Employing nonlinear dynamic concepts for catchment classification using runoff response of catchments

Document Type : Article


1 School of Civil Engineering, Iran University of Science and Technology, Tehran, Iran

2 Department of Water Engineering, University of Tabriz, Tabriz, Iran


Classification has been considered as a fundamental step towards improved science and management data. Introducing methods which describe the underlying dynamics of runoff could be a promising way for catchment classification. In this respect chaos theory and correlation dimension was applied to test its ability to construct a concept to introduce a catchment classification framework in this study. The correlation dimension, as an indicator, was calculated for the daily river flow of sixty grouping stations in different catchments in Iran, ranging in size from 8 to 36500 (km2). The results confirmed that applying this indicator to catchments in varied ranges, from low to high complexity, can also be classified. The results showed that Iran’s catchments can be classified into four groups based on the complexity degree of runoff time series. The group is as flows: low dimension (D2 D2 = 5) as group 2, high dimension (D2 => 6) as group 3 and unidentifiable as group 4.The spatial pattern classification of Iran's catchments indicates that catchments with different climate characteristics which are located at a far distance from each other might yield similar responses along with the same level of complexity.


Main Subjects


1. McDonnell, J.J. and Woods, R.A. On the need for
catchment classi cation", Journal of Hydrology, 299,
pp. 2-3 (2004).
2. Gani, A., Siddiqa, A., Shamshirband, S., and Hanum,
F. A survey on indexing techniques for big data:
taxonomy and performance evaluation", Knowledge
and Information Systems, 46, pp. 241-284 (2016).
3. Grigg, D.B. The logic of regional systems", Annals
of the Association of American Geographers, 55, pp.
465-491 (1965).
4. Wagener, T., Sivapalan, M., Troch, P.A. and Woods,
R.A. Catchment classi cation and hydrologic similarity",
Geography Compass, 1(4), pp. 901-931 (2007).
5. Olden, J.D., Kennard, M.J., and Pusey, B.J. A
framework for hydrologic classi cation with a review
of methodologies and applications in ecohydrology",
Ecohydrology, 5, pp. 503-518 (2011).
6. Sivakumar, B. and Singh, V.P. Hydrologic system
complexity and nonlinear dynamic concepts for a
catchment classi cation framework", Hydrology and
Earth System Sciences, 16, pp. 4119-4131 (2012).
7. Zhang, Y., Xia, J., Bunn, S.E., Arthington, A.H.,
Mackay, S., and Kennard, M. Classi cation of
regimes for environmental
ow assessment in regulated
1130 H. Delafrouz et al./Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 1122{1131
rivers: the Huai River Basin, China", River Research
and Applications, 28, pp. 989-1005 (2011).
8. Bejarano, M.D., Marchamalo, M., De Jalon, D.G., and
De Tanago, M.G. Flow regime patterns and their
controlling factors in the Ebro basin (Spain) ", Journal
of Hydrology, 385, pp. 323-335 (2010).
9. Monk, W.A., Wood, P.J., Hannah, D.M., Wilson,
D.A., Extence, C.A., and Chadd, R.P. Flow variability
and macro invertebrate community response within
riverine systems", River Research and Applications,
22, pp. 595-615 (2006).
10. Rao, A.R. and Srinivas, V.V. Regionalization of
watersheds by fuzzy cluster analysis", Journal of Hydrology,
318(1), pp. 57-79 (2006).
11. Zoppou, C., Nielsen, O.M., and Zhang, L. Regionalization
of daily stream
ow in Australia using
wavelets and K means analysis, CMA Research
Report MRR02-003", Australian National University,
Canberra. Available at: http://wwwmaths.
anu.edu.au/research.reports/mrr/02/003/ (2002).
