1. Introduction
In the context of global warming, assessment of Antarctic temperature change has become a very important issue during the past few years because of the impact that temperature changes may have on land/sea ice changes (Pritchard et al. 2012; Joughin et al. 2012). Based on measurements from regular weather stations and satellite and reanalysis data, temperature trends have been discussed both locally and for the whole continent (Comiso 2000; Marshall 2002; Vaughan et al. 2003; Turner et al. 2005; Monaghan et al. 2008). One well-recognized fact is that the Antarctic Peninsula has been found to be one of the most rapidly warming locations on Earth. This significant warming covers most of West Antarctica (Turner et al. 2005; Thomas et al. 2009; Schneider et al. 2012; Bromwich et al. 2013), whereas in East Antarctica the temperature change seems to be not so remarkable (Steig et al. 2009; Nicolas and Bromwich 2014).
When investigating the possible temperature change in the Antarctic, one main challenge comes from the paucity of surface observations. Even though more and more weather stations have been founded recently, the number is still small and most of them are located near the coast, providing little direct information about the continental interior. Therefore, the very first thing when discussing the temperature changes over the Antarctic is normally to get a reliable dataset, which can provide us with more information. Many efforts have been made during the past years, such as spatial reconstructions made by interpolating the sparse meteorological records (Steig et al. 2009; O’Donnell et al. 2011), as well as the temporal reconstructions made by infilling gaps with global reanalysis data, automatic weather station (AWS) data, and the satellite data (Bromwich et al. 2013; Nicolas and Bromwich 2014). Thanks to these efforts, a rough picture of how the temperatures over Antarctic change during the past decades has been formed, even though the magnitudes are still inconsistent among different researches.
With these reconstructions, the most widely discussed topic is whether the Antarctic is undergoing a significant temperature change (Bromwich et al. 2013; Bunde et al. 2014; Bromwich and Nicolas 2014). Normally, traditional statistical methods such as a Student’s t test or autoregressive model of first order (AR1) are applied to rule out the possible temperature-change intervals owing to statistical noises or autocorrelations (Santer et al. 2000; Bromwich et al. 2013). However, besides these estimations, it is important to emphasize that another concept, long-term climate memory (LTM), should also be taken into account (Koscielny-Bunde et al. 1998; Malamud and Turcotte 1999; Lennartz and Bunde 2011). Long-term memory, or long-term persistence (correlations), is not a new concept. Actually, it has been proposed ever since the middle of the last century, and is thought to be ubiquitous in nature as the Hurst phenomenon (Hurst 1951). But extensive researches on LTM only emerged recently after several well-developed methods were introduced, such as the well-known wavelet analysis (WA; Arneodo et al. 1995) and detrended fluctuation analysis (DFA; Peng et al. 1994). Compared with traditionally short-term correlations, long-term memory, as its name implies, means that the autocorrelations can last for a very long time. From a statistical point of view, if a time series is characterized by LTM, its autocorrelation function will not decay exponentially with time lags but rather decays by a power law, as 
Time series with different long-term memory: (a) white noise without LTM (DFA exponent 
Citation: Journal of Climate 28, 15; 10.1175/JCLI-D-14-00733.1
This paper is organized as follows. In section 2, we make a brief introduction of the data and provide a detailed discussion of the method we apply. Detailed diagnostic results on whether the temperature over Antarctica is long-term correlated or not are shown in section 3. In section 4, we provide further discussion on 1) how to understand the different LTM behaviors found in section 3 and 2) how the LTM may affect the trend evaluation. In section 5, we conclude this paper.
2. Data and methodology
a. Data
In this study, we analyzed monthly temperature records from 12 stations. The data (except the records from Byrd station) are mainly downloaded from the Reference Antarctic Data for Environment Research (READER) dataset (http://www.antarctica.ac.uk/met/READER/surface/), while the records from Byrd are obtained from the Byrd Polar Research Centre (http://polarmet.osu.edu/datasets/Byrd_recon/). We choose these 12 stations according to two criteria: 1) the observed temperature records should be relatively long, with few missing points, and 2) the stations should represent different specific regions of Antarctica, including coastal regions, the inner continent, and islands, as well as both East and West Antarctic. Locations of these 12 stations are shown in Fig. 2, with their altitude and data length explained in Table 1.
Locations of the 12 stations. Six of them (Halley, Syowa, Mawson, Casey, Scott Base, and Bellingshausen) are built along the coastline (CS), two of them (Bellingshausen and Orcadas) are located in small islands (IS), and the last four (South Pole, Vostok, Novolazarevskaya, and Byrd) are classified as Antarctic continental stations (ACS).
Citation: Journal of Climate 28, 15; 10.1175/JCLI-D-14-00733.1
Detailed information about the 12 monthly records used in this study, including the names of the stations, classifications, and their altitudes, beginning years, ending years, and the length.
