Water Resources Management

, Volume 32, Issue 8, pp 2611–2624 | Cite as

A Non-Stationary Reconnaissance Drought Index (NRDI) for Drought Monitoring in a Changing Climate

  • Javad BazrafshanEmail author
  • Somayeh Hejabi


Traditionally, drought indices are calculated under stationary condition, the assumption that is not true in a changing environment. Under non-stationary conditions, it is assumed the probability distribution parameters vary linearly/non-linearly with time or other covariates. In this study, using the GAMLSS algorithm, a time-varying location parameter of lognormal distribution fitted to the initial values (α0) of the traditional Reconnaissance Drought Index (RDI) was developed to establish a new index called the Non-Stationary RDI (NRDI), simplifying drought monitoring under non-stationarity. The fifteen meteorological stations having the longest records (1951–2014) in Iran were chose to evaluate the NRDI performances for drought monitoring. Trend analysis of the α0 series at multiple time windows was tested by using the Mann-Kendall statistics. Although all stations detected decreasing trend in the α0 series, eight of them were significant at the 5% probability level. The results showed that the time-dependent relationship is adequate to model the location parameter at the stations with the significant temporal trend. There were remarkable differences between the NRDI and the RDI, especially for the time windows larger than 6 months, implying monitoring droughts using the NRDI under non-stationarity. The study suggests using the NRDI where the significant time trend appears in the initial values of RDI due to changing climate.


Non-Stationary RDI NRDI Drought GAMLSS Time-Dependent 



This work has been supported by Iran National Science Foundation and executed at University of Tehran-College of Agricultural and Natural Resources (UTCAN).


