Normal Ratio in Multiple Imputation Based on Bootstrapped Sample for Rainfall Data With Mis Singness

Abstract

ABSTRACT:The existence of missing values in rainfall data series is inevitably affects the quality of the data. This problem will influence the results of analysis and subsequently provide imprecise information to the hydrological and meteorological management. A practical and reliable approach is needed in developing estimation methods to impute the missing values. Single imputation is the most commonly used approach for missing values, but, it encounters with the limitation of not considering the uncertainty and natural variability in missing data imputation. Thus, this study has proposed multiple imputation approach based on bootstrap samples in order to overcome the limitation of single imputation approach. Three normal ratio estimation methods are implemented using the proposed approach. The performances of the estimation methods are evaluated at six different levels of missingness. Complete 40 years daily rainfall data from four meteorology stations were considered for the analysis purpose with Johor Bahru station was selected as the target station. The results of the proposed approach were compared to the results obtained from single imputation approach and the widely known built in software for multiple imputation, Amelia II package, in assessing the performance of proposed approach. The results showed that all estimation methods that implemented using proposed approach provided the most accurate estimation results at all percentages of missingness. This proves the advantage of adaption of variability and uncertainty element in the proposed approach in estimating the missing rainfall data at the area of the current study.

Comparison of the Methods to Estimate Missing Values in Monthly Precipitation Data

“…The performances of the estimation methods evaluated at six different percentages of missing data to propose three normal ratio estimation methods to overcome missing data [9]. Forty years daily rainfall data from four meteorology stations considered.…”

Controlled Sampling Approach in Improving Multiple Imputation for Missing Seasonal Rainfall Data

“…Block bootstrap was adopted by Burhanuddin et al (2017b) in their MI that was specifically proposed for rainfall time series. The bootstrapping approach was applied to normal ratio methods to impute Data are divided into several blocks before being resampled Data are directly resampled missing values in the Malaysian daily rainfall dataset.…”

“…The bootstrap was applied separately on each block of the data. The detailed procedure of block bootstrap that has been implemented in the current study is explained below (Burhanuddin et al, 2017b).…”

Identifying the Ideal Number Components of the Bayesian Principal Component Analysis Model for Missing Daily Precipitation Data Treatment

“…For the past decades, a number of imputation algorithms have been proposed, such as a normal ratio algorithm, inverse distance weighting algorithm and coefficient of weighting algorithm, where these conventional imputation algorithms are frequently applied in environmental sciences [1,5,9,10]. Recently, Burhanuddin et al [3] proposed a multiple imputation algorithm, which associate the conventional normal ratio algorithm and moving block bootstrapping. The analysis results rendered their proposed algorithm yielded a more reliable results compared to the single imputation algorithm in missing daily precipitation data treatment.…”

“…Moreover, Burhanuddin et al [4] also proposed an improved normal ratio algorithm by adapting geometric median as an alternative of the arithmetic mean, which invariant respect to outliers. The imputation algorithms proposed by Burhanuddin et al [3,4] are highly dependent on the homogeneous precipitation time series of neighbouring monitoring stations. Contrarily, Saeed et al [9] proposed median algorithm, which the proposed single imputation algorithm is without depending on the homogeneous precipitation time series of neighbouring monitoring stations.…”