability(ILV) than a 13-month window running mean, which does not exclude the annual cycle. It is also betterthan other traditional versions (annual or summer or winter mean) of ILV, which contains a portion of theannual cycle. The analysis reveals that the variability of the annual cycle could be as large as the magnitudeof interannual variability. The possible physical causes of different timescale variability of SAT in China arefurther discussed.

Key words: modulated annual cycle, the Ensemble Empirical Mode Decomposition, climate anomaly, cli-mate normal, variability of surface air temperature in China

Citation: Qian, C., Z. Wu, C. B. Fu, and T. J. Zhou, 2010: On multi-timescale variability of temperature inChina in modulated annual cycle reference frame. Adv. Atmos. Sci., 27(5), 1169–1182, doi: 10.1007/s00376-009-9121-4.

1. Introduction

Most previous studies on climate variability startwith the traditional anomaly (TA), which is a depar-ture from a climate normal. The climate normal underconsideration is typically the traditional annual cycle

(TAC), often defined as the arithmetic mean of a cli-mate quantity over three consecutive decades (WorldMeteorological Organization, WMO, 1989). Such a30-yr climate normal is suggested to be updated byWMO every 10 years and the most recent span in usecovers the period 1971–2000. However, such a calcu-

∗Corresponding author: QIAN Cheng, [email protected]

© China National Committee for International Association of Meteorology and Atmospheric Sciences (IAMAS), Institute of AtmosphericPhysics (IAP) and Science Press and Springer-Verlag Berlin Heidelberg 2010

1170 VARIABILITY OF TEMPERATURE IN MAC REFERENCE FRAME VOL. 27

lation lacks physical uniqueness when the data lengthis extended, leading to many difficulties in interpret-ing and understanding climate variability physically,since many previous studies have found that the an-nual cycles of climate variables have changed signifi-cantly in the past decades. For example, Xue et al.(2003) studied the interdecadal changes of 30-yr seasurface temperature (SST) normals during 1871–2000and suggested updating the normal periodically sincethe standard deviation and persistence of the Nino-3 region (5◦S–5◦N, 90◦–150◦W) SST index changedsignificantly from one 30-yr base period to another.The variations of the 30-yr climate normal surface airtemperature (SAT) were also large, especially duringwinter and spring (Fig. 1). An earlier onset of springhas been reported at many worldwide locations (e.g.,Linderholm, 2006; Qian et al., 2009). Furthermore, itis projected that the climate normals by the end of thiscentury will be significantly different from the presentday (IPCC, 2007, Fig. 10.28). Since the 30-yr climatenormals change significantly both through history andas projected from one 30-yr base period to another, thefrequent changes of climate normals due to the exten-sion of data length have led to changes in the result-ing anomalies and the corresponding physical explana-tions for the same data spans (e.g., 1961–1970). Thisis physically unreasonable since the physical processesof the past cannot be changed by future evolution. Inaddition to the lacking of physical uniqueness that isimplied, the use of a 30-yr climate normal is also log-ically inconsistent, since TAC-based climate normalsare considered fixed year-by-year for a given 30-yr

Fig. 1. (a) Different climate normals for different 30-yrbase periods at Beijing station. (b) Differences between1961–1990 climate normal and that of 1951–1980 (blue)and between 1971–2000 climate normal and that of 1951–1980 (red). Units: ◦C.

base period but are then changed every 10 years bythe extension of new data.

In light of the difficulties listed above, efforts havebeen devoted to the development of an alternative cli-mate normal that is more physically and logically con-sistent. The most commonly used method is to cal-culate anomalies according to pre-1977 climatologicalannual cycle and post-1977 climatological annual cycle(e.g., Zhu and Yang, 2003, since it has been widely rec-ognized that the 20th century climate has experiencedan interdecadal scale change around 1977. This in-terdecadal scale climate change is also evident in EastAsia (Yu and Zhou, 2007; Zhou et al., 2009). However,the climate normal after 1977 is still changing due tothe addition of later data, and such a method alsocannot exclude the annual cycle very well. In recentyears, some studies (e.g., Pezzulli et al., 2005; Shen etal., 2005; Wu et al., 2008) have argued that the annualcycle can contain amplitude-frequency modulation dueto the nonlinearity of the climate system. Wu et al.(2008) further suggested that the annual cycle shouldbe defined temporally locally, and they proposed touse the amplitude-frequency modulated annual cycle(MAC), which allows the annual cycle to change fromyear to year in both frequency and amplitude. Theysuggest that this basis serve as an alternative climatenormal (reference frame) for climate anomalies, andthey also developed the Ensemble Empirical Mode De-composition (EEMD) method (Wu et al., 2008; Huangand Wu, 2008; Wu and Huang, 2009) to adaptively ex-tract the MAC from climate data.

