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An abrupt climate change means that the climate system shifts from a steady state to another steady state. Study on the phenomenon and theory of the abrupt climate change is a new research field of modern climatology, and it is of great significance for the prediction of future climate change. The climate regime shift is one of the most common forms of abrupt climate change, which mainly refers to the statistical significant changes on the variable of climate system at one time scale. These detection methods can be roughly divided into five categories based on different types of abrupt changes, namely, abrupt mean value change, abrupt variance change, abrupt frequency change, abrupt probability density change, and the multivariable analysis. The main research progress of abrupt climate change detection methods is reviewed. What is more, some actual applications of those methods in observational data are provided. With the development of nonlinear science, many new methods have been presented for detecting an abrupt dynamic change in recent years, which is useful supplement for the abrupt change detection methods.

The research on the phenomenon of abrupt climate change and the related theory is an important field in modern climatology, which is one of the core issues concerning the global climate change. It is also important for the prediction of climate change [

Because of the suddenness for the occurrence of abrupt climate change, it has a potentially significant impact on the sustainable development of the ecological environment, the social economy, or even the extinction of species. For example, historically, the drought in the region of Mesopotamia led to the decline of ancient civilizations, such as the ancient Greek civilization, the Egyptian civilization in the Nile Valley, and the ancient Indian civilization in the Indus Valley [

At present, there are mainly three aspects of studies on abrupt climate change: early-warning signals for abrupt climate change, detection methods for abrupt climate change, and attribution studies on abrupt climate change events. Scheffer et al. [

The accurate identification and detection of abrupt climate change is the prerequisite and basis for studies on early-warning signals and attribution studies of abrupt climate change. Many scholars have conducted a lot of relevant studies, such as detection with respect to transition in the climate system state. Rodionov [

In this paper, we mainly review the progress on the theory and methodological studies in China and other countries regarding the detection of regime shifts in the climate system. The discussions are focused on describing the climate regime shifts detection methods, and some applications on actual observation data. This paper is organised as follows. In Section

The detection methods for the abrupt mean value changes can be divided into six categories, which mainly include parameter detection method, non-parameter detection method, cumulative sum method, Bayesian analysis method, sequential method, and detection methods based on regression analysis. The moving

The nonparametric detection methods mainly include the Mann-Kendall test (M-K test) [

The mean and variance of the newly established sequence

The standardization of the newly established sequence

The Mann-Whitney

Original hypothesis

Combine two sets of data, and assign numeric ranks to all the records, beginning with 1 for the smallest value (where there are groups of tied values, assign a rank equal to the midpoint of unadjusted rankings [e.g., the ranks of (3, 5, 5, 9) are (1, 2.5, 2.5, 4)]).

Calculate the sum of the ranks for the two samples, and

Calculate the statistical quantity

If the original hypothesis is true, then the mean value and variance of random variable

If

Make the judgment. Setting the mean value of the first sample as

The Mann-Whitney

The Lepage test is a nonparametric statistical method for testing whether there is a significant difference between the mean values of two independent samples, even if the distributions of parent populations are unknown. If there is a significant difference between the two subsequences at a significant level, it is concluded that there is an abrupt change.

Suppose that the number of samples for the subsequence before the reference point is

Additionally, we then construct another quantity of rank statistics as

A combine of the squares of the standardized Wilcoxon and Ansariy-Braley’s statistics is the Lepage test:

The Lepage test has more powerful functions than the moving

The cumulative sum method is the third type of detection method for the abrupt mean value change, and it mainly includes the cumulative sum test and the cumulative frequency test. The cumulative sum method was proposed by Page [

The Bayesian analysis is the fourth detection method type for the abrupt mean value change, which is developed based on Bayesian theory. Firstly, we can integrate the a priori information and sample information of unknown parameters and then derive the a posteriori information according to Bayesian theory. The unknown parameters can be inferred according to the derived posteriori information. The Markov Chain Monte Carlo (MCMC) approach [

Construct the Markov chain and make it converge with the stationary distribution.

Draw the sample from a target space, apply the chain constructed in Step 1 to sample and simulate, and then generate the sequence.

Conduct the Monte Carlo integration, and the expected estimate of any function is as follows:

Chu and Zhao [

The time series of tropical cyclones number in the central of North Pacific during 1966–2002 and its MCMC detection results [

The sequential method can find the maximum of the mean value from a number of normal distributions with different mean values and then can be used to conveniently and rapidly detect an abrupt mean change. Rodionov [

Bernaola-Galvan et al. [

The two-phase regression technique (TPR) is a typical method for detecting abrupt change based on regression analysis. Hinkley [

The composite analysis [

The methods that detect the change in the probability density distribution of elements include the abrupt density change, skewness and kurtosis coefficient, and sliding skewness index method based on the Box-Cox transformation.

