Geostatistical interpolation of streambed hydrologic attributes with addition of left censored data and anisotropy

Ruba A.M. Mohamed; Scott C. Brooks; Chia Hsing Tsai; Tanzila Ahmed; Dale F. Rucker; April L. Ulery; Eric M. Pierce; Kenneth C. Carroll

doi:10.1016/j.jhydrol.2021.126474

Geostatistical interpolation of streambed hydrologic attributes with addition of left censored data and anisotropy

Ruba A.M. Mohamed, Scott C. Brooks, Chia Hsing Tsai, Tanzila Ahmed, Dale F. Rucker, April L. Ulery, Eric M. Pierce, Kenneth C. Carroll

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Spatial geostatistical interpolation of point measurements of streambed attributes in the hyporheic zone may be constrained by the streambed anisotropy, and data density and spatial distribution may significantly impact the results. Spatial clustering and low spatial data density can be caused by bedrock outcropping at the streambed limiting installation of in-stream piezometers. This study examines parameter error variability of the geostatistical interpolation using anisotropic interpolation methods and increasing the data density by adding left censored values (i.e., data below measurement limit) to locations where measurements were limited by exposed bedrock lining the streambed. The reduction in relative standard error of the interpolation was determined for the spatial distributions of streambed attributes including hydraulic conductivity, seepage flux, and mercury solute flux measured in two different years along a study reach in East Fork Poplar Creek, Tennessee, USA. Two methods to impute the left censored values were compared including the conventional half the detection limit substitution method, and the Stochastic Approximation of Expectation-Maximization (SAEM) algorithm, which both had comparable results. Imputing left censored data increased the data density to recommended ranges, reduced data clustering, increased the spatial dependence for some attributes, and reduced the standard error for each of the three attributes. For the reach considered herein, addition of the left censored values resulted in a larger error reduction than the consideration of anisotropy within the interpolation, which confirms the benefit of data addition to increase data density within data-limited river corridors.

Original language	English
Article number	126474
Journal	Journal of Hydrology
Volume	599
DOIs	https://doi.org/10.1016/j.jhydrol.2021.126474
State	Published - Aug 2021

Funding

This work was supported by the Department of Energy (DOE) Minority Serving Institution Partnership Program (MSIPP) managed by the Savannah River National Laboratory. Additional support was provided by the USDA National Institute of Food and Agriculture (Hatch project 1023257) and the Plant & Environmental Science Department at NMSU, which is greatly appreciated. A portion of this research was sponsored by the Office of Biological and Environmental Research within the Office of Science of the U.S. DOE, as part of the Critical Interfaces Science Focus Area project at the Oak Ridge National Laboratory (ORNL). The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). ORNL is managed by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with DOE. We appreciate the assistance of Kenneth Lowe, Michael Jones, Nikki Jones, Justin Milavec, Autumn Pearson, Chris Kubicki, and Amanda Lara. We thank the anonymous reviewers for their comments, which improved the clarity of this work. This work was supported by the Department of Energy (DOE) Minority Serving Institution Partnership Program (MSIPP) managed by the Savannah River National Laboratory. Additional support was provided by the USDA National Institute of Food and Agriculture (Hatch project 1023257) and the Plant & Environmental Science Department at NMSU, which is greatly appreciated. A portion of this research was sponsored by the Office of Biological and Environmental Research within the Office of Science of the U.S. DOE, as part of the Critical Interfaces Science Focus Area project at the Oak Ridge National Laboratory (ORNL). The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). ORNL is managed by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with DOE. We appreciate the assistance of Kenneth Lowe, Michael Jones, Nikki Jones, Justin Milavec, Autumn Pearson, Chris Kubicki, and Amanda Lara. We thank the anonymous reviewers for their comments, which improved the clarity of this work.

Funders	Funder number
DOE Public Access Plan
MSIPP
NMSU
Plant & Environmental Science Department
U.S. Department of Energy
National Institute of Food and Agriculture	1023257
Biological and Environmental Research
Oak Ridge National Laboratory
Savannah River National Laboratory
UT-Battelle	DE-AC05-00OR22725

Keywords

Geostatistics
Hyporheic
Kriging
Left censored data
Piezometer

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10.1016/j.jhydrol.2021.126474

