Skip to main content

Advertisement

SpringerLink
Log in

Comparative analysis of probability distributions for the Standardized Precipitation Index and drought evolution in China during 1961–2015

  • Original Paper
  • Published:
Theoretical and Applied Climatology Aims and scope Submit manuscript

Abstract

As a representative index for monitoring and assessing drought, the Standardized Precipitation Index (SPI) relies on a suitable probability distribution function (PDF) to describe a precipitation series, which allows interregional comparisons following normalization. In this study, we considered nine PDFs (exponential (EXP), extreme value (EV), gamma (GAM), generalized Pareto (GP), logistic (LO), log-logistic (LOL), log-normal (LON), normal (NOR), and Weibull (WEI)) as candidates for use in SPI calculations. Based on monthly precipitation time series data (1961–2015) from 582 stations across China, together with the Kolmogorov–Smirnov (K–S) and Akaike Information Criterion (AIC) methods, differences in optimal PDFs for SPI calculations were compared comprehensively from the perspectives of timescale, record length, and index value. Based on the SPI calculated using the optimal PDF at the 6-month timescale (SPI6-opt), we analyzed the spatiotemporal characteristics of drought trends in China using the Mann–Kendall method. Results indicated both the timescale and the record length would affect the selection of the optimal PDF. The performance of the WEI and GAM distributions was superior to other distributions in describing monthly precipitation (especially for long precipitation records) at short and multiple timescales, respectively. During the entire study period, areas of China with high frequency of drought have transferred from the northwest (1960s), to the northeast (2000s), and to the southwest (most recent 5 years). Trend analysis revealed a noticeable wetting tendency confined mainly to Northwest, Northeast, and Southeast China and a significant trend toward drought in Southwest China and on the North China Plain.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Abramowitz M, Stegun IA (1965) Handbook of mathematical functions. Dover Publications, New York

    Google Scholar 

  • Ahmed K, Shahid S, Nawaz N (2018) Impacts of climate variability and change on seasonal drought characteristics of Pakistan. Atmos Res 214:364–374

    Google Scholar 

  • Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723. https://doi.org/10.1109/TAC.1974.1100705

    Article  Google Scholar 

  • Allan RP, Soden BJ (2008) Atmospheric warming and the amplification of precipitation extremes. Science 321(5895):1481–1484. https://doi.org/10.1126/science.1160787

    Article  Google Scholar 

  • Ayantobo OO, Li Y, Song SB, Yao N (2017) Spatial comparability of drought characteristics and related return periods in mainland China over 1961–2013. J Hydrol 550:549–567

    Google Scholar 

  • Botai CM, Botai JO, de Wit JP, Ncongwane KP, Adeola AM (2017) Drought characteristics over the Western Cape province, South Africa. Water 9(11):876. https://doi.org/10.3390/w9110876

    Google Scholar 

  • Bozdogan H (2000) Akaike’s information criterion and recent developments in information complexity. J Math Psychol 44(1):62–91. https://doi.org/10.1006/jmps.1999.1277

    Article  Google Scholar 

  • GB/T 20481-2006 (2006) Classification of meteorological drought. Standards Press of China, Beijing

    Google Scholar 

  • Colominas MA, Schlotthauer G, Torres ME (2014) Improved complete ensemble EMD: a suitable tool for biomedical signal processing. Biomed Signal Process Control 14:19–29

    Google Scholar 

  • Donat MG, Lowry AL, Alexander LV, O’Gorman PA, Maher N (2016) More extreme precipitation in the world’s dry and wet regions. Nat Clim Chang 6:508–513

    Google Scholar 

  • Estrela T, Vargas E (2012) Drought management plans in the European Union. The case of Spain. Water Resour Manag 26(6):1537–1553. https://doi.org/10.1007/s11269-011-9971-2

    Article  Google Scholar 

  • Feng Y, Cui NB, Zhao L, Gong DZ, Zhang KD (2017) Spatiotemporal variation of reference evapotranspiration during 1954–2013 in Southwest China. Quat Int 441:129–139

