Generation of a stochastic precipitation model for the tropical climate

Abstract

A tropical country like Malaysia is characterized by intense localized precipitation with temperatures remaining relatively constant throughout the year. A stochastic modeling of precipitation in the flood-prone Kelantan River Basin is particularly challenging due to the high intermittency of precipitation events of the northeast monsoons. There is an urgent need to have long series of precipitation in modeling the hydrological responses. A single-site stochastic precipitation model that includes precipitation occurrence and an intensity model was developed, calibrated, and validated for the Kelantan River Basin. The simulation process was carried out separately for each station without considering the spatial correlation of precipitation. The Markov chains up to the fifth-order and six distributions were considered. The daily precipitation data of 17 rainfall stations for the study period of 1954–2013 were selected. The results suggested that second- and third-order Markov chains were suitable for simulating monthly and yearly precipitation occurrences, respectively. The fifth-order Markov chain resulted in overestimation of precipitation occurrences. For the mean, distribution, and standard deviation of precipitation amounts, the exponential, gamma, log-normal, skew normal, mixed exponential, and generalized Pareto distributions performed superiorly. However, for the extremes of precipitation, the exponential and log-normal distributions were better while the skew normal and generalized Pareto distributions tend to show underestimations. The log-normal distribution was chosen as the best distribution to simulate precipitation amounts. Overall, the stochastic precipitation model developed is considered a convenient tool to simulate the characteristics of precipitation in the Kelantan River Basin.

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References

  1. Abas N, Daud ZM, Yusof F (2014) A comparative study of mixed exponential and Weibull distributions in a stochastic model replicating a tropical rainfall process. Theor Appl Climatol 118:597–607. doi:10.1007/s00704-013-1060-4

    Article  Google Scholar 

  2. Ahmad MN (2015) A comparative study of localized rainfall and air pollution between the urban area of Sungai Penchala with sub-urban and green area in Malaysia. J Energy Environ 7:5–11

    Google Scholar 

  3. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automat Contr 19:716–723. doi:10.1109/TAC.1974.1100705

    Article  Google Scholar 

  4. Allard D, Bourotte M (2015) Disaggregating daily precipitations into hourly values with a transformed censored latent Gaussian process. Stoch Environ Res Risk Assess 29:453–462. doi:10.1007/s00477-014-0913-4

    Article  Google Scholar 

  5. Allcroft DJ, Glasbey CA (2003) A latent Gaussian Markov random-field model for spatiotemporal rainfall disaggregation. J R Stat Soc Ser C Appl Stat 52:487–498. doi:10.1111/1467-9876.00419

    Article  Google Scholar 

  6. Bannayan M, Hoogenboom G (2008) Weather analogue: a tool for real-time prediction of daily weather data realizations based on a modified k-nearest neighbor approach. Environ Model Softw 23:703–713. doi:10.1016/j.envsoft.2007.09.011

    Article  Google Scholar 

  7. Barros VR, Doyle ME, Camilloni IA (2008) Precipitation trends in southeastern South America: relationship with ENSO phases and with low-level circulation. Theor Appl Climatol 93:19–33. doi:10.1007/s00704-007-0329-x

    Article  Google Scholar 

  8. Bernardara P, De Michele C, Rosso R (2007) A simple model of rain in time: an alternating renewal process of wet and dry states with a fractional (non-Gaussian) rain intensity. Atmos Res 84:291–301. doi:10.1016/j.atmosres.2006.09.001

    Article  Google Scholar 

  9. Berrocal VJ, Raftery AE, Gneiting T (2008) Probabilistic quantitative precipitation field forecasting using a two-stage spatial model. Ann Appl Stat 2:1170–1193. doi:10.1214/08-AOAS203

    Article  Google Scholar 

  10. Bowles DS, O’Connell PE (1991) Recent advances in the modeling of hydrologic systems. Springer, Netherlands

    Book  Google Scholar 

  11. Burton A, Kilsby CG, Fowler HJ, Cowpertwait PSP, O’Connell PE (2008) RainSim: a spatial–temporal stochastic rainfall modelling system. Environ Model Softw 23:1356–1369. doi:10.1016/j.envsoft.2008.04.003

    Article  Google Scholar 

  12. Chen W, Chau KW (2006) Intelligent manipulation and calibration of parameters for hydrological models. Int J Environ Pollut 28:432. doi:10.1504/IJEP.2006.011221

