Copula-Based Regional Drought Analysis and Derivation of Severity-Area-Frequency Curve in Lake Urmia Basin

آب و خاک

Article 1, Volume 31, Issue 4 - Serial Number 54, September 2018, Pages 1260-1277   

Document Type: Research Article

DOI: 10.22067/jsw.v31i4.60382

Authors

M. Montaseri^* ; B. Amirataee; H. Rezaei

Urmia University

Abstract

Introduction: Drought is a natural phenomenon and was described when precipitation is less than expected. Since the precipitation amounts in terms of spatial and temporal characteristics are different from one region to another, so this phenomenon is known as a multivariate phenomenon. This phenomenon often characterized by different variables such as drought duration, severity, intensity and spatial extent. Although site specific analysis can provide useful information on drought occurrences in a limited area, but these results have a fundamental uncertainty to drought risk assessment in a large region. Therefore regional drought analysis, provides a more comprehensive assessment in each region, and is essential for short and long term management of water resources. Meanwhile, the copula functions has been developed as a new advanced technique for modeling the two or multivariate joint probability distribution in different fields such as financial, hydrology, water resources and risk management. So, in this research, regional analysis of drought severity and percent of drought area were performed using the copula functions in Lake Urmia basin, as one of the Iran's drought-prone basin. Such study with emphasis on bivariate analysis of drought severity and drought areal extend were conducted for the first time in the study area. The main objectives of this study are: 1) Modeling drought characteristics in Lake Urmia basin, 2) Evaluation of copula functions in modeling the structure of the region's drought characteristics, and 3) Develop the Severity-Area-Frequency curve using the appropriate copula.
Materials and Methods: Copula is the stochastic model and based on probability. In other words, copulas are function for modeling the two or multivariate random variables. Copulas can be easily coupled the marginal distributions to multiple distributions. There are many parametric copula families available, that seven copula functions such as archimedean (Clayton, Frank, Gumbel and Joe), extreme value (Galambos), elliptical (Normal) and others (Plackett) were used. The SPI-1 was determined at each station and then, the whole area was divided into small grids with cell size of 2000×2000. Distances between the grid centers with all the selected stations were calculated with a programming code. Finally, the SPI values in each grid were calculated using IDW method. The severity and percentage of drought area variables were determined and used for regional drought modeling in the study area based on drought threshold equal to zero. After determining the best statistical distribution of two variables, the appropriate copula function was conducted based on different goodness of fit tests. Finally, the Severity-Area-Frequency curve for the study area was developed based on the appropriate copula function and conditional return periods.
Results and Discussion: The correlation between the two variables of percentage of drought area and severity was assessed using different graphical (Kendall plot and Chi plot) and statistical tests (Spearman rand order correlation and Kendal tau). The results showed a positive correlation between the drought severity and percentage of drought area variables. Based on Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) and graphical test, the Lognormal and Beta probability distributions were select as a best fit distribution of severity and percentage of area under drought, respectively. Finally, the Frank copula among other type of copulas was selected as an appropriate copula for modeling joint drought severity and percentage of area under drought for the study area based on Maximum log likelihood, AIC, BIC and RMSE criteria. The S-A-F curve was developed using conditional return periods based on Frank copula. According to S-A-F curve, it can be seen that increase in the percentage of area under drought in the study area led to increase in drought severity and vice versa. For example, drought severity with return period of 20 years and drought with 20 percent areal extend is obtained equal to 0.37.
Conclusions: Copula functions are of great importance in the analysis of drought, due to preserve correlation between variables and not have any limitation to have a same marginal distribution in long-term prediction of drought events. In this study, using best fit copula (Frank copula) and conditional return periods, the relationships between drought severity and percent of area under drought for the study area named S-A-F curve were developed. These curves can be useful for planning and management of drought in the region. Drought risk assessment based on the results of this study can be high priorities for drought monitoring in large areas.

Keywords

Area under drought; Marginal distribution; Severity; SPI

References

1- Abdul Rauf U. and Zeephongsekul P. 2014. Copula based analysis of rainfall severity and duration: a case study. Theoretical and Applied Climatology, 115(1):153–166.

2- Alemaw B.F. and Kileshye-Onema J.M. 2014. Evaluation of drought regimes and impacts in the Limpopo basin. Hydrology and Earth System Sciences Discussion, 11:199-222.

3- Bonaccorso B., Peres D.J., Castano A. and Cancelliere A. 2015. SPI-based probabilistic analysis of drought areal extent in Sicily. Water Resources Management, 29:459–470.

