Warming Amplification of Minimum and Maximum Temperatures over High-Elevation Regions across the Globe

An analysis of the annual mean temperature (TMEAN) (1961–2010) has revealed that warming amplification (altitudinal amplification and regional amplification) is a common feature of major high-elevation regions across the globe against the background of global warming since the mid-20th century. In this study, the authors further examine whether this holds for annual mean minimum temperature (TMIN) and annual mean maximum temperature (TMAX) (1961–2010) on a global scale. The extraction method of warming component of altitude, and the paired region comparison method were used in this study. Results show that a significant altitudinal amplification trend in TMIN (TMAX) is detected in all (four) of the six high-elevation regions tested, and the average magnitude of altitudinal amplification trend for TMIN (TMAX) [0.306±0.086 °C km-1(0.154±0.213 °C km-1)] is substantially larger (smaller) than TMEAN (0.230±0.073 °C km-1) during the period 1961–2010. For the five paired high- and low-elevation regions available, regional amplification is detected in the four high-elevation regions for TMIN and TMAX (respectively or as a whole). Qualitatively, highly (largely) consistent results are observed for TMIN (TMAX) compared with those for TMEAN.

In the latest study, based on a dataset of annual mean temperature (T MEAN ) series  from 2367 stations around the world, Wang et al. [19] revealed that warming amplification (altitudinal amplification and regional amplification) is a common feature of major highelevation regions across the globe against the background of global warming since the mid-20th century. These authors reached this conclusion by developing the altitudinal warming component extraction equation (AWCE equation), and employing the paired region comparison method. In this study, we further examine whether this holds for annual mean minimum temperature (T MIN ) and annual mean maximum temperature (T MAX ).

Data
This study used a dataset of 1,494 T MIN and 1,448 T MAX station series  around the world (Fig 1). Of all the stations, 1334 are the same stations, representing 89.3% (92.1%) of the total T MIN (T MAX ) stations ; and 652 (641) T MIN (T MAX ) stations are sited at the six high-elevation regions tested (Fig 2), of which 636 are the same stations, representing 97.5% (99.2%) of the total high-elevation region T MIN (T MAX ) stations.
The data were compiled from 6 sources: the Global Historical Climatology Network Monthly (GHCNM) version 3.2.0dataset [20]; the National Meteorological Information Center of China (NMICC); MeteoSwiss; the Latin American Climate Assessment and dataset (LACAD) [21]; the European Climate Assessment & Dataset (ECA&D) [22]; and the National Weather Service of Chile (NWSC). The data for the GHCNM, NMICC, ECA&D and NWSC were available for the entire period 1961-2010, while the data for the LACAD were available for the period 1961-2006.
To obtain the annual time series from the daily minimum and maximum temperatures from the ECA&D and NWSC, two steps (or two criteria) were required. A monthly mean value was first calculated for the available days if no more than 3 days of data were missing in that month; then, an annual mean value was computed from the monthly means if 12 monthly values were present in that year. For the monthly data from other sources, the annual time series was calculated using the second criterion. After the establishment of the T MIN and T MAX series , the series that had at least37yearsof complete data (i.e., 12 months per year) were selected for homogeneity testing using RHtests V3 [23]. The series that had obvious inhomogeneity were excluded. However, the series from the LACAD with at least 30 years of complete data were also included in the homogeneity test because the source dataset ended in 2006, the available stations in the Andes were very sparse, and no other data are available at present. The final dataset consisted of 909 (874), 459 (459), 58 (53), 36 (33),17 (17) and 15 (12)T MIN (T MAX ) stations from the GHCNM; NMICC, MeteoSwiss, LACAD, ECA&D and NWSC, respectively, with 37, 41, 37, 30, 41and 40yearsof complete data, respectively.

2.2.1
Test of temperature trend. The trend for a station (or a region as a whole) was extracted from the anomalies (relative to the 1961-1990 mean) using the Mann-Kendall method [24][25]. The trend slope was estimated using Sen's method [26] and the trend significance was determined using the Mann-Kendall test [24][25] with an iterative procedure [27].
