A new detection method has been proposed to study the transition process of abrupt climate change. With this method, the climate system transiting from one stable state to another can be verified clearly. By applying this method to the global sea surface temperature over the past century, several climate changes and their processes are detected, including the start state (moment), persist time, and end state (moment). According to the spatial distribution, the locations of climate changes mainly have occurred in the Indian Ocean and western Pacific before the middle twentieth century, in the 1970s in the equatorial middle-eastern Pacific, and in the middle and southern Pacific since the end of the twentieth century. In addition, the quantitative relationship between the transition process parameters is verified in theory and practice: (1) the relationship between the rate and stability parameters is linear, and (2) the relationship between the rate and change amplitude parameters is quadratic.
Including a variety of factors, the climate system is a gigantic and complex
system. Each member of the system follows a certain rule, and there is a
certain interaction between members. According to previous
work (Goldblatt et al., 2006; Alexander et al., 2012; Baker and Charlson, 1990;
Charney and DeVore, 1979; Zerkle et al., 2012), the climate system has two or more
stable states, and the system transiting from one state to another is called
climate change (Thom, 1972; Lorenz, 1963, 1976; Rial, 2004). Climate change has
an important impact on social politics and economic environments, and it is
closely related to human survival, production, and daily life. The climate change
issue has aroused great concern in the international community (IPCC, 2014).
When climate changes, the system jumps from one state to another, and it
experiences a process (Li et al., 1996; Yan et al., 2012, 2013). Most traditional
theories and detection methods (Wei, 1999; Feng et al., 2011; He et al., 2012)
have been focused on the changes in statistics before and after climate change,
such as Yamamoto (Yamamoto et al., 1986), Mann–Kendall (Mann, 1945; Kendall, 1955; Kendall et
al., 1976), moving
When the climate system transits from one stable state to another via a process, the duration could be identified no matter how long the period lasts. Muldelsee (2000) developed a regression technique to identify such processes with a ramp function. In the present paper, a traditional model (logistic model) is used to regress a real-time sequence. The parameters of the model obtained by regressing the time series. The mode could represent different degrees of change. It has been noticed that climate change has a relationship with the length of time sequence (Yan et al., 2015); thus, a sub-sequence is extracted from the entire sequence for regression. A group of parameters can be obtained when the sub-sequence moves on the entire time sequence. By using the percentile threshold method on the parameters with a given threshold (98 %), climate changes are determined. Based on the concept of climate change process, several climate changes in global sea surface temperature (GSST) have been detected in the past century.
Details of the proposed method have been thoroughly discussed (Yan et al., 2015);
a brief description is as follows. A biological model was created, and it is
a complex system (May, 1976). The model also describes an abrupt change in
mean (Liu and Peng, 2004) and it is expressed as
A piecewise function is created to describe a curve, which is similar to the
preceding one and is divided into three stages:
In stage 2, the system is in transition from state
According to Eq. (
Note that parameter
By applying this method to the Pacific decadal oscillation index, Yan et al. (2015) verified its transition process. In the present paper, this method is applied to analyze the GSST transition process. It is noticed that the sub-sequence could be set as 10a, 20a, 30a, and 40a, and for our purposes the sub-sequence was set as 10a.
The data used in the present paper were reconstructed by the National Oceanic
and Atmospheric Administration (2016,
The detection method is applied to identify the temperature sequence in each grid. In order to confirm the climate change, all start moments and end moments were counted. As shown in Fig. 1, the frequencies of start moments and end moments are displayed from 1854 to 2010. In order to confirm the number of abrupt changes, a threshold of the frequencies was set by an ideal numerical experiment. In the experiment, each original sea surface temperature (SST) series is replaced by a new time series, which is rebuilt by a shuffle algorithm (it is an algorithm to disturb a time series randomly). The new random series has the same mean and variance with the original one. By detecting its abrupt changes with the novel method, the frequencies of start moments and end moments are counted as seen in Fig. 1, and all frequencies are less than 1 %. Then, when the frequencies of start moments in 1878, 1942, 1976, and two other periods (1890–1920, 1990–2010) are larger than 1 % (Fig. 1a), the abrupt changes are considered as the real abrupt changes. While according to end moments (Fig. 1b), the frequencies are in 1886, 1950, and 1982 and two other periods (1900–1930, 1990–2010). By comparing the two frequencies, a certain corresponding relationship shows that the climate changes starting in periods of Fig. 1a and ending in periods of Fig. 1b as marked by the red arrows and blue boxes, respectively. For the climate change starting in 1878 and ending in 1886, the frequency of the former is larger than the latter. The reason maybe that some grids started to change in 1878, while some of these grids did not end in 1886. The same situation occurs in other periods.