Concerning variability of SAT and its potential in-fluential factors in China, it is often believed that TAhas excluded the annual cycle, and thus this methodis widely used for interannual to longer timescale vari-ability (ILV) studies. As stated earlier, this is problem-atic to some extent. Besides TA, there are two othercommonly used methods. One is the frequent use ofwinter or summer ILV, which mixes the annual cycleand ILV and has been argued to be problematic byWu et al. (2008). Since the variability of temperaturein China is influenced by different factors on differenttimescales (e.g., see Wang, 2001), it is necessary toseparately study the annual cycle component, the in-terannual variability, and decadal variability, as well astheir potential influencing factors. The other methodis that many studies simply regress the TA upon a cer-tain climate index (e.g., Arctic Oscillation, AO), and ithas been argued on this basis that the strong positivephase of AO during the last decades was one of themost important reasons for the recent winter warming(e.g., Gong and Wang, 2003; Ju et al., 2004; Wang etal., 2004) or the spring cooling over East Asia (Yu andZhou, 2004). Such a method can hardly exclude the

NO. 5 QIAN ET AL. 1171

influence of a global warming trend during the lastdecades, and thus the result may not be convincingenough. In addition, some climate indices, such asthe AO which is the first empirical orthogonal func-tion (EOF) of the sea level pressure (SLP) anomaly inthe North Atlantic region, are calculated based on TA,and thus are problematic themselves. One alternativeway to reduce the impact of the warming trend oninterannual variability is to separate the interannualvariability from the long-term trend.

Concerning the above difficulties of three com-monly used methods, in this study we take advantageof the newly refined MAC concept and the newly devel-oped nonlinear and non-stationary data analysis toolEEMD to investigate the spatial and temporal char-acteristics of different timescales of variability of tem-perature in China based on homogenized daily data.The daily SAT series is adaptively decomposed intoa high frequency component, a MAC component, aninterannual component, and a decadal-to-trend com-ponent using the EEMD method. We also examinetheir corresponding physical explanations separately.These lines of thinking and approach could potentiallyprovide some insights into atmospheric and climate re-search. As will be shown below, the MAC referenceframe for the past does not change following the ex-tension of data length, satisfying the physical require-ments of temporal locality.

The rest of the paper is organized as follows. In sec-tion 2, data and analysis methods is described. Twocomparisons, i.e., TAC with MAC, and also cases ofvarious traditional ILV with ILV defined with respectto a MAC reference frame are presented in section3.1 and 3.2. In section 3.3, variability of MAC, in-terannual, and decadal-to-trend components of SATin China are discussed separately. A summary anddiscussion is given in section 4.

2. Data and methods

The observed daily SAT data at meteorologicalstations throughout China are not spatially uniformlydistributed and also cover different temporal domains.In order to maximize the temporal coverage whilekeeping adequate spatial coverage, the homogenizeddaily historical SAT dataset (Li et al., 2009) providedby the China Meteorological Administration, from1 January 1952 to 31 December 2004 was used inthis study. The stations containing missing data formore than ten consecutive days were excluded. Forconvenience of the subsequent analysis, the data forFebruary 29th in leap years were excluded, leaving 365daily values for each year. The monthly SLP, zonalwind at 850 hPa (U850), geopotential height at 500

hPa (GHT500), and surface wind from NCEP/NCARreanalysis (Kalnay et al., 1996; Kistler et al., 2001)and monthly SST from NOAA during 1953–2003(http://www.cdc.noaa.gov/cdc/data.noaa.ersst.html)were also used.

To adaptively and temporally locally decomposedaily SAT at each station and obtain its MAC,we applied the recently developed tool for nonlin-ear and non-stationary time-series analysis, EEMD(Wu et al., 2008; Huang and Wu, 2008; Wu andHuang, 2009), which is the most recent improvementof the EMD method (Huang et al., 1998, 1999, 2003;Flandrin et al., 2004; Wu and Huang, 2004; Huangand Wu, 2008). The EMD/EEMD method has al-ready been demonstrated effective in many geophys-ical applications (e.g., Huang and Wu, 2008; Wuet al., 2008; Qian et al., 2009). The Matlab codefor EEMD and a simple tutorial can be found athttp://rcada.ncu.edu.tw/research1.htm. The steps todecompose daily SAT at each station and to extractMAC by the EEMD method are as follows:

(1) for the daily SAT series (e.g., Fig. 2a), a whitenoise series was added with an amplitude of 0.2 (atsome stations 0.3) times the standard deviation of theraw daily SAT series, providing a relatively uniformdistribution of high frequency extrema with which tofacilitate EMD to avoid the possible “mode mixing”problem (see Wu and Huang, 2009 for more details);

(2) decompose the data with added white noise intoIntrinsic Mode Functions (IMFs) using the EMD ap-proach (detailed procedure is in Huang and Wu, 2008);

(3) repeat steps 1 and 2 for 1000 times, but eachtime use different realizations of white noise series withthe same characteristics;

(4) obtain the (ensemble) means of the correspond-ing IMFs of the decompositions;

(5) combine the sixth (almost always from theannual cycle) and the seventh components (contain-ing some annual cycle signal as well as some longertimescale variations) obtained from step 4, and thendo one more single EMD decomposition; the resultingfirst IMF is the final MAC component (Fig. 2c); and

(6) combine the first through fifth components ob-tained from step 4 as the final high frequency compo-nent (Fig. 2b); combine the residual from step 5 andthe eighth through eleventh components from step 4 asthe final interannual component (Fig. 2d); and com-bine the last three components from step 4 as the finaldecadal-to-trend component (Fig. 2e).