Although only a few stations are available, compared to model data or reconstructed spatial data the observational data are more reliable in providing information on LTM. It should be noted that the data from Byrd are also a reconstruction by Bromwich et al. (2013), but considering that the data have been proved to have high quality, and this is the only long observation over west Antarctic, we choose these data for our analysis.
Before analysis, we first remove the effect of periodic annual cycle, as suggested by many previous works, by 
b. Methodology
To diagnose whether a time series is characterized by LTM, there are several methods available, including the autocorrelation analysis, power spectral density (PSD) analysis (Talkner and Weber 2000), structure function method (Lovejoy and Schertzer 2012), and wavelet analysis (Arneodo et al. 1995), as well as methods based on random walking theory, such as the rescaled-range (R/S) analysis (Hurst 1951), fluctuation analysis (FA; Peng et al. 1992), and the detrended fluctuation analysis (Peng et al. 1994; Kantelhardt et al. 2001). Among all these methods, calculating autocorrelation coefficients is the most straightforward way, but it suffers from strong finite size effects at large time scales (Lennartz and Bunde 2009b). PSD has relatively better statistics than the autocorrelation analysis, but still needs special estimators [e.g., the Geweke–Porter-Hudak (GPH) estimator] to guarantee the fitting accuracy (Geweke and Porter-Hudak 1983; Vyushin and Kushner 2009). Structure function method, R/S analysis, and the standard fluctuation analysis FA are all designed for stationary time series, which are claimed not appropriate for time series with external trends mixed (Koscielny-Bunde et al. 1998, 2006; Bashan et al. 2008). Finally, only the WA and DFA can both provide better statistical outputs and are capable in dealing with nonstationary data (Arneodo et al. 1995; Kantelhardt et al. 2001). Compared with WA, the algorithm of DFA is easier for computational purposes; therefore, DFA has become the most widely used method in analyzing LTM. In this study, we also choose to use this method.
Suppose we have a record 
Note that as DFA is based on the random walking theory, one may find it not straightforward in describing temporal variability of a given record. Therefore, we further introduce the Fourier transform–based method, power spectral density analysis, for better understanding. PSD analysis is a conventional and well-known method to characterize the fractal properties (or LTM) of time series (Talkner and Weber 2000). To determine the power spectral density 
Illustration of DFA-2 and PSD analysis, taking temperature anomalies over Byrd station as an example. (a) The DFA-2 result, where we find the exponent 
Citation: Journal of Climate 28, 15; 10.1175/JCLI-D-14-00733.1
We take the temperature anomalies over Byrd station as an example, and show both the DFA-2 and PSD results in Fig. 3. From the fitted exponents (
However, compared with DFA-2, there are two main limitations in PSD analysis. First, PSD is based on the Fourier transform, which assumes that the time series analyzed are stationary. If the considered variable is affected by external trends, or some other nonstationary factors, biased estimation of 
In this study, we choose DFA-2. Before showing the results, we also note that, even for DFA-2, there are still criticisms that require our attention. First, on small time scales (normally 
3. Results
In this study, we focus on the Antarctic region, where little attention was paid before. In fact, by using climate model simulated data, Rybski et al. (2008) discussed LTM properties globally, with Antarctic included. They found that the 2-m temperatures are long-term correlated in West Antarctica with DFA-2 exponent 
According to Fig. 2 and Table 1, one can see that among the 12 stations in our study, six of them are located along the coastline with low altitudes (<50 m), two are located on small islands with even lower altitudes (<20 m), and three are built on the Antarctic continent with very high altitudes (>1500 m). The location of the last station, Novolazarevskaya (70.8°S, 11.8°E), is relatively special. It is located near the ocean, but not directly at the coastline; it is built on the continent with relatively high altitude (119m), but not as high as the other three continental stations. According to Parish and Bromwich (1987), the station is actually located in a region where strong terrain-induced winds blow from the interior Antarctic to the coast. Other forces that shape the near-surface wind field such as the large-scale pressure gradients associated with cyclonic storms may be only of secondary importance. Therefore, climate in Novolazarevskaya may have continental characteristics. In this way, the 12 stations are classified into three groups: coastline stations (CS), island stations (IS), and Antarctic continental stations (ACS), as shown in Table 1. Although there are few stations in our study, they have a good spatial distribution covering different regions of Antarctica (Fig. 2). Therefore, detailed information as to whether there is LTM over Antarctic can be expected.
