Theoretical analysis of errors when estimating snow distribution through point measurements
In recent years, marked improvements in our knowledge of the statistical properties of the spatial distribution of snow properties have been achieved thanks to improvements in measuring technologies (e.g., LIDAR, terrestrial laser scanning (TLS), and ground-penetrating radar (GPR)). Despite this, ob...
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2015
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ftnonlinearchiv:oai:noa.gwlb.de:cop_mods_00016124 2023-05-15T18:32:33+02:00 Theoretical analysis of errors when estimating snow distribution through point measurements Trujillo, E. Lehning, M. 2015-06 electronic https://doi.org/10.5194/tc-9-1249-2015 https://noa.gwlb.de/receive/cop_mods_00016124 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00016079/tc-9-1249-2015.pdf https://tc.copernicus.org/articles/9/1249/2015/tc-9-1249-2015.pdf eng eng Copernicus Publications The Cryosphere -- ˜Theœ Cryosphere -- http://www.bibliothek.uni-regensburg.de/ezeit/?2393169 -- http://www.the-cryosphere.net/ -- 1994-0424 https://doi.org/10.5194/tc-9-1249-2015 https://noa.gwlb.de/receive/cop_mods_00016124 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00016079/tc-9-1249-2015.pdf https://tc.copernicus.org/articles/9/1249/2015/tc-9-1249-2015.pdf uneingeschränkt info:eu-repo/semantics/openAccess article Verlagsveröffentlichung article Text doc-type:article 2015 ftnonlinearchiv https://doi.org/10.5194/tc-9-1249-2015 2022-02-08T22:54:17Z In recent years, marked improvements in our knowledge of the statistical properties of the spatial distribution of snow properties have been achieved thanks to improvements in measuring technologies (e.g., LIDAR, terrestrial laser scanning (TLS), and ground-penetrating radar (GPR)). Despite this, objective and quantitative frameworks for the evaluation of errors in snow measurements have been lacking. Here, we present a theoretical framework for quantitative evaluations of the uncertainty in average snow depth derived from point measurements over a profile section or an area. The error is defined as the expected value of the squared difference between the real mean of the profile/field and the sample mean from a limited number of measurements. The model is tested for one- and two-dimensional survey designs that range from a single measurement to an increasing number of regularly spaced measurements. Using high-resolution (~ 1 m) LIDAR snow depths at two locations in Colorado, we show that the sample errors follow the theoretical behavior. Furthermore, we show how the determination of the spatial location of the measurements can be reduced to an optimization problem for the case of the predefined number of measurements, or to the designation of an acceptable uncertainty level to determine the total number of regularly spaced measurements required to achieve such an error. On this basis, a series of figures are presented as an aid for snow survey design under the conditions described, and under the assumption of prior knowledge of the spatial covariance/correlation properties. With this methodology, better objective survey designs can be accomplished that are tailored to the specific applications for which the measurements are going to be used. The theoretical framework can be extended to other spatially distributed snow variables (e.g., SWE – snow water equivalent) whose statistical properties are comparable to those of snow depth. Article in Journal/Newspaper The Cryosphere Niedersächsisches Online-Archiv NOA The Cryosphere 9 3 1249 1264 |
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article Verlagsveröffentlichung |
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article Verlagsveröffentlichung Trujillo, E. Lehning, M. Theoretical analysis of errors when estimating snow distribution through point measurements |
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article Verlagsveröffentlichung |
description |
In recent years, marked improvements in our knowledge of the statistical properties of the spatial distribution of snow properties have been achieved thanks to improvements in measuring technologies (e.g., LIDAR, terrestrial laser scanning (TLS), and ground-penetrating radar (GPR)). Despite this, objective and quantitative frameworks for the evaluation of errors in snow measurements have been lacking. Here, we present a theoretical framework for quantitative evaluations of the uncertainty in average snow depth derived from point measurements over a profile section or an area. The error is defined as the expected value of the squared difference between the real mean of the profile/field and the sample mean from a limited number of measurements. The model is tested for one- and two-dimensional survey designs that range from a single measurement to an increasing number of regularly spaced measurements. Using high-resolution (~ 1 m) LIDAR snow depths at two locations in Colorado, we show that the sample errors follow the theoretical behavior. Furthermore, we show how the determination of the spatial location of the measurements can be reduced to an optimization problem for the case of the predefined number of measurements, or to the designation of an acceptable uncertainty level to determine the total number of regularly spaced measurements required to achieve such an error. On this basis, a series of figures are presented as an aid for snow survey design under the conditions described, and under the assumption of prior knowledge of the spatial covariance/correlation properties. With this methodology, better objective survey designs can be accomplished that are tailored to the specific applications for which the measurements are going to be used. The theoretical framework can be extended to other spatially distributed snow variables (e.g., SWE – snow water equivalent) whose statistical properties are comparable to those of snow depth. |
format |
Article in Journal/Newspaper |
author |
Trujillo, E. Lehning, M. |
author_facet |
Trujillo, E. Lehning, M. |
author_sort |
Trujillo, E. |
title |
Theoretical analysis of errors when estimating snow distribution through point measurements |
title_short |
Theoretical analysis of errors when estimating snow distribution through point measurements |
title_full |
Theoretical analysis of errors when estimating snow distribution through point measurements |
title_fullStr |
Theoretical analysis of errors when estimating snow distribution through point measurements |
title_full_unstemmed |
Theoretical analysis of errors when estimating snow distribution through point measurements |
title_sort |
theoretical analysis of errors when estimating snow distribution through point measurements |
publisher |
Copernicus Publications |
publishDate |
2015 |
url |
https://doi.org/10.5194/tc-9-1249-2015 https://noa.gwlb.de/receive/cop_mods_00016124 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00016079/tc-9-1249-2015.pdf https://tc.copernicus.org/articles/9/1249/2015/tc-9-1249-2015.pdf |
genre |
The Cryosphere |
genre_facet |
The Cryosphere |
op_relation |
The Cryosphere -- ˜Theœ Cryosphere -- http://www.bibliothek.uni-regensburg.de/ezeit/?2393169 -- http://www.the-cryosphere.net/ -- 1994-0424 https://doi.org/10.5194/tc-9-1249-2015 https://noa.gwlb.de/receive/cop_mods_00016124 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00016079/tc-9-1249-2015.pdf https://tc.copernicus.org/articles/9/1249/2015/tc-9-1249-2015.pdf |
op_rights |
uneingeschränkt info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.5194/tc-9-1249-2015 |
container_title |
The Cryosphere |
container_volume |
9 |
container_issue |
3 |
container_start_page |
1249 |
op_container_end_page |
1264 |
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1766216713631694848 |