Sciences in Cold and Arid Regions ›› 2019, Vol. 11 ›› Issue (5): 340-349.doi: 10.3724/SP.J.1226.2019.00340.

Previous Articles     Next Articles

Analysis of chaotic climatic process in the Tarim River Basin (I)

ZuHan Liu1,2()   

  1. 1. Key Laboratory of the Education Ministry for Poyang Lake Wetland and Watershed Research, Jiangxi Normal University, Nanchang, Jiangxi 330022, China
    2. Jiangxi Province Key Laboratory for Water Information Cooperative Sensing and Intelligent Processing, Nanchang Institute of Technology, Nanchang, Jiangxi 330099, China
  • Received:2019-07-27 Accepted:2019-08-29 Online:2019-10-31 Published:2019-11-12
  • Contact: ZuHan Liu


Based on observational data obtained from 1961 to 2011 in the Tarim River Basin, China, we investigated the chaotic dynamics of temperature, precipitation, relative humidity, and evaporation. The main findings are as follow: (1) The four data series have significant chaotic and fractal behaviors, which are the result of the evolution of a nonlinear chaotic dynamic system. The climatic process in the Tarim River Basin also has deterministic and stochastic characteristics. (2) To describe the temperature, precipitation, relative humidity, and evaporation dynamics, at least three independent variables at daily scale are required; in terms of complexity, their order is evaporation > temperature > precipitation > relative humidity. (3) Their respective largest Lyapunov exponent λ 1 shows the order of their degree of complexity is relative humidity > temperature > precipitation ≈ evaporation; the maximum time scales for which the four systems can be predicted are 17 days, 17 days, 16 days, and 16 days, if calculated separately. (4) The Kolmogorov entropy K illustrates that the complexity of the nonlinear precipitation system is much greater than that of the other three systems. Both temperature and evaporation systems exhibit weaker chaotic behavior, their predictability is better, and the degree of complexity is less than that of the other two factors.

Key words: chaos, climatic process, largest Lyapunov exponent, Kolmogorov entropy, correlation dimension

Figure 1

Locations of meteorological stations in the Tarim River Basin"

Figure 2

The change of delay time τ with mutual information of average daily temperature (a), precipitation (b), relative humidity (c), and evaporation (d) in the Tarim River Basin"

Figure 3

The change of E1 and E2 of average daily temperature (a), precipitation (b), relative humidity (c), and evaporation (d) in the Tarim River Basin"

Figure 4

The trend of a correlation integral according to various embedding dimensions m, and the change of correlation dimension and white noise with m values for the time-series of average daily temperature (a1) and (a2), precipitation (b1) and (b2), relative humidity (c1) and (c2), and evaporation (d1) and (d2)"

Figure 5

The calculated result of largest Lyapunov exponent using the Rosenstein algorithm for the time-series of average daily temperature (a), precipitation (b), relative humidity (c), and evaporation (d)"

Figure 6

The calculated results of Kolmogorov entropy K of the time-series of the average daily temperature (a), precipitation (b), relative humidity (c), and evaporation (d)"

