Estimation of Rainfall Curve by using Functional Data Analysis and Ordinary Kriging Approach

Abstract

Rainfall is an interesting phenomenon to investigate since it is directly related to all aspects of life on earth. One of the important studies is to investigate and understand the rainfall patterns that occur throughout the year. To identify the pattern, it requires a rainfall curve to represent daily observation of rainfall received during the year. Functional data analysis methods are capable to convert discrete data intoa function that can represent the rainfall curve and as a result, try to describe the hidden patterns of the rainfall. This study focused on the distribution of daily rainfall amount using functional data analysis. Fourier basis functions are used for periodic rainfall data. Generalized cross-validation showed 123 basis functions were sufficient to describe the pattern of daily rainfall amount. North and west areas of the peninsula show a significant bimodal pattern with the curve decline between two peaks at the mid-year. Meanwhile,the east shows uni-modal patterns that reached a peak in the last three months. Southern areas show more uniform trends throughout the year. Finally, the functional spatial method is introduced to overcome the problem of estimating the rainfall curve in the locations with no data recorded. We use a leave one out cross-validation as a verification method to compare between the real curve and the predicted curve. We used coefficient of basis functions to get the predicted curve. It was foundthatthe methods ofspatial prediction can match up with the existing spatial prediction methods in terms of accuracy,but it is better as the new approach provides a simpler calculation.