  1. Akantziliotou K, Rigby RA, Stasinopoulos DM (2002) The R implementation of generalized additive models for location, scale and shape. In: Stasinopoulos M, Touloumi G (eds) Statistical modelling in society: Proceedings of the 17th International Workshop on Statistical Modelling, Chania, pp 75–83.
  2. Anderson TW, Darling DA (1954) A test of goodness-of-fit. J Am Stat Assoc 49:765–769. CrossRefGoogle Scholar
  3. Asadi Zarch MA, Malekinezhad H, Mobin MH, Dastorani MT, Kousari MR (2011) Drought monitoring by reconnaissance drought index (RDI) in Iran. Water Resour Manag 25(13):3485–3504. CrossRefGoogle Scholar
  4. Banimahd SA, Khalili D (2013) Factors influencing Markov chains predictability characteristics, utilizing SPI, RDI, EDI and SPEI drought indices in different climatic zones. Water Resour Manag 27(11):3911–3928. CrossRefGoogle Scholar
  5. Bazrafshan J (2017) Effect of air temperature on historical trend of long-term droughts in different climates of Iran. Water Resour Manag 31(14):4683–4698. CrossRefGoogle Scholar
  6. Cancelliere A, Bonaccorso B (2016) A non-stationary analytical framework for the probabilistic characterization of drought events. World Environmental and Water Resources Congress 2016:350–358. Google Scholar
  7. Chanda K, Maity R (2015) Meteorological drought quantification with Standardized Precipitation Anomaly Index for the regions with strongly seasonal and periodic precipitation. J Hydrol Eng:06015007.
  8. Cheng L, AghaKouchak A (2014) Nonstationary precipitation intensity-duration-frequency curves for infrastructure design in a changing climate. Sci Rep 4:7093. CrossRefGoogle Scholar
  9. Cole TJ, Green PJ (1992) Smoothing reference centile curves: the LMS method and penalized likelihood. Stat Med 11(10):1305–1319. CrossRefGoogle Scholar
  10. Debele SE, Strupczewski WG, Bogdanowicz E (2017) A comparison of three approaches to non-stationary flood frequency analysis. Acta Geophysica 65:863–883. CrossRefGoogle Scholar
  11. Gao L, Huang J, Chen X, Chen Y, Liu M (2017) Risk of extreme precipitation under nonstationarity conditions during the second flood season in the Southeastern Coastal Region of China. J Hydrometeorol 18(3):669–681. CrossRefGoogle Scholar
  12. IPCC (2007) Climate Change 2007: The Physical Science Basis. In: Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt KB, Tignor M, Miller HL (eds) Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, p 996Google Scholar
  13. Jiang C, Xiong L, Xu C-Y, Guo S (2015) Bivariate frequency analysis of nonstationary low-flow series based on the time-varying copula. Hydrol Process 29(6):1521–1534. CrossRefGoogle Scholar
  14. Kao S-C, Govindaraju RS (2010) A copula-based joint deficit index for droughts. J Hydrol 380(1–2):121–134. CrossRefGoogle Scholar
  15. Kendall MG (1975) Rank correlation methods. Griffin, LondonGoogle Scholar
  16. Khalili D, Farnoud T, Jamshidi H, Kamgar-Haghighi AA, Zand-Parsa SH (2011) Comparability analyses of the SPI and RDI meteorological drought indices in different climatic zones. Water Resour Manag 25(6):1737–1757. CrossRefGoogle Scholar
  17. Kousari MR, Dastorani MT, Niazi Y, Soheili E, Hayatzadeh M, Chezgi J (2014) Trend detection of drought in arid and semi-arid regions of Iran based on implementation of Reconnaissance Drought Index (RDI) and application of non-parametrical statistical method. Water Resour Manag 28(7):1857–1872. CrossRefGoogle Scholar
  18. Kwon H-H, Lall U (2016) A copula-based nonstationary frequency analysis for the 2012-2015 drought in California. Water Resour Res 52(7):5662–5675. CrossRefGoogle Scholar
  19. Kwon H-H, Lall U, Kim SJ (2016) The unusual 2013–2015 drought in South Korea in the context of a multicentury precipitation record: Inferences from a nonstationary, multivariate, Bayesian copula model. Geophys Res Lett 43(16):8534–8544. CrossRefGoogle Scholar
  20. Li JZ, Wang YX, Li SF, Hu R (2015) A Nonstationary Standardized Precipitation Index incorporating climate indices as covariates. J Geophys Res Atmos 120(23):12082–12095. CrossRefGoogle Scholar
  21. López J, Francés F (2013) Non-stationary flood frequency analysis in continental Spanish rivers, using climate and reservoir indices as external covariates. Hydrol Earth Syst Sci 17(8):3189–3203. CrossRefGoogle Scholar
  22. Mann HB (1945) Nonparametric tests against trend. Econometrica 13:245–259CrossRefGoogle Scholar
  23. McKee TBN, Doesken J, Kleist J (1993) The relationship of drought frequency and duration to time scales, Eight Conference on Applied Climatology. American Meteorological Society, Anaheim, pp 179–184Google Scholar
  24. Mishra AK, Singh VP (2009) Analysis of drought severity-area-frequency curves using a general circulation model and scenario uncertainty. J Geophys Res 114(D6):D06120. CrossRefGoogle Scholar
  25. Mishra AK, Singh VP (2010) A review of drought concepts. J Hydrol 391(1–2):202–216. CrossRefGoogle Scholar
  26. Obeysekera J, Salas J (2016) Frequency of recurrent extremes under nonstationarity. J Hydrol Eng:04016005.
  27. Rashid MM, Beecham S, Chowdhury RK (2016) Statistical downscaling of rainfall: a non-stationary and multi-resolution approach. Theor Appl Climatol 124(3):919–933. CrossRefGoogle Scholar
