Abstract
Several studies have been conducted on droughts, precipitation, and temperature, whereas none have addressed the underlying relationship between nonlinear dynamic properties and patterns of two main hydrological parameters, precipitation and temperature, and meteorological and hydrological droughts. Monthly datasets of Midlands in the UK between 1921 and 2019 were collected for analysis. Subsequent to apply a multifractal approach to attain the nonlinear features of the datasets, the relationship between two hydrological parameters and droughts was investigated through the cross-correlation technique. A similar process was performed to analyze the relationship between multifractal strength variations in time series of precipitation and temperature and droughts. The nonlinear dynamic results indicated that droughts (meteorological and hydrological) were substantially affected by precipitation than temperature. In other words, droughts were more sensitive to precipitation fluctuations than temperature fluctuations. Concerning temperature, meteorological, and hydrological droughts were dependent on the minimum and maximum temperatures (\(T_{{{\text{min}}}}\) and \(T_{{{\text{max}}}}\)), respectively. The correlation between precipitation and meteorological drought was more long-range persistence than precipitation and hydrological drought. Besides, the correlation between \(T_{{{\text{max}}}}\) and droughts was more long-range persistence than \(T_{{{\text{min}}}}\) and droughts. Analysis of nonlinear dynamic patterns proved that the multifractal strength of meteorological drought depended on the multifractal strength of precipitation and \(T_{{{\text{max}}}}\), whereas the multifractal strength of hydrological drought depended on the multifractal strength of the \(T_{{{\text{min}}}}\). The correlation between precipitation and drought indices exhibited more multifractal strength than temperature and drought indices. Finally, the pivotal role of maximum temperature on drought events was quite alerting due to global warming intensification.
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Some or all data and models that support the findings of this study are available from the corresponding author upon reasonable request. The corresponding author is ready to share data with other researchers who send their request to this Email address: fattahi.mh@gmail.com.
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References
Adarsh S, Priya KL (2021) Multifractal description of droughts in western India using detrended fluctuation analysis. Springer, Cham. https://doi.org/10.1007/978-3-030-59148-9_9
Adarsh S, Kumar DN, Deepthi B, Gayathri G, Aswathy SS, Bhagyasree S (2019) Multifractal characterization of meteorological drought in India using detrended fluctuation analysis. Int J Climatol 39:4234–4255. https://doi.org/10.1002/joc.6070
Adarsh S, Dharan DS, Nandhu AR, Vishnu BA, Mohan VK, Watorek M (2020) Multifractal description of streamflow and suspended sediment concentration data from Indian river basins. Acta Geophys 68:519–535. https://doi.org/10.1007/s11600-020-00407-2
Agana NA, Homaifar A (2017) A deep learning based approach for long-term drought prediction. SoutheastCon 2017. Concord, NC, pp. 1–8. DOI: https://doi.org/10.1109/SECON.2017.7925314
Aghelpour P, Bahrami-Pichaghchi H, Kisi O (2020) Comparison of three different bio-inspired algorithms to improve ability of neuro fuzzy approach in prediction of agricultural drought, based on three different indexes. Comput Electron Agric 170:105279. https://doi.org/10.1016/j.compag.2020.105279