To detect LTM, DFA-2 is applied to these 12 temperature records. Considering the possible biases and uncertainties in the results provided by DFA-2, to ensure the accuracy of our detection we also performed a Monte Carlo significance test. As shown in Fig. 4, we take the temperature records over the South Pole (ACS) and Mirny (CS) as examples. From the DFA-2 results (see Figs. 5a,b), one can see that the 
Uncertainties in DFA-2 analysis, based on the temperature anomalies over (a) the South Pole and (b) Mirny station. In each calculation, we shuffled the temperature anomalies randomly and obtained 10 000 surrogated data without LTM. Theoretically, 
Citation: Journal of Climate 28, 15; 10.1175/JCLI-D-14-00733.1
(a),(b) DFA-2 results of the 12 monthly records and (c) the corresponding Monte Carlo significance test. DFA-2 results are shown from coastline stations (CS) in (a), where one can see all the temperatures are characterized by significant LTM with Hurst exponent 
Citation: Journal of Climate 28, 15; 10.1175/JCLI-D-14-00733.1
In Fig. 5, we show the results for all the 12 stations. Figure 5a shows the DFA-2 results of the temperature records from the coastline stations, while Fig. 5b shows the DFA-2 results from the island stations and Antarctic continental stations. Through a Monte Carlo significance test, uncertainty intervals of 
4. Discussion
a. Understanding the different LTM behaviors over Antarctica
Recently, it has been proposed that one possible origin of climate memory may come from the slow-varying effects of the ocean, where the huge heat storage capacity is thought to be the key factor (Monetti et al. 2003; Yuan et al. 2013). One can consider the mechanism from the perspective of stochastic climate processes (Hasselmann 1976; Yuan et al. 2013). That is, the climate regimes are triggered by small time-scale excitations (or forcing) to begin to change, but slower response subsystems, such as the ocean, usually “remember” the forcing first, and then release the influence slowly on a larger time scale, which further result in the so-called climate memory. This view is supported by many former studies. Particularly, it has been found that temperatures over the oceans normally have the strongest LTM properties (with DFA exponent 
Recall the results reported by Rybski et al. (2008), where significant LTM is found for the model simulated 2-m temperatures over West Antarctica but not found over East Antarctica; we prefer to understand the “abnormal” behavior at the Byrd station by using the theory introduced above—that is, to check whether there are close interactions between the West Antarctica (where the Byrd station is located) and external slow-varying systems (ocean). In fact, it has been reported that West Antarctica is a key region for heat and moisture transport (Cullather et al. 1998). Influenced by ocean variations from both far away tropical Pacific/Atlantic water (Ding et al. 2011; Li et al. 2014) and nearby clockwise propagated eddies, we argue that the seemingly abnormal behavior at the Byrd station is not unexpected. Furthermore, because of the Transantarctic Mountains, the influences are limited to West Antarctica. Thus, these mountains form a clear border line between West and East Antarctica (Nicolas and Bromwich 2014). In East Antarctica, however, the continent is only weakly influenced by the ocean. As a result, temperatures over this region have high probabilities to behave as white noise. As shown in Fig. 5c, indeed no significant LTM has been measured in the temperatures over the South Pole, Vostok, and Novolazarevskaya. Therefore, the different LTM behaviors between temperature for the Byrd station and that over other continental stations could be explained as a reflection of the different climatic environments between West and East Antarctica. Furthermore, as for the stations from coastline and from islands, it is obviously not surprising to find significant LTM in temperature, since these stations are all located in regions where close interactions with the ocean can be found.
b. Effect of LTM on trend evaluation
Trend distribution of time series with equal length (
Citation: Journal of Climate 28, 15; 10.1175/JCLI-D-14-00733.1
In Table 2, we show the confidence interval 
Trend evaluation of the 12 monthly records over Antarctica. Data length L, temperature increase 
5. Conclusions
In this study, surface air temperature records of 12 stations from different regions of Antarctica are analyzed by means of DFA. After the Monte Carlo significance test, different LTM behaviors are found. Temperatures observed from coastlines and temperatures observed from islands are all characterized by significant LTM, while temperatures records observed from continental stations behave differently. In East Antarctica, continental temperatures from the South Pole, Vostok, and Novolazarevskayz behave closer to white noise, whereas in West Antarctica significant LTM is found in the Byrd station. These different results may be explained by studying the interactions between local weather system and external slow-varying systems (ocean); therefore, we argue that the difference can be considered as a reflection of the different climatic environments between the West and East Antarctica. Since according to the discussion above (Fig. 6 and Table 2) the existence of LTM can increase the uncertainty of trend evaluation, when studying the warming trend over Antarctica special attention should be paid to the coastline, islands, and West Antarctica, where significant LTM is detected in this study.
After submitting this work, we learned of a closely related study by Ludescher et al. (2015) in which, by using DFA-2, similar exponents for the Antarctic records (not exactly the same 12 stations as we use) have been obtained. Their trend analysis shows that only 1 station (out of 13) has a significant warming trend (
Acknowledgments
The authors acknowledge support from National Natural Science Foundation of China (41405074 and 41206179), the climate change project of CMA (CCSF201332), and the Basic Research Fund of CAMS (Grants 2013Z002). Naiming Yuan and Juerg Luterbacher acknowledge also the LOEWE Large Scale Integrated Program (Excellency in research for the future of Hesse “FACE2FACE”) and the Chinese Polar Environment Investigation and Assessment Program (CHINARE2014-04-04). We are grateful to Armin Bunde for the helpful discussion.
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