    Article  Google Scholar 

  13. Chen J, Brissette FP, Leconte R (2010) A daily stochastic weather generator for preserving low-frequency of climate variability. J Hydrol 388:480–490. doi:10.1016/j.jhydrol.2010.05.032

    Article  Google Scholar 

  14. Chen J, Brissette FP, Leconte R (2012a) WeaGETS—a Matlab-based daily scale weather generator for generating precipitation and temperature. Procedia Environ Sci 13:2222–2235. doi:10.1016/j.proenv.2012.01.211

    Article  Google Scholar 

  15. Chen J, Brissette FP, Leconte R, Caron A (2012b) A versatile weather generator for daily precipitation and temperature. Trans ASABE 55:895–906

    Article  Google Scholar 

  16. Chi X, Yin Z, Wang X, Sun Y (2015) Spatiotemporal variations of precipitation extremes of China during the past 50 years (1960–2009). Theor Appl Climatol. doi:10.1007/s00704-015-1436-8

  17. Cowpertwait PSP (1991) Further developments of the Neyman-Scott clustered point process for modeling rainfall. Water Resour Res 27:1431–1438. doi:10.1029/91WR00479

    Article  Google Scholar 

  18. Cowpertwait PSP (2002) A space-time Neyman-Scott model of rainfall: empirical analysis of extremes. Water Resour Res 38:1–14. doi:10.1029/2001WR000709

    Article  Google Scholar 

  19. Cranbrook EO, Furtado JI (1988) Chapter 16—freshwaters. In: Cranbrook EO (ed) Key environments: Malaysia, 1st edn. Pergamon, Oxford, pp 225–250

    Chapter  Google Scholar 

  20. Dastidar AG, Ghosh D, Dasgupta S, De UK (2010) Higher order Markov chain models for monsoon rainfall over West Bengal, India. Indian J Radio Sp Phys 39:39–44

    Google Scholar 

  21. Deni SM, Jemain AA (2008) Fitting the distribution of dry and wet spells with alternative probability models. Meteorog Atmos Phys 104:13–27. doi:10.1007/s00703-008-0010-7

    Article  Google Scholar 

  22. Deni SM, Jemain AA, Ibrahim K (2008) Fitting optimum order of Markov chain models for daily rainfall occurrences in Peninsular Malaysia. Theor Appl Climatol 97:109–121. doi:10.1007/s00704-008-0051-3

    Article  Google Scholar 

  23. Dubrovský M (1997) Creating daily weather series with use of the weather generator. Environmetrics 8:409–424. doi:10.1002/(SICI)1099-095X(199709/10)8:5<409::AID-ENV261>3.0.CO;2-0

    Article  Google Scholar 

  24. Dubrovský M, Buchtele J, Žalud Z (2004) High-frequency and low-frequency variability in stochastic daily weather generator and its effect on agricultural and hydrologic modelling. Clim Chang 63:145–179. doi:10.1023/B:CLIM.0000018504.99914.60

    Article  Google Scholar 

  25. Fodor N, Dobi I, Mika J, Szeidl L (2010) MV-WG: a new multi-variable weather generator. Meteorog Atmos Phys 107:91–101. doi:10.1007/s00703-010-0074-z

    Article  Google Scholar 

  26. Foufoula-Georgiou E, Lettenmaier DP (1987) A Markov renewal model for rainfall occurrences. Water Resour Res 23:875–884. doi:10.1029/WR023i005p00875

    Article  Google Scholar 

  27. Hansen JW, Mavromatis T (2001) Correcting low-frequency variability bias in stochastic weather generators. Agric For Meteorol 109:297–310. doi:10.1016/S0168-1923(01)00271-4

    Article  Google Scholar 

  28. Harrison M, Waylen P (2000) A note concerning the proper choice for Markov model order for daily precipitation in the humid tropics: a case study in Costa Rica. Int J Climatol 20:1861–1872. doi:10.1002/1097-0088(20001130)20:14<1861::AID-JOC577>3.0.CO;2-9

    Article  Google Scholar 

  29. Huang J, Sun S, Xue Y, Zhang J (2014) Spatial and temporal variability of precipitation indices during 1961–2010 in Hunan Province, central south China. Theor Appl Climatol 118:581–595. doi:10.1007/s00704-013-1087-6

