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Probability structure and return period calculations for multi-day monsoon rainfall events at Subang, Malaysia




Muhammad, Nur Shazwani, author
Julien, Pierre Y., advisor
Roesner, Larry A., committee member
Salas, Jose D., committee member
Arabi, Mazdak, committee member
Wohl, Ellen E., committee member

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Flooding is the most common natural disaster in Malaysia, as a result of heavy rainfall. Malaysia is located in the equatorial zone and experiences a tropical climate with two seasons classified as the Northeast (November to May) and Southwest (May to September) monsoons. Both monsoons bring moisture, and multi-day rainfall events that cause particularly devastating floods on large watersheds. The objectives of this study are the following: (1) examine the probability structure of multi-day rainfall events; (2) determine the most suitable distribution function to represent the multi-day rainfall amounts; (3) select the most appropriate model to simulate the sequence of daily rainfall using the discrete autoregressive family models; and (4) develop and test an approach to calculate the return period of multi-day rainfall events with respect to the duration and amount. Daily monsoon rainfall data recorded at Subang Airport are gathered from the Malaysian Meteorological Department. Subang Airport is located near Kuala Lumpur (the capital city of Malaysia) and has a long and reliable daily rainfall record, with 18,993 daily measurements from 1960 to 2011. The majority of wet and dry events at Subang Airport from 1960 to 2011 are multi-days, with the fraction of 57% and 51%, respectively. The analysis of conditional probabilities for t-consecutive wet and dry days shows that the probability of occurrence for multi-day wet and dry days is increasing as the event duration increases. For example, the probability of rain on any random day is 0.53; and the conditional probability of rain the second day increases to 0.63. Also, the probability of dry on any random day is 0.47; and the probability of the second dry day increases to 0.58. The probability of rain and dry days increases gradually with rainfall duration. This finding shows that the occurrence of rain and dry is time-dependent. The autocorrelation coefficient for the daily rainfall amounts is very low at 0.0283. It is concluded that this parameter is independent from one day to another. The two parameter gamma function is most suitable to fit the daily rainfall precipitation data and the cumulative rainfall from t-consecutive rainy days up to 6 days. A graphical method, i.e. the 1:1 plot confirms the goodness-of-fit of the gamma function. Two discrete autoregressive models are tested in this study, i.e., the low order Discrete Auto Regressive [DAR(1)] and the low order Discrete Auto Regressive and Moving Average [DARMA(1,1)]. These models require data stationarity, therefore the analysis is done separately for the Northeast and Southwest monsoons. The model selection is based on the four-step process suggested by Salas and Pielke (2003). The comparisons between the observed and calculated autocorrelation coefficient and the low sum of squared errors for the probability distributions confirm that DARMA(1,1) is most suitable to simulate daily rainfall sequences at Subang Airport for both monsoons. The return period for 1-day and multi-day rainfall events is defined as a function of wet run length and rainfall amount. A test of return period calculations up to 20 years based on the mean wet and dry run lengths shows good agreement between calculation and observations of multi-day rainfall amounts up to 150 mm. A very long sequence of daily rainfall (1,000,000 days) is generated to extend the analysis of multi-day events with cumulative rainfall up to 350 mm, which gives an estimated return period of more than 2,000 years. The mean, standard deviation, maximum daily rainfall, lag-1 ACF coefficient and maximum wet and dry run lengths of the generated daily rainfall sequence using DARMA(1,1) are also comparable with the observed data. The December 2006 rainstorm event at Kota Tinggi, Johor is used as an example of the application of the algorithms developed in this study. This multi-day rainstorm totaling 350 mm caused devastating floods in the area. The December 2006 rainstorm is extremely rare because the cumulative rainfall amount from the multi-day event gives an estimated return period of greater than 2,000 years. The method proposed in this study is helpful for the design of levees on large watersheds (size of more than 1,000 km2) because multi-day rainstorms are the main cause of flooding to the area. For example, the return period to overtop the current levee at Kota Tinggi is 220 years when considering a 1-day rainstorm, but this period of return decreases to 24 years when considering 4-day rainstorms.


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stochastic modeling
multi-day rainfall
return period
conditional probability
monsoon rainfall precipitation


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