Three-dimensional imputation of missing monthly river flow data

Abstract

Imputation of missing data is a critical part of accurate data analysis and modeling. This paper presents 3D imputation as a new data-driven methodology to estimate missing values in time series data. The method is based on the assumption that all the observed data in a time series are related with each other and with data of the some other series. The available data is placed in a three-dimensional space so that the increasing or decreasing relationships between the observed data are appropriately represented. For the estimation of each missing value, the method searches and determines the best possible group of estimator data within the data space. Different data groups are found and used for the estimations of each individual group of missing data. The method is validated by removing and estimating all the observed monthly flow data of Sarayköy station on Büyük Menderes River in Turkey. Data of the downstream Burhaniye station constituted the second data layer in the model. High correlation values were obtained for all years between observations and estimations and the missing data of Sarayköy station was also estimated by using the proposed method.