4- Chen L., Singh V.P., Guo S., Mishra A.K. and Guo J. 2013. Drought analysis using copulas. Journal of Hydrologic Engineering, 18(7):797–808.

5- Fisher N.I. and Switzer P. 1985. Chi-plots for assessing dependence. Biometrika 72:253-265.

6- Genest C. and Favre A.C. 2007. Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering, 12(4):347–368.

7- Genest C., Ghoudi K. and Rivest L. 1995. A semi-parametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika, 82:543–552.

8- Genest C. and Rivest L.P. 1993. Statistical inference procedures for bivariate archimedean copulas. Journal of the American Statistical Association, 88(423):1034–1043.

9- Genest C. and Boies J.C. 2003. Detecting dependence with Kendall plots, American Statistician, 57:275–284.

10- Ghorbani Aghdam M., Dinpazhuh Y., Fakheri Fard A. and Darbandi S. 2012. Regionalization of Urmia lake basin from the view of drought using factor analysis. Journal of Water and Soil, 26(5):1268-1276. (in Persian with English abstract)

11- Griffiths D.V. and Fenton G.A. 2007. Probabilistic Methods in Geotechnical Engineering. SpringerWien, New York.

12- Hisdal H. and Tallaksen L.M. 2003. Estimation of regional meteorological and hydrological drought characteristics: a case study for Denmark. Journal of Hydrology, 281(3):230-247.

13- Hisdal H., Stahl K., Tallaksen L.M. and Demuth S. 2001. Have streamflow droughts in Europe become more severe or frequent?. International Journal of Climatology, 21:317–333.

14- Hosseini Safa H. and Morid S. 2008. Probabilistic analysis of spatial-temporal characteristics of droughts severity in Tehran province. Journal of Agricultural Science and Natural Resources, 15(15):1-11. (in Persian)

15- Joe H. 1997. Multivariate Models and Dependence Concepts. Chapman and Hall, New York.

16- Joe H. and Xu J.J. 1996. The estimation method of inference functions for margins for multivariate models. Technical Report 166, Department of Statistics, University of British Columbia.

17- Karmakar S. and Simonovic S.P. 2009. Bivariate flood frequency analysis. Part 2: a copula-based approach with mixed marginal distributions. Journal of Flood Risk Management, 2:32–44.

18- Khadr M. 2016. Temporal and spatial analysis of meteorological drought characteristics in the upper Blue Nile river region. Hydrology Research, DOI: 10.2166/nh.2016.194

19- Kim T.W., Valdes J.B. and Aparicio J. 2002. Frequency and spatial characteristics of droughts in the Conchos River basin, Mexico. Water International, 27(3):420-430.

20- Lee T., Modarres R. and Quarda T.B.M.J. 2013. Data-based analysis of bivariate copula tail dependence for drought duration and severity. Hydrological Processes, 27(10):1454–1463.

21- Li T., Guo S., Chen L. and Guo J. 2013. Bivariate flood frequency analysis with historical information based on copula. Journal of Hydrologic Engineering, 10.1061/(ASCE)HE.1943-5584.0000684, 1018-1030.

22- Liu X., Wang S., Zhou Y., Wang F., Yang G. and Liu W. 2016. Spatial analysis of meteorological drought return periods in China using copulas. Natural Hazards, 80(1):367–388.

23- Loukas A., Vasiliades L. 2004. Probabilistic analysis of drought spatiotemporal characteristics in Thessaly region, Greece. Natural Hazards and Earth System Sciences, 4:719–731.

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

25- Mirabbasi R., Fakheri-Fard A. and Dinpashoh Y. 2012. Bivariate drought frequency analysis using the copula method. Theoretical and Applied Climatology, 108:191–206.

26- Mirabbasi R., Fakheri-Fard A., Dinpashoh Y. and Eslamian S.S. 2013. Longterm drought monitoring of urmia using joint deficit index (JDI). Water and Soil Science, 23(4):87-103. (in Persian with English abstract)

27- Mirakbari M. and Ganji A. 2012. A bivariatie analysis of meteorological drought duration and severity (case study: Kermnashah province). Iranian Water Research Journal, 6(11):17-25. (in Persian with English abstract)

28- Mishra A.K. and Desai V.R. 2005. Spatial and temporal drought analysis in the Kansabati river basin, India. International Journal River Basin Management, 3(1):31–41.

29- Mishra A.K. and Singh V.P. 2011. Drought modeling—a review. Journal of Hydrology, 403:157 175.

