Comparison of Three Imputation Methods for Groundwater Level Timeseries

Abstract

This study compares three imputation methods applied to the field observations of hydraulic head in subsurface hydrology. Hydrogeological studies that analyze the timeseries of groundwater elevations often face issues with missing data that may mislead both the interpretation of the relevant processes and the accuracy of the analyses. The imputation methods adopted for this comparative study are relatively simple to be implemented and thus are easily applicable to large datasets. They are: (i) the spline interpolation, (ii) the autoregressive linear model, and (iii) the patched kriging. The average of their results is also analyzed. By artificially generating gaps in timeseries, the results of the various imputation methods are tested. The spline interpolation is shown to be the poorest performing one. The patched kriging method usually proves to be the best option, exploiting the spatial correlations of the groundwater elevations, even though spurious trends due to the the activation of neighboring sensors at times affect their reconstructions. The autoregressive linear model proves to be a reasonable choice; however, it lacks hydrogeological controls. The ensemble average of all methods is a reasonable compromise. Additionally, by interpolating a large dataset of 53 timeseries observing the variabilities of statistical measures, the study finds that the specific choice of the imputation method only marginally affects the overarching statistics.