Ahmed K, Shahid S, Nawaz N (2018) Impacts of climate variability and change on seasonal drought characteristics of Pakistan. Atmos Res 214:364–374. https://doi.org/10.1016/j.atmosres.2018.08.020
An G, Hao Z (2017) Variation of precipitation and streamflow in the upper and middle Huaihe River Basin, China, from 1959–2009. J Coast Res 80:69–79. https://doi.org/10.2112/SI80-010.1
Benesty J, Chen J, Huang Y, Cohen I (2009) Pearson correlation coefficient. In: Noise reduction in speech processing. Springer, Berlin. https://doi.org/10.1007/978-3-642-00296-0_5
Bhardwaj K, Shah D, Aadhar S, Mishra V (2020) Propagation of meteorological to hydrological droughts in India. J Geophys Res Atmos 125(22):e2020JD033455. https://doi.org/10.1029/2020JD033455
Byakatonda J, Parida BP, Moalafhi DB, Kenabatho PK (2018) Analysis of long-term drought severity characteristics and trends across semiarid Botswana using two drought indices. Atmos Res 213:492–508. https://doi.org/10.1016/j.atmosres.2018.07.002
Cao G, Shi Y (2017) Simulation analysis of multifractal detrended methods based on the ARFIMA process. Chaos Soliton Fract 105:235–243. https://doi.org/10.1016/j.chaos.2017.10.038
Chatterjee S, Ghosh D (2021) Impact of Global Warming on SENSEX fluctuations—A study based on Multifractal detrended cross correlation analysis between the temperature anomalies and the SENSEX fluctuations. Phys A 571:125815. https://doi.org/10.1016/j.physa.2021.125815
Cleveland RB, Cleveland WS, McRae J, Terpenning I (1990) STL: A seasonal-trend decomposition procedure based on loess. J off Stat 6:3–73
Crow WT, Kumar SV, Bolten JD (2012) On the utility of land surface models for agricultural drought monitoring. Hydrol Earth Syst Sci 16:3451–3460. https://doi.org/10.5194/hess-16-3451-2012
Hao Z, Hao F, Sing VP, Ouyang W, Cheng H (2017a) An integrated package for drought monitoring, prediction and analysis to aid drought modeling and assessment. Environ Model Softw 91:199–209. https://doi.org/10.1016/j.envsoft.2017.02.008
Hao Z, Yuan X, Xia Y, Hao F, Singh VP (2017b) An Overview of Drought Monitoring and Prediction Systems at Regional and Global Scales. Bull Am Meteorol Soc 98(9):1879–1896. https://doi.org/10.1175/BAMS-D-15-00149.1
Hao Z, Singh VP, Xia Y (2018) Seasonal Drought Prediction: Advances, Challenges, and Future Prospects. Rev Geophys 56(1):108–141. https://doi.org/10.1002/2016RG000549
Harisuseno D (2020) Meteorological drought and its relationship with southern oscillation index (SOI). Civ Eng J 6(10):1864–1875. https://doi.org/10.28991/cej-2020-03091588
Hou W, Feng G, Yan P et al (2018) Multifractal analysis of the drought area in seven large regions of China from 1961 to 2012. Meteorol Atmos Phys 130:459–471. https://doi.org/10.1007/s00703-017-0530-0
Kantelhardt JW, Zschiegner SA, Koscielny-Bunde E, Bunde A, Havlin S, Stanley HE (2002) Multifractal detrended fluctuation analysis of nonstationary time series. Phys A 316:87. https://doi.org/10.1016/S0378-4371(02)01383-3
Kendon M, McCarthy M, Jevrejeva S, Matthews A, Sparks T, Garforth J (2020) State of the UK Climate 2019. Int J Climatol 40:1–69. https://doi.org/10.1002/joc.6726
Li Q, Zeng M, Wang H, Li P, Wang K, Yu M (2015) Drought assessment using a multivariate drought index in the Huaihe River basin of Eastern China. Proc Int as Hydrol Sci 369:61–67. https://doi.org/10.5194/piahs-369-61-2015
Li B, Zhu C, Liang Z, Wang G, Zhang Y (2018) Connections between meteorological and hydrological droughts in a semi-arid basin of the middle Yellow River. Proc Int as Hydrol Sci 379:403–407. https://doi.org/10.5194/piahs-379-403-2018
