The coupled climate model outputs are taken from the CMIP5 multi-model data archive (http://cmip-pcmdi.llnl.gov/cmip5/index.html). In this study, the main focus is on 20th century historical experiments [ 13] and on the projection experiments under the representative concentration pathway (RCP) 4.5 and 8.5 scenarios [ 14] with the base period 1961-1990. RCP4.5 and RCP8.5 are defined such that the radiative forcing will reach about 4.5 W·m^-2 and 8.5 W·m^-2, respectively, by the year 2100. From the archive, we use monthly surface air temperature (SAT) data from 15 coupled models with one initial condition realization (r1i1p1) (Table 1). The models are primarily selected based on data availability, model diversity, and their performances in temporal variability, long-term trend, multidecadal variations, and trends of global annual mean SATa (figures not shown).

For model validation, we used one set of reanalysis monthly data from the Met Office Hadley Centre and the University of East Anglia’s Climatic Research Unit, which comprises combined land and sea surface temperature, version 4 (HadCRUT4) [ 5], with a horizontal resolution of 5° × 5°. The dataset covers the period 1900-2013.

In order to avoid influence from missing data or some singular points to linear fitting, a method of regression coefficients has been proposed, called Sen’s slope estimator [ 15]. In this study, the linear trend and the corresponding confidence interval are calculated by Sen’s estimator. In addition, the nonparametric Mann-Kendall test is used to assess the significance of the linear trend [ 16].

Fig. 1 shows the temporal evolutions and trends of annual mean SATa for the globe, NH and SH, hemispheric land, and hemispheric ocean during the 1900-2013 period. All hemispheric-scale annual mean SATa show a long-term warming with multidecadal variations, as well as larger interannual variations from the global mean. In recent years, SATa increase more in the NH than the globe, and less in the SH than the globe, and show more warming over land than over ocean [ 11]. In addition, the long-term trend magnitude over NH land is greater than that over SH land. Similarly, the long-term trend magnitude over NH ocean is greater than that over SH ocean. Based on the multidecadal transit years in global annual mean SATa, the multidecadal variations are divided into two warming periods (1900-1944 and 1971-2000) with significant increasing trends and two hiatus periods (1945-1970 and 2001-2013) with weaker trends, as shown in Fig. 1(g). Compared to the global mean, similar multidecadal variations over NH land as well as over NH and SH oceans are found, but with different trend magnitudes. However, SATa over SH land show an increasing trend (0.06 °C·decade^-1) during the 1945-1970 period, which is different from the global trend and from other hemispheric scales (Table 2). Among NH land and NH and SH oceans, changes in trend magnitudes over NH land are the largest during the four periods. The trend over NH land is 0.3 °C·decade^-1 during the 1971-2000 period, and decreases to 0.05 °C·decade^-1 during the 2001-2013 period, indicating the warming hiatus in the latter period.

Annual mean SATa over the global and hemispheric scales from the 15 CMIP5 models and the MME are shown in Fig. 2. The model results present a large spread. The MME SATa over the global and hemispheric means are comparable to historical observations, but have smaller interannual variations, as shown in Fig. 2(a)-(g). The multidecadal trends in the global mean SATa of MME during the first three periods further indicate that the models are basically capable of reproducing the temporal shape for the global mean, as shown in Fig. 2(h)-(k); this result is consistent with previous research [ 11]. For hemispheric scale, the multidecadal variations can also be basically reproduced by the models, except for SH land, where the modeled SATa show a decreasing trend during the 1945-1970 period, as shown in Fig. 2(j). In addition, most hemispheric scales show a trend within the 95% confidence level of the observed trend during the two warming periods (1900-1944 and 1971-2000), except for NH and SH oceans, as shown in Fig. 2(i) and (k). It is seen that the trend magnitudes over the NH and SH oceans are less than the observed magnitudes during the 1900-1944 period, resulting in the underestimation of modeled long-term trends over the SH and the globe, as shown in Fig. 2(h). In addition, Jones et al. [ 11] pointed out that many models could capture the multidecadal variations in global mean SATa, and further evaluated the global trends during the 1901-2010, 1901-1950, 1951-2010, and 1979-2010 periods. By contrast, it is found that oceans in which the trend magnitudes are underestimated mainly concentrate in the northern Pacific and Atlantic during the 1900-1944 period, and oceans in which the trend magnitudes are overestimated are mainly located in the SH tropical Pacific and Southern Ocean during the 1971-2000 period. In addition to the warming periods, the characteristics of trends at the hemispheric scale are also analyzed during the hiatus period (1945-1970), and an interesting feature is found. Warming encompasses the SH land, a finding that is not simulated by the models.

Based on the above evaluation of multidecadal trends in large-scale annual mean SATa, it is found that the models can basically reproduce the multidecadal variations in SATa during the 1900-2005 period. Furthermore, global mean SATa show a hiatus since the 21th century [ 3, 4]. How do the models project variations in SATa at global and hemispheric scales during this hiatus period? To answer this question, we will project the hemispheric SATa under the medium-low emissions scenario of RCP4.5 and the high emissions scenario of RCP8.5. The future projection datasets of HadCM3 only cover the 2006-2035 period, and the data from MPI-ESM-P and MRI-ESM1 were unavailable at the time of writing, so these three models were omitted from our RCP analysis.

