Long-Time Memory in Drought via Detrended Fluctuation Analysis


The persistence of drought events largely determines the severity of socioeconomic and ecological impacts, unfortunately the performance of current weather forecasting models (WFM) to simulate such events is subject to great uncertainties. This study is investigating time-domain characteristics of drought persistence over Turkey by applying the detrended fluctuation analysis (DFA) method to the Palmer drought severity index (PDSI). The existence of long-range power-law correlation in PDSI fluctuations is demonstrated for time scales ranging from monthly to decadal. Understanding of such statistical patterns in PDSI values can definitely be a step forward in drought predictability. From a climatological point of view, it is found that the areas with high level DFA scaling exponent (generalized Hurst) indicate the areas of higher sensitivity to droughts and associated risks. Furthermore, the characteristics of the persistence of the PDSI in climate zones have also been examined by applying the Holdridge Life Zones (HLZ) classification. HLZ classification over Turkey leads to two climate-zones: cool-temperate and warm-temperate. In addition, when topography is taken in account, montane (cool-temperate) and lower-montane (warm-temperate) climate zones can be treated as two different zones. It has been observed that the predictable index (PI) of the PDSI derived from the DFA Hurst exponent is relatively high in the cool-temperate and montane climate zones compared to others. In fact, very different PI values were also obtained in a few HLZ climate classes within the same climate zone and with same vegetation index (i.e. steppe, dry-forest, warm-forest etc.).

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6


  1. Alley WM (1984) The Palmer drought severity index: limitations and assumptions. J Clim Appl Meteorol 23(7):1100–1109

  2. Bhardwaj R, Siddiqi AH, Mittal A (2012) Predictability index, fractal dimension and Hurst exponent estimation of carbon monoxide at different locations of Delhi. Indian J Industrial App Math 3(2):94–100

  3. Blender R, Fraedrich K (2003) Long time memory in global warming simulations. Geophys Res Lett 30(14).

  4. Byun HR, Wilhite DA (1999) Objective quantification of drought severity and duration. J Clim 12(9):2747–2756

  5. Carbone A, Castelli G, Stanley HE (2004) Analysis of clusters formed by the moving average of a long-range correlated time series. Phys Rev E 69(2):026105

  6. Cohen J, Saito K, Entekhabi D (2001) The role of the Siberian high in northern hemisphere climate variability. Geophys Res Lett 28(2):299–302

  7. Gibbs WJ, Maher JV (1967) Rainfall Deciles as drought indicators. Bureau of Meteorology: Melbourne, Australia, p 29

  8. Gu GF, Zhou WX (2006) Detrended fluctuation analysis for fractals and multifractals in higher dimensions. Phys Rev E 74:061104

  9. Guttman NB (1998) Comparing the palmer drought index and the standardized precipitation index 1. J Am Water Resour As 34(1):113–121

  10. Heim RR (2000) Drought indices: a review. Drought: a global assessment:159–167

  11. Heim RR (2002) A review of twentieth-century drought indices used in the United States. B Am Meteorol Soc 83(8):1149–1165

  12. Holdridge L (1967) Life zone ecology, Tropical Science Center. San Jose´, Costa Rica

  13. Hou W, Feng G, Yan P, Li S (2018) Multifractal analysis of the drought area in seven large regions of China from 1961 to 2012. Meteor Atm Phys 130:459–471

  14. Hu D, Shu H, Hu H, Xu J (2017) Spatiotemporal regression Kriging to predict precipitation using time-series MODIS data. Cluster Comput 20(1):347–357

  15. Intergovernmental Panel on Climate Change (IPCC) (2013) Climate change 2013: The Physical Science Basis, Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by T. F. Stocker et al., Cambridge University Press, Cambridge, U. K.

  16. Ivanova K, Ausloos M (1999) Application of the detrended fluctuation analysis (DFA) method for describing cloud breaking. Physica A: Statistical Mechanics and its Applications 274:349–354

  17. Kantelhardt JW, Zschiegner SA, Koscielny-Bunde E, Havlin S, Bunde A, Stanley HE (2002) Multifractal detrended fluctuation analysis of nonstationary time series. Physica A 316:87–114

  18. Khalyani AH, Gould WA, Harmsen E, Terando A, Quinones M, Collazo JA (2016) Climate change implications for tropical islands: interpolating and interpreting statistically downscaled GCM projections for management and planning. J App Meteor Climatol 55(2):265–282

  19. Kogan FN (1997) Global drought watch from space. B Am Meteorol Soc 78(4):621–636

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

  21. Marcos-Garcia P, Lopez-Nicolas A, Pulido-Velazquez M (2017) Combined use of relative drought indices to analyze climate change impact on meteorological and hydrological droughts in a Mediterranean basin. J Hydrol 554:292–305

