Theory of an Automatic Seepage Meter and Ramifications for Applications

• Published in: Water resources research 2023-10, Vol.59 (10), p.n/a
• Main Authors: Zlotnik, Vitaly A., Solomon, D. Kip, Genereux, David P., Gilmore, Troy E., Humphrey, C. Eric, Mittelstet, Aaron R., Zlotnik, Anatoly V.
• Format: Article
• Language: English
• Subjects: Accuracy; Algorithms; Approximation; automatic seepage meter; Differential equations; Empirical analysis; Evaporation; Exact solutions; field methods; Field tests; Fluctuations; Fluxes; Groundwater; groundwater fluxes; Hydraulic conductivity; Interfaces; Mathematical analysis; Mathematics; noise; Ordinary differential equations; OTHER INSTRUMENTATION; Parameter estimation; Rainfall; Rivers; Seepage; Streambeds; Surface water; Surface-groundwater relations; Temporal resolution; Test procedures; Water levels
• ISSN: 0043-1397; 1944-7973
• DOI: 10.1029/2023WR034766

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. Key Points A generalized equation of water level dynamics in the Automatic Seepage Meter valid for a variety of field conditions The theory considers surface water level fluctuations, evaporation, rainfall, and ambient noise Water flux and vertical hydraulic conductivity estimation accuracy is analyzed with examples and recommendations