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Hydrology 2018, 5(4), 63;

An Empirical Mode-Spatial Model for Environmental Data Imputation

Department of Civil and Environmental Engineering, Brigham Young University, Provo, UT 84602, USA
Department of Statistics, Brigham Young University, Provo, UT 84602, USA
Author to whom correspondence should be addressed.
Received: 26 September 2018 / Revised: 1 November 2018 / Accepted: 13 November 2018 / Published: 17 November 2018
PDF [4857 KB, uploaded 17 November 2018]


Complete and accurate data are necessary for analyzing and understanding trends in time-series datasets; however, many of the available time-series datasets have gaps that affect the analysis, especially in the earth sciences. As most available data have missing values, researchers use various interpolation methods or ad hoc approaches to data imputation. Since the analysis based on inaccurate data can lead to inaccurate conclusions, more accurate data imputation methods can provide accurate analysis. We present a spatial-temporal data imputation method using Empirical Mode Decomposition (EMD) based on spatial correlations. We call this method EMD-spatial data imputation or EMD-SDI. Though this method is applicable to other time-series data sets, here we demonstrate the method using temperature data. The EMD algorithm decomposes data into periodic components called intrinsic mode functions (IMF) and exactly reconstructs the original signal by summing these IMFs. EMD-SDI initially decomposes the data from the target station and other stations in the region into IMFs. EMD-SDI evaluates each IMF from the target station in turn and selects the IMF from other stations in the region with periodic behavior most correlated to target IMF. EMD-SDI then replaces a section of missing data in the target station IMF with the section from the most closely correlated IMF from the regional stations. We found that EMD-SDI selects the IMFs used for reconstruction from different stations throughout the region, not necessarily the station closest in the geographic sense. EMD-SDI accurately filled data gaps from 3 months to 5 years in length in our tests and favorably compares to a simple temporal method. EMD-SDI leverages regional correlation and the fact that different stations can be subject to different periodic behaviors. In addition to data imputation, the EMD-SDI method provides IMFs that can be used to better understand regional correlations and processes. View Full-Text
Keywords: environmental data imputation; missing values; Empirical Mode Decomposition; time series environmental data imputation; missing values; Empirical Mode Decomposition; time series

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Nelsen, B.; Williams, D.A.; Williams, G.P.; Berrett, C. An Empirical Mode-Spatial Model for Environmental Data Imputation. Hydrology 2018, 5, 63.

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