Early-Warning Signals of Drought-Flood State Transition over the Dongting Lake Basin Based on the Critical Slowing Down Theory

: In this study, the standardized precipitation index (SPI) data in Hunan Province from 1961 to 2020 is adopted. Based on the critical slowing down theory, the moving t -test is ﬁrstly used to determine the time of drought-ﬂood state transition in the Dongting Lake basin. Afterwards, by means of the variance and autocorrelation coefﬁcient that characterize the phenomenon of critical slowing down, the early-warning signals indicating the drought-ﬂood state in the Dongting Lake basin are explored. The results show that an obvious drought-to-ﬂood (ﬂood-to-drought) event occurred around 1993 (2003) in the Dongting Lake basin in recent 60 years. The critical slowing down phenomena of the increases in the variance and autocorrelation coefﬁcient, which are detected 5–10 years in advance, can be considered as early-warning signals indicating the drought-ﬂood state transition. Through the studies on the drought-ﬂood state and related early-warning signals for the Dongting Lake basin, the reliabilities of the variance and autocorrelation coefﬁcient-based early-warning signals for abrupt changes are demonstrated. It is expected that the wide application of this method could provide important scientiﬁc and technological support for disaster prevention and mitigation in the Dongting Lake basin, and even in the middle and lower reaches of the Yangtze River.


Introduction
The Dongting Lake basin is located in the middle reaches of the Yangtze River and the north of the southern Yangtze River, mainly covering the Hunan Province, which is known as a fertile land of fish and rice in China. Historical data show that the Dongting Lake basin has been deeply affected by drought and flood disasters [1]. Particularly since the mid-20th century, flood and drought disasters frequently occur in the Dongting Lake basin under the background of significant global warming. Moreover, the phenomenon of drought-flood state transition (critical transition) has become more and more frequent [2,3]. The duration for the climate maintained in a drought or flood state over the Dongting Lake basin is getting shorter and shorter, that is, the transition cycle of drought-flood state significantly shortens [1,4,5].
The drought-flood state transition often leads to regional flood, drought, or deterioration of water environment [6]. If effective measures of early-warning can be carried out before the drought-flood state transition, local government and relevant departments will have sufficient time for management planning to minimize disaster losses as much before its transition from one phase to another, especially at the critical point, there will be dispersed fluctuations conducive to the formation of new phases. This dispersed fluctuation presents not only increasing amplitude, but also longer duration, slower recovery rate after the perturbation and decreased ability to return to the previous phase. This phenomenon is called "slowing down" [39]. Research on several real systems such as the climate system and the ecosystem has revealed that when the system approaches to the critical point, there will be a critical slowing down phenomenon featured by the slowing down in recovery rate, and the increases in the variance and autocorrelation coefficient after the system perturbation which provides a new idea for investigating the early-warning signals of abrupt changes in complex dynamical systems [14]. Based on the critical slowing down theory, Yan et al. [40] processed the data of radon concentrations in water and revealed that the early-warning signals of increasing variances and autocorrelation coefficients appeared before the Wenchuan earthquake in 2008. In recent years, several scholars [41][42][43][44][45] applied this theory to climate data, such as the regional temperature in China, the Pacific Decadal Oscillation index and the intensity of Aleutian low, aiming to study the earlywarning signals of abrupt climatic changes. On the basis of existing early-warning signals, He et al. [46][47][48] made some improvements and developed a set of quantitative earlywarning signals and methods for abrupt climatic changes. In view of the limitations of the linear method in previous research on the drought-flood state transition and the complex nonlinear processes involved in the drought-flood state transition over the Dongting Lake basin, this kind of state transition can be regarded as a systematic mutation. Therefore, previous research on the early-warning signals of abrupt changes based on the critical slowing down theory can provide effective methods for the research on the early-warning signals of the drought-flood state transition over the Dongting Lake basin.
Considering this, this study investigates the early-warning signals of the droughtflood state transition over the Dongting Lake basin based on the critical slowing theory. Firstly, the moving t-test (MTT) is used to detect the drought-flood state transition over the Dongting Lake basin. Then, by analyzing the variances and autocorrelation coefficients that characterize the phenomenon of critical slowing down, the early-warning signals for drought-flood state transition are explored which provides important reference for the prediction of drought and flood events over the Dongting Lake basin, thereby offering scientific and technological support for disaster prevention and mitigation over the basin.

