Two stage iterative approach for addressing missing values in small-scale water quality data

Abstract

Handling missing values in real water quality monitoring systems is essential for environmental analysis, particularly in some small-scale datasets. In the case of insufficient data size, the observed data cannot provide adequate information, inhibiting some imputing methods from working well. This study proposes a two-stage approach for addressing missing water quality data of small size on the basis of accuracy assessment. Missingness is formulated as the coexistence of ‘random missing over short periods’ and ‘long-term continuous missing’. In the first stage, the traditional mean imputation, median imputation, linear interpolation, k-nearest neighbor imputation, random forest imputation, and multiple imputation by chained equations are compared to select the optimal method. As the most suitable method across all variables, linear interpolation is used to fill in small random missing portions of the original data, providing an opportunity to expand the dataset to perform subsequent imputation. In the second stage, together with the autoregressive integrated moving average, the filling methods are similarly evaluated on the basis of data already filled in the first step. The most suitable method obtained from the comparison is used to populate the remaining long-term continuous missing data. The efficacy of the proposed approach is validated on a real water quality dataset. The results demonstrate that the two-stage iterative approach offers a feasible roadmap to impute missing values on the small-scale water quality dataset.