Frequencies of climate changes based on start moments
Spatial distribution classified based on frequency of start and
end moments of abrupt change.
In order to verify the corresponding relationship between the frequencies,
the spatial distribution of abrupt change, classified based on the start/end
moments, is shown in Fig. 2.
As shown in Fig. 2a, the abrupt change starting in 1878 occurred mainly
in the northern Indian Ocean, part of the central North Pacific and South
Pacific, and the equatorial Atlantic region. These regions coincided with
those of abrupt change ending in 1886 (Fig. 2b), which indicates that they
belonged to the same abrupt change process (ACP). As shown in Fig. 2c, the spatial distribution of abrupt change starting
in 1942 coincided with that ending in 1950 (Fig. 2d), mainly covering the
coastal regions in the northern and western Indian Ocean and part of the
equatorial Atlantic regions. This indicates that they are part of the same
ACP. As shown in Fig. 2e, the abrupt change starting in 1976 mainly occurred
in the middle-eastern equatorial Pacific Ocean and small regions of the
South Pacific near the South Pole. These regions completely coincided with
those of the abrupt change ending in 1982 (Fig. 2f), indicating that they
were part of the same ACP. As shown in Fig. 2g, the abrupt change starting in 1890–1920 may be
divided into three principle periods: that in 1890–1898 occurred mainly in
the Indian and South Pacific oceans; that in 1900–1993 occurred mainly in
the North Pacific and Atlantic; and the largest one in 1908–1909 occurred
mainly in the eastern and western regions of the equatorial Pacific. This
coincides with the spatial distributions (Fig. 2h) of abrupt change ending in
1902–1903, 1896–1898, and 1908–1910, and proves that they are part of the
same ACP. As shown in Fig. 2i, the abrupt change, which occurred in 1990–2010, may be
divided into three periods: that in 1995–1997 occurred mainly in the western
region of the South Pacific; that in 1998–1999 also occurred mainly in the
western South Pacific and some regions of the North Pacific; and the most
recent one occurred in 2005 and 2007, mainly in the Arctic region. In
addition, the abrupt changes starting in 1995–1997 ended in 1997–1999; and
that starting in 1998–1999 and 2005–2007 in the Arctic region ended in
2006–2008 (Fig. 2j). These indicate that they are part of the same abrupt
change.
The above analysis verifies that the abrupt change of a certain grid point
undergoes three steps: start, sustaining, and end. The spatial distribution
situation of the entire ACP coincides to a large degree with the
distribution situation of the abrupt change “point” proposed by
Xiao and Li (2007). This indicates that abrupt changes detected by the traditional
ACP are contained within the ACP.
Time sequence average of abrupt changes occurring under the
background of the same abrupt change:
It is obvious that the abrupt changes starting in 1878 and 1942 mainly occurred in the Indian Ocean, and the Indian Ocean dipole (IOD) for these two years got strong negative phase and strong positive phase respectively (Suryachandra et al., 2002), which could be the trigger of the abrupt changes. The abrupt change starting in 1976 is known as a climate shift, and most climate elements were detected to experience abrupt change. The abrupt changes of 1890–1920 occurred mainly in the Pacific Ocean, and it is associated with the Interdecadal Pacific oscillation (IPO) index, which transits from a negative phase to a positive phase during this period. The abrupt changes starting at the end of 2000s mainly occurred in high latitudes, which leads to a significant increase of temperature in the polar.
