Probability Distribution of Rainfall Depth at Hourly Time-Scale
Rainfall data at fine resolution and knowledge of its
characteristics plays a major role in the efficient design and operation
of agricultural, telecommunication, runoff and erosion control as well
as water quality control systems. The paper is aimed to study the
statistical distribution of hourly rainfall depth for 12 representative
stations spread across Peninsular Malaysia. Hourly rainfall data of 10
to 22 years period were collected and its statistical characteristics
were estimated. Three probability distributions namely, Generalized
Pareto, Exponential and Gamma distributions were proposed to
model the hourly rainfall depth, and three goodness-of-fit tests,
namely, Kolmogorov-Sminov, Anderson-Darling and Chi-Squared
tests were used to evaluate their fitness. Result indicates that the east
cost of the Peninsular receives higher depth of rainfall as compared
to west coast. However, the rainfall frequency is found to be
irregular. Also result from the goodness-of-fit tests show that all the
three models fit the rainfall data at 1% level of significance.
However, Generalized Pareto fits better than Exponential and
Gamma distributions and is therefore recommended as the best fit.
[1] Burlando, P. and R. Rosso, Effects of transient climate change on basin
hydrology. 1. Precipitation scenarios for the Arno River, central Italy.
Hydrol. Process. 16, Wiley Interscience, 2002. 16: p. 1151-1175.
[2] Hutchinson, M.F., Stochastic space-time weather models from groundbased
data Agricultural and Forest Meteorology, 1995. 73(3-4): p. 237-
264.
[3] Semenov, M.A. and E.M. Barrow, Use of a Stochastic Weather
Generator in the Development of Climate Change Scenarios. Climatic
Change, 1997. 35: p. 397-414.
[4] Toews, M.W. and D.M. Allen, Evaluating different GCMs for predicting
spatial recharge in an irrigated arid region. Journal of Hydrology,
Elsevier 2009. 374: p. 265-284.
[5] Bonta, J.V., Stochastic Simulation of Storm Occurrence, Depth,
Duration, And Within−Storm Intensities. Transactions of the American
Society of Agricultural Engineers, ASAE 2004. 47(5): p. 1573-1584.
[6] Khalili, M., R. Leconte, and F. Brissette, Stochastic Multisite Generation
of Daily Precipitation Data Using Spatial Autocorrelation. Journal of
Hydrometeorology, 2006. 8: p. 396-412.
[7] Srikanthan, R., T.A. McMahon, and A. Sharma, Stochastic Generation
of Monthly Rainfall Data, in Technical Report 02/8. 2002, Cooperative
Research Centre for Catchment Hydrology.
[8] Unal, N.E., H. Aksoy, and T. Akar, Annual and monthly rainfall data
generation schemes. Stoch Envir Res and Risk Ass., 2004. 18: p. 245-
257.
[9] Rao, N.J.M. and E. Biazi, Probability Distribution Models for Daily
Rainfall Data for an Interior Station of Brazil. Arch. Met. Geoph. Biocl.,
1983. Set. B(33): p. 261-265.
[10] Koutsoyiannis, D., Statistics of extremes and estimation of extreme
rainfall: II. Empirical investigation of long rainfall records.
Hydrological Sciences-Journal-des Sciences Hydrologiques, 49(4)
August 2004, 2004. 49(4): p. 591-610.
[11] Suhaila, J. and A.A. Jemain, Fitting Daily Rainfall Amount in Peninsular
Malaysia Using Several Types of Exponential Distributions. Journal of
Applied Scinces Research, 2007. 3(10): p. 1027-1036.
[12] Suhaila, J. and A.A. Jemain, Fitting the Statistical Distribution for Daily
Rainfall in Peninsular Malaysia Based on AIC Criterion. Journal of
Applied Sciences Research, 2008. 4(12): p. 1846-1857.
[13] Fadhilah, Y.; Zalina, M.; Nguyen, V. T. V.; Suhaila, S.; and Zulkifli, Y.,
Fitting the Best-Fit Distribution for the Hourly Rainfall Amount in the
Wilayah Persekutuan. Jurnal Teknologi, UTM, 2007. 46(C): p. 49-58.
[14] Burguefio, A.; Codina, B.; Redafio, A.; and Lorente J., Basic Statistical
Characteristics of Hourly Rainfall Amounts in Barcelona (Spain). Theor.
Appl. Climatol. Springer Verlag, 1994. 49: p. 175-181.
[15] Adams, B.J.; Fraser, H.G, Charles, D.D., and Hanafy, M.S.;
Meteorological Data Analysis For Drainage System Design. Journal of
Environmental Engineering, ASCE, 1986. 112(5): p. 827-848.
[16] Guo, J.C.Y., Overflow Risk Analysis for Stormwater Quality Control
Basins. Journal of Hydrologic Engineering, 2002. 7(6): p. 428-434.
[17] Adams, B.J. and F. Papa, Urban Stormwater Management Planning with
Analytical Probabilistic Models. 2000, New York: John Wiley & Sons.
p. 53-79.
[1] Burlando, P. and R. Rosso, Effects of transient climate change on basin
hydrology. 1. Precipitation scenarios for the Arno River, central Italy.
