Detection of Decadal Phase Transition and Early Warning Signals of PDO in Recent and Next 100 Years
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摘要: 本文基于临界慢化的理论，采用太平洋年代际振荡（Pacific Decadal Oscillation, PDO）指数的近百年（1900～2019年）历史数据及未来百年（2006～2100年）模式模拟数据，首先通过滑动t检验确定PDO位相转变的时间，进而借助于表征临界慢化现象的方差和自相关系数，研究了PDO年代际位相转折的早期预警信号。结果表明：（1）近百年来PDO发生了4次显著的位相转变，每次位相转变前的5～10年可以提取到早期预警信号；（2）通过对CMIP5气候模式资料计算得到的PDO进行统计合成得到未来百年的PDO序列，检测结果表明在2040年和2080年前后发生年代际转折，转折前的5～10年能够检测到早期预警信号；（3）近百年和未来百年PDO序列的位相转变及早期预警信号研究证实在PDO发生位相转变之前方差和自相关系数总能提前数年给出预警信号，也揭示了未来PDO的转折时间。
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关键词:
- PDO (Pacific Decadal Oscillation) /
- 非线性 /
- 临界慢化 /
- 转折/突变 /
- 早期预警信号
Abstract: Based on the theory of critical slowing down, this study investigates the decadal phase transition and the early warning signals of the Pacific Decadal Oscillation (PDO) series using the historical monitoring data of PDO in the past 100 years (1900–2019) and the simulation data of the future century (2006–2100) model. First, the phase transition time of the PDO is determined by the moving t test technique. Thereafter, the early warning signal of phase transition is analyzed using the variance and autocorrelation coefficients, which characterize the critical slowing phenomenon. The results show that: (1) Four significant phase changes in the PDO occurred in the recent 100 years, and early warning signals can be given 5–10 years in advance. (2) In the next 100 years, the study of the PDO, which is obtained based on the CMIP5 data, shows that the PDO will have two decadal transitions around 2040 and 2080, and early warning signals can be given 5–10 years in advance. (3) Based on the study of the phase transition detection and early warning signals of PDO sequences in the recent and next 100 years, the variance and autocorrelation coefficients can be detected as the early warning signals of abrupt change several years in advance, which can be utilized to predict the climate changes that will affect the PDO in the future. -
图 1 （a）滑动计算方差、（b）滑动计算自相关系数示意图。L1、L2、L3、···Ln···，L12、L22、L32、···Ln2···代表长度相同的各个窗口（ML），s1、s2、s3、···sn···代表对应窗口长度数据的均方差，L为序列总长度，MT为滑动步长，α1代表L1和L12的自相关系数，α2代表L2和L22的自相关系数，···αn代表Ln和Ln2的自相关系数，LT表示滞后时间
Figure 1. (a) Calculation of the variance and (b) autocorrelation coefficient using the sliding window method. L1, L2, L3, ···, Ln···and L12, L22, L32,···Ln2···denote windows of the same length; s1, s2, s3,···sn··· denote the variances of the corresponding windows; L is the total length of the sequence; MT is the sliding step; α1 denotes the autocorrelation coefficients of L1 and L12, α2 denotes the autocorrelation coefficients of L2 and L22, αn denotes the autocorrelation coefficients of Ln and Ln2; LT denotes the lag time
图 2 近百年PDO指数（柱状；红色：正值；蓝色：负值）的时间变化曲线。黑色曲线为51个月滑动平均提取的趋势信息
Figure 2. Curves of the PDO (Pacific Decadal Oscillation) index (bars; red: positive value; blue: negative value) changing with time in the recent 100 years. Black curve denotes the trend information extracted from the 51-month moving average
图 3 基于MTT方法的近百年PDO序列位相转变检测：（a）滑动窗口t为5年；（b）滑动窗口t为12年。虚线表示显著性水平为0.05