Spatial distribution of abrupt change duration in different
periods:
By studying the abrupt changes, which occurred in 1878, 1942, and 1976 and two other periods (1890–1920, 1990–2010), the averages of the spatial grid points of climate change are calculated. Seven sequences are obtained to describe the transition process as shown in Fig. 3.
In terms of sequence variation, the climate changes occurring before 1960
were characterized by low temperature. For that occurring in 1878, the
temperature of the abrupt changes decreased by an average of 0.12
With the start and end moments of a certain abrupt change given in the method, the period of the abrupt change may be determined. Based on this, the spatial distribution of the abrupt change duration is obtained as shown in Fig. 4: deep azure signifies that the duration is no longer than 30 months, orange signifies that the duration is about 30–60 months, turquoise signifies that the duration is about 60–90 months, and magenta signifies that the duration is about 90–120 months.
Amplitude distributions of abrupt changes in different periods:
Bistability state characteristics study of SST system:
According to the start moment, eight figures of different period ACPs are
analyzed:
For the abrupt changes starting in 1878 shown in Fig. 4a, the duration times
of the abrupt changes occurring in areas of the Northern Hemisphere were
short, such in as the north Indian Ocean, central North Pacific, and some
regions of the North Atlantic, while those of the abrupt changes occurring
in the Southern Hemisphere were long, such as in the central South Pacific. For the abrupt changes starting in 1896–1898 shown in Fig. 4b, mainly
occurring in the south of the Southern Hemisphere, the duration times were
all greater than 60 months. That in the Pacific Ocean was 60–90 months, and
that in the southern Indian Ocean was slightly longer. For the abrupt change starting in 1900–1903, shown in Fig. 4c, mainly
occurring in the Pacific Ocean, the overall duration time was long (more
than 60 months); and that in the eastern part was 90–120 months, longer than
that in the western part, which was 60–90 months. For abrupt change starting in 1908–1909, shown in Fig. 4d, mainly occurring
in parts of the coastal regions of the Pacific and southern Indian oceans,
the regions were small, while the overall duration time was long, all being
longer than 60 months. For the abrupt change starting in 1942, shown in Fig. 4e, the overall
duration times were long throughout the world, especially in the coastal
regions of the western Indian Ocean and central Atlantic, both being about
90–120 months. For the abrupt change starting in 1976, occurring mainly in the equatorial
middle Pacific, as shown in Fig. 4f, the duration time was 60–90 months. The duration time of abrupt change starting in 1989–1999 was relatively
short, as shown in Fig. 4g. The duration time in the polar regions and
western Pacific Ocean were shorter than 60 months, while that in the
middle-east equatorial Pacific was a little longer, being longer than 60
months. For the abrupt change starting in 2005–2006, shown in Fig. 4h, mainly
occurring in the Arctic region, the duration time was less than 30 months.
Through the above analysis, the following observations are made: the duration times of abrupt change before the 1960s were 60–120 months, and most were longer than 90 months; those in the 1970s were 60–90 months; those in the 1980s and 1990s were mostly 30–60 months; and those at the start of the 21st century were shorter than 30 months. Therefore, it is understood that the duration time of abrupt change under the background of global warming has shortened.
Relationships between abrupt change rate
The different degree of abrupt change amplitude in different period is
shown in Fig. 5: deep azure signifies that the cooling amplitude is larger
than 2
According to the start moment, eight abrupt changes of different period are analyzed:
For the abrupt change starting in 1878, as shown in Fig. 5a, only in the
northern region of South Pacific did the temperature increase slightly;
those in the other regions (especially in Indian Ocean) decreased, and the
amplitude was less than 2
The abrupt change starting in 1890–1920 is shown in Fig. 5b, c, and d; the
temperature decreased in most areas, while in some it increased. The
specific situations are as follows: for the abrupt change starting in
1896–1897, shown in Fig. 5b, the temperature increased by a small degree only
in the south of the South Pacific; it decreased in all other regions, and
the amplitude was less than 2
For the abrupt change starting in 1942, shown in Fig. 5e, the temperatures in
the coastal region of the western Indian Ocean mostly decreased (the
amplitude was less than 2
Figure 5f is the abrupt change starting in 1976; the temperatures throughout
the entire region increased, and the amplitude was large (larger than
2
Figure 5g and h show the abrupt changes starting in 1990–2010. The
temperatures increased almost everywhere throughout the world, and decreased
only in some regions of the South Pole starting in 1989–1999. The
temperatures in other regions all increased, and the amplitude in the
central regions of equatorial Pacific was larger than 2
Based on the above analysis, it is believed that the temperatures of abrupt changes before the 1960s mostly decreased; after experiencing the temperature rise in the 1970s, the temperatures of abrupt change throughout the world mostly increased.