30- Montaseri M. and Amirataee B. 2015. Stochastic forecasting of drought probabilities (case study on northwest of Iran). Journal of Civil and Environmental Engineering, 45(78):51-63. (in Persian with English abstract)

31- Montaseri M. and Amirataee B. 2016. Comprehensive stochastic assessment of meteorological drought indices. International Journal of Climatology, doi:10.1002/joc.4755.

32- Nelsen R.B. 2006. An Introduction to Copulas. Springer, New York.

33- Obasi G.O.P. 1994. WMO’s role in the international decade for natural disaster reduction. Bulletin of the American Meteorological Society, 75(9):1655–1661.

34- Peel M.C., Finlayson B.L. and McMahon T.A. 2007. Updated world map of the Köppen-Geiger climate classification. Hydrology and Earth System Sciences, 11:1633-1644.

35- Reddy M. and Ganguli P. 2012. Application of copulas for derivation of drought severity–duration–frequency curves. Hydrological Processes, 26(11):1672–1685.

36- Reddy M.J. and Ganguli P. 2013. Spatio-temporal analysis and derivation of copula-based intensity-area-frequency curves for droughts in western Rajasthan (India). Stochastic Environmental Research and Risk Assessment, 27:1975–1989.

37- Rossi G. Benedini M. Tsakiris G. and Giakoumakis S. 1992. On regional drought estimation and analysis, Water Resources Management, 6:249-277.

38- Saghafian B. and Mehdikhani H. 2014. Drought characterization using a new copula-based trivariate approach. Natural Hazards, 72:1391–1407.

39- Salvadori G., De Michele C., Kottegoda N.T. and Rosso R. 2007. Extremes in Nature: An Approach Using Copulas. Springer, Dordrecht.

40- Santos J.F., Pulido-Calvo I. and Portela M. 2010. Spatial and temporal variability of droughts in Portugal. Water Resources Research, 46:W03503.

41- Santos MA. 1983. Regional droughts: a stochastic characterization, Journal of Hydrology, 66:183-211.

42- Sen Z. 1980. Regional drought and flood frequency analysis: theoretical consideration. Journal of Hydrology, 46:265-279.

43- Sen Z. 1998. Probabilistic formulation of spatio-temporal drought pattern, Theoretical and Applied Climatology, 61:197-206.

44- Shiau J.T. 2006. Fitting drought duration and severity with two dimensional copulas. Water Resources Management, 20(5):795–815.

45- Shiau J.T. and Modarres R. 2009. Copula-based drought severity duration frequency analysis in Iran. Meteorological Applications, 16(4):481–489.

46- Shin H.S. and Salas J.D. 2000. Regional drought analysis based on neural networks. Journal of Hydrologic Engineering, 5(2):145-155.

47- Sklar A. 1959. Functions de repartition a n dimensions et leurs marges. Publ Inst Stat Univ Paris 8:229–231.

48- Song S. and Singh V.P. 2010. Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm. Stochastic Environmental Research and Risk Assessment, 24(5):783–805.

49- Tallaksen L.M. and Hisdal H. 1997. Regional analysis of extreme streamflow drought duration and deficit volume, In: FRIEND’97-Regional Hydrology: Concepts and Models for Sustainable Water Resource Management (ed. by A. Gustard, S. Blazkova, M. Brilly, S. Demuth, J. Dixon, H. van Lanen, C. Llasat, S. Mkhandi & E. Servat), 141-150. IAHS Publ. no. 246.

50- Tase N. 1976. Area-Deficit-Intensity characteristics of droughts, Hydrology Papers, 87, Colorado State University, Fort Collins, USA.

51- Vogt J.V. and Somma F. 2000. Drought and Drought Mitigation in Europe, Kluwer Academic Publishers, the Netherlands.

52- WMO Report, 2006. Drought monitoring and early warning: concepts, progress and future challenges. WMO report no. 1006, World Meteorological Organization.

53- Yusof F., Hui-Mean F., Suhaila J. and Yusof Z. 2013. Characterisation of drought properties with bivariate copula analysis. Water Resources Management, 27(12):4183–4207.

54- Zhang L. and Singh V.P. 2007. Bivariate rainfall frequency distributions using Archimedean copulas. Journal of Hydrology, 332(1-2):93–109.

55- Zhang L. and Singh V.P. 2012. Bivariate rainfall and runoff analysis using entropy and copula theories. Entropy, 14(9):1784-1812.