Data
The data used in this paper are the monthly precipitation during 1961-2020 from 97 national meteorological stations released by the National Meteorological Information Center of China Meteorological Administration. After the stations with missing data were excluded, 82 stations were finally selected. On this basis, the standardized precipitation index (SPI) based on the monthly precipitation data is calculated at each station. The SPI proposed by McKee et al. [49] describes the intensity of moisture. It is calculated by referring to [50], and the intensity grades are shown in Table 1. The SPI calculation program is derived from the National Drought Mitigation Center of the United States (https://drought.unl.edu/droughtmonitoring/SPI/SPIProgram.aspx, accessed on 5 July 2021). In this study, the annual SPI is adopted to investigate the drought-flood state transition and its early-warning signals over the Dongting Lake basins. In this study, the moving variance and autocorrelation coefficient of the sequence are calculated to explore the early-warning signals for the drought-flood state transition in terms of the SPI sequence. The detailed method is shown in Figure 1.

Grades
Category SPI Value In this study, the moving variance and autocorrelation coefficient of the sequence are calculated to explore the early-warning signals for the drought-flood state transition in terms of the SPI sequence. The detailed method is shown in Figure 1. We calculated the variance and autocorrelation coefficient by sliding the window. (a) We calculated variance by sliding the window, L1, L2, L3, …, Ln denote windows of the same length(ML), S1, S2, S3, …, Sn represent the variances of the corresponding windows,L is the total length of the sequence, and MT is the sliding step; (b) we calculated the autocorrelation coefficient by sliding the window, L1(L12), L2(L22), L3(L32), …, Ln(Ln2)represent windows of the same length,  Figure 1. We calculated the variance and autocorrelation coefficient by sliding the window. (a) We calculated variance by sliding the window, L1, L2, L3, . . . , Ln denote windows of the same length(ML), S1, S2, S3, . . . , Sn represent the variances of the corresponding windows,L is the total length of the sequence, and MT is the sliding step; (b) we calculated the autocorrelation coefficient by sliding the window, L1(L12), L2(L22), L3(L32), . . . , Ln(Ln2)represent windows of the same length, α1 denotes the autocorrelation coefficients of L1 and the L12, α2 denotes the autocorrelation coefficient of the L2, while L22, the αn refer to the autocorrelation coefficients of the Ln and Ln2, LT represents the lag time, and L, ML and MT have the same meaning as those in (a).

Relation of the Critical Slowing Down with the Increasing Autocorrelations and Increasing Variances
Critical slowing down often leads to an increase in the autocorrelation and variance of the fluctuations in a stochastically forced system approaching a bifurcation at a threshold value of a control parameter [14,37]. It is assumed that there is a repeated disturbance of the state variable after each period of ∆t (that is, additive noise). Between disturbances, the return to equilibrium is approximately exponential with a certain recovery speed of λ. In a simple autoregressive model, this can be described as follows: where x n is the deviation of the state variable x from the equilibrium state, ε n is a random quantity satisfying the standard normal distribution, and s is the mean square error. If λ and ∆t are independent of x n , this model can be written as a first-order autoregressive (AR(1)) process: where the autocorrelation α = e λ∆t is zero for white noise and close to one for red noise. The variance of an AR(1) is as follows: Generally, when the system approaches the critical point, the return of the disturbance with small amplitude to equilibrium gets slower and slower [51,52], that is, λ approaches zero and the autocorrelation α is close to one. Thus, the variance tends to infinity (Equation (3)). Therefore, the increasing variance and autocorrelation coefficient can be used as the early-warning signals for the system approaching the critical point. In the calculation of this study, s represents the variance of the whole sequence, which is a constant value, while the Var value in Equation (3) changes with the window size and moving step.

Moving t-Test Method
The MTT is used to test the abrupt change in a sequence by examining the significance of the difference between the averages of two samples. The basic idea is as follows. The problem of whether there is a significant difference between the mean values of two subsequences in a climatic sequence can be regarded as the test of the significance of the population means between two samples. If the difference between the mean values of two subsequences exceeds a certain confidence level, it is considered that the mean value has changed qualitatively and thus the abrupt change occurs. Note that in order to avoid the drift of the tipping point caused by the artificially selected subsequence length in the MTT method, the subsequence length can be repeatedly changed for experimental comparison in specific application to improve the reliability of calculation results. In this study, this method is used to detect the abrupt change of sequences.

