The Effectiveness of a Probabilistic Principal Component Analysis Model and Expectation Maximisation Algorithm in Treating Missing Daily Rainfall Data

Abstract

The reliability and accuracy of a risk assessment of extreme hydro-meteorological events are highly dependent on the quality of the historical rainfall time series data. However, missing data in a time series such as this could result in lower quality data. Therefore, this paper proposes a multiple-imputation algorithm for treating missing data without requiring information from adjoining monitoring stations. The proposed imputation algorithms are based on the M-component probabilistic principal component analysis model and an expectation maximisation algorithm (MPPCA-EM). In order to evaluate the effectiveness of the MPPCA-EM imputation algorithm, six distinct historical daily rainfall time series data were recorded from six monitoring stations. These stations were located at the coastal and inland regions of the East-Coast Economic Region (ECER) Malaysia. The results of analysis show that, when it comes to treating missing historical daily rainfall time series data recorded from coastal monitoring stations, the 2-component probabilistic principal component analysis model and expectation-maximisation algorithm (2PPCA-EM) were found to be superior to the single- and multiple-imputation algorithms proposed in previous studies. On the contrary, the single-imputation algorithms as proposed in previous studies were superior to the MPPCA-EM imputation algorithms when treating missing historical daily rainfall time series data recorded from inland monitoring stations.