An assessment of the ability of Bartlett-Lewis type of rainfall models to reproduce drought statistics

Hydrology and Earth System Sciences

Volumn 17, Issue 12, 2013, Pages 5167-5183

  Pham, M T ^a   Vanhaute, W J ^a   Vandenberghe, S ^a   De Baets, B ^a   Verhoest, N E C ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EFFECTIVE DROUGHT INDEX (EDI); ENVIRONMENTAL CONSEQUENCES; HISTORICAL OBSERVATION; IRRIGATION REQUIREMENTS; MULTIVARIATE DISTRIBUTIONS; NATURAL DISASTERS; STOCHASTIC POINT PROCESS; SYNTHETIC RAINFALLS;

COMPUTER SIMULATION; DISTRIBUTION FUNCTIONS; RAIN; STOCHASTIC MODELS; TIME SERIES;

DROUGHT;

ASSESSMENT METHOD; DATA SET; DROUGHT STRESS; ECONOMIC ANALYSIS; HYDROLOGICAL MODELING; IRRIGATION; NUMERICAL MODEL; PARAMETERIZATION; RAINFALL; STATISTICAL ANALYSIS;

BELGIUM;

EID: 84890927981     PISSN: 10275606     EISSN: 16077938     Source Type: Journal    
DOI: 10.5194/hess-17-5167-2013     Document Type: Article

References (59)