    Article  Google Scholar 

  30. Husak GJ, Michaelsen J, Funk C (2007) Use of the gamma distribution to represent monthly rainfall in Africa for drought monitoring applications. Int J Climatol 27:935–944. doi:10.1002/joc.1441

    Article  Google Scholar 

  31. Khazaei MR, Zahabiyoun B, Saghafian B (2012) Assessment of climate change impact on floods using weather generator and continuous rainfall-runoff model. Int J Climatol 32:1997–2006. doi:10.1002/joc.2416

    Article  Google Scholar 

  32. Kim Y, Katz RW, Rajagopalan B, Podestá GP, Furrer EM (2012) Reducing overdispersion in stochastic weather generators using a generalized linear modeling approach. Clim Res 53:13–24. doi:10.3354/Cr01071

    Article  Google Scholar 

  33. Kleiber W, Katz RW, Rajagopalan B (2012) Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes. Water Resour Res 48:1–17. doi:10.1029/2011WR011105

    Article  Google Scholar 

  34. Kwaku XS, Duke O (2007) Characterization and frequency analysis of one day annual maximum and two to five consecutive days’ maximum rainfall of ACCRA, Ghana. ARPN J Eng Appl Sci 2:27–31

    Google Scholar 

  35. Kyselý J, Dubrovský M (2005) Simulation of extreme temperature events by a stochastic weather generator: effects of interdiurnal and interannual variability reproduction. Int J Climatol 25:251–269. doi:10.1002/joc.1120

    Article  Google Scholar 

  36. Lall U, Rajagopalan B, Tarboton DG (1996) A nonparametric wet/dry spell model for resampling daily precipitation. Water Resour Res 32:2803–2823. doi:10.1029/96WR00565

    Article  Google Scholar 

  37. Li C, Singh VP, Mishra AK (2012) Simulation of the entire range of daily precipitation using a hybrid probability distribution. Water Resour Res. doi:10.1029/2011WR011446

  38. Li Z, Brissette F, Chen J (2013) Finding the most appropriate precipitation probability distribution for stochastic weather generation and hydrological modelling in Nordic watersheds. Hydrol Process 27:3718–3729. doi:10.1002/hyp.9499

    Article  Google Scholar 

  39. Li Z, Brissette F, Chen J (2014) Assessing the applicability of six precipitation probability distribution models on the Loess Plateau of China. Int J Climatol 34:462–471. doi:10.1002/joc.3699

    Article  Google Scholar 

  40. Liu Q, Yang Z, Cui B (2008) Spatial and temporal variability of annual precipitation during 1961-2006 in Yellow River Basin, China. J Hydrol 361:330–338. doi:10.1016/j.jhydrol.2008.08.002

    Article  Google Scholar 

  41. Liu Y, Zhang W, Shao Y, Zhang K (2011) A comparison of four precipitation distribution models used in daily stochastic models. Adv Atmos Sci 28:809–820. doi:10.1007/s00376-010-9180-6

    Article  Google Scholar 

  42. Mandal KG, Padhi J, Kumar A, Ghosh S, Panda DK, Mohanty RK, Raychaudhuri M (2014) Analyses of rainfall using probability distribution and Markov chain models for crop planning in Daspalla region in Odisha, India. Theor Appl Climatol 121:517–528. doi:10.1007/s00704-014-1259-z

    Article  Google Scholar 

  43. Mavromatis T, Hansen JW (2001) Interannual variability characteristics and simulated crop response of four stochastic weather generators. Agric For Meteorol 109:283–296. doi:10.1016/S0168-1923(01)00272-6

    Article  Google Scholar 

  44. Mayowa OO, Pour SH, Shahid S, Mohsenipour M, Harun SB, Heryansyah A, Ismail T (2015) Trends in rainfall and rainfall-related extremes in the east coast of peninsular Malaysia. J Earth Syst Sci 124:1609–1622. doi:10.1007/s12040-015-0639-9

    Article  Google Scholar 

  45. Mehrotra R, Sharma A (2007) A semi-parametric model for stochastic generation of multi-site daily rainfall exhibiting low-frequency variability. J Hydrol 335:180–193. doi:10.1016/j.jhydrol.2006.11.011