For a stable dynamic system, the probability density of the system variables has a relatively stable distribution pattern, although, when the dynamic structure of the system changes, it may cause different degrees of change in the distribution patterns of the system variables. From the perspective of identifying small changes in the probability density distribution of the system variables, Cheng et al. [

Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. Coefficient of skewness can be positive or negative, or even undefined. For a time series

Kurtosis is a descriptor of the shape of a probability distribution and, just as for skewness, there are different ways of quantifying it for a theoretical distribution and corresponding ways of estimating it from a sample from a population. Coefficient of kurtosis is mainly used to describe the steep degree of the probability density distribution curve. The standard measure of kurtosis is based on a scaled version of the fourth moment of the data or population, and the coefficient of kurtosis

It should be noted that when the difference in the steepness or skewness of the probability density curve before and after an abrupt change is relatively small, it might need more samples to identify the abrupt change to ensure the statistical reliability of the detection results. Consequently, under certain conditions, the coefficients of skewness and kurtosis most likely have a relatively high requirement regarding the sample size and are likely not applicable to those time series with relatively a small sample size.

He et al. [

Box-Cox transformation [

In order to test the performance of the STP method, the 1000 artificial daily precipitation series have been analyzed, and the results indicate that STP can almost recognize all of the first change point and the accuracy for the second change point is 99.8%. It shows the ability of STP to identify abrupt probability density changes in daily precipitation series. To examine the performances of STP in the observed daily precipitation records, He et al. randomly select six observational stations in China and find that all the STP results for six daily precipitation records display almost identical evolutionary trend. The results indicate that the transformation parameters undergo a rapid shift from one stable state to an alternative stable state with obviously different means between 1979 and 1980 (Figure

The STP results for daily precipitation records (from 1961 to 2010) in six meteorological observational stations in China, and the sample size of sliding window is 1 year: (a) Tonghe in Heilongjiang Province; (b) Hailun in Heilongjiang Province; (c) Qiqihaer in Heilongjiang Province; (d) Zhalantun in Inner Mongolia; (e) Sunwu in Heilongjiang Province; (f) Nenjiang in Heilongjiang Province [

Moreover, Ning and Gupta [

The abrupt variance change can be determined by the change in the second-order statistics of elements. There are few methods to test this type of abrupt change. The Downton-Katz test [

Multivariate analytical methods, such as principal component analysis [

In this paper, we briefly review some advances in the abrupt climate change detection methods in recent years. According to the types of abrupt change, the methods for detecting a state transition in the climate system can be divided into five categories: abrupt mean value change, abrupt variance change, abrupt frequency change, abrupt probability density change, and multivariate analysis. There are relatively numerous research contents on abrupt mean value change and abrupt probability density change. Based on this, we provide a considerably detailed summary. The detection methods for abrupt mean value change mainly have six subcategories, which include the parametric method, the non-parametric method, the cumulative sum method, the Bayesian analysis method, the sequential method, and test algorithms based on regression analysis. The methods for detecting abrupt change in probability density distribution of elements include the coefficient of kurtosis and skewness coefficient and the STP method based on the Box-Cox transformation. There are few testing methods based on an abrupt change in variance, frequency, and multivariate analysis, and the details on the algorithmic methods are not described in the present paper.

In this paper, we mainly describe the methods for climate regime shift detection. These methods have one common shortcoming; that is, the detection results heavily depend on the used sample size. In other words, the detected abrupt change point possesses the characteristics of multiple time scales. The reason for this is that an abrupt change event is often determined according to a statistical significant change of a state variable. So, these detection methods for regime shift are not applicable to the abrupt change in the climate dynamic structure. With the development of nonlinear science, many new methods and new techniques have been presented in recent years, especially for the detection methods for abrupt dynamical change. These methods and techniques are mainly based on the long-range correlation in climate system, the complexity property of time series, and the reconstruction theory of phase space. Different from the detection methods for regime shift, the detection results of these new methods have less dependence on sample size, which are applicable to identify whether there is an abrupt dynamic change in the climate system from single time series.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This paper is supported by the National Basic Research Program of China (973 Program) (2012CB955902) and the National Natural Science Foundation of China (Grant nos. 41275074, 41475073, and 41175084).