Publication

Comparison of Three Imputation Methods for Groundwater Level Timeseries

Andrea Rinaldo
2023
Journal paper
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.

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Related concepts (39)
Missing data
In statistics, missing data, or missing values, occur when no data value is stored for the variable in an observation. Missing data are a common occurrence and can have a significant effect on the conclusions that can be drawn from the data. Missing data can occur because of nonresponse: no information is provided for one or more items or for a whole unit ("subject"). Some items are more likely to generate a nonresponse than others: for example items about private subjects such as income.
Imputation (statistics)
In statistics, imputation is the process of replacing missing data with substituted values. When substituting for a data point, it is known as "unit imputation"; when substituting for a component of a data point, it is known as "item imputation". There are three main problems that missing data causes: missing data can introduce a substantial amount of bias, make the handling and analysis of the data more arduous, and create reductions in efficiency.
Autoregressive–moving-average model
In the statistical analysis of time series, autoregressive–moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the autoregression (AR) and the second for the moving average (MA). The general ARMA model was described in the 1951 thesis of Peter Whittle, Hypothesis testing in time series analysis, and it was popularized in the 1970 book by George E. P. Box and Gwilym Jenkins.
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