近地表气温的变化能够准确地反映全球变暖的程度，气温年循环的变化在气候相关研究中也受到了越来越多的关注。此外，气温年循环对于地球的能量循环、生物循环等都会产生重要影响，成为全球变化领域近年来热点关注的问题之一。国际耦合模式比较计划(Coupled Model Intercomparison Project, CMIP)最新发展的第六个阶段中(CMIP6)的模式对于过去和不同情景下未来气温年循环的模拟能力相关研究仍然不足。中国地区处于中纬度地区，在季节变化等方面会受到气温年循环的影响。所以开展CMIP6模式对中国地区气温年循环的研究，揭示过去和未来情景下CMIP6模式在中国地区的气温年循环特征具有重要意义。
本研究选用了CMIP6模式中20个子模式的日值气温历史数据（1961-2014年），以及13个子模式在三种共享社会经济路径(SSP1-2.6、SSP2-4.5、SSP5-8.5)下未来的月值气温数据（2015-2099年）。通过傅里叶分解将气温年循环的曲线分解为最大相位、最小相位、振幅等变量，计算了CMIP6历史日值数据各个变量的长期趋势与空间模态，并与气象观测站点的观测数据进行验证，分析了未来不同情景下CMIP6模拟的气温年循环特征，并揭示CMIP6模拟过去和未来的气温年循环的空间差异。主要结果如下：
（1）对于中国地区而言，尽管1961–2014年CMIP6模拟的年气温值低于观测结果，其多模式集合平均的气温年循环与观测到的平均气温年循环较为吻合。空间模态上，平均气温在最大相位、最小相位、振幅方面显示出明显的南北梯度，其观测结果分别为200.9天、9.4天、31.11℃，而CMIP6的多模式平均值为202.4天、12天、32.45℃。最大相位中观测值在西南地区相较与其他地区值较低，CMIP6对于最大相位在该地区的误差较大。观测值的最大相位、最小相位及振幅的年际波动较大。但是CMIP6与之相反。长期趋势方面，观测得到的最大相位、最小相位以及振幅的长期趋势为-0.4天/10年、-0.5天/10年、-0.18℃/10年，而CMIP6的多模式平均值为0.3天/10年、0.1天/10年、0.06℃/10年，且各个子模式之间的长期趋势差异较大。
（2）在SSP1-2.6、SSP2-4.5、SSP5-8.5三种未来共享社会经济路径下，气温年循环曲线相较于历史时期均有增加，其中SSP5-8.5下最为显著。最大相位延迟幅度分别为0.1天/10年、0.1天/10年、0.4天/10年，大于最小相位的0.1天/10年、0.1天/10年、0.1天/10年，相位与振幅的长期趋势在空间上存在明显的南北梯度。在SSP2-4.5、SSP5-8.5两种情景下东北地区的振幅长期趋势异常减小，而西北地区与之相反。这与两个地区冬夏季节之间的增温不对称性有关。此外，各个CMIP6子模式与多模式集合平均之间在振幅与相位长期趋势上存在明显的差异。
 

The change of near-surface air temperature can accurately reflect the degree of global warming and the change of annual temperature cycle has been paid more and more attention in climate-related research. In addition, the annual temperature cycle has an important impact on the earth's energy cycle and biological cycle, which has become one of the hot issues in the field of global change in recent years. Coupled Model Intercomparison Project (CMIP), the sixth phase of the latest development (CMIP6), has been poorly studied for the simulation capabilities of past and future annual temperature cycles under different scenarios. China is in the middle latitudes and is affected by the annual temperature cycle in terms of seasonal variation. Therefore, it is of great significance to study the annual temperature cycle of CMIP6 model in China and reveal the characteristics of annual temperature cycle of CMIP6 model in China under past and future scenarios.

In this study, historical daily temperature data of 20 sub-models in CMIP6 (1961-2014) and future monthly temperature data of 13 sub-models in three shared socioeconomic paths (SSP1-2.6, SSP2-4.5, SSP5-8.5) were selected. The curve of annual temperature cycle was decomposed into maximum phase, minimum phase, amplitude and other variables by Fourier decomposition. The long-term trend and spatial modes of each variable in the historical daily value data of CMIP6 were calculated and verified with the observation data of meteorological observation stations. The characteristics of annual temperature cycle simulated by CMIP6 under different scenarios in the future were analyzed. It also reveals the spatial differences between the past and future annual temperature cycles simulated by CMIP6. The main results are as follows:

(1) For China, although the annual temperature simulated by CMIP6 during 1961-2014 is lower than that observed, the annual temperature cycle of the multi-model ensemble average is in good agreement with the observed annual temperature cycle. In terms of spatial mode, the mean temperature showed a significant north-south gradient in terms of maximum phase, minimum phase and amplitude, and the observed results were 200.9day, 9.4day and 31.11℃, respectively, while the multi-mode mean of CMIP6 was 202.4day, 12day and 32.45℃. The observed value of the maximum phase in the southwest region is lower than that in other regions, and the error of CMIP6 for the maximum phase in this region is larger. The maximum phase, minimum phase and amplitude of the observed values fluctuate greatly from year to year. But CMIP6 is the opposite. In terms of long-term trends, the observed long-term trends of maximum phase, minimum phase and amplitude are -0.4day/10yrs, -0.5day/10yrs and -0.18℃ per decade, while the multi-modal average of CMIP6 is 0.3day/10yrs, 0.1day/10yrs and 0.06℃ per decade. And the long-term trend of each sub-model is quite different.

(2) Under the three future shared socioeconomic paths of SSP1-2.6, SSP2-4.5 and SSP5-8.5, the annual cycle curve of temperature increases compared with the historical period, and the most significant one is under SSP5-8.5. The maximum phase delay ranges were 0.1day/10yrs, 0.1day/10yrs and 0.4day/10yrs, respectively, which were larger than the minimum phase ranges of 0.1day/10yrs, 0.1day/10yrs and 0.1day/10yrs. The long-term trend of phase and amplitude showed an obvious north-south gradient in space. Under the two scenarios of SSP2-4.5 and SSP5-8.5, the long-term trend of amplitude in northeast China decreased abnormally, while that in Northwest China was opposite. This is related to the asymmetry of warming between winter and summer seasons in the two regions. In addition, there are significant differences in amplitude and phase long-term trends between the CMIP6 submodes and the multi-mode ensemble averages.