Trends of continental, zonal and seasonal land temperatures in the 20th century
11 Trends of continental, zonal and seasonal land temperatures in the20th century
Jouni Takalo and Kalevi Mursula
Space physics and astronomy research unit, University of Oulu, POB 3000,FIN-90014, Oulu, Finland, email: jouni.j.takalo@oulu.fi
Abstract
We study the evolution of continental, zonal and seasonal land tem-perature anomalies especially in the early 20th century warming (ETCW) period,using principal component analysis (PCA) and reverse arrangement trend anal-ysis. ETCW is significant in all other continents except for Oceania. Warmingin South America is significant from the ETCW onwards, but significant recentwarming started in North America and Europe only around 1990. The continen-tal PC2 is related to North Atlantic Oscillation and mainly shows short perioddifferences between North America and Eurasia. The continental PC3 componentincluding the ETCW depicts a 60-70-year oscillation, which is related to Atlanticmultidecadal oscillation (AMO).The zonal and seasonal PC2s are both correlated with AMO index, but zonalPC3 is related to Southern oscillation index (SOI) and seasonal PC3 best corre-lated with wintertime El Ni˜no (NINO34 DJF index). In the southern hemisphere,the recent warming starts first closest to the equator in the 1950s and latest inthe southernmost zone in the late 1970s. In the two lowest northern zones (EQ-N24, N24-N44) the warming is significant since the ETCW, and increased warmingstarts in 1970s, but in two northernmost zones (N44-N64, N64-N90) the coolingafter the ETCW delays the start of recent warming until around 1990. All seasonsof the northern hemisphere but no season in the southern hemisphere depict a sig-nificant ETCW. Significant recent warming starts in the southern seasons alreadyaround 1960, but in the north the start of significant recent warming is delayedup to 1990.All the three PCA have almost common PC1 component for the analyzes 1910-2017, i.e., gradual increase of temperature until 1940s, period of declining towardsthe end of 1950s, a flat phase until the second half of 1970s and steep rise after that.However, the continental PC1 explains only 75.2 % of the variation of the data,while zonal and seasonal PC1s explain 81.7 % and 87.6 % of the correspondingdata, respectively.
Keywords
Temperature anomaly · Trend test · Principal component analysis · Change-point analysis
Global climate is greatly dominated by the increasing temperature since morethan 100 years ago (Cook et al. , 2016). The systematic increase of global temper-ature was broken during the middle of the 20th century. Temperature increased a r X i v : . [ phy s i c s . a o - ph ] A ug between 1920-1950 (so-called early 20th century warming, ETCW), especially inthe northern hemisphere, but cooled after that until the end of 1960s (Davy, Chen,and Hanna, 2018; Fu et al. , 1999; Hegerl et al. , 2018; Johannessen et al. , 2016; Ryb-ski et al. , 2006; Schlesinger and Ramankutty, 1994; Wood et al. , 2010; Yamanouchi,2011).There has been a debate on to what extent these temperature changes weredue to natural variability and/or external forcing (Bengtsson, Semenov, and Jo-hannessen, 2004; Egorova et al. , 2018; Hegerl et al. , 2018; Meehl et al. , 2003; Nozawa et al. , 2005; Reid, 2013; Suo et al. , 2013). Using a one-dimensional climate-oceanmodel Reid came to conclusion that solar and anthropogenic greenhouse-gas forc-ing made roughly equal contributions to the rise in global temperature during theETCW. Meehl et al. showed that their model required a combination of solar andanthropogenic forcing to produce the ETCW, while the radiative forcing of theincreasing greenhouse-gases was dominant for the recent warming effect. Suo et al. presented, based on model simulations and observations, that intensified solar ra-diation and the absence of volcanic activity during the 1920s-1950s can explainmuch of the early 20th century warming. The anthropogenic forcing could play arole in getting the timing of the peak warming correct. Increased heat inflow inthe Barents Sea, or anomalous atmospheric circulation patterns in the northernEurope or north