3.1. Direct comparison of the historical experiments
3.1.1. Trend of temperature change
The ensemble mean SAT over all the simulations was calculated. From Fig.1a, it is clear that the model-simulated temperature captures the main temperature fluctuations, but the amplitudes are small when compared to observations. The CRU data show three distinct periods: 1900-50, 1950-70 and 1970 to present. The temperature increases in both the first period (1900-50) and the third period (1970 to present), but decreases in the second period (1950-70). Note that the third period spans more than 40 years, which is longer than the second period. Furthermore, in this last period, the temperature over China is extraordinarily higher than at any other time, particularly in recent years. The CMIP5 model simulations also exhibit this trend, but do not accurately predict the slope of the post-1970s increase. On a shorter time scale, the cold periods of 1900-20, 1950-60, 1967-70 and 1984 are very significant in the CRU data. While the simulated ensemble means have corresponding cold periods, the high peaks or deep troughs in observations are not well represented, and so the high frequency fluctuations are not well modeled. Some of the models do appear to be able to accurately forecast the extreme nature of some cold periods, but not the correct time.
According to the CRU temperature in Fig. 1b, the summer-high temperature peaks in the 20 years following 1990 appear somewhat comparable to the peaks in the 1940s. This suggests that the increase in summer temperatures is not as significant as annual temperatures. In the CMIP5 simulations, despite some deep drops over very short time periods, the increasing temperature trend is much stronger after 1990 than it is in the 1940s. This means that the comparatively weak warming increasing trend in June-July-August (JJA) is not well modeled.
The IMFs obtained from seven models of the CMIP5 simulations.
For winter temperature, the CMIP5 simulations display similar trends as summer temperatures, except that the winter fluctuations seem larger than summer and annual fluctuations. The simulated fluctuations are not comparable to the very large fluctuations in the CRU data.
3.1.2. Correlation coefficients of yearly series
To quantify the performance of the simulations from different models, the correlation coefficients (R) of the yearly SAT series (1901-2005) of each model with the CRU temperature were calculated, with the results shown in Table 2. The R values of annual series range from 0.19 to 0.69 and have a mean value of 0.50. The HadGEM2-AO, INMCM4 and MIROC5 models yielded the smallest R values of approximately 0.4. The R values larger than 0.6 were produced by the single run of BNU-ESM (0.62), three runs of CCSM4 (0.63-0.65), one run of CSIRO-Mk (0.62), two runs of FGOALS (0.61, 0.68) and two runs of BCC-CSM1.1 (0.61, 0.64). It is worth noting that the runs of those models developed by institutes in China gave the comparatively larger R values.
When the ensemble mean of a single model was considered, the R values were larger than almost all of the single runs. The overall ensemble mean over all runs and all models obtained a correlation of 0.77, which was overwhelmingly larger than any value from single model ensembles.
The correlation coefficients for JJA and December-January-February (DJF) indicated that both their values were smaller than that calculated from the annual series. The R values for the ensemble from all runs and models were 0.57 and 0.46 for JJA and DJF, respectively.
3.1.3. Seasonal characteristics
According to some previous studies, the warming trend is more significant for winter temperatures than for summer temperatures. This phenomenon is also present in the CRU data (see Fig.1). Comparing JJA, DJF and the whole year (Figs.1a-c), the highest to lowest warming rates in CMIP5 model-simulated SAT are in DJF (winter), the whole year, and then JJA (summer). However, this difference in warming rates is not as obvious in the CMIP5 simulations. When comparing the amplitude of fluctuations of summer, winter and annual temperatures, it is clear that the interannual fluctuation of winter temperature is stronger than for summer or annual temperature. This is the case for both the CRU temperature (see Fig. 1) and the CMIP5 simulations.
3.1.4. Historical warming rates
The warming rates between 1956 and 2005 were estimated for each single run and for the ensemble mean. (Ren et al., 2005) reported the mean temperature warming rate over China between 1951 and 2001 to be 0.22°C (10 yr)-1, while (Li et al., 2010) found a rate of 0.26°C (10 yr)-1
± 0.032°C (10 yr)-1 over the period 1954-2006. In a recent study by the present authors, records from more than 570 weather stations between 1962-2011 were used to obtain a rate of 0.284
± 0.142°C (10 yr)-1.
In the present study, we found an average warming rate of 0.173°C (10 yr)-1
± 0.075°C (10 yr)-1 for all of the single runs of CMIP5 and a warming rate of 0.248°C (10 yr)-1 from the CRU data. No model run resulted in a negative warming rate. For the overall ensemble mean of all runs and all models, the warming rate was estimated to be 0.173°C (10 yr)-1, which was equal to the average of all the single runs. Considering individual models, the highest rates were obtained by FGOALS [0.32°C (10 yr)-1] and CCSM4 [0.24°C (10 yr)-1]. The next highest rates were obtained by CESM1-CAM5, bcc-csm and NorESM with values of approximately 0.17°C (10 yr)-1, which was close to the value of the overall ensemble mean. The lowest warming rates were obtained by MIROC5, with a value of 0.08°C (10 yr)-1. The warming rates obtained from CMIP5 simulations were small compared to those from the observations, and we believe that this is due to the underestimation of the amplitudes of fluctuations.
