Comparison of Stochastic Point Process Models of Rainfall in Singapore

Authors: Y. Lu, X. S. Qin

Abstract:

Extensive rainfall disaggregation approaches have been developed and applied in climate change impact studies such as flood risk assessment and urban storm water management.In this study, five rainfall models that were capable ofdisaggregating daily rainfall data into hourly one were investigated for the rainfall record in theChangi Airport, Singapore. The objectives of this study were (i) to study the temporal characteristics of hourly rainfall in Singapore, and (ii) to evaluate the performance of variousdisaggregation models. The used models included: (i) Rectangular pulse Poisson model (RPPM), (ii) Bartlett-Lewis Rectangular pulse model (BLRPM), (iii) Bartlett-Lewis model with 2 cell types (BL2C), (iv) Bartlett-Lewis Rectangular with cell depth distribution dependent on duration (BLRD), and (v) Neyman-Scott Rectangular pulse model (NSRPM). All of these models werefitted using hourly rainfall data ranging from 1980 to 2005 (which was obtained from Changimeteorological station).The study results indicated that the weight scheme of inversely proportional variance could deliver more accurateoutputs for fitting rainfall patterns in tropical areas, and BLRPM performedrelatively better than other disaggregation models.

Keywords: Rainfall disaggregation, statistical properties, poisson processed, Bartlett-Lewis model, Neyman-Scott model.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079672

References:

[1] C. G. Kilsby,A. Butron,S. J. Birkinshaw,A. M. Hashemi, P. E. O-Connell,"Extreme rainfall and flood frequency distribution modeling for present and future climates,"Proceedings of the British Hydrological Society Seventh National Hydrology Symposium, 2000, pp. 3.51-3.56.
[2] I. Rodriguez-Iturbe, V. K. Gupta, E. Waymire,. "Scale consideration in the modeling of temporal rainfall,"Water Resources Research 20 (11), 1984, 1611-1619.
[3] C. Onof,R. E. Chandler, A. Kakou,P. Northrop,H. S. Wheater,V. Isham, "Rainfall modeling using Poisson-Cluster processes: a review of developments,"Stochastic Environmental Research and Risk Assessment 14(6), 2000, 384-411.
[4] I. Rodriguez-Iturbe,D. R. Cox,V. Isham,. "Some models for rainfall based on stochastic point processes,"Proceedings of the Royal Society of London, Series A 410, 1987a, 269-288.
[5] I. Rodriguez-Iturbe,B. Febres de Power,J. B. Valdes,"Rectangular pulses point process models for rainfall: analysis of empirical data,"Journal of Geophysical Research 92, 1987b, 9645-9656.
[6] A. N. Engida, M. Esteves,"Characterization and disaggregation of daily rainfall in the Upper Blue Nile Basin in Ethiopia,"Journal of Hydrology 399, 2011, 226-234.
[7] C. Onof,"DEFRA Project: Improved methods for national spatialtemporal rainfall and evaporation modeling for BSM," 2003,unpublished.
[8] P. S. P. Cowpertwait, "A generalized point process model for rainfall,"Proceedings of Royal Society of London 447, 1994, 23-27.
[9] P. S. P. Cowpertwait,"A generalized spatial-temporal model of rainfall based on a clustered point process,"Proceedings of Royal Society of London 450, 1995, 163-175.
[10] A. Burton,C. G. Kilsby,H. J. Fowler, P. S. P. Cowpertwait, P. E. O-Connell,"RainSim: A spatial-temporal stochastic rainfall modeling system,"Environmental Modelling & Software 23, 2008, 1356-1369.
[11] I. S. Hanaish, K. Ibrahim,A. A. Jemain,"Stochastic modeling of rainfall in Peninsular Malaysia using Bartlett-Lewis rectangular pulse models,"Modelling and Simulation in Engineering, 2011.
[12] A. Kakou, "Point process based models for rainfall," Ph.D. thesis, University of London, 1997, unpublished.
[13] Meteorological Services Division, National Environmental Agency, http://www.nea.gov.sg
[14] Geography of Singapore, WIKIPEDIA, http://en.wikipedia.org/wiki/Geography_of_Singapore
[15] R. Chandler,G. Lourmas,J. Jesus, "Software for moment-based on fitting of single-site stochastic rainfall models,"2010, unpublished.
[16] J. Jesus and R. Chandler, "Estimating functions and the generalized method of moments," Interface Focus, 1(6), 2011, 871-885.