Fig. 3 shows the linear trends in annual mean SATa for RCP4.5 and RCP8.5 for the 2001-2013 period. The trends of the global and hemispheric mean vary greatly from one model to another. It is obvious that most models overestimate the trends for the hemispheric scales, and a similar result is seen for the global scale [ 6]. By comparison, the SATa trends of BCC-CSM1-1-m, CMCC-CM, GFDL-ESM2M, and NorESM1-ME are closest to the observed trends. Previous studies indicate that changes in global SATa are jointly influenced by increasing anthropogenic greenhouse gas, internal climate variability, and so on [ 2]. The overestimation of anthropogenic forces, different sensitivities to external forces of models, and inconsistent model capabilities in reflecting internal climate variability are possible reasons for the widely different and overestimated trends at the hemispheric and global scales during the 2001-2013 period [ 2, 7, 18]. This issue needs to be further discussed in future.

The result in Fig. 3 indicates that the models of BCC-CSM1-1-m, CMCC-CM, GFDL-ESM2M, and NorESM1-ME show better projection capability during the 2001-2013 period. Hence, the simulation abilities of these four models are evaluated according to their multidecadal trends at the global and hemispheric scales during different periods (Table 3). As can be seen, the performance in reproducing multidecadal variations differs among the four models on hemispheric scales. Compared with historical observations (Table 2), the characteristics of the global mean are best represented by the four models during the four periods, and the trends for the global and hemispheric means of these four models are closest to the observed trends during the 1945-1970 and 1971-2000 periods. For the 1900-1944 period, like the MME results shown in Fig. 2(g), the four models give similar trends but with less trend magnitudes at the global and hemispheric scales. In general, the four models can mostly reproduce the temporal shape at the global and hemispheric scales. Due to these models’ capability in simulating and projecting the multidecadal trends of SATa, we selected them for analyzing future SATa variations during the 2006-2099 period.

Fig. 4 shows the changes in annual mean SATa of the MME over the global and the hemispheric scales from BCC-CSM1-1-m, CMCC-CM, GFDL-ESM2M, and NorESM1-ME for the 2006-2099 period under RCP4.5 and RCP8.5. For the globe and for each hemispheric scale, SATa show an overall increase in the future. However, SATa increase more over the NH (land, ocean) than over the SH (land, ocean) under both scenarios, and linear trends are larger under the high emissions scenario of RCP8.5 than under the medium-low emissions scenario of RCP4.5 during the 2006-2099 period. Moreover, for the global and hemispheric scales, SATa show a linear increase under RCP8.5 since 2006, and the increase in SATa is greater under RCP8.5 than under RCP4.5 starting about 2020. On the other hand, SATa reach a peak around 2080 and then do not increase under RCP4.5. Variations of SATa under RCP8.5 and RCP4.5 are closely related to variations of global anthropogenic radiative forcing for the two scenarios [ 14]. The different emissions of global anthropogenic forces are a possible reason for the distinct divergence in SATa under the two scenarios.

In addition, the trends in annual SATa for the globe, NH, SH, NH land, SH land, NH ocean, and SH ocean under RCP4.5 are 0.17, 0.22, 0.11, 0.26, 0.16, 0.19, and 0.10 °C·decade^-1, respectively, and are significantly less than those under RCP8.5 (0.29, 0.36, 0.23, 0.43, 0.33, 0.31, and 0.21 °C·decade^-1, respectively; figure not shown). Moreover, the trends in annual SATa from the MME results of the 12 models for the globe, NH, SH, NH land, SH land, NH ocean, and SH ocean under RCP4.5 (RCP8.5) are 0.20 (0.41), 0.24 (0.49), 0.15 (0.33), 0.29 (0.58), 0.21 (0.45), 0.21 (0.42), and 0.14 (0.30) °C·decade^-1 (figures not shown). The projected trends at the global and hemispheric scales with model selection are clearly lower than the MME results of the 12 models and the results without model selection in the previous study [ 19] under RCP4.5 and RCP8.5. Moreover, both years (2063 and 2053) in which global warming reaches 2 °C under the two scenarios occur later than in the MME (2047 and 2038) without model selection when using the same base period [ 19]. The results at hemispheric scales are similar to the global mean.

CMIP5 models perform well in simulating the long-term trends of SATa [ 2]; however, the performance in reproducing the multidecadal variations of SATa differs among the models. It can be seen from Fig. 5 that some models, including FGOALS-g2, FIO-ESM, GFDL-CM2p1, GISS-E2-R-CC, INMCM4, and MPI-ESM-LR, are not capable of reproducing the multidecadal variations in annual mean SATa for the globe, as well as for each hemispheric scale (Fig. 5(a)-(g)). Obviously, these models give increasing trends over the global and hemispheric means during the 1945-1970 period, indicating the overestimation of modeled trends during this period. In addition, during the 1900-1944 and 1945-1970 periods, the trend magnitudes of each hemispheric mean from these models are close to the long-term global mean, suggesting that the linear increase of SATa may be due to linear responses of these models to increasing anthropogenic greenhouse gases, and may be insufficient in simulating the internal climate variability that modulates the decadal variation in SATa [ 4, 20- 22] in these models. The result implies that the capabilities of these models in reproducing the internal climate variability may need to be improved.