The warming rates obtained from the overall ensemble mean were 0.163°C (10 yr)-1 and 0.204°C (10 yr)-1 for JJA and DJF, respectively, which were both smaller than the values of 0.2°C (10 yr)-1 and 0.39°C (10 yr)-1 obtained in a recent study by the present authors. The ensemble means of the models CCSM4, BNU-ESM, FGOALS, CanESM2 and bcc-csm1 obtained larger warming rates than the observed 0.2°C (10 yr)-1 in JJA. In DJF, only the runs by ACCESS1 and CanESM2 were able to obtain warming rates larger than the observed 0.39°C (10 yr)-1. The FGOALS model obtained comparatively large warming rates in DJF, but only one of three runs attained the observed warming rate of 0.39°C (10 yr)-1. In summary, the majority of models underestimate the observed warming rates of the past 50 years.
In the past 100 years (1906-2006), considering all seasons, the warming rates obtained by the overall ensemble mean temperature of the CMIP5 simulations was 0.64°C (100 yr)-1. This was smaller than the global warming rate of 0.74°C (100 yr)-1 estimated by the (IPCC, 2007). The warming rates in JJA and DJF were estimated as 0.55°C (100 yr)^-1 and 0.80°C (100 yr)-1, respectively. Out of 50 individual model runs, 12 obtained 100-yr warming rates larger than 1.0°C (100 yr)-1. Those runs were produced by FGOALS, BNU-ESM, CCSM4 and bcc-csm. Three runs gave negative warming rates, but the magnitudes were very close to zero.
3.2. EEMD decompositions for historical experiments
3.2.1. Periods of different IMFs
The EEMD method is able to decompose raw series into IMFs with different periods. The periods are empirically determined according to the properties in the raw data; therefore, each IMF may not correspond to a fixed cycle length. In this study, each single run and ensemble mean from each model were processed using the EEMD algorithm. The period between 1901 and 2005 was selected. Each set of CMIP5 simulation data produced six IMFs, where the sixth IMF was the main temperature trend. Table 3 shows the details of the IMFs obtained from the simulations of 15 CMIP5 models. The first to the fifth IMF correspond to approximate periods at 3.16, 7.17, 14.70, 35.25 and 79.30 years. The standard deviation of these periods are 0.19, 0.73, 1.95, 8.33 and 19.70 years, respectively. The periods of IMF1 for all models are in the range of 2.84-3.5 years, and those of IMF2 are 5.83-8.4 years. The corresponding periods of the CRU data are 2.69 and 7.24. The periods of the third and fourth IMFs of the models are in the range of 11.67-19.09 and 26.25-52.5 respectively, corresponding to periods of 16.15 and 52.5 from the CRU data. It is known that the periods of the IMFs decomposed by the EEMD algorithm are not completely stationary. In fact, they are only stationary within a narrow range. Only the average values for each IMF of each model are presented. The periods of the first and second IMFs represent temperature oscillations of 2-7 years, and the periods of the third and fourth IMFs represent a multi-decadal oscillation of climate change. Most models are able to catch these frequency characteristics to some extent, but the majorities underestimate high frequency oscillations and overestimate one of the low frequency oscillations. The periods of the fourth and fifth IMFs vary widely across the models, but they correspond to very low frequencies that are hard to determine with a limited amount of data.
The standard deviation of an IMF can indicate the intensity of its signal. In descending order of standard deviations, the IMFs of the CRU data are 1, 5, 4, 2, 3 (see Table 3). The IMFs exhibit differing relative intensities for different models, but the first and fifth IMFs generally have the strongest intensities, while the third and fourth are the weakest. In summary, the CRU data also exhibit stronger high frequency signals of 2-3 years and weaker multi-decadal signals.
The IMFs obtained from eight models of the CMIP5 simulations.
SAT anomalies (relative to the mean of 2006-15) obtained from the model simulations under different RCPs.
3.2.2. Trend from historical experiments
Figures 2 and 3 display the second to fifth IMFs from different models. Clearly, the IMFs from the majority of the models are consistent with the IMFs of the CRU temperature.
The second order IMFs are better represented by the models than the third order IMFs. When only the second order IMFs are considered, the period from 1970 to 2005 is better represented than the period before 1970.
