The Applied of Functional Data Analysis to Comparison 100 Times Simulated Monthly Rainfall Using Some Two Parameters Distribution

Abstract

Three probability models of mothly rainfall such as Gamma, Weibull and Log Normal distribution are evaluated in terms of their ability to reproduce the mean statistics derived from 100 times simulation of monthly rainfall in the Pekanbaru City, Indonesia. One of the important studies is to investigate and understand the simulate mean monthly rainfall patterns that occur throughout the year. To identify the pattern, it requires a rainfall curve to represent monthly observation of rainfall received during the year. Functional data analysis (FDA) methods are capable to convert discrete data into a function that can represent the rainfall curve and as a result, try to describe the hidden patterns of the rainfall. This study is focused on investigating 100 curve average monthly rainfall simulatated by three different quantile functions using the FDA. The mean and standard deviation of FDA for average monthly precipitation are obtained. Through these two statistics a the confidence interval curves of the mean curve are presented represent 95% pointwise confidence intervals. In this study, most of the monthly average rainfall from the actual data were around the FDA mean and the monthly average rainfall was within the FDA confidence interval. In this study, 100 times monthly rainfall simulations using the quantile function of the gamma and log normal distributions found that the mean FDA can capture most of the mean monthly rainfall from historical data, and within the FDA interval. The contradictory results shown by the monthly rainfall simulations using the Weibull distribution, most of the monthly average rainfall historical data cannot be captured by the FDA mean and are outside the FDA confidence interval. Based on the Mean Absolute Error (MAE) value of the average monthly rainfall of historical data and the monthly average of the FDA, it can be concluded that the gamma distribution can produce simulated rain better than the log normal distribution.