The above decomposition and reconstruction pro-cess separates a raw daily SAT series from each sta-tion into four major timescale components, i.e., a highfrequency component, a MAC component, an inter-annual component, and a decadal-to-trend component


Fig. 2. (a) Daily SAT at Beijing station for 1953–2003 and its fourcomponents using EEMD method, i.e., (b) high frequency component;(c) MAC component; (d) interannual component; and (e) decadal-to-trend component. Units: ◦C.

(e.g., Fig. 2). In order to eliminate the minor influ-ence of data end effects, the first and last year of thedecomposed results were excluded, leaving only the re-maining period of 1953–2003 to be further analyzed.

Wavelet analysis was also used to analyze thetemperature series of Beijing after a 13-month run-ning mean. The wavelet program is taken fromhttp://paos.colorado.edu/research/wavelets. To ob-tain spatial and temporal structures, EOF analysiswas applied to the MAC components, interannualcomponents, and decadal-to-trend components, re-spectively, from the decompositions of the SAT se-ries at all selected stations. The monthly SLP, U850,GHT500, and SST during 1953–2003 were used to cal-culate correlation coefficients with the first two princi-pal components (PCs) resulting from the EOF analysisfor the interannual component. Based on the charac-teristics of the PCs, the composite analysis for monthlysurface wind was further carried out. The significanceof differences between the two composites was deter-mined by using a variant of the student-t test.

3. Results

3.1 Comparison between TAC and MAC

The mean of MACs of daily SAT at Beijing stationfor 1953–2003, which is a smooth curve, clearly fits theclimatological annual cycle (Fig. 3). The average ofthe difference between the mean of MACs and the cli-matological annual cycle is only −0.013◦C. This minordifference is mainly due to the high frequency fluctua-tions contained in the climatological annual cycle and

is negligible compared with the amplitude of the clima-tological annual cycle, which is 31.7◦C. The year-to-year MACs show that the variations of MACs are largeand can be significantly different from the climatologi-cal annual cycle (climatological mean of the whole dataspan). The difference of year-to-year MACs for anindividual day can reach as large as 2.5◦C, which isof the same magnitude as the interannual variability(Fig. 2d), indicating that the anomalies defined withrespect to different annual cycles could potentially leadto different physical understandings when they are an-alyzed.

Fig. 3. Comparison between climatological annual cycle(white line) and MACs (red line) of daily SAT at Beijingstation for 1953–2003. Black line indicates the mean ofMACs. Green lines indicate raw daily SAT in each year.Unit: ◦C.


Fig. 4. A piece of the MAC for daily SAT at Beijingstation. Blue line indicates the last four years for 1952–2004 while red line indicates the last eight years for dataextended to 2008. Unit: ◦C.

To illustrate that the anomalies defined with re-spect to MAC at any temporal location are not af-fected by the addition of later data in the temporaldomain, the MAC component of daily SAT at the Bei-jing station is displayed as an example (Fig. 4). In thisillustration, we first extracted the MAC component ofdaily SAT for 1952–2004, and then extracted it for thedata updated to 2008. Note that the MAC remainedalmost the same for 1952–2004 when later data wasadded. This result also shows that EEMD is a tempo-rally local analysis method. Indeed, EEMD is basedon the distribution of local extremes at any temporaldomain; once the data is given, its local extremes arefixed and will not be altered by the extension of datalength. Therefore, the EEMD components in the samedata span are fixed regardless of the addition of laterdata. It should be noted that the minor discrepancyin the year of 2004, which is the last year of the for-mer data, is due to a minor end effect of the EEMDmethod. Since the first and last year have been ex-cluded from analysis in this study, it is expected thatthe anomaly with respect to MAC as well as its cor-responding physical explanation for 1953–2003 shouldremain almost the same when future data is added.

3.2 Comparisons between different versionsof ILV

Several studies have shown that anomalies withrespect to MAC exclude more cleanly the variabilityat and near annual cycle frequencies (e.g., Wu et al.,2008; Zhao and Qian, 2010) than many other meth-ods. It is also suggested that the low frequency com-ponent with respect to MAC (the combination of in-terannual and decadal-to-trend components in Fig. 2)is more suitable to represent ILV than TA, which con-

tains both residual annual cycle and high frequencyinformation (e.g., Zhao and Qian, 2010).