Results and Analysis
Since the mid-20th century, the drought-flood state transition over the Dongting Lake basin occurs more and more frequently under significant global warming, and correspondingly, the duration for the climate maintained in a drought or flood state is getting shorter and shorter. The drought-flood state transition often leads to regional flood, drought or deterioration of water environment [1,6]. Therefore, it is of great significance to study the early-warning signals for the drought-flood state transition over the Dongting Lake basin. In this section, the early-warning signals for the drought-flood state transition over the Dongting Lake basin are explored based on the critical slowing down theory.

Detection of the Drought-Flood State Transition over the Dongting Lake Basin
Firstly, the SPI values over the Dongting Lake basin are calculated through the gridarea-weighted average method [53]. This section mainly investigates the decadal variation characteristics of the SPI and the characteristics of the drought-flood state transition (abrupt change) over the Dongting Lake basin. Figure 2 shows that the SPI sequence over the Dongting Lake basin in recent 60 years is featured by obvious decadal changes. The trend of the moving averages reveals that there are obvious more precipitation-to-less precipitation (less precipitation-to-more precipitation) events in 1983 and 2003 (1993 and 2016). All these events are collectively referred to as the drought-flood state transition events (abrupt change). Studies have shown that there are obvious decadal changes for the drought and flood conditions over the Dongting Lake basin. In particular, the less precipitation-to-more precipitation events around 1993 are widely concerned [4,5].
characteristics of the SPI and the characteristics of the drought-flood state transition (abrupt change) over the Dongting Lake basin. Figure 2 shows that the SPI sequence over the Dongting Lake basin in recent 60 years is featured by obvious decadal changes. The trend of the moving averages reveals that there are obvious more precipitation-to-less precipitation (less precipitation-to-more precipitation) events in 1983 and 2003 (1993 and 2016). All these events are collectively referred to as the drought-flood state transition events (abrupt change). Studies have shown that there are obvious decadal changes for the drought and flood conditions over the Dongting Lake basin. In particular, the less precipitation-to-more precipitation events around 1993 are widely concerned [4,5].

Figure 2.
Temporal variation of the SPI sequence over the Dongting Lake basin in recent 60 years. The bar represents the SPI value (red bar indicates positive SPI and blue bar indicates negative SPI), and the black curve represents the trend extracted from 51month moving average. Figure 3 shows the detection curve for the abrupt change in the SPI sequence over the Dongting Lake basin based on the MTT method. When the size of the sliding window is set as 5 years, multiple abrupt changes will be found in the SPI sequence, which are especially significant in 1985, 1993 and 2003. When is set as 10 years, two obvious abrupt changes in 1993 and 2003 can also be found. Therefore, it can be considered that the SPI sequence over the Dongting Lake basin has two obvious abrupt changes (droughtflood state transition) in 1993 and 2003. In the following section, the early-warning signals for these two abrupt changes are explored based on the critical slowing down theory.  Figure 3 shows the detection curve for the abrupt change in the SPI sequence over the Dongting Lake basin based on the MTT method. When the size t of the sliding window is set as 5 years, multiple abrupt changes will be found in the SPI sequence, which are especially significant in 1985, 1993 and 2003. When t is set as 10 years, two obvious abrupt changes in 1993 and 2003 can also be found. Therefore, it can be considered that the SPI sequence over the Dongting Lake basin has two obvious abrupt changes (drought-flood state transition) in 1993 and 2003. In the following section, the early-warning signals for these two abrupt changes are explored based on the critical slowing down theory.     tion) in 1993 and 2003. Therefore, the state of the drought or flood over the Dongting Lake basin can be divided into three periods: 1961-1992, 1993-2002 and 2003-2020, all of which experience the state transition of less precipitation-more precipitation-less precipitation ( Figure 4). Specifically, during 1961-1992, the drought intensity in central and southeast Hunan is stronger; during 1993-2002, the waterlogging in western and northern Hunan is more obvious; during 2003-2020, the drought intensity in the east of central Hunan and the waterlogging in northern and western Hunan are stronger. The spatial distribution of the SPI values demonstrates that there are significant differences in the spatial distributions of the drought-flood conditions before and after the transition in 1993.

