Abstract
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.
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References
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. https://www.statmod.org/workshops_archive_proceedings_2002.htm
Anderson TW, Darling DA (1954) A test of goodness-of-fit. J Am Stat Assoc 49:765–769. https://doi.org/10.1007/978-3-642-04898-2_118
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. https://doi.org/10.1007/s11269-011-9867-1
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. https://doi.org/10.1007/s11269-013-0387-z
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. https://doi.org/10.1007/s11269-017-1773-8
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. https://doi.org/10.1061/9780784479858.036
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. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001236
Cheng L, AghaKouchak A (2014) Nonstationary precipitation intensity-duration-frequency curves for infrastructure design in a changing climate. Sci Rep 4:7093. https://doi.org/10.1038/srep07093
Cole TJ, Green PJ (1992) Smoothing reference centile curves: the LMS method and penalized likelihood. Stat Med 11(10):1305–1319. https://doi.org/10.1002/sim.4780111005
Debele SE, Strupczewski WG, Bogdanowicz E (2017) A comparison of three approaches to non-stationary flood frequency analysis. Acta Geophysica 65:863–883. https://doi.org/10.1007/s11600-017-0071-4
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. https://doi.org/10.1175/jhm-d-16-0119.1
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 996
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. https://doi.org/10.1002/hyp.10288
Kao S-C, Govindaraju RS (2010) A copula-based joint deficit index for droughts. J Hydrol 380(1–2):121–134. https://doi.org/10.1016/j.jhydrol.2009.10.029
Kendall MG (1975) Rank correlation methods. Griffin, London
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. https://doi.org/10.1007/s11269-010-9772-z
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. https://doi.org/10.1007/s11269-014-0558-6
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. https://doi.org/10.1002/2016WR018959
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. https://doi.org/10.1002/2016GL070270
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. https://doi.org/10.1002/2015JD023920
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. https://doi.org/10.5194/hess-17-3189-2013
Mann HB (1945) Nonparametric tests against trend. Econometrica 13:245–259
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 179–184
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. https://doi.org/10.1029/2008JD010986
Mishra AK, Singh VP (2010) A review of drought concepts. J Hydrol 391(1–2):202–216. https://doi.org/10.1016/j.jhydrol.2010.07.012
Obeysekera J, Salas J (2016) Frequency of recurrent extremes under nonstationarity. J Hydrol Eng:04016005. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001339
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. https://doi.org/10.1007/s00704-015-1465-3
Rigby RA, Stasinopoulos DM (1996a) A semi-parametric additive model for variance heterogeneity. Stat Comput 6(1):57–65. https://doi.org/10.1007/bf00161574
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 215–230
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. 249–256
Rigby RA, Stasinopoulos DM (2005) Generalized additive models for location, scale and shape. Appl Stat 54(3):507–554. https://doi.org/10.1111/j.1467-9876.2005.00510.x
Rigby R, Stasinopoulos D, Voudouris V (2013) Discussion: A comparison of GAMLSS with quantile regression. Stat Model 13(4):335–348. https://doi.org/10.1177/1471082x13494316
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. https://doi.org/10.3934/environsci.2017.3.502
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. https://doi.org/10.1002/jgrd.50571
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. https://doi.org/10.1002/2015WR018525
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):507–510
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, London
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. https://doi.org/10.1126/science.290.5499.2133
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. https://doi.org/10.1016/j.protcy.2016.05.005
Thornthwaite CW (1948) An approach toward a rational classification of climate. Geogr Rev 38:55–94
Thuiller W (2004) Patterns and uncertainties of species' range shifts under climate change. Glob Chang Biol 10(12):2020–2027. https://doi.org/10.1111/j.1365-2486.2004.00859.x
Tsakiris G (2004) Meteorological drought assessment. Paper prepared for the needs of the European Research Program MEDROPLAN (Mediterranean Drought Preparedness and Mitigation Planning), Zaragoza
Tsakiris G, Vangelis H (2005) Establishing a drought index incorporating evapotranspiration. Eur Water 9-10:1–9
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)
Tsakiris G, Pangalou D, Vangelis H (2007) Regional drought assessment based on the reconnaissance drought index (RDI). Water Resour Manag 21(5):821–833
Verdon-Kidd DC, Kiem AS (2010) Quantifying drought risk in a nonstationary climate. J Hydrometeorol 11(4):1019–1031. https://doi.org/10.1175/2010jhm1215.1
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. https://doi.org/10.1175/2009jcli2909.1
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. https://doi.org/10.1016/j.advwatres.2009.05.003
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. https://doi.org/10.1007/s11269-015-1138-0
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. https://doi.org/10.1016/j.wace.2014.01.002
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. https://doi.org/10.1007/s11269-016-1380-0
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. https://doi.org/10.1007/s11269-016-1501-9
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. https://doi.org/10.1007/s11069-015-1638-5
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. https://doi.org/10.1007/s11269-017-1877-1
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This work has been supported by Iran National Science Foundation and executed at University of Tehran-College of Agricultural and Natural Resources (UTCAN).
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Bazrafshan, J., Hejabi, S. A Non-Stationary Reconnaissance Drought Index (NRDI) for Drought Monitoring in a Changing Climate. Water Resour Manage 32, 2611–2624 (2018). https://doi.org/10.1007/s11269-018-1947-z
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DOI: https://doi.org/10.1007/s11269-018-1947-z