Alexandersson H , 1986. A homogeneity test applied to precipitation data. Journal of Climatology, 6(6): 661-675. DOI: 10.1002/joc.3370060607 .
doi: 10.1002/joc.3370060607
Branstator G , Teng HY , 2010. Two limits of initial-value decadal predictability in a CGCM. Journal of Climate, 23: 6292-6311. DOI: 10.1175/2010JCLI3678.1 .
doi: 10.1175/2010JCLI3678.1
Buishand TA , 1982. Some methods for testing the homogeneity of rainfall records. Journal of Hydrology, 58(1-2): 11-27. DOI: 10.1016/0022-1694(82)90066-X .
doi: 10.1016/0022-1694(82)90066-X
Cao LY , 1997. Practical method for determining the minimum embedding dimension of a scalar time series. Physica D, 110(1-2): 43-50. DOI: 10.1016/s0167-2789(97)00118-8 .
doi: 10.1016/s0167-2789(97)00118-8
Chen Z , Pch I , Hu K , et al. , 2002. Stanley effect of nonstationarities on detrended fluctuation analysis. Physical Review E, 65(4): 110-126. DOI: 10.1103/PhysRevE.65.041107 .
doi: 10.1103/PhysRevE.65.041107
Fraser AM , Swinney HL , 1986. Independent coordinates for strange attractors from mutual information. Physical Review A, 33(2): 1134-1140. DOI: 10.1103/PhysRevA.33.1134 .
doi: 10.1103/PhysRevA.33.1134
Grassberger P , Procaccia I , 1983a. Estimation of the Kolmogorov entropy from a chaotic signal. Physical Review A, 28(4): 2591-2593. DOI: 10.1103/PhysRevA.28.2591 .
doi: 10.1103/PhysRevA.28.2591
Grassberger P , Procaccia I , 1983b. Measuring the strangeness of strange attractor. Physica D, 9(1-2): 189-208. DOI: 10. 1016/0167-2789(83)90298-1 .
doi: 10. 1016/0167-2789(83)90298-1
AGDSM Honorato , GBLD Silva , Santos CAG , 2019. Monthly streamflow forecasting using neuro-wavelet techniques and input analysis. Hydrological Sciences Journal, 63(15-16): 2060-2075. DOI: 10.1080/02626667.2018.1552788 .
doi: 10.1080/02626667.2018.1552788
Kolokolov AS , Lyubinskii IA , 2019. Measuring the pitch of a speech signal using the autocorrelation function. Automation and Remote Control, 80(2): 317-323. DOI: 10.1134/S0005117919020097 .
doi: 10.1134/S0005117919020097
Liston GE, Pielke RA , 2000. A climate version of the regional atmospheric modeling system. Theoretical and Applied Climatology, 66(1-2): 29-47. DOI: 10.1007/s007040070031 .
doi: 10.1007/s007040070031
Liu ZH , Xu JH , Shi K , 2014a. Self-organized criticality of climate change. Theoretical and Applied Climatology, 115(3-4): 685-691. DOI: 10.1007/s00704-013-0929-6 .
doi: 10.1007/s00704-013-0929-6
Liu ZH , Xu JH , Chen ZS , et al. , 2013. Multifractal and long memory of humidity process in the Tarim River Basin. Stochastic Environmental Research and Risk Assessment, 28(6): 1383-1400. DOI: 10.1007/s00477-013-0832-9 .
doi: 10.1007/s00477-013-0832-9
Lorenz EN , 1962. Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2): 130-141. DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 .
doi: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
Lorenz EN , 1963. The mechanics of vacillation. Journal of the Atmospheric Sciences, 20(5): 448-465. DOI: 10.1175/1520-0469(1963)0202.0.CO;2 .
doi: 10.1175/1520-0469(1963)0202.0.CO;2
Millan H , Kalauzi A , Llerena G , et al. , 2009. Meteorological complexity in the Amazonian area of ecuador: an approach based on dynamical system theory. Ecological Complexity, 6(3): 278-285. DOI: 10.1016/j.ecocom.2009.05.004 .
doi: 10.1016/j.ecocom.2009.05.004
Nguelifack BM , Kemajou-Brown I , 2019. Robust rank-based variable selection in double generalized linear models with diverging number of parameters under adaptive Lasso. Journal of Statistical Computation and Simulation, 89(1): 1-22. DOI: 10.1080/00949655.2019.1607346 .
doi: 10.1080/00949655.2019.1607346
Palmer TN , 1999. A nonlinear dynamical perspective on climate prediction. Journal of Climate, 12(2): 575-591. DOI: 10.1175/1520-0442(1999)012<0575:ANDPOC>2.0.CO;2 .
doi: 10.1175/1520-0442(1999)012<0575:ANDPOC>2.0.CO;2
Palmer TN , Buizza R , Molteni F , et al. , 1994. Chaos and forecasting-Singular vectors and the predictability of weather and climate. Philosophical Transactions: Physical Sciences and Engineering, 348(1688): 459-475. DOI: 10.2307/54222 .
doi: 10.2307/54222
Pettitt AN , 1979. A non-parametric approach to the change-point problem. Journal of the Royal Statistical Society. Series C (Applied Statistics), 28(2): 126-135. DOI: 10.2307/2346729
doi: 10.2307/2346729
Qian XS , 1994. On Geographical Science, pp. 46. (In Chinese)
Rocha J , Varandas P , 2018. On sensitivity to initial conditions and uniqueness of conjugacies for structurally stable diffeomorphisms. Nonlinearity, 31(293): 293-313. DOI: 10.1088/1361-65 4 4/aa8 d78 .
doi: 10.1088/1361-65 4 4/aa8 d78
Segond ML , Onof C , Wheater HS , 2006. Spatial-temporal disaggregation of daily rainfall from a generalized linear model. Journal of Hydrology, 331(3-4): 674-689. DOI: 10. 1016/j.jhydrol.200 6.0 6.019 .
doi: 10. 1016/j.jhydrol.200 6.0 6.019
Takens F , 1981. Detecting strange attractors in fluid turbulence. In: Dynamical Systems and Turbulence. Berlin: Springer Verlag.
Tsonis AA , 1996. Widespread increases in low-frequency variability of precipitation over the past century. Nature, 382(6593): 700-702. DOI: 10.1038/382700a0 .
doi: 10.1038/382700a0
Wang JX , Yang Y , Huang JK , et al. , 2019. Adaptive irrigation measures in response to extreme weather events: empirical evidence from the North China plain. Regional Environmental Change, 19(4): 1009-1022. DOI: 10.1007/s10113-018-1442-3 .
doi: 10.1007/s10113-018-1442-3
Wan J , Ding L , Yao JF , et al. , 2018. A hybrid CHAOS-PSO algorithm for dimensional synthesis of a redundant manipulator based on tracking trajectories without or with singularities. Production Engineering, 12(5): 579-587. DOI: 10. 1016/j.physleta.2005.04.048 .
doi: 10. 1016/j.physleta.2005.04.048
Wen XX , Duan WS , 2019. Errors in current velocity in the low-latitude north pacific: results from the regional ocean modeling system. Advances in Atmospheric Sciences, 36(4): 397-416. DOI: 10.1007 /s00376-018-8140-4 .
doi: 10.1007 /s00376-018-8140-4
Wernitz BA, Hoffmann NP , 2012. Recurrence analysis and phase space reconstruction of irregular vibration in friction brakes: signatures of chaos in steady sliding. Journal of Sound and Vibration, 331(16): 3887-3896. DOI: 10.1016/j.jsv.2012.04.003 .
doi: 10.1016/j.jsv.2012.04.003
Wolf A , Swift JB , Swinney HL , et al. , 1985. Determining Lyapunov exponents from a time series. Physica D, 16(3): 285-317. DOI: 10.1016/0167-2789(85)90011-9 .
doi: 10.1016/0167-2789(85)90011-9
Xu JH , Chen YN , Li WH , et al. , 2016. Understanding temporal and spatial complexity of precipitation distribution in Xinjiang, China. Theoretical and Applied Climatology, 123(1): 1-13. DOI: 10.1007 /s00704-014-1364-z .
doi: 10.1007 /s00704-014-1364-z
Zheng C , Yao HT , 2019. Segmentation for remote-sensing imagery using the object-based Gaussian-Markov random field model with region coefficients. International Journal of Remote Sensing, 40(11): 4441-4472. DOI: 10.1080/01431161. 2018.1563841 .
doi: 10.1080/01431161. 2018.1563841
No related articles found!
Full text