12. Krasovskaia, I. Entropy-based grouping of river
regimes", Journal of Hydrology, 202, pp. 173-191
13. Sen, A.K. Complexity analysis of river
ow time
series", Stochastic Environmental Research and Risk
Assessment, 23, pp. 361-366 (2009).
14. Chou, C. Complexity analysis of rainfall and runo
time series based on sample entropy in di erent temporal
scales", Stochastic Environmental Research and
Risk Assessment, 28, pp. 1401-1408 (2014).
15. Sivakumar, B. Dominant processes concept in hydrology:
moving forward", Hydrological Processes, 18, pp.
2349-2353 (2004).
16. Sivakumar, B., Jayawardena, A.W., and Li, W.K.
Hydrologic complexity and classi cation: a simple
data reconstruction approach", Hydrological Processes,
21, pp. 2713-2728 (2007).
17. Sivakumar, B., Woldemeskel, F.M., and Puente, C.E.
Nonlinear analysis of rainfall variability in Australia",
Stochastic Environmental Research and Risk Assessment,
28, pp. 17-27 (2014).
18. Vignesh, R., Jothiprakash, V. and Sivakumar, B.
ow variability and classi cation using false
nearest neighbour method", Journal of Hydrology,
531, pp. 706-715 (2015).
19. Hrachowitz, M., Savenije, H.H.G., Bloschl, G.,
McDonnell, J.J., Sivapalan, M., Pomeroy, J.W.,
Arheimer, B., Blume, T., Clark, M.P., Ehret, U.,
Fenicia, F., Freer, J.E., Gelfan, A., Gupta, H.V.,
Hughes, D.A., Hut, R.W., Montanari, A., Pande, S.,
Tetzla , D., Troch, P.A., Uhlenbrook, S., Wagener, T.,
Winsemius, H.C., Woods, R.A., Zehe, E., and Cudennec,
C. A decade of predictions in ungaged basins
(PUB) - a review", Hydrological Science Journal, 58,
pp. 1198-1255 (2013).
20. Sivakumar, B., Singh, V.P., Berndtsson, R., and Khan,
S.K. Catchment classi cation framework in hydrology:
Challenges and directions", Journal of Hydrologic
Engineering, 20(1), 4014002-4014002 (2015).
21. Liu, Q., Islam, S., Rodriguez-Iturbe, I., and Le, Y.
Phase-space analysis of daily stream
ow: characterisation
and prediction", Advances in Water Resources,
21, pp. 463-475 (1998).
22. Fan, Q., Wang, Y., and Zhu, Li. Complexity analysis
of spatial-temporal precipitation system by PCA and
SDLE", Applied Mathematical Modelling, 37, pp. 4059-
4066 (2013).
23. Takens, F. Detecting strange attractors in turbulence",
Lecture Notes in Mathematics, 898, pp. 366-
381 (1981).
24. Grassberger, P., and Procaccia, I. Measuring the
strangeness of strange attractors", Physica D: Nonlinear
Phenomena, 9(2-1), pp. 189-208 (1983).
25. Ghorbani, M.A., Kisi, O., and Aalinezhad M. A
probe into the chaotic nature of daily stream
ow time
series by correlation dimension and largest lyapunov
methods", Applied Mathematical Modelling, 34, pp.
4050-4057 (2010).
26. Schertzer, D., Tchiguirinskaia, I., Lovejoy, S., Hubert,
P., and Bend-joudi, H. Which chaos in the rainfallruno
process? A discussion on Evidence of chaos
in the rainfall-runo process by Sivakumar et al.",
Hydrological Sciences Journal, 47, pp. 139-147 (2002).
27. Sivakumar, B. Correlation dimension estimation of
hydrologic series and data size requirement: myth and
reality", Hydrological Sciences Journal, 50, pp. 591-
604 (2005).
28. Sivakumar, B., Berndtsson, R., Olsson, J., and Jinno,
K. Reply to Which chaos in the rainfall-runo
process?" by Schertzer et al.", Hydrological Sciences
Journal, 47, pp. 149-158 (2002).
29. Sivakumar, B., Persson, M., Berndtsson, R., and Uvo,
C.B. Is correlation dimension a reliable indicator
of low-dimensional chaos in short hydrological time
series?", Water Resources Research, 38(2), pp. 1-8
30. Tongal, H. and Berndtsson, R. Impact of complexity
on daily and multi-step forecasting of stream
ow with
chaotic, stochastic, and black-box models", Stochastic
Environmental Research and Risk Assessment, 31(3),
pp. 661-682 (2017).