    Article  Google Scholar 

  46. Mhanna M, Bauwens W (2012) A stochastic space-time model for the generation of daily rainfall in the Gaza Strip. Int J Climatol 32:1098–1112. doi:10.1002/joc.2305

    Article  Google Scholar 

  47. Ng WW, Panu US (2010) Comparisons of traditional and novel stochastic models for the generation of daily precipitation occurrences. J Hydrol 380:222–236. doi:10.1016/j.jhydrol.2009.11.002

    Article  Google Scholar 

  48. Nguyen V-T-V, Mayabi A (1991) Probabilistic analysis of summer daily rainfall for the Montreal region. Can Water Resour J 16:65–80. doi:10.4296/cwrj1601065

    Article  Google Scholar 

  49. Racsko P, Szeidl L, Semenov M (1991) A serial approach to local stochastic weather models. Ecol Model 57:27–41. doi:10.1016/0304-3800(91)90053-4

    Article  Google Scholar 

  50. Ramos-Calzado P, Gómez-Camacho J, Pérez-Bernal F, Pita-López MF (2008) A novel approach to precipitation series completion in climatological datasets: application to Andalusia. Int J Climatol 28:1525–1534. doi:10.1002/joc.1657

    Article  Google Scholar 

  51. Rao AR, Hamed KH (2000) Flood frequency analysis. CRC Press, Boca Raton

    Google Scholar 

  52. Richardson CW (1981) Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resour Res 17:182–190. doi:10.1029/WR017i001p00182

    Article  Google Scholar 

  53. Safeeq M, Fares A (2011) Accuracy evaluation of ClimGen weather generator and daily to hourly disaggregation methods in tropical conditions. Theor Appl Climatol 106:321–341. doi:10.1007/s00704-011-0438-4

    Article  Google Scholar 

  54. Sahai AK, Soman MK, Satyan V (2000) All India summer monsoon rainfall prediction using an artificial neural network. Clim Dyn 16:291–302. doi:10.1007/s003820050328

    Article  Google Scholar 

  55. Schoof JT, Arguez A, Brolley J, O’Brien JJ (2005) A new weather generator based on spectral properties of surface air temperatures. Agric For Meteorol 135:241–251. doi:10.1016/j.agrformet.2005.12.004

    Article  Google Scholar 

  56. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464

    Article  Google Scholar 

  57. Semenov MA (2008) Simulation of extreme weather events by a stochastic weather generator. Clim Res 35:203–212. doi:10.3354/cr00731

    Article  Google Scholar 

  58. Semenov MA, Barrow EM (1997) Use of a stochastic weather generator in the development of climate change scenarios. Clim Chang 35:397–414. doi:10.1023/A:1005342632279

    Article  Google Scholar 

  59. Sharma MA, Singh JB (2010) Use of probability distribution in rainfall analysis. New York Sci J 3:40–49

    Google Scholar 

  60. Singh P, Borah B (2013) Indian summer monsoon rainfall prediction using artificial neural network. Stoch Environ Res Risk Assess 27:1585–1599. doi:10.1007/s00477-013-0695-0

    Article  Google Scholar 

  61. So B-J, Kwon H-H, Kim D, Lee SO (2015) Modeling of daily rainfall sequence and extremes based on a semiparametric Pareto tail approach at multiple locations. J Hydrol 529:1442–1450. doi:10.1016/j.jhydrol.2015.08.037

    Article  Google Scholar 

  62. Sonnadara DUJ, Jayewardene DR (2014) A Markov chain probability model to describe wet and dry patterns of weather at Colombo. Theor Appl Climatol 119:333–340. doi:10.1007/s00704-014-1117-z

    Article  Google Scholar 

  63. Srikanthan R, Harrold TI, Sharma A, McMahon TA (2005) Comparison of two approaches for generation of daily rainfall data. Stoch Environ Res Risk Assess 19:215–226. doi:10.1007/s00477-004-0226-0

    Article  Google Scholar 

  64. Stern RD, Coe R (1984) A model fitting analysis of daily rainfall data. J R Stat Soc Ser A 147:1–34. doi:10.2307/2981736

    Article  Google Scholar 

  65. Suhaila J, Deni SM, Zin WZW, Jemain AA (2010) Trends in Peninsular Malaysia rainfall data during the southwest monsoon and northeast monsoon seasons: 1975-2004. Sains Malays 39:533–542. doi:10.1007/s00703-010-0108-6