However, one may argue that the data from amonthly series after a 13-month window runningmean should exclude the annual cycle and high fre-quency components, leaving only components whosetimescales are larger than one year, as is often be-lieved. It is also well known that the running meancan provide temporally local interannual and longertimescale anomalies, and this method appears mucheasier for ILV studies than obtaining the low frequencycomponent with respect to MAC. However, while thetemporal locality is true for the running mean, theexclusion of the annual cycle is not complete. Thisargument can be verified by applying a wavelet analy-sis to a time series after applying a 13-month runningmean (e.g., for the temperature at Beijing shown inFig. 5a). It is evident that the running mean basedanomaly still contains a significant amount of annualcycle signal (Figs. 5b and 5c), making the runningmean approach much less appealing for cleanly iso-lating the ILV. This result suggests that a 13-monthrunning mean can only dampen the amplitude of theannual cycle to some extent, but can not exclude it.

Another commonly used method to study ILV isto define interannual and longer timescale variabilitybased on the mean of a particular season. Here, weagain use the SAT data at Beijing station to exam-ine these traditional versions of ILV with the low fre-quency with respect to MAC (Fig. 6). It is shown thatthe traditional ILV represented by annual and summermean differs significantly (Fig. 6a). However, for thelow frequency component with respect to MAC, theannual mean and summer mean series are almost thesame (Fig. 6b). If the hidden variations of MAC (Fig.6d), i.e., annual mean of MAC and summer mean ofMAC, are subtracted from the traditional versions ofILV, respectively, their residuals are almost the same,and they are much the same as those with respect toMAC (Fig. 6d). This result further supports the find-ings in Wu et al. (2008) and suggests that the tra-ditional versions of ILV still contain a portion of theannual cycle, which is different from what has beenwidely perceived. The uniqueness of ILV with respectto MAC provides the necessary condition for pursuinga unique physical explanation.

3.3 Variability of SAT in China in MAC ref-erence frame

Since the MAC reference frame and the corre-sponding anomalies with respect to MAC remain thesame for a given data span as the data length is ex-tended, MAC is more suitable for physical interpreta-tion. So, in the following, we will study the temporal-


Fig. 5. Morlet wavelet analysis for a time series of monthly SAT during 1953–2003 at Beijing station after application of a 13-month window running mean(a) (Unit: ◦C), its wavelet power spectrum (b), and its global wavelet spec-trum (c) (Unit: (◦C)2), respectively. In panel (c), solid line indicates globalwavelet power and dotted line indicates a significance level of p <0.05.

Fig. 6. Comparison between annual mean (thick line)and summer (thin line) interannual to longer timescalevariability of SAT at Beijing station for 1953–2003. (a)is based on a traditional calculation; (b) is for the low fre-quency component with respect to MAC; (c) is for MAC;and (d) is a comparison between (b) and the residuals(dotted line) of (a) minus (c). Unit: ◦C.

spatial variability of SAT in China in the MAC ref-erence frame on three major timescales: MAC, in-terannual, and decadal-to-trend, by using data from1953–2003. It should be noted here that the dominantspatial patterns and their corresponding temporal evo-lutions of MAC, the interannual component, and thedecadal-to-trend component of SAT in China are not

significantly affected by the enhancement of spatialresolution of data (figure not shown), as long as theenhancement of the spatial resolution is spatially rela-tively homogeneous. Therefore, only the results basedon the station data from 1953 to 2003 are displayed.The coherent spatial and temporal patterns of variabil-ity of SAT on those different timescales are diagnosedusing EOF analysis (Fig. 7).

3.3.1 MAC variabilityThe dominant pattern of the MAC of daily SAT

of China exhibits a zonal orientation with its ampli-tude increasing with latitude (Fig. 7a). In the north-ern part of China (45◦–55◦N), the mean amplitude ofMAC is about twice than that in the southern partof China (20◦–30◦N). This distribution pattern can beexplained largely by the winter-summer solar radia-tion difference as a function of latitude. The corre-sponding PC (Fig. 7b) shows that the amplitude isrelatively large around 1968 (1.54 standard deviation)and relatively small around 1987 (1.37 standard devia-tion), a reduction of seasonality of 11% compared with1968. Previously, there have been reports concerningthe changing annual cycles of other climate variables,e.g., Hu et al. (2003) found that the seasonality of pre-cipitation has become slightly weaker in recent decadesin southern and eastern China. It remains to be in-vestigated how and why the MAC of various climatevariables are changing, in order to piece together a co-


Fig. 7. EOF analysis for different timescale components of daily SAT in China during1953–2003. (a) Leading mode (explains 98.7% of the total variance of that timescale)of MAC component; (b) its corresponding PC. (c) Leading mode (explains 40.0% ofthe total variance of that timescale) of interannual component; (d) its correspondingPC. (e) The second mode (explains 20.0% of the total variance of that timescale)of interannual component; (f) its corresponding PC. In panels (d) and (f), dottedlines indicate one standard deviation. (g) Leading mode (explains 77.8% of the totalvariance of that timescale) of decadal-to-trend component; (h) its corresponding PC.

herent view of the changes in the climate system onthe annual timescale.