The difference between different states of the ACP is counted in Fig. 6, and Fig. 6a shows the statistics of the start states. It is observed that the statistical probabilities of two states are high, which indicates that these states are stable. The statistics of the end states are shown in Fig. 6b, and the statistical probabilities of the multiple states are large, which indicates that multiple stability states appear after abrupt changes of the system. After further study of the abrupt change amplitude parameter of the system, as shown in Fig. 6c, it is observed that the change amplitude parameter of the system presents a double-peak structure, and the two peaks are distributed symmetrically around the “zero point”. This indicates that the system shifts in different states, and abrupt change is formed. Scholars have previously achieved similar conclusions in the study of climate system theories, i.e. the climate system is a multistability system (Baker and Charlson, 1990; Alexander et al., 2012). The results shown in Fig. 7 further prove that bistability or multistability states exist in the sea surface temperature.
The quantitative relationship among abrupt change rate
Relationship between abrupt change rate
Figure 7 shows the relationship between abrupt change rate
Figure 8 shows the relationship between abrupt change rate
In the results above, the Figs. 7–8 prove the quantitative relationship
provided in Eq. (
The climate is a gigantic, complex, and chaotic system with
bistable (multistable) states. Its transition from one state to another is
considered to be an abrupt climate change. In the present paper, by applying a
novel transition process detection method, the SST system is verified to be
bistable and several abrupt changes are detected. The results also provide
an understanding of the transition period, in which the system has already
left its original state, but has still not reached its new state:
The transition process is a significant period of an abrupt change
event. According to the start and end moment, the abrupt change event can be
divided into three stages. Based on GSST series, several abrupt changes have
been identified in the past 100 years, and the spatial distribution reveals
that abrupt change amplitudes in low-latitude regions are small, but those
in regions of middle and high latitude are large. In view of these characteristics of the abrupt change process, the
spatial distribution of abrupt change duration is analyzed. It is discovered
that abrupt changes in different periods have different durations. The
durations of abrupt changes before 1942 were generally long (about 5–10 years);
that in 1976 was about 5–8 years; and those after this time were
short (about 5 years). This indicates that the durations being shortened by
abrupt change are consistent with global warming. The spatial distribution of abrupt change amplitudes indicates that the
temperature decreased throughout the world mostly before 1942, but mostly
increased after that. The statistical results for abrupt change amplitude
verifies that the SST is bistable and that the system state variables have
shifted many times from one stable state to another. By analyzing the parameters estimated from the SST system, a
quantitative relationship is demonstrated that the relationship between the
rate of abrupt change and stability is linear, and the relationship between
the rate of abrupt change and change amplitude is quadratic. This
observation reveals the cause of the high rate and large amplitude of abrupt
climate change.
In the present paper, the transition process of abrupt climate change is
detected, based on reanalysis data from (NOAA) National Oceanic and Atmospheric Administration, and a quantitative relationship is exposed.
With the quantitative relationship, further research about the prediction of
abrupt climate change is worthy of further examination.
The authors acknowledge the National Oceanic and Atmospheric Administration
(Earth System Research Laboratory, 2016) for providing extended reconstructed
sea surface temperature (SST) V4
(
This study was jointly sponsored by the National Natural Science Foundation of China (grants 41305056, 41530531, 41375069), the key Special Scientific Research Fund of Meteorological Public Welfare Profession of China (grant GYHY201506001), and the State Key Development Program for Basic Research of China (grant 2013CB430204). Edited by: V. Perez-Munuzuri Reviewed by: two anonymous referees