Circulation Background of the Drought-Flood Transition over the Dongting Lake Basin
The above analysis shows that the Dongting Lake basin has experienced less precipitation-more precipitation-less precipitation state transitions in three periods of 1961-1992, 1993-2002 and 2003-2020. In order to explore the circulation backgrounds for drought-flood state transitions over the Dongting Lake basin under different decadal backgrounds, the 500-hPa geopotential height and 200-hPa zonal wind are analyzed in this section.

Circulation Background of the Drought-Flood Transition over the Dongting Lake Basin
The above analysis shows that the Dongting Lake basin has experienced less precipitation-more precipitation-less precipitation state transitions in three periods of 1961-1992, 1993-2002 and 2003-2020. In order to explore the circulation backgrounds for drought-flood state transitions over the Dongting Lake basin under different decadal backgrounds, the 500-hPa geopotential height and 200-hPa zonal wind are analyzed in this section.
The low-pass filtering is carried out on the 500-hPa geopotential height to filter out the inter-annual components below 10 years. Figure 5 shows the fields of 500-hPa geopotential height and the composite anomalies corresponding to different decades over the Dongting Lake basin. In the first stage of the drought-flood transition (Figure 5a), the intensity of the polar vortex in Asian is strong, and there are significant negative anomalies over the Ural Mountains and the Okhotsk Sea, which is unfavorable to the development of the blocking highs over the Ural Mountains and Okhotsk Sea. For the mid-latitude region over the Asia continent, there are also significant negative anomalies, resulting in the relatively straight westerly circulation, which is unfavorable for the southward movement of cold air. Meanwhile, the western Pacific subtropical high (WPSH) is significantly weak, which is not beneficial to the transportation of the warm and humid airflow from the western Pacific and the South China Sea to southern China. This circulation configuration leads to less rainfall in this decade over the Dongting Lake basin. In the second stage of the drought-flood transition (Figure 5b), the field of 500-hPa geopotential height and corresponding composite anomalies show that the polar vortex is slightly weaker, and the Eurasian mid-high latitudes present a distribution of two-trough and one-ridge. Specifically, the Ural Mountains and its western area as well as the Okhotsk Sea are controlled by significant negative anomalies of geopotential height, indicating weak blocking highs over the Ural Mountains and the Okhotsk Sea. The Lake Baikal and its southern area are dominated by the ridge with obvious meridional circulations, which is beneficial to the southward movement of the cold air to affect China. Meanwhile, the westward extension and enhancement of the WPSH are more significant compared with that in the previous stage, and the Dongting Lake basin is located in the southward water vapor conveyor belt to the west side of the WPSH, which are favorable to more precipitation in this decade over this region. In the third stage of the drought-flood transition over the Dongting Lake basin (Figure 5c), the Eurasian mid-high latitudes are controlled by positive anomalies of geopotential height. The blocking highs over the Ural Mountains and the Okhotsk Sea significantly strengthen, which is not conducive to the southward movement of cold air. This is also consistent with the overall background of higher decadal temperature. At this stage, the WPSH is obviously stronger with larger area and westward position, and the ridge line is obviously northward to its normal position. The main rain belt is located in northern China, while the weather to the south of the Yangtze River is sunny, hot with less rain under the control of the WPSH. stage, and the Dongting Lake basin is located in the southward water vapor conveyor belt to the west side of the WPSH, which are favorable to more precipitation in this decade over this region. In the third stage of the drought-flood transition over the Dongting Lake basin (Figure 5c), the Eurasian mid-high latitudes are controlled by positive anomalies of geopotential height. The blocking highs over the Ural Mountains and the Okhotsk Sea significantly strengthen, which is not conducive to the southward movement of cold air. This is also consistent with the overall background of higher decadal temperature. At this stage, the WPSH is obviously stronger with larger area and westward position, and the ridge line is obviously northward to its normal position. The main rain belt is located in northern China, while the weather to the south of the Yangtze River is sunny, hot with less rain under the control of the WPSH.  Figure 6 shows the 200-hPa zonal wind and the composite anomalies corresponding to different decades over the Dongting Lake basin. In the first stage (Figure 6a), the 200-hPa zonal wind over the mid-latitude region in eastern Asia presents a significant "positive-negative" distribution, where positive zonal wind anomalies appear over the northern region of China, and negative zonal wind anomalies over the southern region. This reveals that the location of the westerly jet is more northerly and easterly than its normal position. Therefore, it is difficult for the cyclonic disturbance in the westerlies to affect the southern region of China, leading to less rainfall in the Dongting Lake basin. In the second stage (Figure 6b), the circulation is obviously opposite to that of the previous stage. Negative zonal wind anomalies prevail over the northern region of China, while positive zonal wind anomalies over the southern region, which implies that the location of westerly jet is more south than its normal location, thus leading to significantly more-than-normal precipitation over the Dongting Lake basin. In the third stage (Figure 6c), the distribution of 200-hPa zonal wind over the eastern part of the mid-latitude in the Asia continent is similar to that in the first stage, posing a "positive and negative" distribution pattern from  Figure 6 shows the 200-hPa zonal wind and the composite anomalies corresponding to different decades over the Dongting Lake basin. In the first stage (Figure 6a), the 200-hPa zonal wind over the mid-latitude region in eastern Asia presents a significant "positivenegative" distribution, where positive zonal wind anomalies appear over the northern region of China, and negative zonal wind anomalies over the southern region. This reveals that the location of the westerly jet is more northerly and easterly than its normal position. Therefore, it is difficult for the cyclonic disturbance in the westerlies to affect the southern region of China, leading to less rainfall in the Dongting Lake basin. In the second stage (Figure 6b), the circulation is obviously opposite to that of the previous stage. Negative zonal wind anomalies prevail over the northern region of China, while positive zonal wind anomalies over the southern region, which implies that the location of westerly jet is more south than its normal location, thus leading to significantly more-than-normal precipitation over the Dongting Lake basin. In the third stage (Figure 6c), the distribution of 200-hPa zonal wind over the eastern part of the mid-latitude in the Asia continent is similar to that in the first stage, posing a "positive and negative" distribution pattern from north to south. The location of westerly jet stream is slightly norther than normal, causing less precipitation over the Dongting Lake basin, but not as significant as that in the first stage. The results are consistent with the conclusions in previous studies [4,54].

