A nonlinear method for detecting climate mutation: a case study for summer climate change in China

In this paper, we explored the dynamical mechanism of anomalous summer climate late 1970s in China applying a new method, i.e., a dynamics index-Q based on phasespace reconstruction. The interesting results show that different climate variable have the similar dynamics property in different regions, they reflect an intrinsic dynamics 5 interior climate system, which may be associated with the teleconnection wave trains mainly triggered by the Tibetan Plateau, and reveals some of causes making North China drought indirectly. However, the Phenomena are hardly possible found via any statistic methodology.


Introduction
Climate mutation is a specific representation of the dynamical structures of climate system, its dynamical processes or mechanisms are largely unknown (Feng et al., 2001Li and Chou, 2003;Li and Wang, 2003). Statistical techniques, such as low pass filtering, moving t-test, Cramer method (Fu and Wang, 1992), Yamamoto method (Yamamoto et al., 1985(Yamamoto et al., , 1986, and M-K method (Goossens and Berger, 1986), 15 etc., are still the main tools for diagnosing the climate mutation. These methods have advantages to certain extent, but can't show confidence level due to certain subjectivity involved sometimes (Fu and Wang, 1992). Furthermore, most of these methods can't be used to deal with complicated time series.
Although the climate mutation studies based on the statistical techniques have in- 20 dicated that under the background of global climate changes, many climate elements jumped late1970s, however, the property and mechanism associated with the climate jump remain to be established (Shi, 1996;Shi et al., 2000Shi et al., , 2003Dai et al., 2003). Aiming at exploring the question, the dynamics index-Q (Li and Pei, 2003), which has the superior performance in distinguishing different dynamics and is suitable for the 25 cases of small sample (Feng et al., 2005(Feng et al., , 2006, is introduced in this paper to iden-tify the nonlinear dynamics climate system. In present paper, we use the dynamics index-Q to diagnose climate mutation in the summer climatic elements. The data sets and methodology are exposed in Sect. 2. Results of the analyses on temperature and precipitation in China are given in Sect. 3. Reconstruction of climate dynamical backgrounds is shown in Sect. 4. Conclusions and discussion appear in Sect. 5.

Daily weather observations
Daily precipitation and temperature in mainland China for the period 1960-2000 was obtained from a recent developed comprehensive daily meteorological dataset . The dataset contains 729 stations that have long-term precipitation and 10 temperature observations. The data had been subjected to a series of quality control, which includes homogeneity testing and adjustments to assure their reliability . The 1960-2000 complete summer (JJA) daily data at 547 stations without any missing value selected ( Fig. 1) and divided into 1960-1977 and 1983-2000 groups in order to avoid the influence of the mutation periods (Shi, 1996) (namely the 5 years 15 of 1978-1982 were not included).

The optimizing algorithm
In this section, we introduce the methodology for the application of Q-index. The Qindex method is designed to detect dynamical structures of time series recorded at various locations, based on phase-space reconstruction. The dynamical reconstruc-20 tion of a nonlinear time series with the size N{x (t i ) , i =1, 2, . . ., N} can be performed according to the following expression: 1049 where the lag time τ=α·∆t, α is a lag parameter, ∆t the sampling interval, and m the dimension number of the embedding space (Sauer, 1994). Thus a vector matrix of (N−α (m−1)) ×m dimensions is constructed, and its self-correlation function is defined as (Grassberger and Procaccia, 1983) which denotes the probability of finding an adjacent point within distance in the reconstructed space (Grassberger and Procaccia, 1983). Θ denotes the Heaviside function. C xx ( ) has certain ability to distinguish potential dynamics for chaotic signals (Provanzale et al., 1992), however, it is far from the most important standard for 10 discerning the closeness of chaotic time series (Grassberger and Procaccia, 1983;Grassberger, 1990). Then, how to identify the dynamical differences of chaotic time series? Let x (i ) and x (j ) be two points of discrete series x (n) (n is size of samples), when )| has stronger forecast ability than self-correlation (Savit and Green, 1991;Manuca and 15 Savit, 1996). Similarly, for two time series {x i } and {y i }, the dynamical self-correlation factor can be defined as (Li and Pei, 2003) which means that when Q xy is statistically small enough, series {x i } and {y i } at least have a close dynamical structure, otherwise, they do not have close dynamical charac-20 ters. It can directly measure the "distance" of different chaotic time series (Grassberger, 1990), i.e., when Q xy ≈0, it represents that two series originate from the same dynamics system.