  22. McKee TB, Doesken NJ, Kleist J (1993) The relationship of drought frequency and duration to time scales. In Proceedings of the 8th Conference on Applied Climatology (Vol. 17, no. 22, pp. 179-183). Boston, MA: American Meteorological Society

  23. Mishra AK, Singh VP (2010) A review of drought concepts. J Hydrol 391(1–2):202–216

  24. Mukherjee S, Mishra A, Trenberth KE (2018) Climate change and drought: a perspective on drought indices. Current Climate Change Reports:1–19

  25. Palmer WC (1965) Meteorological drought. Research paper no. 45. Office of Climatology. U.S. weather bureau, Washington

  26. Peng CK, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL (1994) Mosaic organization of DNA nucleotides. Phys Rev E 49(2):1685

  27. Podobnik B, Horvatic D, Petersen AM, Stanley HE (2009) Cross-correlations between volume change and price change. P Natl A Sci India A 106(52):22079–22084

  28. Rego CRC, Frota HO, Gusmão MS (2013) Multifractality of Brazilian rivers. J Hydrol 495:208–215

  29. Rossi G, Benedini M, Tsakiris G, Giakoumakis S (1992) On regional drought estimation and analysis. Water Resour Manag 6:249–277

  30. Shafer BA, Dezman LE (1982) Development of a surface water supply index (SWSI) to assess the severity of drought conditions in snowpack runoff areas. In proceedings of the Western snow conference, Colorado State University, Fort Collins, CO, USA, 19–23 April 1982; pp. 164–175

  31. Shukla S, Wood AW (2008) Use of a standardized runoff index for characterizing hydrologic drought. Geophys Res Lett 35(2):1–7

  32. Surendran U, Kumar V, Ramasubramoniam S, Raja P (2017) Development of drought indices for semi-arid region using drought indices calculator (DrinC)–a case study from Madurai District, a semi-arid region in India. Water Resour Manag 31:3593–3605

  33. Szelepcsényi Z, Breuer H, Kis A, Pongrácz R, Sümegi P (2018) Assessment of projected climate change in the Carpathian region using the Holdridge life zone system. Theor Appl Climatol 131(1–2):593–610

  34. Tatli H, Dalfes HN (2016) Defining Holdridge's life zones over Turkey. Int J Climatol 36(11):3864–3872

  35. Tatli H, Türkeş M (2011) Empirical orthogonal function analysis of the Palmer drought indices. Agric For Meteorol 151(7):981–991

  36. Thornthwaite CW (1948) An approach toward a rational classification of climate. Geogr Rev 38(1):55–94

  37. Tsakiris G, Pangalou D, Vangelis H (2007) Regional drought assessment based on the reconnaissance drought index (RDI). Water Resour Manag 21:821–833

  38. Vicente-Serrano SM, Beguería S, López-Moreno JI (2010) A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index. J Clim 23(7):1696–1718

  39. Voss RF (1991) Random fractals: characterization and measurement. In Scaling Phenomena In Disordered Systems (pp. 1-11). Springer, Boston, MA

  40. Webb R, Rosenzweig CE, Levine ER (2000) Global soil texture and derived water-holding capacities. ORNL DAAC., data set. Available from oak Ridge National Laboratory distributed active archive center, oak ridge, Tennessee, USA. (accessed 1 May 2017)

  41. Wilhite DA (2000) Drought as a natural hazard: concepts and definitions. In Drought: A Global Assessment Wilhite; Routledge: London, UK 1:3–18

  42. Wilhite DA, Glantz MH (1985) Understanding: the drought phenomenon: the role of definitions. Water Int 10(3):111–120

  43. Wilhite DA, Svoboda MD, Hayes MJ (2007) Understanding the complex impacts of drought: a key to enhancing drought mitigation and preparedness. Water Resour Manag 21:763–774

  44. Yuan X, Ji B, Tian H, Huang Y (2014) Multiscaling analysis of monthly runoff series using improved MF-DFA approach. Water Resour Manag 28(12):3891–3903

  45. Zargar A, Sadiq R, Naser B, Khan FI (2011) A review of drought indices. Environ Rev 19(NA):333–349

Download references

Author information

Correspondence to Hasan Tatli.

Ethics declarations

Conflict of Interest

The authors have no conflict of interest to publish this research.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tatli, H., Dalfes, H.N. Long-Time Memory in Drought via Detrended Fluctuation Analysis. Water Resour Manage (2020).

Download citation


  • DFA
  • Drought
  • PDSI
  • HLZ
  • Long-memory
  • Turkey