Early-Warning Signals for the Drought-Flood State Transition over the Dongting Lake Basin Based on the Variance
At the beginning of the 21st century, scientists found that the critical slowing down theory has important potentials in studying the early-warning signals for complex dynamical systems. This section explores the early-warning signals for the drought-flood state transition over the Dongting Lake basin by the variance that characterizes the phenomenon of critical slowing down. Figure 7 shows the detection of the abrupt changes in the SPI sequence over the Dongting Lake basin based on the variance signal. Here, ML in this study is set to 120 months (10 years), and the MT is set to 3 months. For the variance of the sequence, the window width and the MT, please refer to Figure 1. Figure 7a shows the variance-based detection of the SPI sequence for the abrupt change in 1993. As shown in Figure 1, by sliding forward a fixed-width window with fixed MT in the SPI sequence, a new sequence is obtained in the fixed-width window with the new location. The variance is further calculated for this new sequence. The arrow in Figure 7a illustrates that the variance starts to increase around 1985. The above theoretical analysis shows that the critical slowing down leads to the decrease in the internal change rate of the drought-flood state, and the similarity between the states at any time and the previous state in the complex nonlinear system as well. Thus, the autocorrelation coefficient is close to one, and the variance is close to infinity according to Formula (3). Therefore, the critical slowing down phenomenon of increasing variance when the complex nonlinear system approaches to the critical point might be an early-warning signal for the abrupt change in complex nonlinear sys-