Results
Researches based on the statistical techniques indicated that under the climate background of global changes, climate elements in China jumped late 1970s. Shi (Shi, 1996;Shi et al., 2003) investigated the climate change in China in terms of annual temperature, annual precipitation and characteristic quantities of the Northern Hemi-5 spheric general circulation, and pointed out that the regional characters of the precipitation and temperature in the 1980s in China are as follows: north China was warm and dry, southwest China cold and dry, northeast China warm and wetter, and the Yangtze River valley cold and wet; while the intensities of teleconnection patterns including the WA and PNA had jumped, respectively, in the early 1980s and the middle 10 1970s; The discontinuous change of the subtropical high happened in 1976 and the early 1980s. Recently, Dai (Dai et al., 2003) pointed out that the interdecadal dry/wet subrogation occurred in most areas of China, and north China has been severely dry in the 1980s-1990s.  (Dai et al., 2003;Shi et al., 2003Shi et al., , 2000Shi, 1996). However, whether the jump of mean-value means the change in the dynamics of the governing system or not? This is the key issue to be analyzed and solved in this paper by using the latest research achievement of the nonlinear 25 dynamics. The dynamics index-Q calculated via Eq. (4) suggests that the dynamical mutation areas (shaded) generally do not accord with the mean-value jump areas, but 1051 both coincide well in north China (C1 in Fig. 2b). namely, remarkable mean-value jump and dynamical mutation both occur in North China. Although the mean-value jump in the lower-middle reaches of the Yangtze River is more notable than that in North China, there is no evidence for dynamical mutation to appear in this region (Fig. 2b). Similarly, the distributions of the mean-value and dynamical mutation of temperature 5 are shown in Fig. 2c and d, respectively. It is clear that there was a warming in North China and a cooling in the Yangtze River valley for mean temperature (Shi, 1996;Shi et al., 2003) and the situation of temperature is in agreement with that of precipitation for dynamical mutation The contrast analysis shows that the mean-value jump centers for precipitation and temperature do not coincide with each other (Fig. 2a and c) while 10 the dynamical mutation centers (including eastern Tibetan Plateau, North China and north Northeast China) of precipitation and temperature coincide well (A1, B1 and C1 coincide basically with A2 ,B2 and C2, respectively). Figure 3 is summer (JJA) total precipitation at Shanghai (Fig. 3a), Wutaishan (Fig. 3b), respectively. Figure 3a shows that although the first and second segments of 15 the precipitation series at Shanghai (located in the Yangtze River valley) differ greatly in the mean value, they are very similar in the shape, indicating that the mean value jump of precipitation in the middle and lower reaches of the Yangtze River results from the different phases (namely wave peak and trough scenarios) of the same system. That is to say, the dynamical structure of precipitation in Shanghai does not change. The 20 boreal spring SAM (Southern Hemisphere annular mode) variation provides a potential valuable signal for predicting the summer precipitation in the lower-middle reaches of the Yangtze River valley. However, situations in Wutaishan (Fig. 3b, located in North China) is different from that in Fig. 3a. Two segments of the precipitation series differ in the shape, amplitude, even period, reflecting the difference in the dynamical struc-25 ture of the two segment curves. Therefore, the mean-value jump does not mean any change in dynamics.

Possible mechanism for climate mutation
The teleconnection show the synchro-variation feature of the atmospheric circulation, and are the products of the remote-responses triggered by topography and quasistationary heat source. And the interaction between external forcing (topography and heat source) and basic flow is the fundamental cause for the genesis of teleconnection 5 wave trains. Figure 4a and b exhibit the 300-hPa geopotential height response patterns triggered by a circular mountain (30 • N) and an elliptic heat source (15 • N), respectively, in a 5-layers baroclinic model under an initial condition of northern winter zonal flow, which suggests that the topography and heat source are able to trigger, respectively, a teleconnection wave rain that propagates (north-northeast-wards) towards the high latitude (Hoskins and Karoly, 1981). This is the "great circle theory" used to interpret the teleconnection phenomenon. Likewise, the Tibetan Plateau as the global heating center can also trigger similar wave trains, which propagate along a great circle on the sphere surface (see the circles in Fig. 2b and d), namely from the Tibetan Plateau (A1/B1, A2/B2), through north China (C1, C2), to northeast China (D1, D2), and dis-15 perse downstream-wards. North China just lies on its propagating path (B1, B2); hence the persistent drought in north China after late 1970s might be dominated by Tibetan Plateau teleconnection wave trains (TPT).
The recent studies point out that the atmospheric circulation of the Tibetan Plateau not only responses to the global warming jump around 1980, but also on the inter-20 decadal scale, the state of its heat source also show an evident jump around 1977 (Shi and Zhu, 1993), which gives possible cause and mechanism for the enhanced drought condition in north China after late 1970s.

Reproducibility of the climate dynamical backgrounds
It has been mentioned above that the mean value jump of precipitation and temperature 25 can't be superimposed spatially, but all of the dynamical mutation are basically uniform.

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What essence does it reveal?
As well known, the climate system is a complicated dynamical system, it can be described by differential equations of different variables such as potential height, pressure, temperature, or precipitation etc. meteorological elements. Each of them can reproduce the climatic backgrounds. The nonlinear research outcomes of the 1970s 5 reveal that the dynamics of a climate variable is the sub domain of the climate system, which can reflects the character of the governing system. That is to say, after the reconstruction of phase space, whether precipitation or temperature can reveal the character of the dynamical structure and the evolution of climate system, namely the climate dynamical backgrounds can be reconstructed via various weather elements 10 respectively.

Discussion and conclusions
Based on the phase reconstruction of precipitation and temperature, the characteristics of the dynamical structure of climate system are revealed. The similar phenomena are found between precipitation and temperature, indicating that they are governed by the 15 same dynamical system. This insight can not be provided by conventional statistical techniques.
As a source center, the Tibetan Plateau is sensitive to the abnormity of the global climate system and might play an important role as the heat source over the Philippines, which induces teleconnection pattern. It becomes a key part making the climate 20 system abnormal in the Northern Hemisphere.
1059 Figure 3 Summer total precipitation at Shanghai (a) and Wutaishan (b).The dash lines denote mean values for the first (1960~1977) and second (1983~2000) periods, respectively, and the smooth thick lines the 10-order polynomial fitting.