[1] Mohan Bahadur Chand,Rijan Bhakta Kayastha. Study of thermal properties of supraglacial debris and degree-day factors on Lirung Glacier, Nepal[J]. Sciences in Cold and Arid Regions, 2018, 10(5): 357 -368 .
[2] AiHong Xie,ShiMeng Wang,YiCheng Wang,ChuanJin Li. Comparison of temperature extremes between Zhongshan Station and Great Wall Station in Antarctica[J]. Sciences in Cold and Arid Regions, 2018, 10(5): 369 -378 .
[3] YanZai Wang,YongQiu Wu,MeiHui Pan,RuiJie Lu. Comparison of two classification methods to identify grain size fractions of aeolian sediment[J]. Sciences in Cold and Arid Regions, 2018, 10(5): 413 -420 .
[4] YinHuan Ao,ShiHua Lyu,ZhaoGuo Li,LiJuan Wen,Lin Zhao. Numerical simulation of the climate effect of high-altitude lakes on the Tibetan Plateau[J]. Sciences in Cold and Arid Regions, 2018, 10(5): 379 -391 .
[5] Zhuo Ga,Za Dui,Duodian Luozhu,Jun Du. Comparison of precipitation products to observations in Tibet during the rainy season[J]. Sciences in Cold and Arid Regions, 2018, 10(5): 392 -403 .
[6] Rong Yang,JunQia Kong,ZeYu Du,YongZhong Su. Altitude pattern of carbon stocks in desert grasslands of an arid land region[J]. Sciences in Cold and Arid Regions, 2018, 10(5): 404 -412 .
[7] Yang Qiu,ZhongKui Xie,XinPing Wang,YaJun Wang,YuBao Zhang,YuHui He,WenMei Li,WenCong Lv. Effect of slow-release iron fertilizer on iron-deficiency chlorosis, yield and quality of Lilium davidii var. unicolor in a two-year field experiment[J]. Sciences in Cold and Arid Regions, 2018, 10(5): 421 -427 .
[8] Ololade A. Oyedapo,Joseph M. Agbedahunsi,H. C Illoh,Akinwumi J. Akinloye. Comparative foliar anatomy of three Khaya species (Meliaceae) used in Nigeria as antisickling agent[J]. Sciences in Cold and Arid Regions, 2018, 10(4): 279 -285 .
[9] YuMing Wei,XiaoFei Ma,PengShan Zhao. Transcriptomic comparison to identify rapidly evolving genes in Braya humilis[J]. Sciences in Cold and Arid Regions, 2018, 10(5): 428 -435 .
[10] FangLei Zhong,AiJun Guo,XiaoJuan Yin,JinFeng Cui,Xiao Yang,YanQiong Zhang. Sociodemographic characteristics, cultural biases, and environmental attitudes: An empirical application of grid-group cultural theory in Northwestern China[J]. Sciences in Cold and Arid Regions, 2018, 10(5): 436 -446 .