Atlantic could also contribute to warming. They concluded thatthe early 20th century warming was largely externally forced.Bengtsson, Semenov, and Johannessen state that natural variability was alikely cause for the ETCW, with reduced sea ice cover being crucial for the warm-ing. A robust sea ice vs. air temperature relationship was demonstrated by sim-ulations with the atmospheric model forced with observed SST and sea ice con-centrations. Also the climate model analysis of Nozawa et al. suggest that trendsin the external natural factors, e.g., the recovery from volcanic eruptions and thesolar irradiance variability, caused more warming in the early 20th century thananthropogenic factors. Further investigation of the variability of Arctic surfacetemperature and sea ice cover was performed by analyzing data from a coupledocean-atmosphere model. The analysis showed that the simulated temperature in-crease in the Arctic was related to enhanced wind-driven oceanic inflow into theBarents Sea with an associated sea ice retreat.The review article of Hegerl et al. discusses the observed changes during theETCW and the underlying causes and mechanisms. Attribution studies estimatethat about a half of the global warming from 1901 to 1950 was forced by a combi-nation of increasing greenhouse gases and natural forcing, offset to some extent byaerosols. Natural variability also made a large contribution, particularly to regionalanomalies like the Arctic warming in the 1920s and 1930s. Egorova et al. madea comprehensive study of ETCW using their atmosphere-ocean chemistry-climatemodel driven by different combinations of forcing agents. They found a 0.3 o C global warming during 1910-1940, which is about 0.1 o C lower than the observedwarming. They, furthermore, found that about half of the explained warming wascaused by well-mixed greenhouse-gases, and about one third by the solar UV, visible and infrared irradiance in 250 − et al. , 2011).The global cooling after the ETCW is an interesting phenomenon. Althoughthe greenhouse-gases were still rising, the temperatures decreased, especially inthe NH in 1960s and 1970s. Hodson, Robson, and Sutton suggest that the mostlikely drivers for the cooling are the ”Great Salinity Anomaly” of the late 1960s (Belkin et al. , 1998), the earlier warming of the sub-polar North Atlantic, whichmay have led to a slowdown in the Atlantic meridional overturning circulation(Robson, Sutton, and Smith, 2014) and the increase in anthropogenic aerosols,especially sulfur dioxide emissions (Booth et al. , 2012; Haywood and Boucher,2000; Ohmura, 2009).As to global warming, Callendar predicted a 0.03 degrees/decade rise in tem-perature due to the increasing amount of carbon dioxide (Hawkins and Jones,2013). In the late 1950s it was understood that the concentration of carbon diox-ide was indeed increasing in the atmosphere and it was suggested that, sooner orlater, this would affect climate (Harris, 2010; Revelle and Suess, 1957). Sawyerpredicted global warming and calculated the rate of warming until 2000 (Nicholls,2007). In the late 1970s it was widely understood that the previous cooling wastemporary and that climate warming caused by greenhouse gases, especially CO ,would dominate over the cooling effect of smog, aerosols and volcanic dust in thefuture (Hansen et al. , 1981; Robock and Free, 1995; Mann, Bradley, and Hughes,1998; Myhre, 2009; Friedman et al. , 2013).In this paper we study continental, zonal and seasonal land air temperatureanomalies in 1880-2017 using principal component (PC) analysis and reverse ar-rangement (RA) trend analysis. Furthermore, we find greatest change-points in thetemperature anomalies combined with their profiles. Particular attention is paidto the role of ETCW in the evolution of temperatures during the 20th century,because it has been largely disregarded in the studies global warming. This paperis organized as follows. Section 2 presents the data and methods used in this study.In Section 3 we analyze continental temperature anomalies and in Section 4 zonaltemperature anomalies. In Section 5 we discuss hemispheric seasonal anomaliesand give our conclusions in Section 6. et al. , 