    Google Scholar 

  • Fischer T, Su BD, Luo Y, Scholten T (2012) Probability distribution of precipitation extreme for weather index based insurance in the Zhujiang River basin, south China. J Hydrometeorol 13(3):1023–1037. https://doi.org/10.1175/JHM-D-11-041.1

    Article  Google Scholar 

  • Gu XH, Zhang Q, Singh VP, Shi PJ (2017) Changes in magnitude and frequency of heavy precipitation across China and its potential links to summer temperature. J Hydrol 547:718–731. https://doi.org/10.1016/j.jhydrol.2017.02.041

    Article  Google Scholar 

  • Guo EL, Zhang JQ, Si H, Dong ZH, Cao TH, Lan W (2017) Temporal and spatial characteristics of extreme precipitation events in the Midwest of Jilin Province based on multifractal detrended fluctuation analysis method and copula functions. Theor Appl Climatol 130:597–607

    Google Scholar 

  • Guttman NB (1998) Comparing the palmer drought index and the standardized precipitation index. J Am Water Resour Assoc 34(1):113–121. https://doi.org/10.1111/j.1752-1688.1998.tb05964.x

    Article  Google Scholar 

  • Guttman NB (1999) Accepting the standardized precipitation index: a calculation algorithm. J Am Water Resour Assoc 35(2):311–322. https://doi.org/10.1111/j.1752-1688.1999.tb03592.x

    Article  Google Scholar 

  • Hao ZC, Hao FH, Singh VP, Shen XY (2016) A theoretical drought classification method for the multivariate drought index based on distribution properties of standardized drought indices. Adv Water Resour 92:240–247. https://doi.org/10.1016/j.advwatres.2016.04.010

    Article  Google Scholar 

  • Hong NM, Lee TY, Chen YJ (2016) Daily weather generator with drought properties by copulas and standardized precipitation indices. Environ Monit Assess 188(6):383. https://doi.org/10.1007/s10661-016-5395-z

  • Hong XJ, Guo SL, Xiong LH, Liu ZJ (2015) Spatial and temporal analysis of drought using entropy-based standardized precipitation index: a case study in Poyang Lake basin, China. Theor Appl Climatol 122:543–556

    Google Scholar 

  • Jiang SZ, Liang C, Cui NB, Zhao L, Du TS, Hu XT, Feng Y, Guan J, Feng Y (2019) Impacts of climatic variables on reference evapotranspiration during growing season in Southwest China. Agr Water Manag 216:365–378

    Google Scholar 

  • Karl TR, Gleason BE, Menne MJ, McMahon JR, Heim RR, Brewer MJ, Kunkel KE, Arndt DS, Privette JL, Bates JJ, Groisman PY, Easterling DR (2012) U.S. temperature and drought: recent anomalies and trends. EOS Trans Am Geophys Union 93(47):473–474. https://doi.org/10.1029/2012EO470001

    Article  Google Scholar 

  • Li C, Wang RH (2017) Recent changes of precipitation in Gansu, Northwest China: an index-based analysis. Theor Appl Climatol 129:397–412. https://doi.org/10.1007/s00704-016-1783-0

    Google Scholar 

  • Liu SL, Kang WP, Wang T (2016) Drought variability in Inner Mongolia of northern China during 1960–2013 based on standardized precipitation evapotranspiration index. Environ Earth Sci 75:145

  • Lloyd-Hughes B, Saunders MA (2002) A drought climatology for Europe. Int J Climatol 22(13):1571–1592. https://doi.org/10.1002/joc.846

    Google Scholar 

  • Lorenzo-Lacruz J, Morán-Tejeda E, Vicente-Serrano SM, Lopez-Moreno JI (2013) Streamflow droughts in the Iberian Peninsula between 1945 and 2005: spatial and temporal patterns. Hydrol Earth Syst Sci 17(1):119–134. https://doi.org/10.5194/hess-17-119-2013

    Article  Google Scholar 

  • Lu GY, Wong DW (2008) An adaptive inverse-distance weighting spatial interpolation technique. Comput Geosci 34(9):1044–1055