3.3.2 Interannual variabilityIn order to reduce the potential influence of global

warming on the attribution of interannual variability,we have separated the interannual component fromthe decadal-to-trend component of SAT and will an-alyze their EOFs and corresponding PCs separately.The two leading EOFs of the interannual variabilityof SAT in China (explaining 40.0% and 20.0% of thetotal variance of that timescale, respectively) and their

corresponding PCs are shown in Fig. 7. The spatialpattern of the first two EOFs resemble those in Nittaand Hu (1996), Pu et al. (2007), Zhu et al. (2007),and Kang et al. (2009), and also resemble those of TA(Fig. 8). Since those studies applied the EOF anal-ysis to ILV defined based on either summer or winterdata, i.e., which contains a mixture of the annual cycleand ILV, or on summer or winter interannual variabil-ity, i.e., which contains a mixture of the annual cycleand interannual variability, the contribution of vari-ance associated with the spatial patterns of differenttimescales of variability cannot be identified, and nei-


Fig. 8. EOF analysis for traditional monthly SAT anomaly (departure from 1971–2000) in China during 1953–2003. (a) Leading mode (explains 50.0% of the totalvariance); (b) the first PC; (c) second mode (explains 18.0% of the total variance);(d) the second PC.

ther can the contributions of annual cycle changes orof global warming to the spatial pattern. The resultsshown here indicate that the interannual variabilitywas the main contributor to the spatial pattern of vari-ability revealed in these studies.

The first EOF shows a monopole pattern exceptfor some areas in Sichuan province (roughly 26◦–34◦N,98◦–108◦E) (Fig. 7c). The magnitude of the inter-annual variability of SAT in northern China (35◦–55◦N), especially in Northeast China (40◦–55◦N, 115◦–135◦E), is significantly larger than that in southernChina (20◦–35◦N). The corresponding first PC showslarge variations throughout the data span, with localminima exceeding one standard deviation in 1957/2(year/month, hereafter), 1964/1, 1968/12, 1977/1,1980/3, 1984/4, 1989/10, 1993/7, 2000/1, and 2003/1,and with local maxima exceeding one standard devi-ation at 1953/11, 1955/11, 1959/3, 1961/11, 1973/2,1975/10, 1978/12, 1981/12, 1988/8, 1994/9, 1998/12,2002/1, and 2003/12 (Fig. 7d). January 1977 corre-sponds to the largest negative anomaly (−3.7 standarddeviations), which implies the coldest year for mostof China. This result is consistent with the recordsin the Almanac of Cold Waves (Laboratory of Cli-mate Application of National Meteorological Center,1986), in which it was recorded that during that periodmost part of China (and especially Northeast China)suffered from severe low temperature disasters asso-

ciated with extremely strong cold surges seldom ob-served in history. The second largest negative anomalyappears during February 1957 (−2.1 standard devia-tions), which is also in agreement with records statingthat during that period most areas suffered from se-vere low temperatures with heavy snow or frozen rain,including an especially severe low temperature disasterin Northeast China. Most other local minima exceed-ing one standard deviation, such as 1954/12, 1969/1,1984/4, and 2000/1, are consistent with nationwidestrong cold surge events. These results imply that thestrength of the winter Asian Monsoon has a large influ-ence on the interannual variability of SAT in China.The largest positive anomaly appeared in December1998 (2.3 standard deviations), which coincides wellwith the record highest temperatures in the winter of1998–1999.

To understand the possible mechanisms of interan-nual variability of SAT in China, correlation analysisis conducted using the monthly mean of the first PC ofinterannual variability of SAT and the monthly SLP,GHT500, and SST, respectively. It is shown that dur-ing warmer (colder) periods in most parts of China,the Siberian High and the Aleutian Low are weaker(strong) (Fig. 9a). This result further implies that thestrength of the winter Asian Monsoon has a large in-fluence on the interannual variability of SAT in China.There exists no significant correlationbetweenGHT500


Fig. 9. (a) Correlation coefficient between monthly PC1of interannual component of SAT and monthly SLP.Shading indicates areas significant at better than the 5%level. (b) Difference between warm minus cold compos-ites of surface wind related to the first PC of interan-nual component of SAT. Shading indicates differencessignificant at better than the 5% level, as determinedby t test. Warm periods are 1953/11, 1955/11, 1959/3,1961/11, 1973/2, 1975/10, 1978/12, 1981/12, 1988/8,1994/9, 1998/12, 2002/1, and 2003/12; and cold periodsare 1957/2, 1964/1, 1968/12, 1977/1, 1980/3, 1984/4,1989/10, 1993/7, 2000/1, and 2003/1.