2018), and NASA Goddard Space Flight Center GISTEMP(GISS Surface Temperature Analysis) data for hemispheric, zonal and seasonalland temperature analysis for 1880-2017 (Lenssen et al. , 2019). In zonal analysisboth hemispheres are divided into four latitude zones 0-24 , 24-44, 44-64 and 64-90 degrees (Willmott and Matsuura, 2018). The SH zone S90-S64 (Antarctica),however, has been recorded since 1903 only by few stations and is omitted fromthis analysis.Annual temperature anomalies (in o C ) are calculated from the correspondingannual temperature mean values by subtracting the average base period valueof the temperature from the temperature values. Similarly monthly (seasonal) anomalies are calculated by subtracting the average value of the correspondingmonth (season) of the base period from the monthly (seasonal) temperature values.The base periods used in this study are 1910-2000. However, we note that the baseperiod does not affect results provided in this paper, it only changes the level of thezero point of the anomalies. For cumulative sums (later called anomaly profile) the base period is, of course, the whole time series. Furthermore, principal componentanalysis and reverse arrangement trend test are independent of the base period. Forseasons we use conventional definition: northern winter DJF (December, January,February), northern spring MAM (March, April, May), northern summer JJA(June, July, August) and northern fall SON (September, October, November).2.2 PCA methodPrincipal component analysis has been used in many fields of science, e.g., inchemometrics (Bro and Smilde, 2014), in data compression (Kumar, Rai, and Ku-mar, 2008), in information extraction (Hannachi, Jolliffe, and Stephenson, 2007),and in studying the solar and geomagnetic data (Bhattacharyya and Okpala, 2015;Holappa et al. , 2014; Takalo and Mursula, 2018). For a large number of correlatedvariables PCA finds combinations of a few uncorrelated variables that describethe largest possible fraction of variability in the data. It should be mentionedthat many climate indices, e.g., the Atlantic multidecadal oscillation (AMO) andAtlantic oscillation (AO) are defined as modes of PC analysis (Baez et al. , 2013;Schlesinger and Ramankutty, 1994; Trenberth and Shea, 2006). (For more infor-mation of the method see (Takalo and Mursula, 2018)).2.3 Anomaly profile analysisFor time series of temperature anomalies X ( t i ) , i = 1 ...N , let X be the meanvalue of the anomalies of the whole investigated interval X ( t i ). We calculate thecumulative sum time series, i.e., sum of the deviations from the mean anomalyuntil time t j Y ( t j ) = t j (cid:88) i =1 (cid:0) X ( t i ) − X (cid:1) . (1)We use here this cumulative sum of the deviation of the anomalies for analysisand call it the ”anomaly profile”.2.4 Reverse arrangement testWe use the following method for finding trends in time series. Let us have discretetime series { x i } , i = 1 , ..., N . Beginning from the first value x i = x , we thencount the number of times that x i > x j for i < j = 2 , , ..., p . Each such inequalityis called a reverse arrangement (RA). This process is then repeated for x i = x , x ,..., x p − . Let the total number of reverse arrangement be A p . If the sequence { x i } is a set independent random variables, then the number of reverse arrangements, i.e. A p , is a random normally distributed variable with mean µ A p = p ( p − σ Ap = 2 p + 3 p − p . (3)The z -score of A p (also called standardized A p ) can then be calculated usingthe following equation (Beck et al. , 2006; Bendat and Piersol, 2000; Kendall andStuart, 1967; Siegel, 1988) z p = A p − µ Ap σ Ap . (4)The null hypothesis of the test is that the data points in the time series { z p } , p = 2 , , .., N are independent observations from a random variable. Thealternative hypothesis is that the data points are related and show that there isa significant trend underlying the original time series { x i } , i = 1 , ..., N . The 95%and 99% acceptance criteria for null hypothesis are that − . < z < .
96 and − . < z < .
58, respectively. A z -value outside these intervals means rejectionof the null hypothesis with p < .
05 and p < .