Early-Warning Signals for the Drought-Flood State Transition over the Dongting Lake Basin Based on the Variance
At the beginning of the 21st century, scientists found that the critical slowing down theory has important potentials in studying the early-warning signals for complex dynamical systems. This section explores the early-warning signals for the drought-flood state transition over the Dongting Lake basin by the variance that characterizes the phenomenon of critical slowing down. Figure 7 shows the detection of the abrupt changes in the SPI sequence over the Dongting Lake basin based on the variance signal. Here, ML in this study is set to 120 months (10 years), and the MT is set to 3 months. For the variance of the sequence, the window width and the MT, please refer to Figure 1. Figure 7a shows the variance-based detection of the SPI sequence for the abrupt change in 1993. As shown in Figure 1, by sliding forward a fixed-width window with fixed MT in the SPI sequence, a new sequence is obtained in the fixed-width window with the new location. The variance is further calculated for this new sequence. The arrow in Figure 7a illustrates that the variance starts to increase around 1985. The above theoretical analysis shows that the critical slowing down leads to the decrease in the internal change rate of the drought-flood state, and the similarity between the states at any time and the previous state in the complex nonlinear system as well. Thus, the autocorrelation coefficient is close to one, and the variance is close to infinity according to Formula (3). Therefore, the critical slowing down phenomenon of increasing variance when the complex nonlinear system approaches to the critical point might be an early-warning signal for the abrupt change in complex nonlinear system. It is considered that the early-warning signal for the drought-flood state transition over the Dongting Lake basin occurs around 1985. It can be seen that the early-warning signal is about 8 years ahead of the abrupt change in the SPI sequence, indicating that the variance acts as a good indicator for the prediction of the drought-flood state transition. Similarly, the variance signal for the abrupt change of the SPI sequence in 2003 over the Dongting Lake basin appears in 1998 (in Figure 7b). The critical slowing down based on increasing variance is a potential early-warning signal for the drought-flood state transition over the Dongting Lake basin. Similarly, the variance signal for the abrupt change of the SPI sequence in 2003 over the Dongting Lake basin appears in 1998 (in Figure 7b). The critical slowing down based on increasing variance is a potential early-warning signal for the drought-flood state transition over the Dongting Lake basin.

Early-Warning Signals for the Drought-Flood State Transition over the Dongting Lake Basin Based on the Autocorrelation Coefficient
According to the above studies, the critical slowing down phenomenon based on the increasing variance can be used as an early-warning signal for the drought-flood state transition over the Dongting Lake basin. In this section, another quantity that characterizes the critical slowing down theory, the autocorrelation coefficient, is used to explore the early warning signals for the drought-flood state transition over the Dongting Lake. Figure 8 shows the autocorrelation coefficient signal-based detection of the abrupt changes in the SPI sequence over the Dongting Lake basin. Similarly, ML in this study is set to 120 months (10 years), the MT is set to 6 months, and the lag time (LT) is set to 1 month. The variance of the sequence, window width and MT are shown in Figure 1. As shown in Figure 1, by sliding forward a fixed-width window with one fixed LT in the original SPI sequence, another sequence with the same length as the sequence in the original window is obtained. The correlation between the obtained sequence and the original sequence is calculated, thus obtaining the lag autocorrelation for the sequence itself. The MT is the same as described in the variance signal section. Figure 8a displays the autocorrelation coefficient-based detection for the abrupt change of the SPI sequence in 1993. The autocorrelation coefficient begins to increase from year marked with an arrow in Figure  8a. As the critical slowing down leads to the decrease of the internal change rate in the drought-flood state and the state of complex nonlinear system at any time is becoming more and more similar to its previous state, the autocorrelation coefficient of the SPI sequence is close to one. It is considered that the early-warning signal for the drought-flood state transition in 1993 appears around 1985. Therefore, the early-warning signal of the increasing autocorrelation coefficient appears eight years before the drought-flood state transition over the Dongting Lake basin in 1993, which serves as a good indicator for the prediction of the drought-flood state transition over the Dongting Lake basin. Similarly, the autocorrelation coefficient signal for the abrupt change over the Dongting Lake basin