Figure 3. Phase transition detection of the PDO sequence in the recent 100 years based on the MTT (Moving t-test) method: (a) Sliding window t is 5 years; (b) sliding window t is 12 years. Dashed lines denote the 0.05 significance level
图 4 近百年PDO序列方差信号检测：（a）1921年位相转变的方差信号检测；（b）1942年位相转变的方差信号检测；（c）1976年位相转变的方差信号检测；（d）1998年位相转变的方差信号检测。滑动窗口（ML）为10年，滑动步长（MT）为3个月
Figure 4. Signals detection of the variance of the PDO sequence in the recent 100 years: (a) Variance signal detection of phase transitions in 1921; (b) variance signal detection of phase transitions in 1942; (c) variance signal detection of phase transitions in 1976; (d) variance signal detection of phase transitions in 1998. ML (sliding window) is 10 years and MT (sliding step) is 3 months
图 5 近百年PDO序列自相关系数信号检测：（a）1921年位相转变的自相关系数信号检测；（b）1942年位相转变的自相关系数信号检测；（c）1976年位相转变的自相关系数信号检测；（d）1998年位相转变的自相关系数信号检测。ML为10年、MT为3个月、滞后时间（LT）为1个月
Figure 5. Signals detection of the autocorrelation coefficient of the PDO sequence in the recent 100 years: (a) Autocorrelation signal detection of phase transitions in 1921; (b) autocorrelation signal detection of phase transitions in 1942; (c) autocorrelation signal detection of phase transitions in 1976; (d) autocorrelation signal detection of phase transitions in 1998. ML is 10 years, MT is 3 months, and LT (lag time) is 1 month
图 6 未来百年PDO指数（柱状；红色：正值；蓝色：负值）的时间变化曲线。黑色曲线为51个月滑动平均提取的趋势信息
Figure 6. Curves of the PDO index (bars; red: positive value; blue: negative value) changing with time in the next 100 years. Black curve denotes the trend information extracted from the 51-month moving average
图 7 基于MTT方法的未来百年PDO序列位相转变检测：（a）滑动窗口t为10年；（b）滑动窗口t为12年。虚线表示显著性水平为0.05
Figure 7. Phase transition detection of the PDO sequence in the next 100 years based on the MTT method: (a) Sliding window t is 10 years; (b) the sliding window t is 12 years. Dashed lines denote the 0.05 significance level
图 8 未来百年PDO序列方差信号检测：（a）2040年位相转变的方差信号检测；（b）2080年位相转变的方差信号检测。ML为10年，MT为3个月
Figure 8. Signals detection of the variance of the PDO sequence in the next 100 years: (a) Variance signal detection of phase transitions in 2040; (b) variance signal detection of phase transitions in 2080. ML is 10 years and MT is 3 months
图 9 未来百年PDO序列自相关系数信号检测：（a）2040年位相转变的自相关系数信号检测；（b）2080年位相转变的自相关系数信号检测。ML为10年，MT为3个月，LT为1个月
Figure 9. Signals detection of the autocorrelation coefficient of the PDO sequence in the next 100 years: (a) Autocorrelation signal detection of phase transitions in 2040; (b) autocorrelation signal detection of phase transitions in 2080. ML is 10 years, MT is 3 months, and LT is 1 month
表 1 CMIP5（phase 5 of Coupled Model Intercomparison Project）的36个气候模式
Table 1. The 36 climate models of CMIP5 (phase 5 of Coupled Model Intercomparison Project)
编号 模式名称 编号 模式名称 编号 模式名称 编号 模式名称 1 ACCESS1-0 10 CMCC-CMS 19 GISS-E2-H-CC 28 IPSL-CM5B-LR 2 ACCESS1-3 11 CNRM-CM5 20 GISS-E2-R 29 MIROC-ESM 3 BCC-CSM1-1 12 CSIRO-Mk3-6-0 21 GISS-E2-R-CC 30 MIROC-ESM-CHEM 4 BCC-CSM1-1-M 13 FGOALS-g2 22 HadGEM2-AO 31 MIROC5 5 BNU-ESM 14 FIO-ESM 23 HadGEM2-CC 32 MPI-ESM-LR 6 CanESM2 15 GFDL-CM3 24 HadGEM2-ES 33 MPI-ESM-MR 7 CCSM4 16 GFDL-ESM2G 25 inmcm4 34 MRI-CGCM3 8 CESM1-BGC 17 GFDL-ESM2M 26 IPSL-CM5A-LR 35 NorESM1-M 9 CMCC-CM 18 GISS-E2-H 27 IPSL-CM5A-MR 36 NorESM1-ME 注：加粗字体模式表示选中的最具代表性的模式。 
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