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title = "Geostatistical interpolation of streambed hydrologic attributes with addition of left censored data and anisotropy",

abstract = "Spatial geostatistical interpolation of point measurements of streambed attributes in the hyporheic zone may be constrained by the streambed anisotropy, and data density and spatial distribution may significantly impact the results. Spatial clustering and low spatial data density can be caused by bedrock outcropping at the streambed limiting installation of in-stream piezometers. This study examines parameter error variability of the geostatistical interpolation using anisotropic interpolation methods and increasing the data density by adding left censored values (i.e., data below measurement limit) to locations where measurements were limited by exposed bedrock lining the streambed. The reduction in relative standard error of the interpolation was determined for the spatial distributions of streambed attributes including hydraulic conductivity, seepage flux, and mercury solute flux measured in two different years along a study reach in East Fork Poplar Creek, Tennessee, USA. Two methods to impute the left censored values were compared including the conventional half the detection limit substitution method, and the Stochastic Approximation of Expectation-Maximization (SAEM) algorithm, which both had comparable results. Imputing left censored data increased the data density to recommended ranges, reduced data clustering, increased the spatial dependence for some attributes, and reduced the standard error for each of the three attributes. For the reach considered herein, addition of the left censored values resulted in a larger error reduction than the consideration of anisotropy within the interpolation, which confirms the benefit of data addition to increase data density within data-limited river corridors.",

keywords = "Geostatistics, Hyporheic, Kriging, Left censored data, Piezometer",

author = "Mohamed, {Ruba A.M.} and Brooks, {Scott C.} and Tsai, {Chia Hsing} and Tanzila Ahmed and Rucker, {Dale F.} and Ulery, {April L.} and Pierce, {Eric M.} and Carroll, {Kenneth C.}",

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doi = "10.1016/j.jhydrol.2021.126474",

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AU - Mohamed, Ruba A.M.

AU - Brooks, Scott C.

AU - Tsai, Chia Hsing

AU - Ahmed, Tanzila

AU - Rucker, Dale F.

AU - Ulery, April L.

AU - Pierce, Eric M.

AU - Carroll, Kenneth C.

PY - 2021/8

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N2 - Spatial geostatistical interpolation of point measurements of streambed attributes in the hyporheic zone may be constrained by the streambed anisotropy, and data density and spatial distribution may significantly impact the results. Spatial clustering and low spatial data density can be caused by bedrock outcropping at the streambed limiting installation of in-stream piezometers. This study examines parameter error variability of the geostatistical interpolation using anisotropic interpolation methods and increasing the data density by adding left censored values (i.e., data below measurement limit) to locations where measurements were limited by exposed bedrock lining the streambed. The reduction in relative standard error of the interpolation was determined for the spatial distributions of streambed attributes including hydraulic conductivity, seepage flux, and mercury solute flux measured in two different years along a study reach in East Fork Poplar Creek, Tennessee, USA. Two methods to impute the left censored values were compared including the conventional half the detection limit substitution method, and the Stochastic Approximation of Expectation-Maximization (SAEM) algorithm, which both had comparable results. Imputing left censored data increased the data density to recommended ranges, reduced data clustering, increased the spatial dependence for some attributes, and reduced the standard error for each of the three attributes. For the reach considered herein, addition of the left censored values resulted in a larger error reduction than the consideration of anisotropy within the interpolation, which confirms the benefit of data addition to increase data density within data-limited river corridors.

AB - Spatial geostatistical interpolation of point measurements of streambed attributes in the hyporheic zone may be constrained by the streambed anisotropy, and data density and spatial distribution may significantly impact the results. Spatial clustering and low spatial data density can be caused by bedrock outcropping at the streambed limiting installation of in-stream piezometers. This study examines parameter error variability of the geostatistical interpolation using anisotropic interpolation methods and increasing the data density by adding left censored values (i.e., data below measurement limit) to locations where measurements were limited by exposed bedrock lining the streambed. The reduction in relative standard error of the interpolation was determined for the spatial distributions of streambed attributes including hydraulic conductivity, seepage flux, and mercury solute flux measured in two different years along a study reach in East Fork Poplar Creek, Tennessee, USA. Two methods to impute the left censored values were compared including the conventional half the detection limit substitution method, and the Stochastic Approximation of Expectation-Maximization (SAEM) algorithm, which both had comparable results. Imputing left censored data increased the data density to recommended ranges, reduced data clustering, increased the spatial dependence for some attributes, and reduced the standard error for each of the three attributes. For the reach considered herein, addition of the left censored values resulted in a larger error reduction than the consideration of anisotropy within the interpolation, which confirms the benefit of data addition to increase data density within data-limited river corridors.

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Geostatistical interpolation of streambed hydrologic attributes with addition of left censored data and anisotropy

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