01, respectively.2.5 Finding change-pointsWe find points, where time series, { x i } , i = 1 , ..., N , has greatest change in meanvalues by minimizing the functional (Lavielle, 2005; Killick, Fearnhead, and Eckley,2012) J ( k ) = k − (cid:88) i =1 (cid:16) x i − (cid:104) x (cid:105) k − (cid:17) + N (cid:88) i = k (cid:16) x i − (cid:104) x (cid:105) Nk (cid:17) , (5)i.e., findingmin k { ( k − var ([ x , x , ..., x k − ]) + ( N − k + 1) var ([ x k , x k +1 , ..., x N ]) } . (6) Figure 1 shows the monthly anomalies and their profiles for North America, Europeand Asia for 1910-2017. (For continents and zones we divide the profile with 40 tobetter adjust the anomaly and its profile to same figure). We chose here to presentmaximum five change-points to better find the differences between continents.Thesimplest development of the temperature has been in Asia, which have continuousrise after 1910, but been stronger after late 1980s. In North America there was anETCW between about 1937-1945, after which there was a cooler interval to thelate 1970s. The warming period started gradually in 1980s but has been steepersince late 1990s (total variance during 1910-2017 is 1.10 for North America) . Thetemperature in Europe has been very similar to North America (variance 1.07),but the warming period was earlier, starting about 1934, and ending 1940. Afterthat, simultaneously with second world war, Europe experienced very cold period, which lasted three years. The recent warming in Europe started at the end of1980s.Figure 2 shows the monthly anomalies and their profiles for South America,Africa and Oceania (mainly Australia and New Zealand) for 1910-2017. The tem-perature development of South Africa is very similar to that of Asia. However, the variance of the anomalies is much smaller in South America, i.e, 0.83 for Asiaand 0.29 for South America. Also the rise of the temperature is much smootherin South America with only moderate increase recently. Africa has even smallervariance, 0.23, than for South America. Africa had cooler period between 1936-1948, but started warming after that. The recent warming in Africa started inthe beginning of 1980s. Oceania, which has largest variation in the anomalies forsouthern hemisphere continents (variance 0.50) had short warmer period in the1910s, and after that somewhat cooler until late 1950s. Oceania has had similarmoderate increase in temperature after that as South America.We have made a PCA for the yearly averaged temperature anomalies of the sixcontinents. Figure 3a,b and c show the three first PCs, which explain more than91% of total variance (PC1 explains 75.2 %, PC2 9.0 % and PC3 7.2 %). PC1 doesnot exhibit a strong ETCW phenomenon. After the initial increase, there is onlya small decrease from the 1940s until the late 1970s (and an increase thereafter).However, the ETCW is also partly included in PC3, which shows a clear increasefrom 1910s until 1950s, and a subsequent decrease until 1970s. There is also arecent decline of PC3, which makes PC3 to depict a quasi-periodicity of about60-70 years. It should be noted that PC3 is related to the linearly detrended AMOindex (Enfield, Mestas-Nu˜nez, and Trimble, 2001; Frajka-Williams, Beaulieu, andDuchez, 2017) with correlation coefficient 0.411 (p < − ). PC2 has a rather flattrend and mainly consists of short period fluctuations that are largest around 1940and 1990. PC2 is, however, related to the North Atlantic Oscillation index withcorrelation coefficient 0.478 (p < − ).Figure 3d shows the first three EOFs of the continental PCA. While EOF1depicts very similar values for all continents, EOF2 is largest (and positive) forEurope and second largest (but negative) for North America. It is evident thatPC2 mainly describes the short-term differences between these two continents(with smaller differences between other continents). EOF3 is far from zero onlyfor North America and Oceania, with opposite signs. The large positive EOF3means that North America has an enhanced temperature with respect to all othercontinents, especially Oceania, between 1930-1960. Accordingly, the ETCW phe-nomenon is mainly seen in the North America, and least for Oceania. For Oceaniathe negative EOF3 implies relatively higher temperatures in 1970-1980 with re-spect to other continents, which leads to an early start of the recent warming inOceania. The early start was also seen in South