Li Q, He P, He Y et al (2020) Investigation to the relation between meteorological drought and hydrological drought in the upper Shaying River Basin using wavelet analysis. Atmos Res 234:104743. https://doi.org/10.1016/j.atmosres.2019.104743
Liu Y, Ren L, Singh VP, Yong B, Jiang S, Yuan F, Yang X (2019a) Understanding the Spatiotemporal Links Between Meteorological and Hydrological Droughts from a Three-Dimensional Perspective. J Geophys Res Atmos 124(6):3090–3109. https://doi.org/10.1029/2018JD028947
Liu Y, Zhu Y, Ren L, Singh VP, Yong B, Jiang S, Yuan F, Yang X (2019b) Understanding the Spatiotemporal Links Between Meteorological and Hydrological Droughts from a Three-Dimensional Perspective. J Geophys Res Atmos 124(6):3090–3109. https://doi.org/10.1029/2018JD028947
Livina V, Kizner Z, Braun P, Molnar T, Bunde A, Havlin S (2007) Temporal scaling comparison of real hydrological data and model runoff records. J Hydrol 336(1–2):186–198. https://doi.org/10.1016/j.jhydrol.2007.01.014
Lyerly SB (1952) The average spearman rank correlation coefficient. Psychometrika 17:421–428. https://doi.org/10.1007/BF02288917
Malik A, Kumar A, Singh RP (2019) RP Application of heuristic approaches for prediction of hydrological drought using multi-scalar streamflow drought index. Water Resour Manage 33:3985–4006. https://doi.org/10.1007/s11269-019-02350-4
Manimaran P, Narayana AC (2018) Multifractal detrended cross-correlation analysis on air pollutants of University of Hyderabad Campus, India. Phys A 502:228–235. https://doi.org/10.1016/j.physa.2018.02.160
McKee TB, Doesken NJ, Kleist J (1993) The relationship of drought frequency and duration to time scales. Proceedings of the Eighth Conference on Applied Climatology, American Meteorological Society 179–184.
Miloş LR, Haţiegan C, Miloş MC, Barna FM, Boțoc C (2020) Multifractal detrended fluctuation analysis (MF-DFA) of stock market indexes empirical evidence from seven central and eastern european markets. Sustainability 12(2):535. https://doi.org/10.3390/su12020535
Morales Martínez JL, Segovia-Domínguez I, Quiros Rodríguez I, Horta-Rangel FA, Sosa-Gómez G (2021) A modified Multifractal detrended fluctuation analysis (MFDFA) approach for multifractal analysis of precipitation. Phys A 565:125611. https://doi.org/10.1016/j.physa.2020.125611
Nabipour N, Dehghani M, Mosavi A, Shamshirband S (2020) Short-term hydrological drought forecasting based on different nature-inspired optimization algorithms hybridized with artificial neural networks. IEEE Access 8:15210–15222. https://doi.org/10.1109/ACCESS.2020.2964584
Nalbantis I, Tsakiris G (2009) Assessment of hydrological drought revisited. Water Resour Manage 23:881–897. https://doi.org/10.1007/s11269-008-9305-1
Ozkaya A, Zerberg Y (2019) A 40-Year analysis of the hydrological drought indexfor the tigris basin. Turkey Water 11:657. https://doi.org/10.3390/w11040657
Peña-Gallardo M, Vicente-Serrano SM, Hannaford J et al (2019a) Complex influences of meteorological drought time-scales on hydrological droughts in natural basins of the contiguous Unites States. J Hydrol 568:611–625. https://doi.org/10.1016/j.jhydrol.2018.11.026
Peña-Gallardo M, Vicente-Serrano SM, Hannaford J, Lorenzo-Lacruz J, Svoboda M, Domínguez Castro F, Maneta M, Tomas-Burguera M, El Kenawy A (2019b) Complex influences of meteorological drought time-scales on hydrological droughts in natural basins of the contiguous Unites States. J Hydrol 568:611–625. https://doi.org/10.1016/j.jhydrol.2018.11.026
Rahmani F, Fattahi MH (2021) Phase space mapping of pivotal climatic and non-climatic elements affecting basin’ drought. Arab J Geosci 14:397. https://doi.org/10.1007/s12517-021-06734-y