(SST) and PC1 (figure not shown). Composite sur-face wind associated with warm minus cold monthlyPC1 further shows that during colder periods in China,most parts of China are under the control of anomalousnorthernly wind associated with the anomalous anti-cyclone near Kala Sea (Russian Arctic Ocean), whichsuggests that the Siberian High is stronger (Fig. 9b).There is an anomalous cyclone over Sichuan basin,where the anomalous northernly wind and the anoma-lous southernly wind from the Indian Ocean and theSouth China Sea converges. This difference in surfacewind might explain to some extent the temperaturedifference between Sichuan province and other parts ofChina in Fig. 7c. Meanwhile, there is an anomalouscyclone (although not significant) in the North PacificOcean, which suggests that during colder period inChina, the Aleutian Low is stronger. This result isconsistent with the above mentioned analysis.

The second EOF shows a sea-saw variation patternbetween Northeast China and the other parts of China(Fig. 7e), i.e., when the temperature anomaly is high(low) in Northeast China, it is low (high) in other partsof China. This result is a little different from that of

Kang et al. (2009), who reported that the variationsin Northeast China and the northern parts of the Xin-jiang Autonomous Region (roughly 34◦–50◦N, 74◦–96◦E) are simultaneous. The difference may partlyarise from different datasets used. The correspond-ing second PC also shows large variations throughoutthe whole temporal span of the data, with local max-ima exceeding one standard deviation during 1953/1,1965/1, 1966/2, 1969/11, 1977/3, 1978/9, 1986/12,1990/3, 2001/1, and with local minima exceeding onestandard deviation during 1955/1, 1958/9, 1962/2,1963/11, 1968/8, 1974/4, 1976/1, 1982/8, 1988/12,1992/2, 1995/1, 1997/12, 1999/11, 2002/2 (Fig. 7f).January 2001 recorded the largest positive anomaly(3.5 standard deviations), which indicates unusuallycold conditions in Northeast China along with unusualwarmth in other parts of China. At that time, the firstPC is also negative which also indicates cold anoma-lies in Northeast China. The combination of these twoPCs intensifies the cold anomaly in Northeast Chinaduring January 2001, which is in agreement with therecord that Northeast China and the east part of In-ner Mongolia Autonomous Region (roughly 38◦–55◦N,96◦–126◦E) suffered from severe cold weather duringthe winter of 2000–2001. For the period that appearedto have a minimum in the first PC (Fig. 7d), i.e., Jan-uary 1977, the second PC had a larger (exceeding onestandard deviation) positive value (Fig. 7f), whichcoincided with a cold anomaly in Northeast China.The combination of the first and the second PC is at-tributed to the observed severe freezing in NortheastChina during this period. A correlation analysis isconducted between the monthly mean of the secondPC and the monthly SLP, U850, GHT500, and SST,respectively. The results are also compared with thoseanalyzed from the second PC of TA (Fig. 10). As faras the second PC of interannual variability with re-spect to MAC (“IPC2 w.r.t MAC” hereafter) is con-cerned, cold (warm) periods in Northeast China areassociated with a strong (weak) Polar High, a weak(strong) Azores High, and a strong (weak) AleutianLow (Fig. 10a). The correlation map resembles theAO pattern, which suggests that the IPC2 w.r.t. MACmight be related to the variability of the AO. Thisresult is also in agreement with that using TA (Fig.10e). For U850, it is shown that there is a wave-trainin the northern East Asia region (Fig. 10b). Such awave-train also exists in PC2 of TA (Fig. 10f). FromFig. 10c, it is shown that the cold (warm) periods inNortheast China are associated with a strong (weak)Polar Vortex and increasing (decreasing) GHT500 inthe tropics above the Indian Ocean to West Pacificregion (“IWR” hereafter). The possible influence ofthe Polar Vortex also exists in PC2 of TA; however,


Fig. 10. Correlation coefficient between monthly PC2 of interannual component w.r.t MAC of SATand monthly SLP (a), U850 (b), GHT500 (c), and SST (d), respectively. (e), (f), (g), and (h) arethe same, but for PC2 of TA. Shaded areas indicate significance at better than the 5% level. (i)Difference between strong minus weak composites of surface wind related to PC2 of interannualcomponent w.r.t MAC. Shading indicates differences that are significant at better than the 5%level, as determined by t test. Strong PC2 periods are 1953/1, 1965/1, 1966/2, 1969/11, 1977/3,1978/9, 1986/12, 1990/3, 2001/1; and weak PC2 periods are 1955/1, 1958/9, 1962/2, 1963/11,1968/8, 1974/4, 1976/1, 1982/8, 1988/12, 1992/2, 1995/1, 1997/12, 1999/11, 2002/2.