America, the only other conti-nent with a significant negative EOF3. The interconnection between the northern(North America) and southern (South America, Oceania) Pacific hemispheres de-picted by the oscillating PC3 is called the Interdecadal Pacific Oscillation (IPO)(Salinger, Renwick, and Mullan, 2001). We find that this interconnection oscillatesat the period of about 60-70 years, and may be related to Pacific Decadal Oscilla-tion (Mantua and Hare, 2002; Newman et al. , 2016), and to Atlantic MultidecadalOscillation (AMO) (Polyakov et al. , 2010; Schlesinger and Ramankutty, 1994).Figure 4a shows the PCA proxies (sums of PC1, PC2 and PC3) for the threenorthern continents and Figure 4b for the two southern hemisphere continents and Africa. The PCA proxies of NH continents have larger short-term fluctuations andrelative differences than the PCA proxies of SH continents, most likely reflectingthe larger fraction of oceans in the southern hemisphere. Note also that many largeshort-scale fluctuations are in opposite phase between North America and Eurasia(Europe and Asia), especially those around 1940, in 1980 and around 2010. These
Fig. 1
Monthly anomalies and anomaly profiles of the North America, Europe and Asia. Theblack dashed lines show the greatest changes in anomalies and vertical red lines show theaverage of the anomalies between change lines. (The anomaly profile in all figures is dividedby 40 to fit the same figure with anomalies themselves.)
Fig. 2
Same as Fig.1, but for South America, Africa and Oceania.
Fig. 3 a) PC1 b) PC2 and c) PC3 of the PCA of continental yearly temperature anomalies.d)The EOFs of the PC1, PC2 and PC3. are among the periods when the corresponding PC2 (see Fig. 3b) shows the largestvalues.Figure 5 shows the reverse arrangement tests of the trend for all the six con-tinents. It is obvious that the z-score of South-America diverges from the 99%confidence level already at about 1930. Moreover, the divergence after 1960 is ap-proximately linear in time with p-value decreasing much below 0.01. This meansthat in South-America the warming in the 1930s is part of a fairly systematicrise with no clear subsequent temperature decrease, nor ETCW. Another conti-nent, which differs from others in Figure 5 is Oceania. Its z-score starts decreasingaround 1960 but stays within p < .
01 until 1970s. This coincides with the timewhen the temperature in New Zealand started rising during 1960s (Salinger andGunn, 1975). Accordingly, no ETCW is observed in Oceania. The z-scores of theother continents behave quite similarly until about 1980 when Asia and Africadiverge conclusively below p < .
01, while Europe and North-America diverge onlyat about 1990. All these four continents depict a significant warming during theETCW. The maximum of ETCW is in the 1940s, but the exact timing and lengthof the ETCW varies between the continents.
Figures 6 and 7 show the monthly land temperature anomalies and their anomalyprofiles for four northern hemisphere and three southern hemisphere latitudinalzones 1910-2017, respectively. Since the anomaly profile depends on the selectedperiod, we limit the data period to 1910-2017 in order to better compare seasonalprofiles with continental profiles. We also show the five greatest changes in anoma- lies during 1910-2017 for each zone. It is evident that the more north (south) we gothe larger (smaller, respectively) is the total range of the anomaly profile. The totalvariances, however, increase when going further north or south from the equator.The variances are 0.194, 0.320, 1.143 and 1.585 for EQ-N24, N24-N44, N44-N64and N64-N90, respectively, and 0.161, 0.294 and 0.722 for S24-EQ, S44-S24 and Fig. 4 a) PCA proxies (PC1+PC2+PC3) for a) the northern b) southern hemisphere conti-nents in 1910-2017.
S64-S44, respectively. The ETCW is seen only in the northern hemisphere zonesand is strongest in the N64-90. This is the only zone, where anomaly is over theaverage of the whole period, i.e., above zero line between 1920-1955. However, inS64-S44 there was ETCW-like short warming period 1941-46. This zone is alsoexceptional such that consecutive changes of temperature are alternating up anddowns, and there is only a slight recent warming. The anomaly profile minimaare earlier in time, in the 1970s to early 1980s, for the southern zones, while theminima for the three northernmost zones are found some 10 years later.