    Google Scholar 

  • Madadgar S, AghaKouchak A, Farahmand A, Davis SJ (2017) Probabilistic estimates of drought impacts on agricultural production. Geophys Res Lett 44. https://doi.org/10.1002/2017GL073606

    Google Scholar 

  • Mandal S, Choudhury BU (2015) Estimation and prediction of maximum daily rainfall at Sagar Island using best fit probability models. Theor Appl Climatol 121:87–97

    Google Scholar 

  • Mann ME, Gleick PH (2015) Climate change and California drought in the 21st century. Proc Natl Acad Sci 112:3858–3859

    Google Scholar 

  • McGrath GS, Sadler R, Fleming K, Tregoning P, Hinz C, Veneklaas EJ (2012) Tropical cyclones and the ecohydrology of Australia’s recent continental-scale drought. Geophys Res Lett 39(3):L03404. https://doi.org/10.1029/2011GL050263

    Article  Google Scholar 

  • 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. Boston, MA: American Meteorological Society 17(22): 179-183

  • Meng L, Ford T, Guo Y (2017) Logistic regression analysis of drought persistence in East China. Int J Climatol 37:1444–1455

    Google Scholar 

  • Mishra AK, Singh VP (2010) A review of drought concepts. J Hydrol 391:202–216. https://doi.org/10.1016/j.jhydrol.2010.07.012

    Article  Google Scholar 

  • Morid S, Smakhtin V, Moghaddasi M (2006) Comparison of seven meteorological indices for drought monitoring in Iran. Int J Climatol 26(7):971–985. https://doi.org/10.1002/joc.1264

    Article  Google Scholar 

  • Mosaedi A, Zare Abyaneh H, Ghabaei Sough M, Samadi SZ (2015) Quantifying changes in reconnaissance drought index using equiprobability transformation function. Water Resour Manag 29:2451–2469

    Google Scholar 

  • Nielsen DR, Bouma J (1985) Soil spatial variability. In: Proceedings of a Workshop of the international soil science society and the soil science society of America. Pudoc, Wageningen, p 243

    Google Scholar 

  • Rahmstorf S, Coumou D (2011) Increase of extreme events in a warming world. Proc Natl Acad Sci 108(44):17905–17909

    Google Scholar 

  • Raziei T, Saghafian B, Paulo AA, Pereira LS, Bordi I (2009) Spatial patterns and temporal variability of drought in Western Iran. Water Resour Manag 23:439–455. https://doi.org/10.1007/s11269-008-9282-4

    Article  Google Scholar 

  • Ren GY, Ren YY, Zhan YJ, Sun XB, Liu YJ, Chen Y, Wang T (2015) Spatial and temporal patterns of precipitation variability over mainland China: II: recent trends. Adv Water Sci 26(4):451–465 (in Chinese)

    Google Scholar 

  • Shi YF, Shen YP, Li DL, Zhang GW, Ding YJ, Hu RJ, Kang ES (2003) Discussion on the present climate change from warm-dry to warm-wet in northwest China. Q Sci 23(2):152–164 (in Chinese)

    Google Scholar 

  • Sienz F, Bothe O, Fraedrich K (2012) Monitoring and quantifying future climate projections of dryness and wetness extremes: SPI bias. Hydrol Earth Syst Sci 16:2143–2157. https://doi.org/10.5194/hess-16-2143-2012

    Article  Google Scholar 

  • Song SB, Cai HJ, Jin JL, Kang Y (2012) Copulas function and its application in hydrology. Science Publications, Beijing

    Google Scholar 

  • Song SB, Singh VP (2010) Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stoch Env Res Risk A 24:425–444. https://doi.org/10.1007/s00477-009-0331-1

    Article  Google Scholar 

  • Stagge JH, Kingston DG, Tallaksen LM, Hannah DM (2017) Observed drought indices show increasing divergence across Europe. Sci Rep 7:14045. https://doi.org/10.1038/s41598-017-14283-2