  28. Rigby RA, Stasinopoulos DM (1996a) A semi-parametric additive model for variance heterogeneity. Stat Comput 6(1):57–65. CrossRefGoogle Scholar
  29. Rigby RA, Stasinopoulos DM (1996b) Mean and dispersion additive models. In: Hardle W, Schimek MG (eds) Statistical Theory and Computational Aspects of Smoothing. Physica, Heidelberg, pp 215–230CrossRefGoogle Scholar
  30. Rigby RA, Stasinopoulos DM (2001) The GAMLSS project: a flexible approach to statistical modelling. In: Klein B and Korsholm L (eds.), New Trends in Statistical Modelling: Proceedings of the 16th International Workshop on Statistical Modelling, Odense, pp. 249–256Google Scholar
  31. Rigby RA, Stasinopoulos DM (2005) Generalized additive models for location, scale and shape. Appl Stat 54(3):507–554. Google Scholar
  32. Rigby R, Stasinopoulos D, Voudouris V (2013) Discussion: A comparison of GAMLSS with quantile regression. Stat Model 13(4):335–348. CrossRefGoogle Scholar
  33. Romero L, Pérez-Sánchez M, López Jiménez PA (2017) Improvement of sustainability indicators when traditional water management changes: a case study in Alicante (Spain). AIMS Environ Sci 4(3):502–522. CrossRefGoogle Scholar
  34. Russo S, Dosio A, Sterl A, Barbosa P, Vogt J (2013) Projection of occurrence of extreme dry-wet years and seasons in Europe with stationary and nonstationary Standardized Precipitation Indices. J Geophys Res Atmos 118(14):7628–7639. CrossRefGoogle Scholar
  35. Sarhadi A, Burn DH, Ausín MC, Wiper MP (2016) Time-varying nonstationary multivariate risk analysis using a dynamic Bayesian copula. Water Resour Res 52(3):2327–2349. CrossRefGoogle Scholar
  36. Shah R, Manekar VL, Christian RA, Mistry NJ (2013) Estimation of Reconnaissance Drought Index (RDI) for Bhavnagar District, Gujarat, India. International Journal of Environmental, Chemical, Ecological, Geological and Geophysical Engineering 7(7):507–510Google Scholar
  37. Stasinopoulos DM, Rigby RA, Akantziliotou C (2008) Instructions on how to use the GAMLSS package in R, 2nd edn. STORM Research Centre, London Metropolitan University, LondonGoogle Scholar
  38. Stott PA, Tett FB, Jones GS, Allen MR, Mitchell JFB, Jenkins GJ (2000) External control of 20th century temperature by natural and anthropogenic forcings. Science 290(5499):2133–2137. CrossRefGoogle Scholar
  39. Thomas T, Jaiswal RK, Galkate RV, Nayak TR (2016) Reconnaissance drought index based evaluation of meteorological drought characteristics in Bundelkhand. Procedia Technology 24:23–30. CrossRefGoogle Scholar
  40. Thornthwaite CW (1948) An approach toward a rational classification of climate. Geogr Rev 38:55–94Google Scholar
  41. Thuiller W (2004) Patterns and uncertainties of species' range shifts under climate change. Glob Chang Biol 10(12):2020–2027. CrossRefGoogle Scholar
  42. Tsakiris G (2004) Meteorological drought assessment. Paper prepared for the needs of the European Research Program MEDROPLAN (Mediterranean Drought Preparedness and Mitigation Planning), ZaragozaGoogle Scholar
  43. Tsakiris G, Vangelis H (2005) Establishing a drought index incorporating evapotranspiration. Eur Water 9-10:1–9Google Scholar
  44. Tsakiris G, Rossi G, Iglesias A, Tsiourtis N, Garrote L, Cancelliere A (2006) Drought Indicators Report. Report made for the needs of the European Research Program MEDROPLAN (Mediterranean Drought Preparedness and Mitigation Planning)Google Scholar
  45. Tsakiris G, Pangalou D, Vangelis H (2007) Regional drought assessment based on the reconnaissance drought index (RDI). Water Resour Manag 21(5):821–833CrossRefGoogle Scholar
  46. Verdon-Kidd DC, Kiem AS (2010) Quantifying drought risk in a nonstationary climate. J Hydrometeorol 11(4):1019–1031. CrossRefGoogle Scholar
  47. 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. CrossRefGoogle Scholar
  48. Villarini G, Smith JA, Serinaldi F, Jerad B, Paul DB, Krajewski WF (2009) Flood frequency analysis for nonstationary annual peak records in an urban drainage basin. Adv Water Resour 32(8):1255–1266. CrossRefGoogle Scholar
  49. Wang Y, Li J, Feng P, Hu R (2015) A time-dependent drought index for non-stationary precipitation series. Water Resour Manag 29:5631–5647. CrossRefGoogle Scholar
  50. Wilhite DA, Sivakumar MVK, Pulwarty R (2014) Managing drought risk in a changing climate: The role of national drought policy. Weather and Climate Extremes 3:4–13. CrossRefGoogle Scholar
  51. Zarei AR, Moghimi MM, Mahmoudi MR (2016a) Analysis of changes in spatial pattern of drought using RDI index in south of Iran. Water Resour Manag 30(11):3723–3743. CrossRefGoogle Scholar
  52. Zarei AR, Moghimi MM, Mahmoudi MR (2016b) Parametric and non-parametric trend of drought in arid and semi-arid regions using RDI index. Water Resour Manag 30(14):5479–5500. CrossRefGoogle Scholar
  53. Zhang D-D, Yan D-G, Wang Y-C, Lu F, S-H L (2015) GAMLSS-based nonstationary modeling of extreme precipitation in Beijing–Tianjin–Hebei region of China. Nat Hazards 77(2):1037–1053. CrossRefGoogle Scholar
  54. Zou L, Xia J, She D (2018) Analysis of impacts of climate change and human activities on hydrological drought: a case study in the Wei River Basin, China. Water Resour Manag 32(4):1421–1438. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Irrigation and Reclamation EngineeringUniversity of TehranKarajIran

Personalised recommendations