Figure 8a, b and c show the first three PCs for the seven zonal yearly averagedanomalies over the whole extent 1880-2017, respectively. PC1 explains now 81.8 %,PC2 8.5 %, and PC3 4.7 % of the total variance. Note, that the ETCW is quite aweak and short maximum in PC1. However, both PC2 and PC3 include a fairlystrong ETCW evolution (we show also 21 year trapezoidal smoothed curves of PC2 Fig. 5 z-scores of the reverse arrangements for continental anomalies. (Note the reversedvertical axis). The 95 % (99 %) confidence limits are denoted by black (magenta) lines.
Fig. 6 a) NH zonal monthly anomalies and anomaly profiles with five greatest change-pointsof the anomaly.2
Fig. 7 a) SH zonal monthly anomalies and anomaly profiles with five greatest change-pointsof the anomaly. and PC3). Figure 8d shows the related EOFs. EOF1 has an almost equal powerin all zonal anomalies, only somewhat smaller for S64-S44. Zone S64-S44 has avery large negative value of EOF2, while zone N64-N90 has the largest positivevalue. It is clear that PC2 aims to characterize the difference between S64-S44from the other zones, in particular from the two northernmost zones. Similarly,PC3 takes into account the difference between the most poleward zones (on eitherhemisphere) and the equatorial (and low southern) zones. Note also that, becauseof the similar long-term variation of PC2 and PC3, the ETCW evolution is largelysuppressed for those zones whose EOF2 and EOF3 have opposite signs. This istrue for the southernmost zone and the two equatorial zones. As to the abovediscussion, it is no wonder that the correlation coefficients between zonal PC2 andAMO index is 0.380 (p=0.000049) and PC3 and SOI index is 0.479 (p < − ).Note, especially, that EOF3 is large negative for S44-S24, S24-EQ and EQ-N24.Figures 9a and 9b show the trend analysis for northern and southern hemi-sphere zones, respectively. We restricted the trend analysis again to the period1910-2017 so that it is comparable to the earlier trend analyzes. Note that, as forthe seasonal analysis, the ETCW is significant in all NH zones. In the two lower-latitude NH zones the ETCW warming continues as a significant increase until the recent warming. However, higher in the north the cooling after the ETCW islarger and the recent warming is delayed to start until about 1990. No significantwarming is found during the ETCW interval in the SH zones, although marginalwarming is seen in S24-EQ in the 1940s. Recent warming becomes significant inS24-EQ around 1960, in the two other SH zones in the 1970s. Fig. 8 a) PC1, b) PC2 and c) PC3 of zonal temperature anomalies. d) EOFs of zonal PC1,PC2 and PC3.
Fig. 9 z-scores of the reverse arrangement test for a) the northern b) the southern hemispherezonal temperatures. (Note reverse vertical axes.) The 95 % (99 %) confidence limits are denotedby black (magenta) lines.4
Fig. 10 a) Northern hemisphere seasonal anomalies and c) their profiles. b) Southern hemi-sphere seasonal anomalies and d) their profiles. Small vertical bars in c) and d) show theminimum years of the continental cumulative anomalies, also given in parenthesis in the leg-ends.