1. Anderson, T.W. and Darling, D. A.: A test of goodness of fit, J. Am. Stat. Assoc., 49, 765-769, 1954.
2. Bhalme, H. N. and Mooley, D. A.: Large-scale droughts/floods and monsoon circulation, Mon. Weather Rev., 108, 1197-1211, 1980.
3. Burton, A., Kilsby, C. G., Fowler, H. J., Cowpertwait, P. S. P., and O'Connell, P. E.: Rain Sim: a spatial-temporal stochastic rainfall modelling system, Environ. Model. Softw., 23, 1356-1369, 2008.
4. Byun, H.-R. and Wilhite, D. A.: Objective quantification of drought severity and duration, J. Climate, 12, 2747-2756, 1999. (Pubitemid 30039775)
5. Byun, H.-R., Sun-Ju, L., Saeid, M., Ki-Seon, C., Sang-Min, L., and Do-Woo, K.: Study on the periodicities of droughts in Korea, Asia-Pac. J. Atmos. Sci., 44, 417-441, 2008.
6. Cameron, D., Beven, K., and Tawn, J.: An evaluation of three stochastic rainfall models, J. Hydrol., 228, 130-149, 2000. (Pubitemid 30156972)
7. Cameron, D., Beven, K., and Tawn, J.: Modelling extreme rainfalls using a modified random pulse Bartlett-Lewis stochastic rainfall model (with uncertainty), Adv. Water Resour., 24, 203-211, 2001. (Pubitemid 32033804)
8. Cowpertwait, P., Isham, V., and Onof, C.: Point process models of rainfall: developments for fine-scale structure, P. Roy. Soc. A, 463, 2569-2587, 2007.
9. De Jongh, I. L. M., Verhoest, N. E. C., and De Troch, F. P.: Analysis of a 105-year time series of precipitation observed at Uccle, Belgium, Int. J. Climatol., 26, 2023-2039, 2006. (Pubitemid 44823234)
10. Démarée, G. R.: Le pluviographe centenaire du plateau d'Uccle: son histoire, ses données et ses applications (The centennial recording raingauge of the Uccle Plateau: its history, its data and its applications), La Houille Blanche, 4, 95-102, 2003. (Pubitemid 37190250)
11. Dogan, S., Berktay, A., and Singh, V. P.: Comparison of multimonthly rainfall-based drought severity indices, with application to semi-arid Konya closed basin, Turkey, J. Hydrol., 470-471, 255-268, 2012.
12. Duan, Q., Sorooshian, S., and Gupta, V. K.: Optimal use of the SCEUA global optimization method for calibrating watershed models, J. Hydrol., 158, 265-284, 1994. (Pubitemid 281640)
13. Genest, C. and Favre, A.: Everything you always wanted to know about copula modeling but were afraid to ask, J. Hydrol. Eng., 12, 347-368, 2007. (Pubitemid 47023282)
14. Genest, C. and Rivest, L.-P.: On the multivariate probability integral transformation, Stat. Probabil. Lett., 53, 391-399, 2001. (Pubitemid 33396271)
15. Genest, C., Quessy, J.-F., and Rémillard, B.: Goodness-of-fit procedures for copula models based on the probability integral transformation, Scand. J. Stat., 33, 337-366, 2006. (Pubitemid 43937525)
16. Gommes, R. A. and Petrassi, F.: Rainfall variability and drought in sub-Saharan Africa since 1960, Technical Report, Food and Agriculture Organization of the United Nations, Research and Technology Development Division, Agrometeorology Group, Rome, Italy, 1994.
17. González, J. and Valdés, J. B.: New drought frequency index: definition and comparative performance analysis, Water Resour. Res., 42, W11421, doi:10.1029/2005WR004308, 2006. (Pubitemid 46134891)
18. Gräler, B., van den Berg, M. J., Vandenberghe, S., Petroselli, A., Grimaldi, S., De Baets, B., and Verhoest, N. E. C.: Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation, Hydrol. Earth Syst. Sci., 17, 1281-1296, doi:10.5194/hess-17-1281-2013, 2013.
19. Jesus, J. and Chandler, R. E.: Estimating functions and the generalized method of moments, Interface Focus, 1, 871-885, 2011.
20. Kaczmarska, J.: Further development of Bartlett-Lewis models for fine-resolution rainfall, Technical Report, Department of Statistical Science, University College London, London, 011.
21. Kendall, D. and Dracup, J.: On the generation of drought events using an alternating renewal-reward model, Stoch. Hydrol. Hydraul., 6, 55-68, 1992.
22. Kim, D.-W., Byun, H.-R., and Choi, K.-S.: Evaluation, modification, and application of the Effective Drought Index to 200-year drought climatology of Seoul, Korea, J. Hydrol., 378, 1-12, 2009.
23. Kim, T.-W., Valdés, J. B., and Aparicio, J.: Spatial characterization of droughts in the Conchos river basin based on bivariate frequency analysis, Water Int., 31, 50-58, 2006a.
24. Kim, T.-W., Valdés, J. B., and Yoo, C.: Nonparametric approach for bivariate drought characterization using palmer drought index, J. Hydrol. Eng., 11, 134-143, 2006b. (Pubitemid 43263836)
25. Li, N., Liu, X., Xie, W., Wu, J., and Zhang, P.: The return period analysis of natural disasters with statistical modeling of bivariate joint probability distribution, Comput. Stud., 33, 134-145, 2012.
26. Mathier, L., Perreault, L., Bobée, B., and Ashkar, F.: The use of geometric and gamma-related distributions for frequency analysis of water deficit, Stoch. Hydrol. Hydraul., 6, 239-254, 1992.
27. McKee, T. B., Doesken, N. J., and Kleist, J.: The relationship of drought frequency and duration to time scales, Proceedings of the 8th Conference on Applied Climatology, American Meteorological Society, Anaheim, California, USA, 179-184, 1993.
28. Morid, S., Smakhtin, V., and Moghaddasi, M.: Comparison of seven meteorological indices for drought monitoring in Iran, Int. J. Climatol., 26, 971-985, 2006.
29. Morid, S., Smakhtin, V., and Bagherzadeh, K.: Drought forecasting using artificial neural networks and time series of drought indices, Int. J. Climatol., 27, 2103-2111, 2007. (Pubitemid 350268751)