Early-Warning Signals for the Drought-Flood State Transition over the Dongting Lake Basin Based on the Autocorrelation Coefficient
According to the above studies, the critical slowing down phenomenon based on the increasing variance can be used as an early-warning signal for the drought-flood state transition over the Dongting Lake basin. In this section, another quantity that characterizes the critical slowing down theory, the autocorrelation coefficient, is used to explore the early warning signals for the drought-flood state transition over the Dongting Lake. Figure 8 shows the autocorrelation coefficient signal-based detection of the abrupt changes in the SPI sequence over the Dongting Lake basin. Similarly, ML in this study is set to 120 months (10 years), the MT is set to 6 months, and the lag time (LT) is set to 1 month. The variance of the sequence, window width and MT are shown in Figure 1. As shown in Figure 1, by sliding forward a fixed-width window with one fixed LT in the original SPI sequence, another sequence with the same length as the sequence in the original window is obtained. The correlation between the obtained sequence and the original sequence is calculated, thus obtaining the lag autocorrelation for the sequence itself. The MT is the same as described in the variance signal section. Figure 8a displays the autocorrelation coefficient-based detection for the abrupt change of the SPI sequence in 1993. The autocorrelation coefficient begins to increase from year marked with an arrow in Figure 8a. As the critical slowing down leads to the decrease of the internal change rate in the drought-flood state and the state of complex nonlinear system at any time is becoming more and more similar to its previous state, the autocorrelation coefficient of the SPI sequence is close to one. It is considered that the early-warning signal for the droughtflood state transition in 1993 appears around 1985. Therefore, the early-warning signal of the increasing autocorrelation coefficient appears eight years before the drought-flood state transition over the Dongting Lake basin in 1993, which serves as a good indicator for the prediction of the drought-flood state transition over the Dongting Lake basin. Similarly, the autocorrelation coefficient signal for the abrupt change over the Dongting Lake basin in 2003 appears in 1998 in the SPI sequence. Therefore, in view of the two drought-flood state transitions of the SPI sequence over the Dongting Lake basin, the early-warning signal of increasing autocorrelation coefficient for abrupt changes appears 5-10 years before the state transition. The critical slowing down phenomenon based on the increasing autocorrelation coefficient is a potential early warning signal for the drought-flood state transition over the Dongting Lake basin.
the state transition. The critical slowing down phenomenon based on the increasing autocorrelation coefficient is a potential early warning signal for the drought-flood state transition over the Dongting Lake basin.
Note that when the data amount remains constant, the larger the window width and the longer the MT, the more stable the result will be. Variations in window width and LT do not influence the occurrence of the signal, but only affect the signal stability. Related studies are detailed in Wu et al. [25][26][27][28], which will not be covered here.
In summary, when the drought-flood system approaches the critical point, the phenomena of critical slowing down will occur, featured by increasing variance and increasing autocorrelation coefficient, indicating the occurrence of a drought-flood state transition. Based on the variance and autocorrelation coefficient, the occurrence times of the early-warning signals for the drought-flood state transition are basically the same, which further proves the feasibility to explore the early warning signals for the drought-flood state transition based on the critical slowing down theory.

Conclusions and Discussions
In view of the complex nonlinear characteristics of the drought-flood state transition, the theories and methods related to the nonlinear science are adopted for investigation in this study. First, the MTT method is performed on the SPI sequence over the Dongting Lake basin in recent 60 years for detecting the drought-flood state transitions. Afterwards, the physical basis and statistical significance of the critical slowing down phenomenon are further introduced. On this basis, the theory of critical slowing down is used to explore the early-warning signals for abrupt changes in the SPI sequence over the Dongting Lake basin. The conclusions are as follows.
Detection on the SPI sequence over the Dongting Lake basin reveals that there are two significant drought-flood state transitions, namely the drought-to-flood event in 1993 and the flood-to-drought event in 2003.
(1) By analyzing the 500-hPa geopotential height and 200-hPa zonal wind, it is found that the circulation backgrounds during 1961-1992 and 2003-2020 are favorable for less precipitation and drought over the Dongting Lake Basin. While the circulation backgrounds during 1993-2002 results in more precipitation and even floods over the Dongting Lake basin.
(2) The critical slowing down phenomena with the increases in variances and autocorrelation coefficients appear 5-10 years before the two drought-flood state transitions, indicating the feasibility of exploring the early-warning signals for drought-flood state transitions based on the critical slowing down theory. Note that when the data amount remains constant, the larger the window width and the longer the MT, the more stable the result will be. Variations in window width and LT do not influence the occurrence of the signal, but only affect the signal stability. Related studies are detailed in Wu et al. [25][26][27][28], which will not be covered here.
In summary, when the drought-flood system approaches the critical point, the phenomena of critical slowing down will occur, featured by increasing variance and increasing autocorrelation coefficient, indicating the occurrence of a drought-flood state transition. Based on the variance and autocorrelation coefficient, the occurrence times of the earlywarning signals for the drought-flood state transition are basically the same, which further proves the feasibility to explore the early warning signals for the drought-flood state transition based on the critical slowing down theory.