  • Stagge JH, Tallaksen LM, Gudmundsson L, Van Loon AF, Stahl K (2015) Candidate distributions for climatological drought indices (SPI and SPEI). Int J Climatol 35(13):4027–4040. https://doi.org/10.1002/joc.4267

    Google Scholar 

  • Stott P (2016) How climate change affects extreme weather events. Science 352(6293):1517–1518. https://doi.org/10.1126/science.aaf7271

    Article  Google Scholar 

  • Su BD, Huang JL, Fischer T, Wang YJ, Kundzewicz ZW, Zhai JQ, Sun HM, Wang AQ, Zeng XF, Wang GJ, Tao H, Gemmer M, Li XC, Jiang T (2018) Drought losses in China might double between the 1.5 °C and 2.0 °C warming. Proc Natl Acad Sci 115:10600–10605

    Google Scholar 

  • Svensson C, Hannaford J, Prosdocimi I (2017) Statistical distributions for monthly aggregations of precipitation and streamflow in drought indicator applications. Water Resour Res 53(2):999–1018. https://doi.org/10.1002/2016WR019276

    Article  Google Scholar 

  • Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res 106(D7):7183–7192. https://doi.org/10.1029/2000JD900719

    Article  Google Scholar 

  • Teuling AJ (2018) A hot future for European droughts. Nat Clim Chang 8:364–365

    Google Scholar 

  • Tu XJ, Singh VP, Chen XH, Ma MW, Zhang Q, Zhao Y (2016) Uncertainty and variability in bivariate modeling of hydrological droughts. Stoch Env Res Risk A 30:1317–1334

    Google Scholar 

  • Vergni L, Di Lena B, Todisco F, Mannocchi F (2017) Uncertainty in drought monitoring by the standardized precipitation index: the case study of the Abruzzo region (central Italy). Theoret Appl Climatol 128:13–26. https://doi.org/10.1007/s00704-015-1685-6

    Google Scholar 

  • Vicente-Serrano SM, Begueria 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

    Article  Google Scholar 

  • Wang H, Yan DH, Qin DY, Wang JH (2005) A study of the spatial shift of 400 mm rainfall contours in the Yellow River basin. Adv Earth Science 20(6):649–655 (in Chinese)

    Google Scholar 

  • Wang R, Chen JY, Chen XW, Wang YF (2017) Variability of precipitation extremes and dryness/wetness over the southeast coastal region of China, 1960-2014. Int J Climatol 37:4656–4669

    Google Scholar 

  • Waseem M, Ajmal M, Kim TW (2015) Development of a new composite drought index for multivariate drought assessment. J Hydrol 527:30–37. https://doi.org/10.1016/j.jhydrol.2015.04.044

    Article  Google Scholar 

  • Wu H, Hayes MJ, Wilhite DA, Svoboda MD (2005) The effect of the length of record on the standardized precipitation index calculation. Int J Climatol 25(4):505–520. https://doi.org/10.1002/joc.1142

    Article  Google Scholar 

  • Wu H, Svoboda MD, Hayes MJ, Wilhite DA, Wen FJ (2007) Appropriate application of the standardized precipitation index in arid locations and dry seasons. Int J Climatol 27(1):65–79

    Google Scholar 

  • Wu SF, Zhang X, Wang JC, Liu JF, Pan GY (2016) Calculation of the standardized precipitation index based on the best fitted distribution functions to the precipitation series. Arid land Geogr 39(3):555–564 (in Chinese)

    Google Scholar 

  • Yan GX, Wu ZY, Li DH, Xiao H (2018) A comparative frequency analysis of three standardized drought indices in the Poyang Lake basin, China. Nat Hazards 91:353–374

    Google Scholar 

  • Yang HC, Wang HX, Fu GB, Yan HM, Zhao PP (2018) Evaluation of HHT approach for estimating agricultural drought trend and frequency based on modified soil water deficit index (MSWDI). Theor Appl Climatol 137:1825–1842

