Normal ratio in multiple imputation based on bootstrapped sample for rainfall data with missingness

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.