2.2.2 Test of altitudinal amplification. The methodology for evaluation of the altitudinal amplification trend for T MIN (T MAX ) within a high-elevation region was exactly the same as for T MEAN in the previous study [19], consisting of the following four steps: 1. Transformation of altitude (in meter), latitude (in degree) and longitude (in degree) into ALT, LAT and LONG (all in km) for each station using the following equations, LAT ¼ latitude Â 111:317; ð2Þ where 111.317 (expressed in km) is the distance constant per degree of latitude, and R is the radius of the Earth. Because the distance between two degrees of longitude changes with latitude, eq (3) is necessary.
2. Estimation of the effect coefficients of altitude, latitude and longitude (EC ALT , EC LAT and EC LONG , respectively) on a regional scale using stepwise regression. This procedure was performed with the model of fit y = b 1 x 1 + b 2 x 2 +b 3 x 3 + c, where the long-term (1961-2010) average T MIN and T MAX values (T AVG in general,°C) and the ALT, LAT and LONG values of the individual stations within a region were taken as the dependent (y) and independent variables (x 1 , x 2 , and x 3 ), respectively. The negative values of the regression coefficients (b 1 , b 2 andb 3 ) estimated for ALT, LAT and LONG (i.e., the temperature lapse rates along the altitudinal, latitudinal and longitudinal gradients) were taken as EC ALT , EC LAT and EC LONG , respectively. When an independent variable was not introduced (i.e., the partial correlation coefficient for it was not significant at the 0.05 level), its effect coefficient was considered to be zero.
3. Extraction of the warming component of altitude (Q ALT ) from the station warming rate (Q TOTAL ) for each station within a high-elevation region using the following equation, where Q TOTAL in T MIN and T MAX is expressed in°C 50-yrs -1 , and ALT, LAT and LONG are all expressed in km for each station, and EC ALT , EC LAT and EC LONG are constant values for every station within the region, and are expressed in°C km -1 . The result, Q ALT , is also expressed in°C 50-yrs -1 .
4. Test of the altitudinal amplification trend for each region. Based on the Q ALT values extracted from the individual stations, the altitudinal amplification trend was evaluated by regressing Q ALT against ALT to obtain the amplification factor (Q ALTAMP , in°C km -1 50-yrs -1 ) over the period 1961-2010.
Besides, if assuming that the temperature change in a high-elevation region is predominately controlled by altitude and latitude, then the EC ALT , and EC LAT will be estimated using the model of fit y = b 1 x 1 + b 2 x 2 + c, where the long-term average T MEAN (T MIN or T MAX ; in°C), and the ALT and LAT at individual stations within the region will be used as the dependent (y) and independent variables (x 1 and x 2 ), respectively. The negative values of b 1 and b 2 will be taken as the EC ALT and EC LAT , respectively. The extraction of Q ALT from Q TOTAL for each station is conducted either using eq (4), where the EC LONG is assumed to be zero, or using the following equation: Furthermore, if assuming that the temperature change in a high-elevation region is only controlled by altitude (both EC LAT and EC LONG are considered to be zero), Q ALT will be equal to Q TOTAL , It is clear that this equation is a special case of eq (4) or eq (5). 2.2.3 Test of regional amplification. The regional amplification was tested using the paired-region comparison method [19]. Each of the paired high and lower elevation regions were selected using a method similar to the belt transect method. Each paired regions are located at the same latitudes, and has the equal longitude range. The sampled area is a northeast-southwest parallelogram for the Appalachian Mountains, and its west low-lying counterpart (Table 1).
However, the regional amplification was not only evaluated for T MIN and T MAX as for T MEAN [19], but also for T MIN and T MAX as a whole. (1) The regional amplification was evaluated for T MIN and T MAX separately when a similar asymmetric warming in T MIN and T MAX occurs between one paired regions; that is, the magnitude of the trend is greater for T MIN than T MAX (or for T MAX than T MIN ) in both high-and low-elevation regions. (2) The regional amplification was evaluated for T MIN and T MAX as a whole (the average magnitude of T MIN and T MAX trends was used for comparison) when an opposite asymmetric warming in T MIN and T MAX occurs between one paired regions; that is, the magnitude of the trend is greater for T MIN than T MAX in one region, whereas the magnitude of the trend is greater for T MAX than T MIN in its counterpart. In this situation, the separate analysis of regional amplification for T MIN and T MAX would not only make the difference in T MIN or T MAX (or both) appear very large between the paired regions, but would also make the warming in T MIN or T MAX look even weaker at times for the high-elevation region than its lower counterpart, and vice versa, even if the average warming (the magnitude of the T MEAN trend) is greater in the high-elevation region than its lower counterpart.