Santos da Silva H, Rodrigo Santos Silva J, Stosic T (2020) Multifractal analysis of air temperature in Brazil. Phys A 549:124333. https://doi.org/10.1016/j.physa.2020.124333
Stefan S, Ghioca M, Rimbu N, Boroneant C (2004) Study of meteorological and hydrological drought in southern Romania from observational data. Int J Climatol 24(7):871–881. https://doi.org/10.1002/joc.1039
Sun X, Chen H, Wu Z, Yuan Y (2001) Multifractal analysis of hang seng index in hong kong stock market. Phys A 291(1–4):553–562. https://doi.org/10.1016/S0378-4371(00)00606-3
Tatli H, Dalfes HN (2020) Long-time memory in drought via detrended fluctuation analysis. Water Resour Manage 34:1199–1212. https://doi.org/10.1007/s11269-020-02493-9
Tatli H, Menteş ŞS (2019) Detrended cross-correlation patterns between North Atlantic oscillation and precipitation. Theor Appl Climatol 138:387–397. https://doi.org/10.1007/s00704-019-02827-7
Tian Y, Xu Y, Wang G (2018) Agricultural drought prediction using climate indices based on Support Vector Regression in Xiangjiang River basin. Sci Total Environ 622–623:710–720. https://doi.org/10.1016/j.scitotenv.2017.12.025
Tigkas D (2008) Drought characterization and monitoring in regions of Greece. Eur Water 23:29–39
Tigkas D, Vangelis H, Tsakiris G (2015) DrinC: a software for drought analysis based on drought indices. Earth Sci Inform 8(3):697–709. https://doi.org/10.1007/s12145-014-0178-y
Toluwalope Ogunjo S (2021) Multifractal properties of meteorological drought at different time scales in a tropical location. Fluct Noise Lett 20(1):2150007. https://doi.org/10.1142/S0219477521500073
Toluwalope Ogunjo S, Fuwape I, Rabiu AB (2021) Samuel Oluyamo S (2021) Multifractal analysis of air and soil temperatures. Chaos 31:033110. https://doi.org/10.1063/5.0029658
Tzanis CG, Koutsogiannis I, Philippopoulos K, Kalamaras N (2020) Multifractal detrended cross-correlation analysis of global methane and temperature. Remote Sens 12(3):557. https://doi.org/10.3390/rs12030557
Uddin MJ, Hu J, Islam ARMT, Eibek KU, Nasrin ZM (2020) A comprehensive statistical assessment of drought indices to monitor drought status in Bangladesh. Arab J Geosci 13:323. https://doi.org/10.1007/s12517-020-05302-0
Ullah I, Ma X, Yin J, Asfaw TG, Azam K, Syed S, Liu M, Arshad M, Shahzaman M (2021) Evaluating the meteorological drought characteristics over Pakistan using in situ observations and reanalysis products. Int J Climatol. https://doi.org/10.1002/joc.7063
Van Loon AF, Laaha G (2015) Hydrological drought severity explained by climate and catchment characteristics. J Hydrol 526:3–14. https://doi.org/10.1016/j.jhydrol.2014.10.059
Wang B, Wei Y, Xing Y, Ding W (2019) Multifractal detrended cross-correlation analysis and frequency dynamics of connectedness for energy futures markets. Phys A 527:121194. https://doi.org/10.1016/j.physa.2019.121194
Wei X, Zhang H, Gong X, Wei X, Dang C, Zhi T (2020) Intrinsic cross-correlation analysis of hydro-meteorological data in the Loess Plateau, China. Int J Environ Res Public Health 17:2410. https://doi.org/10.3390/ijerph17072410
Wu Y, He Y, Wu M et al (2018) Multifractality and cross-correlation analysis of streamflow and sediment fluctuation at the apex of the Pearl River Delta. Sci Rep 8:16553. https://doi.org/10.1038/s41598-018-35032-z
Wu L, Wang M, Zhao T (2020) Joint multifractal analysis and source testing of river level records based on multifractal detrended cross-correlation analysis. Complexity. https://doi.org/10.1155/2020/1532805