Comparing the fourth order IMFs over the last 30 years, the CRU series shows an increasing trend instead of the wave cycle that the majority of models suggest. Nevertheless, some models do simulate such a trend, such as CSIRO-MK, MIROC-ESM, and NorESM1-M. The CCSM4, CESM1-BGC, BNU-ESM, MRI-CGCM3, FGOALs and inmcm4 models show a strong wave cycle. However, other models exhibit weak cycles and a comparatively high temperature in the last 30 years, which corresponds somewhat to the increasing trend of the last three decades.
All of the models except for inmcm4 have a fifth order IMF that simulates a single wave cycle spanning the entire 105 years. The FGOALs model exhibits a single wave cycle, but with an amplitude far larger than that from other models and from the CRU temperature data. This exceptionally large amplitude does not occur in the other order IMFs of the same model.
The residuals of EEMD show an increasing trend for all models, but with different magnitudes. Among all the models, six have a rate larger than the CRU temperature. The historical warming suggested by the models between 1901 and 2005 was obtained directly from the sixth IMF (the residual) by subtracting the value at 1901 from the value at 2005 (see the last column in Table 3). The value obtained from the overall ensemble mean is close to the warming of 0.97°C calculated from the CRU temperature data.Ordering the models by temperature increase, from high to low, we get: FGOALS, CCSM4, BNU-ESM, BCC-CSM1.1, CESM1, CanESM2, INMCM4, MRI-CGCM3, NorESM1-M, CESM1-CAM5, MIROC-ESM, ACCESS1.0, HadGEM2-AO, CSIRO-Mk3.6.0 and MIROC5. The temperature increase calculated from the CRU data falls in the middle of these values. The increases calculated from MRI-CGCM3 and inmcm4 are closest to the value calculated from the CRU data. This result is not consistent with the directly estimated warming rates, which as previously discussed, underestimated the increase.
3.3. The warming rates for RCP experiments
As shown in Fig. 4, the simulated SAT trends for each RCP have specific properties. For RCP2.6, the significant increase in temperature continues until 2030, where it peaks. After 2030, the temperature becomes stable and begins to slowly decrease or increase for different simulations. For RCP4.5, the significant temperature increase continues until approximately 2060, and is followed by a slower increase that continues until the end of the century. For RCP6.0, the increasing rate in the second half of the century is larger than that in the first half of the century. This high increasing rate decreases slightly near the end of the century. For RCP8.5, the warming rate remains high over the whole century.
Table 4 displays the ensemble mean warming rates of the four RCPs for the periods 2006-55, 2006-2100 and 2006-2300. They forecast that the temperature in this century could increase by approximately 0.9°C, 2.4°C, 3.2°C and 6.1°C for the RCP2.6, RCP4.5, RCP6.0, and RCP8.5 scenarios, respectively.
Under the scenario of RCP2.6, the largest warming rate of 0.26°C (10 yr)-1
± 0.11°C (10 yr)-1 was obtained for the period 2006-55. For the periods 2006-2100 and 2006-2300, the warming rates under RCP2.6 were close to 0.09°C (10 yr)-1 and －0.01°C (10 yr)-1. This means the scenario of RCP2.6 mostly influences the climate over the first half of the century. Similarly, the results for RCP4.5 forecast that there will be significant warming over the next 50 years, which will continue for 100 to 300 years, but with slowly decreasing warming rates.
However, the warming rates of RCP6.0 and RCP8.5 for 2006-55 are smaller than the period from 2006 until the end of this century. This indicates that the highest peak of warming rate will occur in the second half of the century. It is also clear that the warming rates in summer are slightly lower than in winter.
Table 5 displays the different warming rates for each model.The largest increasing rates were obtained by MIROC5, FGOALS, and HadGEM2-AO, and were near or larger than 0.8°C (10 yr)-1 in the long-term period to 2100. The Earth system models (BNU-ESM, CanESM2, MIROC-ESM, NorESM1-M) obtained medium warming rates in the range of 0.5°C (10 yr)-1-0.7°C (10 yr)-1 (to 2100), but it is not clear whether these complex Earth system models produce more accurate predictions. Note that FIO-ESM obtained a low warming rate of 0.44°C (10 yr)-1 (to 2100).
As discussed in previous sections, the majority of models underestimate the historical warming rate. If this is an indication of the accuracy of the different models, then the warming rates should be close to the results of models such as FGOALS. This suggests that the best forecast of the temperature increase over this century, for the four RCPs, should be larger than 3°C, 4°C, 5°C and 7°C. However, the models contain many uncertainties. The models CCSM4 and BNU-ESM exhibit larger warming rates in the last 50 years than other models, but they forecast a comparatively small increase for future scenarios. The model MIROC5 simulates very low historical warming rates, but gives very large increases under RCP8.5. Nevertheless, models such as FGOALS and BNU-ESM appear to give consistent results.