significant correlation above the IWR is not evidentwhen using TA (Fig. 10g). The correlation with SSTshows that the IPC2 w.r.t MAC is positively corre-lated with SST in the central equatorial Pacific re-gion, with the peak in between 180◦ and 150◦W (Fig.10d). This pattern is a little different from the canoni-cal ENSO pattern, but is much like the ENSO Modoki(Ashok et al., 2007) pattern. This result implies thatthe ENSO Modoki might be associated with the IPC2w.r.t. MAC. However, the ENSO Modoki signal is notevident when using TA (Fig. 10h). Composite anal-ysis of the surface wind associated with strong andweak monthly PC2 shows that during the cold periodsin Northeast China, there is an anomalous anticyclonenear Kala Sea, an anomalous cyclone centered around(60◦N, 90◦E), an anomalous transverse trough in thewest part of China, and an anomalous dipole in theNorth Pacific Ocean (Fig. 10i). Northeast China isdominated by an anomalous north wind from the po-lar region while the other parts of China are controlledby anomalous northwest airflow ahead of the anoma-lous transverse trough. This might explain, to someextent, the contrasts between Northeast China and theother parts of China shown in Fig. 7e.

3.3.3 Decadal to trend variabilityThe first EOF of the decadal-to-trend variability

(explains 77.8% of the total variance of that timescale)is distinguishable from other EOFs. Its spatial pat-tern shows co-variability in almost all part of Chinaexcept some parts of Sichuan province (Fig. 7g). Thispattern resembles that of Kang et al. (2006) wherethey analyzed winter interdecadal variability (its firstEOF explained 66% of the total variance) showing amixture of the annual cycle and an interdecadal com-ponent. Our result also agrees with that of Pu et al.,(2007) in that the first EOF is independent of sea-sonal cycle and different data spans when analyzingtraditional temperature anomalies in China. In detail,the amplitudes in Northern China, especially North-east China, mid-Inner Mongolia Autonomous Region,and the northwest part of Xinjiang Autonomous Re-gion, are larger than those in Southern China (Fig.7g). The corresponding PC shows an overall warm-ing trend, with some fluctuations during 1960s–1970sand a maximum in 1998 (Fig. 7h). This is a littledifferent from the result of Ren et al. (2005), who re-ported that before the 1980s, temperature in Chinawas fluctuating within a small range. This differencemay be explained as following: (1) it is shown in Fig.2 of Ren et al. (2005) that before the 1980s, the tem-perature in China is also fluctuating and increasing atthe decadal timescale along with the similar patternof fluctuating increases/decreases found in our study;

(2) the end effect of the EEMD method may overes-timate the warming rate to some extent in the early1950s; however, it does not influence the latter pe-riod. From further analysis, the turning point fromnegative phase to positive phase appears during May1985. This is consistent with the result in Zhu et al.(2007), who used a Mann-Kendall test to analyze win-ter temperature variability (departures from the meanof 1971–2000) in China from 1951/1952 to 2005/2006and reported an abrupt change during the 1984/1985winter. Note we regard it as a decadal change insteadof an “abrupt change.” In addition, the maximum in1998 identified in this study is also in agreement withWang et al. (2004) where they reported that 1998 wasthe warmest year in China since 1880. All of theseresults again show the adaptive and temporally localcharacteristics of the EEMD method.

From Figs. 7g and 7h, it is shown that dur-ing 1953–2003, most parts of China are undergoingan overall warming trend, with fluctuations, and thenorthern part of the country, especially NortheastChina, mid-Inner Mongolia Autonomous Region, andthe northwest part of Xinjiang Autonomous Region,has a warming trend stronger than that in southernpart. This is in agreement with the results in Tu etal. (2000), Ren et al. (2005), and Sun and Lin (2007).In Sichuan province, the SAT trend is debatable inprevious studies due to different data spans used. Forexample, when data from 1951 to 1996 is analyzed, it isfound that there is basically a decreasing trend (Tu etal., 2000; Chen et al., 1998); however, when data from1951 to 2002 is analyzed, no obvious trend is found(Tang and Zhai, 2005; Ren et al., 2005; Sun and Lin,2007). To see the source of this discrepancy, we ap-ply an adaptive multi-decadal trend (Wu et al., 2007;Qian et al., 2009) by using the EEMD method to thedaily SAT series at some locations in Sichuan province,e.g., at Nanchong (30◦N, 106◦E), which is quite dif-ferent from the others (Fig. 7g). The multi-decadaltrend (the combination of the last two components ofthe EEMD result) of SAT at Nanchong is displayedin Fig. 11. It is shown that there is an increasingtrend from 1953 to the late 1960s, a deceasing trendin the 1970s and 1980s, and an increasing trend sincethe mid-1980s. Since the linear trends used in the pre-vious studies were calculated according to the wholedata span, they implicitly assumed that the trend hasa timescale of infinity and hence the extension of datapast 1996 has led to the discrepancy in the previousstudies. This shows the advantage of an adaptive trendover a linear trend.