Altitudinal amplification
Figs 3 and 4 depict the relationship between the altitudinal warming components (Q ALT s) and station altitudes within each high-elevation region for T MIN and T MAX , respectively. A significant altitude amplification trend in T MIN is detected in all the high-elevation regions tested (the Tibetan Plateau, Loess Plateau, Yunnan-Guizhou Plateau, Alps, US Rocky Mountains, and Appalachian Mountains), whereas a significant or a marginally significant altitude amplification trend in T MAX is observed in four of the high-elevation regions (significant: the Yunnan- Guizhou Plateau, Alps, and Appalachian Mountains; marginally significant: the Tibetan Plateau). No altitudinal amplification in T MAX is detected in the Loess Plateau, and US Rocky Mountains.
In the regions where altitudinal amplification trends have been confirmed for T MIN and T MAX , the magnitudes of the amplification trends are generally greater for T MIN than for T MAX ( Table 2). If the magnitude of the altitudinal amplification trend is taken as zero when no altitudinal amplification trend is detected, the average magnitude of altitudinal amplification trends for the six regions is 0.306 ± 0.086°C km -1 50-yrs -1 and 0.154 ± 0.213°C km -1 50-yrs -1 for T MIN and T MAX , respectively. This indicates a remarkable asymmetry in the altitudinal amplification between T MIN and T MAX . The average magnitude of amplification trends is 0.33 times greater for T MIN but 0.33 times smaller for T MAX compared with the magnitude for T MEAN (0.230 ± 0.073°C km -1 ) during the period 1961-2010.
Similar results are obtained (Table 3) provided that temperature change in high-elevation regions is predominately controlled by two variables (altitude and latitude) rather than three variables (altitude, latitude and longitude). The average magnitude of the altitudinal amplification trends for the six regions is0.300 ±0.089°C km -1 50-yrs -1 and 0.155±0.212°C km -1 50-yrs -1 for T MIN and T MAX , respectively;0.32 times greater for T MIN but 0.32 times smaller for T MAX compared with that (0.228 ±0.069°C km -1 ) for T MEAN during the same period. This indicates that the longitude effect, though significant in three of the regions tested, is almost negligible in quantifying the altitudinal amplification trends in high-elevation regions.
However, if assuming that temperature change in high-elevation regions is only controlled by altitude, contrasting results are obtained for T MEAN [19], T MIN and T MAX ( Table 4). The differing results for T MEAN , T MIN and T MAX among the high-elevation regions could be attributed to the difference in signal intensity of the Q TOTAL values [28] and the region-specific interactions between altitude and latitude [19]in the individual regions (see the 'Discussion'section for details).

Regional amplification
Figs 5 and 6 depict the monotonic trends  in the paired regions for T MIN and T MAX , respectively. Among the five paired regions, the magnitude of the T MAX trend is larger than the T MIN trend for the Alps and its low-lying counterpart, whereas the magnitude of the T MIN trend is larger than the T MAX trend for the Appalachian Mountains and its low-lying counterpart. Despite this difference between these two paired regions, similar asymmetric warming is detected in each paired regions. It is clear that greater warming is only observed in T MIN for the Alps than its east low-lying counterpart, whereas greater warming is detected in both T MIN and T MAX in the Appalachian Mountains than in its low-lying counterpart.
For other three paired regions, opposite asymmetric warming is observed between each paired regions. The magnitude of the T MIN trend is larger than the T MAX trend on the Northern Tibetan Plateau, whereas the magnitude of the T MIN trend is smaller than that of the T MAX trend in its eastern lower-elevation counterpart (the sampled Loess Plateau). The magnitude of the T MIN trend is smaller than that of the T MAX trend in the East Loess Plateau and the Southeast Rocky Mountains, whereas the T MIN trend is larger than the T MAX trend in their low-lying counterparts (the North China Plain and the eastern low-lying region, respectively). When the regional amplification is estimated for T MIN and T MAX as a whole, the warming is greater on the North Tibetan Plateau than the sampled Loess Plateau (2.26 versus 1.60°C)and in the Southeast Rocky Mountains than its eastern low-lying region (1.54 versus 1.05°C) during 1961-2010. Greater warming also occurred in the East Loess Plateau than on the North China Plain (1.53 versus 1.42°C) during the same period.