Conclusions and Discussions
In view of the complex nonlinear characteristics of the drought-flood state transition, the theories and methods related to the nonlinear science are adopted for investigation in this study. First, the MTT method is performed on the SPI sequence over the Dongting Lake basin in recent 60 years for detecting the drought-flood state transitions. Afterwards, the physical basis and statistical significance of the critical slowing down phenomenon are further introduced. On this basis, the theory of critical slowing down is used to explore the early-warning signals for abrupt changes in the SPI sequence over the Dongting Lake basin. The conclusions are as follows.
Detection on the SPI sequence over the Dongting Lake basin reveals that there are two significant drought-flood state transitions, namely the drought-to-flood event in 1993 and the flood-to-drought event in 2003.
(1) By analyzing the 500-hPa geopotential height and 200-hPa zonal wind, it is found that the circulation backgrounds during 1961-1992 and 2003-2020 are favorable for less precipitation and drought over the Dongting Lake Basin. While the circulation backgrounds during 1993-2002 results in more precipitation and even floods over the Dongting Lake basin.
(2) The critical slowing down phenomena with the increases in variances and autocorrelation coefficients appear 5-10 years before the two drought-flood state transitions, indicating the feasibility of exploring the early-warning signals for drought-flood state transitions based on the critical slowing down theory. (3) The critical slowing down phenomena with the increases in variances and autocorrelation coefficients appear 5-10 years before the two drought-flood state transitions, indicating the feasibility of exploring the earlywarning signals for drought-flood state transitions based on the critical slowing down theory.
Through the study on the drought-flood state and related early-warning signals over the Dongting Lake basin, the reliability of the early-warning signals of the variance and autocorrelation coefficient characterizing the critical slowing down phenomenon in detecting abrupt changes is demonstrated. Besides, the introduction of the critical slowing down theory is of important practical significance and scientific value for deep understanding of drought-flood state transition and for exploring the early warning signals of its state transition based on the SPI sequence. Furthermore, the extensive application of this method is expected to provide important scientific and technological support for disaster prevention and mitigation over the Dongting Lake basin and even in the middle and lower reaches of the Yangtze River. Note that although the the results of the present manuscript show that the increasing variances and autocorrelation coefficients caused by the critical slowing down phenomenon are potential early warning signals, and more robust conclusions require more experiments and applications to confirm. The confidence probability of early warning signals, the circulation characteristics, the characteristics of external forcing changes, and the relationship between the critical slowing down phenomenon and the intensity/amplitude of abrupt changes before and after the transitions still need to be further studied.
This paper studies a method that can identify the early warning signal of Drought-Flood state transition in a long period of time in the future, which strictly belongs to the category of climate shift. The climate shift is not necessarily a hazard per se, but it will have a great impact on the frequency, intensity and duration of hazards. The early warning signal of climate shift can warn the change and remind people to be prepared for the possible consequences of this change. For example, we can study some specific disasters and determine the threshold of precipitation which can lead to disaster, such as flood and landslide [55]; in addition, the high-risk locations of disasters can be determined in the region with reference to the disasters that have occurred in the previous more Rainy period or less rainy period and their impacts, and the probability of possible disasters in the future can be estimated in combination with the current exposure and vulnerability.
EWS involves six aspects [27]: (1) What is happening with respect to the hazards and/vulnerabilities? (2) When are the impacts likely to occur? (3) Where are at risk? (4) Who are at risk? (5) What causes the risk? (6) How can EWS play a better role, whether it is for a specific hazard or guiding a long-term risk response process? For drought or flood disasters, the early warning signal of Drought-Flood state transition can answer the first question about hazards and the second question, as well as help to solve the sixth question. On the premise that the accuracy of climate model prediction needs to be further improved, the method in this paper can use the existing observation data to provide a new technology for early warning of climate transition. In addition, it can also analyze the influencing factors such as atmospheric circulation and sea surface temperature in time, so as to provide comparison and reference for improving the climate model.