Natural Hazards

, Volume 71, Issue 2, pp 1017–1024 | Cite as

Investigation of karst hydrological processes by using grey auto-incidence analysis

Original Paper


The karst hydrological processes are the response of karst groundwater system to precipitation. The precipitation penetrates through the vadose zone, the subsequent groundwater pressure wave propagates to a spring outlet, and then, the spring discharge changes. This paper proposes a grey auto-incidence analysis for studying the karst hydrological processes. The method can detect the periodicity of a time series, for example, precipitation and spring discharge. Then the approach is applied to Liulin Springs Basin, China. The results show that the auto-incidence degree of precipitation reaches to the maximum (i.e., 0.816) when time delay equals to 8 years. The auto-incidence degree of spring discharge reaches to the maximum (i.e., 0.865) when time delay equals to 3 years. These results show that the periodicity of precipitation is 8 years, and of spring discharge is 3 years. The difference of periodicity between the precipitation and the spring discharge reveals that the processes of precipitation recharging groundwater and groundwater transport are regulated or controlled by karst aquifer. Because of heterogeneity of karst aquifer, the quick flow and base flow occur during the groundwater propagation, which causes the periodicity of spring discharge is not coincidence with of precipitation.


Grey auto-incidence analysis Karst groundwater Aquifer Heterogeneity 



This work is partially funded by the National Natural Science Foundation of China (41272245, 40972165, 40572150), the Opening Fund of Tianjin Key Laboratory of Water Resources and Environment 52XS1015, and 2012 National College Students’ Innovative Entrepreneurial Training Program 201210065025. We are also grateful to the two anonymous reviewers who have spent enormous efforts reviewing the manuscript and provided very encouraging, insightful, and constructive comments.


