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Analysis of Irrigation Water Use Efficiency Based on the Chaos Features of a Rainfall Time Series

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Abstract

The chaos theory is used to analyze the mechanism behind the response of irrigation water use efficiency (IWUE) to rainfall in irrigation districts of the Heilongjiang Province in China. The Lyapunov exponent and correlation dimension of the monthly rainfall time series of eight large- and medium-sized irrigation districts are calculated, and the correlations between IWUE and certain factors are analyzed. The results indicate that the monthly rainfall time series of each district sample exhibits chaotic characteristics, and high correlations exist between IWUE and the chaos features of the monthly rainfall time series. Furthermore, the scale of the irrigation district has some correlations with IWUE. The research results show that the difference in the temporal distribution of rainfall and the difference in the scale of an irrigation district both impact IWUE. This study provides a theoretical basis for improving the usage efficiency of water resources in the irrigation districts of Heilongjiang Province and for increasing the IWUE.

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References

  1. Ali MK, Klein KK (2014) Water use efficiency and productivity of the irrigation districts in southern Alberta. Water Resour Manag 28(10):2751–2766

  2. Cao L (1997) Practical method for determining the minimum embedding dimension of a scalar time series. Physica D Nonlinear Phenomena 110(1):43–50

  3. Cheng K, Fu Q, Li TX, Jiang QX, Liu W (2015) Regional food security risk assessment under the coordinated development of water resources. Nat Hazards 78(1):603–619

  4. Cui Y, Dong B, Li YH, Cai XL (2007) Assessment indicators and scales of water saving in agricultural irrigation. Transactions of the Chinese Society of Agricultural Engineering 23(7):1–7 (in Chinese)

  5. Deng XP, Shan L, Zhang H, Turner NC (2006) Improving agricultural water use efficiency in arid and semiarid areas of china. Agric Water Manag 80(1–3):23–40

  6. Deng J, Chen X, Du Z, Zhang Y (2011) Soil water simulation and predication using stochastic models based on LS-SVM for red soil region of China. Water Resour Manag 25(11):2823–2836

  7. Dhanya CT, Kumar DN (2010) Nonlinear ensemble prediction of chaotic daily rainfall. Adv Water Resour 33(3):327–347

  8. Dhanya CT, Kumar DN (2011) Multivariate nonlinear ensemble prediction of daily chaotic rainfall with climate inputs. J Hydrol 403(3–4):292–306

  9. Diaz-Ramirez JN, Mcanally WH, Martin JL (2011) Analysis of hydrological processes applying the HSPF model in selected watersheds in alabama, mississippi, and puerto rico. Appl Eng Agric 27(6):937–954

  10. Ding RQ, Li JP (2007) Nonlinear finite-time lyapunov exponent and predictability. Phys Lett A 364(5):396–400

  11. Ding J, Wang WS, Zhao YL (2003) Characteristics of daily flow variation in the Yangtze River, 1, optimum determination of delay time for reconstruction of a phase space. Adv Water Sci 14(4):407–411 (in Chinese)

  12. Ding RQ, Li JP, Ha K-J (2008) Nonlinear local lyapunov exponent and quantification of local predictability. Chin Phys Lett 25(5):1919–1922

  13. Fu Q, Liu W, Liu D, Li TX (2015) Spatial distribution of irrigation water use efficiency index system in Heilongjiang Province. Transactions of the Chinese Society for Agricultural Machinery 46(12):127–132 (in Chinese)

  14. Fu Q, Li TX, Li TN, Li H (2016) Temporal-spatial evolution patterns of the annual precipitation considering the climate change conditions in the sanjiang plain. Journal of Water & Climate Change 7(1):198–211

  15. Grassberger P, Procaccia I (1983a) Measuring the strangeness of strange attractors. Physica D 9:189–208

  16. Grassberger P, Procaccia I (1983b) Characterization of strange attractors. Phys Rev Lett 50(5):346–349

  17. Hassanli AM, Ahmadirad S, Beecham S (2010) Evaluation of the influence of irrigation methods and water quality on sugar beet yield and water use efficiency. Agric Water Manag 97(2):357–362

  18. Hu Z, Zhang C, Luo G, Teng Z, Jia C (2013) Characterizing cross-scale chaotic behaviors of the runoff time series in an inland river of Central Asia. Quat Int 311(9):132–139

  19. Karagiannis G, Tzouvelekas V, Xepapadeas A (2003) Measuring irrigation water efficiency with a stochastic production frontier. Environ Resour Econ 26(1):57–72

  20. Li JP, Ding RQ (2011) Temporal-spatial distribution of atmospheric predictability limit by local dynamical analogs. Mon Weather Rev 139(10):3265–3283