    Google Scholar 

  66. Suhaila J, Ching-Yee K, Fadhilah Y, Hui-Mean F (2011) Introducing the mixed distribution in fitting rainfall data. Open J Mod Hydrol 1:11–22. doi:10.4236/ojmh.2011.12002

    Article  Google Scholar 

  67. Syafrina AH, Zalina MD, Juneng L (2014) Historical trend of hourly extreme rainfall in Peninsular Malaysia. Theor Appl Climatol 120:259–285. doi:10.1007/s00704-014-1145-8

    Article  Google Scholar 

  68. Varikoden H, Preethi B, Samah AA, Babu CA (2011) Seasonal variation of rainfall characteristics in different intensity classes over Peninsular Malaysia. J Hydrol 404:99–108. doi:10.1016/j.jhydrol.2011.04.021

    Article  Google Scholar 

  69. Verhoest N, Troch PA, De Troch FP (1997) On the applicability of Bartlett–Lewis rectangular pulses models in the modeling of design storms at a point. J Hydrol 202:108–120. doi:10.1016/S0022-1694(97)00060-7

    Article  Google Scholar 

  70. Verhoest NEC, Vandenberghe S, Cabus P, Onof C, Meca-Figueras T, Jameleddine S (2010) Are stochastic point rainfall models able to preserve extreme flood statistics? Hydrol Process 24:3439–3445. doi:10.1002/hyp.7867

    Article  Google Scholar 

  71. Wan H, Zhang X, Barrow EM (2005) Stochastic modelling of daily precipitation for Canada. Atmosphere-Ocean 43:23–32. doi:10.3137/ao.430102

    Article  Google Scholar 

  72. Wijngaard JB, Klein AMG, Konnen GP (2003) Homogeneity of 20th century European daily temperature and precipitation series. Int J Climatol 23:679–692. doi:10.1002/joc.906

    Article  Google Scholar 

  73. Wilks DS (1999) Interannual variability and extreme-value characteristics of several stochastic daily precipitation models. Agric For Meteorol 93:153–169. doi:10.1016/S0168-1923(98)00125-7

    Article  Google Scholar 

  74. Wilks DS (2011) Statistical methods in the atmospheric sciences, 3rd edn. Academic Press, London

    Google Scholar 

  75. Wilks DS, Wilby RL (1999) The weather generation game: a review of stochastic weather models. Prog Phys Geogr 23:329–357. doi:10.1177/030913339902300302

    Article  Google Scholar 

  76. Wong CL, Venneker R, Uhlenbrook S, Jamil ABM, Zhou Y (2009) Variability of rainfall in Peninsular Malaysia. Hydrol Earth Syst Sci Discuss 6:5471–5503. doi:10.5194/hessd-6-5471-2009

    Article  Google Scholar 

  77. Woolhiser DA, Roldán J (1982) Stochastic daily precipitation models: 2. A comparison of distributions of amounts. Water Resour Res 18:1461–1468. doi:10.1029/WR018i005p01461

    Article  Google Scholar 

  78. Wu CL, Chau KW (2013) Prediction of rainfall time series using modular soft computing methods. Eng Appl Artif Intell 26:997–1007. doi:10.1016/j.engappai.2012.05.023

    Article  Google Scholar 

  79. Wu CL, Chau KW, Li YS (2008) River stage prediction based on a distributed support vector regression. J Hydrol 358:96–111. doi:10.1016/j.jhydrol.2008.05.028

    Article  Google Scholar 

  80. Wu CL, Chau KW, Fan C (2010) Prediction of rainfall time series using modular artificial neural networks coupled with data-preprocessing techniques. J Hydrol 389:146–167. doi:10.1016/j.jhydrol.2010.05.040

    Article  Google Scholar 

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Acknowledgements

The authors are appreciative of and thankful to the Malaysian Meteorological Department (MMD) for providing the daily precipitation data and the Ministry of Education Malaysia (MOE) for the financial support. The authors also acknowledge and sincerely appreciate the valuable comments of the reviewers.

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Correspondence to Jing Lin Ng.

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Ng, J.L., Abd Aziz, S., Huang, Y.F. et al. Generation of a stochastic precipitation model for the tropical climate. Theor Appl Climatol 133, 489–509 (2018). https://doi.org/10.1007/s00704-017-2202-x

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