We have made a PC analysis for NH and SH seasonal land temperature anomalies.Figure 10 shows the temperature anomalies and anomaly profiles for each season,NH on panels a and c, and SH on panels b and d, respectively. Since the anomalyprofile depends on the selected period, we limit the data period to 1910-2017 inorder to better compare seasonal profiles with continental profiles. (We do nottry to find change-points here, because we have, of course, only yearly data forseasons, and consequently the resolution is too sparse to make reliable analysis).Figure 10 shows that most seasonal anomalies of the southern hemisphere reachtheir minima at about 1970, about ten years earlier than most of the northernhemisphere seasons. As for the above presented PCA of continents, this is mainlydue to the ETCW and subsequent cooling period in the NH, which delays the startof the recent warming in the northern hemisphere. Note also that the NH seasonsdiffer considerably from each other with ETCW being more strongly present inthe summer and fall seasons of the NH.Figure 11a shows the three leading PCs for the seasonal temperature anomaliesusing the full length of seasonal data in 1880-2017. PC1 accounts for as much as86.6%, PC2 4.9% and PC3 2.4% of the total variance. The high percentage of PC1means that all eight seasonal anomalies follow quite a similar temporal evolutionof PC1, where temperature rises systematically from 1880 to a weak maximum of the ETCW around 1940, with only a short subsequent decrease lasting until thelate 1950s. PC2 again describes the different fraction of ETCW in the differentseasons. Figure 11b shows the corresponding EOFs with NH and SH EOF2s havingopposite signs. The highest positive EOF2 is found in NH fall, while the other threeseasons in the SH have the largest negative EOF2s. That is why it is not surprising Fig. 11 a) PC1, PC2 and PC3 of the hemispheric seasonal anomaly PCA. b) CorrespondingEOF1, EOF2 and EOF3. that PC2 is correlated with linearly detrended AMO index with coefficient 0.557( p < − ).Seasonal anomaly PC3 accounts only for 2.4% of the variance of seasonalanomalies. Note that the corresponding EOF3 is highly positive during both northand south DJF. Although PC3 looks quite noisy, it correlates significantly withwintertime (DJF) NINO34 with coefficient 0.358 (p=0.00015). The correlationwith spring (MAM) NINO34 component is still 0.246 (p=0.011), but for otherseasons insignificant. This reminds us about the origin of naming El Ni˜no phe-nomenon, which was first noticed in winter and called ”El Ni˜no de Navidad”(Christmas Child) by the fishermen (Winchester, 2017).Figures 12a and 12b show the seasonal z-scores of the reverse arrangementstest for northern and southern hemisphere, respectively. Note the significance ofthe ETCW for all seasons in the northern hemisphere. The NH z-scores move out of the p=0.01 limit in the 1920s to 1930s. In most NH seasons the ETCWcontinues as a significant rise until the recent warming. However, in NH fall thetemperature decreases relatively more after the ETCW, and the recent warmingstarts only in the 1990s (as a significant trend). The z-scores in the SH decreasefairly systemically since 1930s but remain random (within p=0.01) until the late Fig. 12 z-scores of the reverse arrangements for a) the northern b) the southern hemisphereseasons. (Note reverse vertical axes). The 95 % (99 %) confidence limits are denoted by black(magenta) lines.
We have used the principal component analysis, reverse arrangement (RA) trendtest and anomaly profiles to study land temperature anomalies from 1880 onwards.The RA trend test is, as far as we know, used the for the first time in temperatureanalysis. Also combining anomaly profile (cumsum), with change-points analysisclarifies the temperature evolution remarkably.The principal component analysis of the yearly temperature anomalies of thesix continents reveals that the continents depict the ETCW very differently. PC1,which explains 75.2 % of inter-annual variability includes warming from 1910s to to 1940s, but a very modest cooling thereafter and a notable recent warming sincethe 1970s. PC2, which includes 9.0 % of the variance between the continents, and isrelated to NAO index, includes no trend and describes mainly the short-term fluc-tuations which are in opposite phase between North America and Eurasia (Europeand Asia), especially around 1940 and around 1990. The different appearance of the ETCW in the six continents is mainly included in PC3, which describes 7.2 %of variance, and is highly correlated with detrended AMO index.Trend analysis shows that there is a significant ETCW warming in all othercontinents except for Oceania. However, there are differences in the start timeand duration of significant warming and the ETCW maximum between thesefive continents. Most of them have their ETCW maximum in the 1940s. TheEOF3 