  21. Li Z, Sun Z (2016) Optimized single irrigation can achieve high corn yield and water use efficiency in the corn belt of northeast china. Eur J Agron 75:12–24

  22. Li X, Gao G, Hu T, Ma H, Li T (2014) Multiple time scales analysis of runoff series based on the chaos theory. Desalin Water Treat 52(52):2741–2749

  23. Liu D, Luo MJ, Fu Q, Zhang YJ, Imran KM, Zhao D, Li TX, Abrar FM (2016) Precipitation complexity measurement using multifractal spectra empirical mode decomposition Detrended fluctuation analysis. Water Resour Manag 30(2):505–522

  24. Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20(2):130–141

  25. Mañé R (1980) On the dimension of the compact invariant sets of certain non-linear maps. Dyn Syst Turbulence Warwick 1980:230–242

  26. Rontani D, Locquet A, Sciamanna M, Citrin DS, Ortin S (2009) Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view. IEEE J Quantum Electron 45(7):879–1891

  27. Rosenstein MT, Collins JJ, Luca CJD (1993) A practical method for calculating largest Lyapunov exponents from small data sets. Physica D-nonlinear Phenomena 65(93):117–134

  28. Sangoyomi TB, Lall U, Abarbanel HDI (1996) Nonlinear dynamics of the great salt lake: dimension estimation. Water Resour Res 32(32):149–159

  29. Smith LA, Ziehmann C, Fraedrich K (1999) Uncertainty dynamics and predictability in chaotic systems. Q J R Meteorol Soc 125(560):2855–2886

  30. Sun H, Zhang X, Wang E, Chen S, Shao L (2015) Quantifying the impact of irrigation on groundwater reserve and crop production – a case study in the north china plain. Eur J Agron 70:48–56

  31. Takens F (1981) Detecting strange attractors in turbulence. Dyn Syst Turbulence Warwick 1981:366–381

  32. Trentacoste ER, Puertas CM, Sadras VO (2015) Effect of irrigation and tree density on vegetative growth, oil yield and water use efficiency in young olive orchard under arid conditions in mendoza, argentina. Irrig Sci 33(6):1–12

  33. Wang W, Xu WC (2005) Some issues on the characterization of chaotic properties of hydrologic time series. Adv Water Sci 16(4):609–616 (in Chinese)

  34. Wang XJ, Zhang Q, Gu XQ (2012) Fractal-based effective utilization coefficient of irrigation water space scale variability. Acta Geograph Sin 67(9):1201–1212 (in Chinese)

  35. Wang XJ, Zhang Q, Yi XB (2015) Annual variation of irrigation water effective utilization coefficient and analysis of influencing factors in Guangdong Province. J Irrig Drain 34(1):64–68 (in Chinese)

  36. Wang G, Liang Y, Zhang Q, Jha SK et al (2016) Mitigated CH4 and N2O emissions and improved irrigation water use efficiency in winter wheat field with surface drip irrigation in the north china plain. Agric Water Manag 163:403–407

  37. Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Determining lyapunov exponents from a time series. Physica D Nonlinear Phenomena 16(3):285–317

  38. Yu CY, Chen XW (2008) Chaotic characteristics on multi-time scales of precipitation series in Fuzhou urban region[J]. Journal of Fujian Normal University (Natural Science Edition) 24(5):96–100 (in Chinese)

  39. Zhou H, Zhang M, Zhou Q, Sun Z, Chen J (2013) Analysis of agricultural irrigation water-using coefficient in Xinjiang arid region. Transactions of the Chinese Society of Agricultural Engineering 29(22):100–107 (in Chinese)

  40. Zounemat-Kermani M, Kisi O (2015) Time series analysis on marine wind-wave characteristics using chaos theory. Ocean Eng 100:46–53

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Acknowledgements

This research was supported by funds from the National Natural Science Foundation of China (51479032, 51679039, 51609039, 51579044), the Yangtze River Scholars in Universities of Heilongjiang Province and the Water Conservancy Science and Technology project of Heilongjiang Province (201318, 201503), and the Outstanding Youth Fund of Heilongjiang Province (JC201402).

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Correspondence to Qiang Fu.

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Fu, Q., Liu, Y., Li, T. et al. Analysis of Irrigation Water Use Efficiency Based on the Chaos Features of a Rainfall Time Series. Water Resour Manage 31, 1961–1973 (2017). https://doi.org/10.1007/s11269-017-1624-7

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Keywords

  • Irrigation district
  • Irrigation water use efficiency
  • Heilongjiang Province
  • Rainfall time series
  • Chaos theory
  • Lyapunov exponent
  • Correlation dimension