Application of Recursive Estimation to Heat Tracing for Groundwater/Surface‐Water Exchange

Abstract

Heat has been used as a tracer to estimate groundwater/surface-water exchange and hydraulic properties since pioneering work by Stallman in the 1960s (Anderson, 2005;Constantz, 2008;Stallman, 1965). The measurement technology (e.g., thermistors and thermocouples) is relatively inexpensive, long-term field installations are possible, and data analysis is straightforward. The increasing interest in hyporheic, hypolentic, and hypopaludal processes over the last two decades has led to burgeoning applications of heat tracing below the sediment water interface (e.g.,

Shallow and local or deep and regional? Inferring source groundwater characteristics across mainstem riverbank discharge faces

“…The recursive estimation methods require an estimate of discharge process variance, a parameter related to expected system noise and true short‐term discharge flux variability. As in the McAliley et al (2022) study, we found that setting the process variance parameter values from 1 × 10 −4 to 1 × 10 −5 m/day for EKF models reduced model output noise and preserved real, abrupt changes in discharge flux. Smaller values of process variance tended to overly smooth the discharge flux patterns to show little change at multiweek timescales even during known variation in river flow.…”

“…Kalman Filters have recently been more commonly applied to hydrologic problems (e.g., Kang et al, 2018;Shapiro & Day-Lewis, 2021, 2022Sun et al, 2016). The methodology used here has been previously tested on both synthetic and field data in McAliley et al (2022) where EKF methods were shown to converge to step changes in synthetic discharge data on sub-daily timescales, and residuals between observed (i.e., field observations) and estimated (i.e., EKF predictions) temperature observations were generally within 0.1 C, consistent with expected measurement precision. Further information on the numerical implementation, comparisons to synthetic and field observations, as well as links to open-source code can be found in McAliley et al (2022).…”

A multi-scale temperature-based strategy to map hydrologic exchange flows in highly dynamic systems

“…We use the recently published tempest1d library (McAliley et al, 2022a;McAliley et al, 2022b) to analyze the VTP data. tempest1d includes tools for analysis of VTP data collected in highly dynamic systems subject to rapid changes and reversals in flux.…”

“…Temperature measurement error was assumed to be Frontiers in Earth Science frontiersin.org gaussian white noise with a standard error, σ, of 0.04 °C based on the sensor resolution and the relation σ R/ 3 √ . The process noise was also assumed to be gaussian white, with zero mean and a variance found according to the discrepancy principle (McAliley et al, 2022a); this automated approach identifies the process variance such that the measurement misfit is consistent with the assumed standard error. Data from the 0.05-m and 0.35-m thermistors were used to define boundary conditions for the 1D heat-transport model, and data from the interior thermistors were used for calibration.…”

Geoelectric Characterization of Hyporheic Exchange Flow in the Bedrock‐Lined Streambed of East Fork Poplar Creek, Oak Ridge, Tennessee

“…Heat‐tracing methods, used in alluvial rivers since the 1960s, generally have limited uses in bedrock riverbeds with the exception of the use thermal infrared cameras that image the temperature distribution of the stream surface and distributed temperature sensing (DTS) methods used on the riverbed and within the stream (Anderson, 2005; Briggs et al., 2012; Hare et al., 2015; Mamer & Lowry, 2013; McAliley et al., 2022; Mohamed, Gabrielli, et al., 2021; Rosenberry et al., 2016). DTS methods provide near‐continuous temperature data on the riverbed or within the SW through time at fine spatial scales of about 1 m over distances of a few kilometers (Rosenberry et al., 2016) and offer a plausible alternative to point‐scale heat tracing in bedrock rivers, because SW is strongly affected by diurnal and annual temperature variations whereas GW temperature remains close to the mean annual air temperature.…”