4. Summary and discussions

In this study, the MAC is used as a reference frame


Fig. 11. Adaptive trend extracted by EEMD methodat Nanchong station (30◦N, 106◦E) in Sichuan Provincefrom 1953 to 2003. Solid line indicates the combination ofthe last two components of EEMD result, and dotted lineindicates the combination of the last three components.

for climate anomalies instead of the traditional every10-yr change of climatological mean annual cycle (cli-mate normals), to study the multi-timescale variabilityof SAT in China during 1953–2003. The results showthat the EEMD method, which is used to isolate thehigh frequency component, MAC component, interan-nual component, and decadal to trend component fromdaily SAT, can reflect historical events relatively well,indicating its adaptive and temporally local character-istics. The main results are summarized below:

(1) For the MAC component, the MAC referenceframe is temporally local and does not change follow-ing the extension of data length, and thus the cor-responding anomalies and their physical explanationsare physically unique. This is more physically rea-sonable than the traditional anomaly reference frame,which changes for the same data span with the exten-sion of new data, and so is the corresponding TA aswell as its physical explanation. Moreover, the year-to-year difference of MAC for one individual day atthe Beijing station can reach as large as 2.5◦C, whichis of the same magnitude as interannual variability.Furthermore, the low frequency component with re-spect to MAC is found more suitable to study ILVthan the 13-month window running mean, which can-not exclude the annual cycle, and than other versionsof ILV (e.g., annual mean or summer mean or win-ter mean), which still contain a portion of the annualcycle.

(2) For the interannual component, the first EOF(explains 40.0% of the total variance of that timescale)is a nationwide monopole pattern except for someparts of Sichuan province. During cold periods in mostparts of China, the Siberian High and the AleutianLow is stronger; most parts of China are dominatedby anomalous north wind from the polar region; andthis anomalous north wind and the anomalous southwind from the Indian Ocean and the South China Sea

converge in Sichuan province, which explains to someextent the difference in interannual variability betweenSichuan province and other parts of China. The sec-ond EOF (explains 20.0% of the total variance of thattimescale) shows a sea-saw pattern between NortheastChina and the other parts of China, which might berelated to the AO, the Polar Vortex, and the ENSOModoki, whereas the ENSO Modoki signal cannot beseen when using traditional anomaly methods.

(3) For the decadal-to-trend component, mostparts of China except for some parts of Sichuanprovince undergo an overall (but fluctuating) warmingtrend, with the northern part (especially the NortheastChina, mid-Inner Mongolia Autonomous Region, andthe northwestern part of Xinjiang Autonomous Re-gion) has a warming trend stronger than that of thesouthern part. The turning point from negative phaseto positive phase appears in May 1985. The multi-decadal trend in Sichuan province shows an increasingtrend from 1953 to the late 1960s, a deceasing trendin the 1970s and 1980s, and an increasing trend sincethe mid-1980s.

It should be acknowledged that concerning the at-tribution of the decadal-to-trend variability of SAT inChina, we can hardly exclude the influence of globalwarming from that of other potential factors simply byusing regression method. Therefore, the result fromprevious studies showing that the leading EOF modeof decadal-to-trend variability is associated with theAO might not be convincing enough, since the green-house effect might simultaneously affect SAT in Chinaand the AO. Many previous studies (e.g., Hu et al.,2003; Zhao et al., 2005; Ding et al., 2006; Zhou andYu, 2006; Zhou and Zhao, 2006) report that for thelast 50 years, the interdecadal variability is to a largeextent due to external greenhouse effect forcing, whilethe increase of sulfur aerosols may affect local SAT tosome extent (see Zhou et al., 2009 for a review). How-ever, climate models also have their uncertainties (e.g.Wang et al. 2009). Up to now, there are still manyuncertainties in the detection and attribution studiesof 20th century climate warming in China. Therefore,more solid work needs to be done in this field.

As noted in this paper, the advantage of the EEMDmethod in removing the annual cycle is obvious. How-ever, through the comparison, we have learned thatthe EEMD method actually separates some seasonallydependent anomalies into a so-called non-stationaryannual cycle. This makes the variations longer thanseasons less seasonally-dependent. A consequence ofthe separation is that we have to study/predict boththe changing annual cycle and the relevant anomaly.This is an important and distinct feature of EEMD.Wu et al. (2008) discussed the prediction model for a


changing annual cycle and the respective interannualvariability. Though such a method gives us differentinsight for climate prediction, there are still many openquestions for further study.

Acknowledgements. This work was jointly sup-

ported by Grant 2006CB400504 from the National Basic

Research Program of China, and Grant LCS-2006-03 from

the Laboratory for Climate Studies, China Meteorological

Administration; Wu was sponsored by the National Science

Foundation of USA (ATM-0653136, ATM-0917743). Zhou

was sponsored by National Key Technologies R&D Pro-

gram under Grant No. 2007BAC29B03. Qian is grateful

for Prof. WANG Dongxiao and MU Mu for their helpful

comments. The authors thank two anonymous reviewers

for their helpful suggestions to improve the paper.

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