30. Nelsen, R. B.: An Introduction to Copulas, Springer, New York, 2006.
31. Onof, C. and Wheater, H. S.: Improvements to the modelling of British rainfall using a modified random parameter Bartlett-Lewis rectangular pulse model, J. Hydrol., 157, 177-195, 1994. (Pubitemid 279828)
32. Onof, C., Meca-Figueras, T., Kaczmarska, J., Chandler, R., and Hege, L.: Modelling rainfall with a Bartlett-Lewis process: thirdorder moments, proportion dry, and a truncated random parameter version, Technical Report, Department of Civil and Environmental Engineering, Imperial College London, London, 2013.
33. Pandey, R. P., Dash, B. B., Mishra, S. K., and Singh, R.: Study of indices for drought characterization in KBK districts in Orissa (India), Hydrol. Process., 22, 1895-1907, 2008. (Pubitemid 351983224)
34. Rodriguez-Iturbe, I., Cox, D. R., and Isham, V.: Some models for rainfall based on stochastic point processes, P. Roy. Soc. Lond. A, 410, 269-288, 1987a. (Pubitemid 17599343)
35. Rodriguez-Iturbe, I., De Power, B. F., and Valdes, J. B.: Rectangular pulses point process models for rainfall: analysis of empirical data, J. Geophys. Res., 92, 9645-9656, 1987b.
36. Rodriguez-Iturbe, I., Cox, D. R., and Isham, V.: A point process model for rainfall: further developments, P. Roy. Soc. Lond. A, 417, 283-298, 1988.
37. Rooy, M. P. V.: A rainfall anomaly index (RAI) independent of time and space, Notos, 14, 43-48, 1965.
38. Salvadori, G.: Bivariate return periods via 2-copulas, Stat. Methodol., 1, 129-144, 2004. (Pubitemid 43339379)
39. Salvadori, G. and De Michele, C.: Frequency analysis via copulas: theoretical aspects and applications to hydrological events, Water Resour. Res., 40, W12511, doi:10.1029/2004WR003133, 2004.
40. Salvadori, G. and De Michele, C.: Statistical characterization of temporal structure of storms, Adv. Water Resour., 29, 827-842, 2006.
41. Salvadori, G. and De Michele, C.: On the use of copulas in hydrology: theory and practice, J. Hydrol. Eng., 12, 369-380, 2007. (Pubitemid 47023283)
42. Salvadori, G. and De Michele, C.: Multivariate multiparameter extreme value models and return periods: a copula approach, Water Resour. Res., 46, W10501, doi:10.1029/2009WR009040, 2010.
43. Salvadori, G., Michele, C. D., Kottegoda, N., and Rosso, R.: Extremes in Nature: an Approach Using Copulas, Springer, New York, 2007.
44. Shiau, J. T.: Return period of bivariate distributed extreme hydrological events, Stoch. Env. Res. Risk A., 17, 42-57, 2003. (Pubitemid 36922606)
45. Shiau, J. T.: Fitting drought duration and severity with twodimensional copulas, Int. Ser. Prog. Wat. Res., 20, 795-815, 2006. (Pubitemid 44263973)
46. Shiau, J. T. and Modarres, R.: Copula-based drought severityduration- frequency analysis in Iran, Meteorol. Appl., 16, 481-489, 2009.
47. Shiau, J. T. and Shen, H. W.: Recurrence analysis of hydrologic droughts of differing severity, J. Water Res. Pl.-ASCE, 127, 30-40, 2001. (Pubitemid 32140097)
48. Sklar, A.: Fonctions de répartition àn dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris, 8, 229-231, 1959.
49. Vandenberghe, S.: Copula-based Models for Generating Design Rainfall, PhD dissertation, Ghent University, Faculty of Bioscience Engineering, Ghent, Belgium, 2012.
50. Vandenberghe, S., Verhoest, N. E. C., Onof, C., and De Baets, B.: A comparative copula-based bivariate frequency analysis of observed and simulated storm events: a case study on Bartlett-Lewis modeled rainfall, Water Resour. Res., 47, W07529, doi:10.1029/2009WR008388, 2011.
51. Vanhaute, W. J., Vandenberghe, S., Scheerlinck, K., De Baets, B., and Verhoest, N. E. C.: Calibration of the modified Bartlett-Lewis model using global optimization techniques and alternative objective functions, Hydrol. Earth Syst. Sci., 16, 873-891, doi:10.5194/hess-16-873-2012, 2012.
52. Verhoest, N., Troch, P. A., and De Troch, F. P.: On the applicability of Bartlett-Lewis rectangular pulses models in the modeling of design storms at a point, J. Hydrol., 202, 108-120, 1997. (Pubitemid 28118038)
53. Verhoest, N. E. C., Vandenberghe, S., Cabus, P., Onof, C., Meca-Figueras, T., and Jameleddine, S.: Are stochastic point rainfall models able to preserve extreme flood statistics?, Hydrol. Process., 24, 3439-3445, 2010.
54. Wheater, H. S., Chandler, R. E., Onof, C. J., Isham, V. S., Bellone, E., Yang, C., Lekkas, D., Lourmas, G., and Segond, M. L.: Spatial-temporal rainfall modelling for flood risk estimation, Stoch. Env. Res. Risk A., 19, 403-416, 2005. (Pubitemid 41801066)
55. Wilby, R. L. and Wigley, T. M. L.: Precipitation predictors for downscaling: observed and general circulation model relationships, Int. J. Climatol., 20, 641-661, 2000. (Pubitemid 30320046)
56. Wilhite, D., Svoboda, M., and Hayes, M.: Understanding the complex impacts of drought: a key to enhancing drought mitigation and preparedness, Int. Ser. Prog. Wat. Res., 21, 763-774, 2007. (Pubitemid 46672158)
57. Wong, G., Lambert, M. F., Leonard, M., and Metcalfe, A. V.: Drought analysis using trivariate copulas conditional on climatic states, J. Hydrol. Eng., 15, 129-141, 2010.
58. Yu-Won, K. I. M. and Hi-Ryong, B.: On the cause of summer droughts in Korea and their return to normal, Asia-Pac. J. Atmos. Sci., 42, 237-251, 2006.
59. Zelenhasi, E. and Salvai, A.: A method of streamflow drought analysis, Water Resour. Res., 23, 156-168, 1987.