Discussion
Many factors might have played a role in shaping the patterns of temperature change in highelevation regions across the globe. However, it is worth noting that these factors might have distinct effects in terms of their magnitudes and directions, and can be defined as basic and non-basic factors in terms of their relative status in the complex interaction hierarchy.
Barry [2] stated that climate in mountain regions is controlled by four basic factors: altitude, latitude, continentality, and topography. A previous study has shown that altitude and latitude are major factors in determining the geographical pattern of temperature change in the Alps [12]. Notably, the effect of energy balance variation on surface temperature was found to be amplified with decreasing temperature in the environment as a result of the functional shape of the Stefan-Boltzmann law [29][30]. Provided that this energy balance effect is a fundamental theoretical basis on warming amplification under lower temperature rather than a partial explanation of larger temperature trends in polar and high-altitude climate [29][30], because the higher the altitude (latitude), the lower the temperature [2], the magnitudes of station temperature trends across a high-elevation region will be closely related to both ALT and LAT. Furthermore, provided that there is a clear temperature gradient with longitude due to continentality, then this will remain true for LONG as well. It is based on these observations and deductions that Wang et al. [19] have developed the altitudinal warming component extraction equation (AWCE equation). In fact, a significant negative relationship between T AVG and ALT, LAT and LONG (between T AVG and ALT and LAT) was detected for three (five) of the eight high-elevation regions tested [19]. A significant altitudinal amplification trend in T MEAN was detected in each region by extracting Q ALT from Q TOTAL at the individual stations in each region using the AWCE equation [19]. Because the same holds good for T MIN and T MAX for the regions where a significant negative relationship exists between T AVG and ALT, LAT and LONG or between T AVG and ALT and LAT, significant altitudinal amplification trends are detected for T MIN and T MAX in four regions, consistent with the T MEAN results from these regions. In the Loess Plateau and the US Rocky Mountain regions, significant altitudinal amplification trends are detected for T MIN , Quantitatively, the asymmetric altitudinal amplification trends in T MIN and T MAX are consistent with the regional temperature trends in T MIN and T MAX for all the regions, with the exception of the US Rocky Mountains ( Table 2). The elevation-dependent warming in minimum temperatures on and around the Tibetan Plateau has been demonstrated by plotting the trends at individual elevation bands versus elevation in the previous studies [11,14]. In contrast, You et al. [13] failed to substantiate altitudinal amplification trends in most temperature extreme indices derived from daily minimum and maximum temperatures in the eastern and central Tibetan Plateau.
The asymmetric changes in T MIN and T MAX have been reported for a number of large regional series [31][32] and for certain high-elevation regions [15,[33][34][35][36]. A stronger warming Table 4. Relationships between station warming rates (Q TOTAL ,°C 50-yrs -1 ) and station altitudes (km) in the high-elevation regions across the globe. given with the two-tailed p value for each case. Significant trends (at the 0.05 level) are set in bold, with the marginally significant ones (at the 0.10 level) in italic bold. The results for annual mean temperature are cited from Wang et al. [19]. doi:10.1371/journal.pone.0140213.t004 Warming of Minimum (Maximum) Temperatures over High-Elevation Regions for T MIN than T MAX has been observed in the Tibetan Plateau [35][36], the eastern Loess Plateau [37] and the stations located in different elevation ranges in the latitudinal bands 30°N-70°N [34]. Greater warming has been observed in T MIN than T MAX in the Swiss Alps over the period1901-1992 [33], whereas similar changes in the minimum and maximum temperatures have been detected in the mountainous regions of Central Europe over the period1901-1990 [17]. The greater warming for T MAX than T MIN observed in this study indicates a shift from stronger warming in T MIN to stronger warming in T MAX for the Alps during 1961-2010. Moreover, McGuire et al. [15] found significant warming in T MAX but not in T MIN in the Rocky Mountain Front Range during 1953-2008. The presence of a cooling signal in T MIN along the Front Range [15] and the weaker warming for T MIN than T MAX for the entire US Rocky Mountain region observed in the current study are likely related to changes in regional and local land-use practices [15] and possible changes in atmospheric circulation [38]. In terms of the longitude effect, it is difficult to interpret the meaning of EC LONG except for the above deduction. Nevertheless, similar results are observed for T MEAN , T MIN and T MAX in the high-elevation regions tested (Table 3) when two variables (altitude and latitude) are considered instead of three variables (altitude, latitude and longitude). This indicates that the altitudinal amplification trend in a high-elevation region can be well approximated when these two basic variables are taken into account.