    Google Scholar 

  • Yao N, Li Y, Lei TJ, Peng LL (2018) Drought evolution, severity and trends in mainland China over 1961-2013. Sci Total Environ 616-617:73–89. https://doi.org/10.1016/j.scitotenv.2017.10.327

    Article  Google Scholar 

  • Yu HY, Liu SH, Zhao N, Li D, Yu YT (2011) Characteristics of air temperature and precipitation in different regions of China from 1951 to 2009. J Meteorol Environ 27(4):1–11 (in Chinese)

    Google Scholar 

  • Yue S, Hashino M (2007) Probability distribution of annual, seasonal and monthly precipitation in Japan. Hydrol Sci J 52:863–877

    Google Scholar 

  • Zarch MAA, Sivakumar B, Sharma A (2015) Droughts in a warming climate: a global assessment of standardized precipitation index (SPI) and reconnaissance drought index (RDI). J Hydrol 526:183–195. https://doi.org/10.1016/j.jhydrol.2014.09.071

    Article  Google Scholar 

  • Zhai JQ, Liu B, Hartmann H, Su BD, Jiang T, Fraedrich K (2010) Dryness/wetness variations in ten large river basins of China during the first 50 years of the 21st century. Quat Int 226:101–111. https://doi.org/10.1016/j.quaint.2010.01.027

    Article  Google Scholar 

  • Zhang J, Shen YJ (2019) Spatio-temporal variations in extreme drought in China during 1961–2015. J Geogr Sci 29:67–83

    Google Scholar 

  • Zhang RR, Chen X, Cheng QB, Zhang ZC, Shi P (2016) Joint probability of precipitation and reservoir storage for drought estimation in the headwater basin of the Huaihe River, China. Stoch Env Res Risk A 30(6):1641–1657. https://doi.org/10.1007/s00477-016-1249-z

    Article  Google Scholar 

  • Zhang Q, Xu CY, Chen XH (2011) Reference evapotranspiration changes in China: natural processes or human influences? Theor Appl Climatol 103:479–488

    Google Scholar 

  • Zhao Q, Zou CH, Wang KF, Gao Q, Yao T (2019) Spatial and temporal distribution characteristics of drought and its influencing factors in Heilongjiang province, China from 1956 to 2015. Appl Ecol Environ Res 17:2631–2650

    Google Scholar 

  • Zhou H, Liu YB (2016) SPI based meteorological drought assessment over a humid basin: effects of processing schemes. Water 8(9):373. https://doi.org/10.3390/w8090373

    Article  Google Scholar 

  • Zhu Y, Liu Y, Ma XY, Ren LL, Singh VP (2018) Drought analysis in the Yellow River basin based on a short-scalar palmer drought severity index. Water 10(11):1526. https://doi.org/10.3390/w10111526

    Google Scholar 

Download references

Acknowledgments

We gratefully acknowledge the China Meteorological Administration for providing climate datasets.

Funding

This work is supported financially by the National Key Research and Development Program of China (Grant No. 2017YFC0404603), National Natural Science Foundation of China (Grant No. 51779009), 111Project(B18006), and Geology and Mineral Resources Survey Project (Grant No. DD20190652).

Author information

Authors and Affiliations

  1. Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water Sciences, Beijing Normal University, No. 19, Xinjiekouwai Street, Haidian District, Beijing, 100875, China

    Ruxin Zhao, Huixiao Wang & Yuxuan Dong

  2. Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, 100101, China

    Chesheng Zhan & Shi Hu

  3. School of Geographic and Environmental Sciences, Tianjin Normal University, Tianjin, 300387, China

    Meihong Ma

Authors
  1. Ruxin Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huixiao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chesheng Zhan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shi Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Meihong Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yuxuan Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huixiao Wang.

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, R., Wang, H., Zhan, C. et al. Comparative analysis of probability distributions for the Standardized Precipitation Index and drought evolution in China during 1961–2015. Theor Appl Climatol 139, 1363–1377 (2020). https://doi.org/10.1007/s00704-019-03050-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00704-019-03050-0

Search

Navigation