of Oceania is strongly negative, and its evolution in the early 1900s wasalmost opposite to ETCW with a decrease of temperature from the early centuryto a minimum in the 1940s and 1950s. In four ETCW continents (Africa, Asia,Europe and North America) the cooling after the ETCW was strong enough toconsiderably delay the start of recent warming. Recent warming started in NorthAmerica in the late 1980s and in Europe only around 1990. In South Americathere is little cooling before the ETCW, and surprisingly warming is systematicallysignificant since the start of the ETCW around 1930. As far as we know, this slowbut continuous rise in the temperature of South America has not been reportedearlier. We also find that PC3, and thereby the ETCW phenomenon, depict a60-70-year oscillation, which is related, at least, to AMO. If the AMO index isdecreasing after present maximum, PC3 can be used to forecast that there will bea slight cooling in the Northern hemisphere continents, especially North America.Note, however, that PC3 accounts only about 7% of the whole variation of theanomalies.The principal component analysis of the temperature anomalies of seven lati-tude zonal regions (we leave out Antarctica) shows that, as for seasonal data, thePC1 (about 81.8 % of variance) depicts fairly systematic warming throughout thestudied time interval, with a weak ETCW maximum around 1940 and only a weakcooling thereafter until 1970s. However, both PC2 (about 8.7% of variance) andPC3 (about 4.7% of variance) include a fairly similar, roughly in-phase evolution.PC2 and PC3 mainly deviate in their different short-term variation. According thethe EOF2 and EOF3, the ETCW warming is strongest in the two northernmostzones (N44-N64 and N64-N90).Trend analysis shows that most NH zones have the ETCW maximum in 1940s,but have mutual differences in the start time and duration of significant warmingand the level of cooling after the ETCW. The southern zones depict no significantETCW warming, only marginally significant warming in the equatormost zone(S24-EQ), and a short warming period in S64-S44 during the first half on 1940s.In fact, the southernmost zone (S64-S44) seems to have a cooling phase during theETCW period, but the trend analysis shows that this is only marginally significant(at p < . We also studied the hemispheric temperature anomalies during four seasons(winter, spring, summer, and fall). The high percentage of PC1 (about 86.6 % ofvariance) for hemispheric seasons means that all eight seasonal anomalies followquite a similar temporal evolution. However, the eight seasons are divided byPC2 (about 4.9 % of variance) into the four northern hemisphere seasons with Fig. 13
The PC1s of continental, zonal and seasonal anomaly PC analyzes. Magenta linesshow the average linear trends and vertical dashed lines the change-points. positive EOF2 and for southern hemisphere seasons with negative EOF2. PC2 ishighly correlated with detrended AMO index, at least in the period 1910-2017,and includes not only the ETCW phenomenon and the subsequent cooling, whichends in the 1970s, but also an earlier warming at the end of 19th century and acooling in the beginning of 20th century.The PC2 type evolution is strongest inNH fall season and less strong in all other NH seasons.In trend analysis all NH seasons also depict a significant ETCW warming.While most NH seasons have the ETCW maximum in the 1940s, there are mutualdifferences in the timing of ETCW and level of subsequent cooling. No SH sea-son depict significant warming during the ETCW period. In 1950s a systematicincrease in all SH seasons starts, which becomes significant in the late 1950s forspring and summer and in the late 1960s for fall and winter. In the NH the startof final warming is delayed until 1990s for NH fall, and 1970s for other seasons.Although we have studied the global temperature evolution during 20th cen-tury in three different PCA analysis, there is almost common PC1 for all analyzes(see Fig. 13). It is evident, that the overall development of the anomalies are verysimilar. (Here we use PC analyzes for zonal 1910-2017 and seasonal 1910-2017data). All the PC1s show slight warming towards the end of 1940s, a period of de-cline in anomalies until second half of 1950s, a rather flat interval until second halfof 1970s, and a steep rise after that. There are some minima, which are deeper inthe continental PC1. These are, e.g., years 1956-57 and 1984-85, when there wereextremely cold winters, at least, in Europe (Twardosz and Kossowska-Cezak, 2016;Dizerens et al. , 2017). These events are smoothed out in the zonal and seasonalPC analyzes. Notice, however, that the continental PC1 explains only 75.2 % of the variation of the data, while zonal and seasonal PC1s explain 81.7 % and 87.6% of the corresponding data, respectively.
Acknowledgements
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