Why is Q ALT so different from Q TOTAL when they are each regressed against ALT? First, this is due to Q TOTAL s being predominately controlled by both altitude and latitude over a high-elevation region, while Q ALT s are associated only with altitude, as the name suggests. Consequently, the correlation between Q TOTAL and ALT can be reduced by a huge amount of noise, whereas no noise affects the correlation between Q ALT and ALT. Relative to the effect (signal) of the target independent variable (ALT), the effect of the non-target independent variable (LAT), as well as the interacting effect of LAT and ALT, should be considered noise in the statistical analysis. Second, the magnitude of the noise impact on the correlation between Q TO-TAL and ALT varies from region to region, depending on the signal intensity (SI) of Q TOTAL in individual regions. According to the SI concept [28], the Q TOTAL SI (signal quantity per unit area) in a region is approximately proportional to the number of available stations in a region and is inversely proportional to the total area of the region. It is probably due to the very high Q TOTAL SI for the Loess Plateau, the Yunnan-Guizhou Plateau, and the US Rockies, but very low Q TOTAL SI for the Tibetan Plateau and the Appalachian Mountains, that a significant correlation between Q TOTAL and ALT is detected for the former, but not for the latter in terms of T MEAN ( Table 4). The same holds true for T MIN , excepting that a positive but non-significant correlation between Q TOTAL and ALT is observed for the Loess Plateau (Table 4).
Furthermore, the contrasting correlations between Q TOTAL and ALT among these regions (particularly between the two sub-regions of the Tibetan Plateau) could be partly attributable to the effect of topography (the underlying feature of the available stations)on them. As revealed in a previous study [19], the underlying topography of the available stations in the Northern Tibetan Plateau (NTP) is characterized by a significant negative spatial correlation between the station altitudes and station latitudes (SCOALLA), whereas no significant negative SCOALLA occurs in the Southern Tibetan Plateau (STP); indicating that the altitude effect could be cancelled out (or overwhelmed) by the latitude effect in the NTP while not in the STP [19]. Therefore, the correlation between Q TOTAL and ALT is non-significant (negatively significant) for T MEAN and T MIN (T MAX ) over the NTP, while the correlation between Q TOTAL and ALT is positively significant (marginally significant) for T MEAN and T MIN (T MAX ) over the STP (Table 4). Owing to that, the correlation between Q TOTAL and ALT for the entire Tibetan Plateau is a reflection of those two sub-regions, and the number of stations from the NTP is obviously larger than that from the STP, the correlation between Q TOTAL and ALT for the entire Tibetan Plateau is closer to that of the NTP rather than the STP (Table 4).
In addition, it should be noted that although the negative SCOALLA has no direct influence on the correlation between Q ALT and ALT, it may more or less affect the long-term average values of T MEAN , T MIN and T MAX , and consequently the EC ALT and EC LAT . This, in turn, could have affected the magnitudes of Q ALT s, and therefore the relationship between Q ALT and ALT. It is probably due to this indirect influence that the magnitudes of altitudinal amplification trends appear underestimated for the Tibetan Plateau and the Northern Tibetan Plateau relative to the Southern Tibetan Plateau (Table 2). However, the topographical effect is difficult to quantify, and this effect can only be taken as noise relative to the direct effects of altitude and latitude. Hence it is not taken into account in the quantitative estimation of Q ALT s.