  1. Custodio E (2002) Aquifer overexploitation: what does it mean? Hydrogeol J 10:254–277CrossRefGoogle Scholar
  2. Deng JL (1982) Control problems of grey systems. Syst Control Lett 2(5):288–294Google Scholar
  3. Dreiss SJ (1982) Linear kernels for karst aquifers. Water Resour Res 18:865–876CrossRefGoogle Scholar
  4. Fleury P, Plagnes V, Bakalowicz M (2007) Modelling of the functioning of karst aquifers with a reservoir model: application to fontaine de vaucluse (south of France). J Hydrol 345:38–49CrossRefGoogle Scholar
  5. Guo CQ (1993) Grey system theory and method for karst groundwater assessment. Geological Publishing House, Beijing (in Chinese)Google Scholar
  6. Han XR, Lu RA, Li QS (1993) Karst water system: a study on Shanxi’s big karst spring. Geological Publishing House, Shanxi, pp 294–305 (in Chinese)Google Scholar
  7. Hao YH, Yeh TJ, Gao ZQ, Wang YR, Zhao Y (2006) A gray system model for studying the response to climatic change: the Liulin karst springs, China. J Hydrol 328(3–4):668–676CrossRefGoogle Scholar
  8. Hao YH, Yeh TJ, Wang YR, Zhao Y (2007) Analysis of karst aquifer spring flows with a gray system decomposition model. Ground Water 45(1):46–52CrossRefGoogle Scholar
  9. Hao YH, Wang W, Wang GQ, Du X, Zhu YE, Wang XM (2009) The role of climate and human influences in karst springs in the north of China. Acta Geologica Sinca 83:139–144 (in Chinese)Google Scholar
  10. Hao YH, Cao BB, Zhang PC, Wang QY, Li ZT, Yeh TJ (2012a) Differences in karst processes between northern and southern China. Carbonates Evaporites 27:331–342CrossRefGoogle Scholar
  11. Hao YH, Zhao JJ, Li HM, Cao BB, Li ZT, Yeh TJ (2012b) Karst hydrological processes and grey system model. J Am Water Resour As 48(4):656–666CrossRefGoogle Scholar
  12. Hao YH, Cao BB, Che X, Yin J, Sun RL, Yeh TJ (2013) A piecewise grey system model for study the effects of anthropogenic activities on karst hydrological processes. Water Resour Manage 27(5):1207–1220CrossRefGoogle Scholar
  13. Hiscock KM, Rivett MO, Davison RM (2002) Sustainable groundwater development. Geol Soc London Special Publ 193:1–14CrossRefGoogle Scholar
  14. Hua SL (1981) Progress of karst hydrology in China. Prog Phys Geogr 5(4):563–574CrossRefGoogle Scholar
  15. Janža M (2011) Impact assessment of projected climate change on the hydrological regime in the SE Alps, Upper Soča River basin, Slovenia. Nat Hazards. doi: 10.1007/s11069-011-9892-7
  16. Kalf FRP, Woolley DR (2005) Applicability and methodology of determining sustainable yield in groundwater systems. Hydrogeol J 13:295–312CrossRefGoogle Scholar
  17. Konikow LF, Kendy E (2005) Groundwater depletion: a global problem. Hydrogeol J 13:317–320CrossRefGoogle Scholar
  18. Labat D, Ababou R, Mangin A (2000a) Rainfall-runoff relations for karstic springs. Part I: convolution and spectral analyses. J Hydrol 238:123–148CrossRefGoogle Scholar
  19. Labat D, Ababou R, Mangin A (2000b) Rainfall-runoff relations for karstic springs. Part II: continuous wavelet and discrete orthogonal multiresolution analyses. J Hydrol 238:149–178CrossRefGoogle Scholar
  20. Liu SF, Lin Y (2006) Grey information-theory and practical applications. Spring-Verlag London Limited, USAGoogle Scholar
  21. Liu SF, Dang YG, Fang ZG (2004) Grey system theory and application. Science Press, Beijing (in Chinese)Google Scholar
  22. Loucks DP (2000) Sustainable water resources management. Water Int 25(1):3–10CrossRefGoogle Scholar
  23. Lundy L, Wade R (2011) Integrating sciences to sustain urban ecosystem services. Prog Phys Geogr 35:653–669CrossRefGoogle Scholar
  24. Quinlan JF, Davies GJ, Jones SW, Huntoon PW (1996) The application of numerical models to adequately characterized ground-water flow in karstic and other triple-porosity aquifers. Subsurface Fluid-flow (Ground-Water and Vadose Zone) Modeling, ASTM STP 1288, American Society for Testing and Materials, pp 114–133Google Scholar
  25. Ren XW, Tang YQ, Li J, Yang Q (2012) A prediction method using grey model for cumulative plastic deformation under cyclic loads. Nat Hazards. doi:  10.1007/s11069-012-0248-8
  26. Sweeting MM (1995) Karst in China: its geomorphology and environment. Springer, BerlinCrossRefGoogle Scholar
  27. Wang XM, Nie HS (1989) Application of the grey system model to an agriculture economy. Huazhong University of Science and Technology Press, Wuhan (in Chinese)Google Scholar
  28. Wang Y, Ma T, Luo Z (2001) Geostatistical and geochemical analysis of surface water leakage into groundwater on a regional scale: a case study in the Liulin karst system, northwestern China. J Hydrol 246(1–4):223–234CrossRefGoogle Scholar
  29. Wang HJ, Chen YN, Chen ZS, Li WH (2012) Changes in annual and seasonal temperature extremes in the arid region of China, 1960–2010. Nat Hazards. doi: 10.1007/s11069-012-0454-4
  30. White WB (1969) Conceptual models for limestone aquifers. Ground Water 7(3):15–21CrossRefGoogle Scholar
  31. White WB (1977) Conceptual models for carbonate aquifers: revisited. In: Dilamarter RR, Csallany SC (eds) Hydrologic problems in karst terrain, Western Kentucky University, Bowling Green, Kentucky, pp 176–187Google Scholar
  32. Xia J (2000) Grey system hydrology: theory, methodology and application. Huazhong University of Science and Technology Press, Wuhan (in Chinese)Google Scholar
  33. Xiao XP, Song ZM, Li F (2005) Basic of grey system technology and application. Science Press, Beijing (in Chinese)Google Scholar
  34. Yuan DX (1993) Karst of China. Geological Publishing House, Beijng, pp 149–164 (in Chinese)Google Scholar
  35. Yuan DX (1997) Sensitivity of karst process to environmental change along the PEP II Transect. Quatern Int 37:105–113CrossRefGoogle Scholar
  36. Zhou J, Tang YQ, Yang P, Zhang XH, Zhou NQ, Wang JX (2012) Inference of creep mechanism in underground soil loss of karst conduits I. Conceptual model. Nat Hazards. doi: 10.1007/s11069-012-0143-3

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Tianjin Key Laboratory of Water Resources and EnvironmentTianjin Normal UniversityTianjinPeople’s Republic of China
  2. 2.College of Urban and Environment ScienceTianjin Normal UniversityTianjinPeople’s Republic of China
  3. 3.Institute of Agricultural Resources and EconomyShanxi Academy of Agricultural SciencesTaiyuanPeople’s Republic of China

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