Theory of an Automatic Seepage Meter and Ramifications for Applications
Abstract A new approach for measuring fluxes across surface water—groundwater interfaces was recently proposed. The Automatic Seepage Meter (ASM) is equipped with a precise water level sensor and digital memory that analyzes water level time series in a vertical tube inserted into a streambed (Solom...
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| Format: | Article |
| Language: | English |
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Wiley
2023-10-01
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| Series: | Water Resources Research |
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| Online Access: | https://doi.org/10.1029/2023WR034766 |
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| author | Vitaly A. Zlotnik D. Kip Solomon David P. Genereux Troy E. Gilmore C. Eric Humphrey Aaron R. Mittelstet Anatoly V. Zlotnik |
| author_facet | Vitaly A. Zlotnik D. Kip Solomon David P. Genereux Troy E. Gilmore C. Eric Humphrey Aaron R. Mittelstet Anatoly V. Zlotnik |
| author_sort | Vitaly A. Zlotnik |
| collection | DOAJ |
| description | Abstract A new approach for measuring fluxes across surface water—groundwater interfaces was recently proposed. The Automatic Seepage Meter (ASM) is equipped with a precise water level sensor and digital memory that analyzes water level time series in a vertical tube inserted into a streambed (Solomon et al., 2020, https://doi.org/10.1029/2019WR026983). The ability to infer flux values with high temporal resolution relies on an accurate interpretation of water level dynamics inside the tube. Here, we reduce the three‐dimensional hydrodynamic problem that describes the ASM water level in a variety of field conditions to a single ordinary differential equation. This novel general analytical solution for estimating ASM responses is more comprehensive and flexible than previous approaches and is applicable to the entire range of field conditions, including steady or transient stream stages, evaporation, rainfall, and noise. For example, our analysis determines the timing of the nonmonotonic ASM response to a monotonic linear stream stage variation and explains previously used empirical parabolic approximation for estimating fluxes. We present algorithms for simultaneous inference of vertical interface flux and hydraulic conductivity values together with an example code. We quantify how the accuracy of parameter estimation depends on test duration and noise amplitude and propose how our analysis can be used to optimize field test protocols. On this basis, changing the ASM geometry by increasing the radius and decreasing tube insertion depth may enable ASM field test protocols that estimate interface flux and hydraulic conductivity faster while maintaining desired accuracy. Potential applications of joint parameter estimation are suggested. |
| format | Article |
| id | doaj-art-1dc69217be1e4a0f9fbc2a8fc5059414 |
| institution | Kabale University |
| issn | 0043-1397 1944-7973 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Wiley |
| record_format | Article |
| series | Water Resources Research |
| spelling | doaj-art-1dc69217be1e4a0f9fbc2a8fc50594142025-08-20T03:32:27ZengWileyWater Resources Research0043-13971944-79732023-10-015910n/an/a10.1029/2023WR034766Theory of an Automatic Seepage Meter and Ramifications for ApplicationsVitaly A. Zlotnik0D. Kip Solomon1David P. Genereux2Troy E. Gilmore3C. Eric Humphrey4Aaron R. Mittelstet5Anatoly V. Zlotnik6Department of Earth and Atmospheric Sciences University of Nebraska‐Lincoln Lincoln NE USADepartment of Geology and Geophysics University of Utah Salt Lake City UT USADepartment of Marine, Earth, and Atmospheric Sciences North Carolina State University Raleigh NC USASchool of Natural Resources University of Nebraska‐Lincoln Lincoln NE USADepartment of Geology and Geophysics University of Utah Salt Lake City UT USABiological Systems Engineering Department University of Nebraska‐Lincoln Lincoln NE USAApplied Mathematics and Plasma Physics (T‐5) Los Alamos National Laboratory Los Alamos NM USAAbstract A new approach for measuring fluxes across surface water—groundwater interfaces was recently proposed. The Automatic Seepage Meter (ASM) is equipped with a precise water level sensor and digital memory that analyzes water level time series in a vertical tube inserted into a streambed (Solomon et al., 2020, https://doi.org/10.1029/2019WR026983). The ability to infer flux values with high temporal resolution relies on an accurate interpretation of water level dynamics inside the tube. Here, we reduce the three‐dimensional hydrodynamic problem that describes the ASM water level in a variety of field conditions to a single ordinary differential equation. This novel general analytical solution for estimating ASM responses is more comprehensive and flexible than previous approaches and is applicable to the entire range of field conditions, including steady or transient stream stages, evaporation, rainfall, and noise. For example, our analysis determines the timing of the nonmonotonic ASM response to a monotonic linear stream stage variation and explains previously used empirical parabolic approximation for estimating fluxes. We present algorithms for simultaneous inference of vertical interface flux and hydraulic conductivity values together with an example code. We quantify how the accuracy of parameter estimation depends on test duration and noise amplitude and propose how our analysis can be used to optimize field test protocols. On this basis, changing the ASM geometry by increasing the radius and decreasing tube insertion depth may enable ASM field test protocols that estimate interface flux and hydraulic conductivity faster while maintaining desired accuracy. Potential applications of joint parameter estimation are suggested.https://doi.org/10.1029/2023WR034766groundwater fluxeshydraulic conductivityfield methodsautomatic seepage meternoiseaccuracy |
| spellingShingle | Vitaly A. Zlotnik D. Kip Solomon David P. Genereux Troy E. Gilmore C. Eric Humphrey Aaron R. Mittelstet Anatoly V. Zlotnik Theory of an Automatic Seepage Meter and Ramifications for Applications Water Resources Research groundwater fluxes hydraulic conductivity field methods automatic seepage meter noise accuracy |
| title | Theory of an Automatic Seepage Meter and Ramifications for Applications |
| title_full | Theory of an Automatic Seepage Meter and Ramifications for Applications |
| title_fullStr | Theory of an Automatic Seepage Meter and Ramifications for Applications |
| title_full_unstemmed | Theory of an Automatic Seepage Meter and Ramifications for Applications |
| title_short | Theory of an Automatic Seepage Meter and Ramifications for Applications |
| title_sort | theory of an automatic seepage meter and ramifications for applications |
| topic | groundwater fluxes hydraulic conductivity field methods automatic seepage meter noise accuracy |
| url | https://doi.org/10.1029/2023WR034766 |
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