For comparative purpose, the global base EC ALT and EC LAT were also estimated for T MIN and T MAX . The base EC ALT and EC LAT were computed according to the data from all the high (!200 m above sea level) and low (<200 m above sea level) elevation stations, respectively, for either index using the same method as for T MEAN [19]. The result shows that the global base EC ALT values in T MEAN , T MIN and T MAX (4.9±0.9, 5.0±1.2and 3.1±2.8°C km -1 , respectively) are smaller than the average EC ALT values in T MEAN , T MIN and T MAX (5.3±0.8, 5.4±0.9 and 3.9±3.2°C km -1 , respectively) for the six high-elevation regions, and the global base EC LAT values in T MEAN , T MIN and T MAX (0.0049±0.0037, 0.0045 ±0.0028, and 0.0048 ±0.0036°C km -1 , respectively) are clearly smaller than the average EC LAT values in T MEAN , T MIN and T MAX (0.0074 ±0.0020, 0.0074±0.0016, and 0.0050±0.0044°Ckm -1 , respectively) for these regions. This suggests that there exists not only an enhanced EC ALT but also an enhanced EC LAT in the high-elevation regions. Therefore, a greater warming usually occurs in high-elevation regions relative to their lower elevation counterparts.
The slightly greater warming in T MIN and even weaker warming in T MAX in the Alps relative to its low-lying counterpart are likely associated with the greater urban heat effect in the lowelevation area because the urban heat effect is generally greater at low-elevation sites [9,17]. On the other hand, the unusually stronger warming in T MIN relative to T MAX over the North China Plain could have partially resulted from the unusually large urban heat effect on T MIN relative to T MAX . The urban heat effect is primarily a nocturnal phenomenon in certain places around the world [39][40]. The North China Plain may be one such place. The large difference between changes in T MIN and T MAX between the East Loess Plateau and the North China Plain is also likely related to the barrier effect of the Taihang Mountains, which run from north to south in North China, forming a natural boundary between the paired regions and a physical barrier to the southeast summer monsoon in China. In fact, the trends in various precipitation indices also differ between the East Loess Plateau and the North China Plain due to this barrier effect. For instance, Fan et al. [37] observed a significant decreasing trend (-15.05mm 50-yrs -1 ) in annual total precipitation on wet days (PRCPTOT) over the entire Shanxi Province, whereas a non-significant trend was observed in PRCPTOT over the northern half of the North China Plain. These two regions are nearly equivalent to the East Loess Plateau and North China Plain in this study.
Considerable seasonal variations in trend magnitude have been observed [11,14,30,38]. The warming amplifications in high-elevation regions may vary greatly on sub-annual scales due to changes in atmospheric circulation and local processes, such as snow albedo and water vapor feedbacks [38,41]. An improved understanding of altitudinal amplification on subannual scales may have more important bearings on societal, ecological and physical systems in high-elevation regions. Therefore it is of great important to characterize the seasonal and monthly pictures of warming amplification of T MEAN , T MIN and T MAX on a global scale.

Conclusions
In this study, analysis of T MIN and T MAX series (1961-2010) show a significant altitudinal amplification trend in T MIN (T MAX ) in six (four) of the high-elevation regions tested. The average magnitude of altitudinal amplification trends for the six high-elevation regions is substantially larger (smaller) for T MIN (T MAX ) [0.306±0.086°C km -1 (0.154±0.213°C km -1 )] than T MEAN (0.230±0.073°C km -1 ) in the period 1961-2010. Similar results are obtained when the effects of two variables (altitude and latitude) are considered instead of three variables (altitude, latitude and longitude). For the five paired high-and low-elevation regions available, regional amplification is detected in four high-elevation regions for T MIN and T MAX (respectively or as a whole), whereas it is only observed for T MIN in the fifth high-elevation region. Qualitatively, highly (largely) consistent results are observed for T MIN (T MAX ) compared with those for T MEAN . The results for T MIN (T MAX ) are basically in conformity with our expectations. These results confirm the effectiveness of the AWCE equation in quantifying altitudinal amplification trend within a high-elevation region. Future study is required to explore the seasonal and monthly patterns of warming amplification trends in T MEAN , T MIN and T MAX on a global scale.