Xie C, Zhou Y, Wang G, Yan X (2017) Analyzing the cross-correlation between onshore and offshore RMB exchange rates based on multifractal detrended cross-correlation analysis (MF-DCCA). Fluct Noise Lett 16(1):1750004. https://doi.org/10.1142/S0219477517500043
Xu L, Chen N, Zhang Z, Chen Z (2018) An evaluation of statistical, NMME and hybrid models for drought prediction in China. J Hydrol 566:235–249. https://doi.org/10.1016/j.jhydrol.2018.09.020
Yang Y, McVicar TR, Donohue RJ, Zhang Y, Roderick ML, Chiew FHS, Zhang L, Zhang J (2017) Lags in hydrologic recovery following an extreme drought: assessing the roles of climate and catchment characteristics. Water Resour Res 53(6):4821–4837. https://doi.org/10.1002/2017WR020683
Yao N, Zhao H, Li Y, Biswas A, Feng H, Liu F, Pulatov B (2020) National-scale variation and propagation characteristics of meteorological, agricultural, and hydrological droughts in China. Remote Sens 12(20):3407. https://doi.org/10.3390/rs12203407
Yu MX, Liu XL, Wei L, Li QF, Zhang JY, Wang GQ (2016) Drought Assessment by a Short-/Long-Term Composited Drought Index in the Upper Huaihe River Basin, China. Adv. Meteorol. 1–10. Artn798656810.1155/2016/7986568
Zarei AR, Shabani A, Mahmoudi MR (2021) Susceptibility assessment of winter wheat, barley and rapeseed to drought using generalized estimating equations and cross-correlation function. Environ Process 8:163–197. https://doi.org/10.1007/s40710-021-00496-1
Zhang W, Wang P, Li X, Shen D (2018) Multifractal detrended cross-correlation analysis of the return-volume relationship of bitcoin market. Complexity. https://doi.org/10.1155/2018/8691420
Zhang L, Li H, Liu D et al (2021) Application of an improved multifractal detrended fluctuation analysis approach for estimation of the complexity of daily precipitation. Int J Climatol. https://doi.org/10.1002/joc.7092
Zhao A, Zhang A, Cao S, Liu X, Liu J, Cheng D (2018) Responses of vegetation productivity to multi-scale drought in Loess Plateau, China. CATENA 163:165–171. https://doi.org/10.1016/j.catena.2017.12.016
Zhou WX (2008) Multifractal detrended cross-correlation analysis for two non-stationary signals. Phys Rev E 77:066211. https://doi.org/10.1103/PhysRevE.77.066211
Zhu Y, Liu Y, Wang W, Singh VP, Ma X, Yu Z (2019) Three-dimensional characterization of meteorological and hydrological droughts and their probabilistic links. J Hydrol 578:124016. https://doi.org/10.1016/j.jhydrol.2019.124016
Zou S, Zhang T (2020) Multifractal detrended cross-correlation analysis of the relation between price and volume in European carbon futures markets. Phys A 537:122310. https://doi.org/10.1016/j.physa.2019.122310
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The authors thank the Met Office and National River Flow Archive websites because of providing us with raw data of precipitation, temperature, and flow data. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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Rahmani and Fattahi contributed to conceptualization; Rahmani and Fattahi contributed to methodology; Rahmani contributed to formal analysis and investigation; Rahmani contributed to writing—original draft preparation; Rahmani and Fattahi contributed to Writing— review, and editing; Fattahi contributed to supervision.
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Rahmani, F., Fattahi, M.H. A multifractal cross-correlation investigation into sensitivity and dependence of meteorological and hydrological droughts on precipitation and temperature. Nat Hazards 109, 2197–2219 (2021). https://doi.org/10.1007/s11069-021-04916-1
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DOI: https://doi.org/10.1007/s11069-021-04916-1