Hydrol. Process. 16, Wiley Interscience, 2002. 16: p. 1151-1175.
[2] Hutchinson, M.F., Stochastic space-time weather models from groundbased
data Agricultural and Forest Meteorology, 1995. 73(3-4): p. 237-
264.
[3] Semenov, M.A. and E.M. Barrow, Use of a Stochastic Weather
Generator in the Development of Climate Change Scenarios. Climatic
Change, 1997. 35: p. 397-414.
[4] Toews, M.W. and D.M. Allen, Evaluating different GCMs for predicting
spatial recharge in an irrigated arid region. Journal of Hydrology,
Elsevier 2009. 374: p. 265-284.
[5] Bonta, J.V., Stochastic Simulation of Storm Occurrence, Depth,
Duration, And Within−Storm Intensities. Transactions of the American
Society of Agricultural Engineers, ASAE 2004. 47(5): p. 1573-1584.
[6] Khalili, M., R. Leconte, and F. Brissette, Stochastic Multisite Generation
of Daily Precipitation Data Using Spatial Autocorrelation. Journal of
Hydrometeorology, 2006. 8: p. 396-412.
[7] Srikanthan, R., T.A. McMahon, and A. Sharma, Stochastic Generation
of Monthly Rainfall Data, in Technical Report 02/8. 2002, Cooperative
Research Centre for Catchment Hydrology.
[8] Unal, N.E., H. Aksoy, and T. Akar, Annual and monthly rainfall data
generation schemes. Stoch Envir Res and Risk Ass., 2004. 18: p. 245-
257.
[9] Rao, N.J.M. and E. Biazi, Probability Distribution Models for Daily
Rainfall Data for an Interior Station of Brazil. Arch. Met. Geoph. Biocl.,
1983. Set. B(33): p. 261-265.
[10] Koutsoyiannis, D., Statistics of extremes and estimation of extreme
rainfall: II. Empirical investigation of long rainfall records.
Hydrological Sciences-Journal-des Sciences Hydrologiques, 49(4)
August 2004, 2004. 49(4): p. 591-610.
[11] Suhaila, J. and A.A. Jemain, Fitting Daily Rainfall Amount in Peninsular
Malaysia Using Several Types of Exponential Distributions. Journal of
Applied Scinces Research, 2007. 3(10): p. 1027-1036.
[12] Suhaila, J. and A.A. Jemain, Fitting the Statistical Distribution for Daily
Rainfall in Peninsular Malaysia Based on AIC Criterion. Journal of
Applied Sciences Research, 2008. 4(12): p. 1846-1857.
[13] Fadhilah, Y.; Zalina, M.; Nguyen, V. T. V.; Suhaila, S.; and Zulkifli, Y.,
Fitting the Best-Fit Distribution for the Hourly Rainfall Amount in the
Wilayah Persekutuan. Jurnal Teknologi, UTM, 2007. 46(C): p. 49-58.
[14] Burguefio, A.; Codina, B.; Redafio, A.; and Lorente J., Basic Statistical
Characteristics of Hourly Rainfall Amounts in Barcelona (Spain). Theor.
Appl. Climatol. Springer Verlag, 1994. 49: p. 175-181.
[15] Adams, B.J.; Fraser, H.G, Charles, D.D., and Hanafy, M.S.;
Meteorological Data Analysis For Drainage System Design. Journal of
Environmental Engineering, ASCE, 1986. 112(5): p. 827-848.
[16] Guo, J.C.Y., Overflow Risk Analysis for Stormwater Quality Control
Basins. Journal of Hydrologic Engineering, 2002. 7(6): p. 428-434.
[17] Adams, B.J. and F. Papa, Urban Stormwater Management Planning with
Analytical Probabilistic Models. 2000, New York: John Wiley & Sons.
p. 53-79.
@article{"International Journal of Earth, Energy and Environmental Sciences:60673", author = "S. Dan'azumi and S. Shamsudin and A. A. Rahman", title = "Probability Distribution of Rainfall Depth at Hourly Time-Scale", abstract = "Rainfall data at fine resolution and knowledge of its
characteristics plays a major role in the efficient design and operation
of agricultural, telecommunication, runoff and erosion control as well
as water quality control systems. The paper is aimed to study the
statistical distribution of hourly rainfall depth for 12 representative
stations spread across Peninsular Malaysia. Hourly rainfall data of 10
to 22 years period were collected and its statistical characteristics
were estimated. Three probability distributions namely, Generalized
Pareto, Exponential and Gamma distributions were proposed to
model the hourly rainfall depth, and three goodness-of-fit tests,
namely, Kolmogorov-Sminov, Anderson-Darling and Chi-Squared
tests were used to evaluate their fitness. Result indicates that the east
cost of the Peninsular receives higher depth of rainfall as compared
to west coast. However, the rainfall frequency is found to be
irregular. Also result from the goodness-of-fit tests show that all the
three models fit the rainfall data at 1% level of significance.
However, Generalized Pareto fits better than Exponential and
Gamma distributions and is therefore recommended as the best fit.", keywords = "Goodness-of-fit test, Hourly rainfall, Malaysia,Probability distribution.", volume = "4", number = "12", pages = "670-5", }