Assessing the accuracy of 1‐D analytical heat tracing for estimating near‐surface sediment thermal diffusivity and water flux under transient conditions

Abstract

Amplitude decay and phase delay of oscillating temperature records measured at two vertical locations in near-surface sediments can be used to infer water fluxes, thermal diffusivity, and sediment scour/deposition. While methods that rely on the harmonics-based analytical heat transport solution assume a steady state water flux, many applications have reported transient fluxes but ignored the possible violation of this assumption in the method. Here we use natural heat tracing as an example to investigate the extent to which changes in the water flux, and associated temperature signal nonstationarity, can be separated from other influences. We systematically scrutinize the assumption of steady state flow in analytical heat tracing and test the capabilities of the method to detect the timing and magnitude of flux transients. A numerical model was used to synthesize the temperature response to different step and ramp changes in advective thermal velocity magnitude and direction for both a single-frequency and multifrequency temperature boundary. Time-variable temperature amplitude and phase information were extracted from the model output with different signal-processing methods. We show that a worst-case transient flux induces a temperature nonstationarity, the duration of which is less than 1 cycle for realistic sediment thermal diffusivities between 0.02 and 0.13 m 2 /d. However, common signal-processing methods introduce erroneous temporal spreading of advective thermal velocities and significant anomalies in thermal diffusivities or sensor spacing, which is used as an analogue for streambed scour/deposition. The most time-variant spectral filter can introduce errors of up to 57% in velocity and 33% in thermal diffusivity values with artifacts spanning ±2 days around the occurrence of rapid changes in flux. Further, our results show that analytical heat tracing is unable to accurately resolve highly time-variant fluxes and thermal diffusivities and does not allow for the inference of scour/depositional processes due to the limitations of signal processing in disentangling flux-related signal nonstationarities from those stemming from other sources. To prevent erroneous interpretations, hydrometric data should always be acquired in combination with temperature records.

Estimating interaction between surface water and groundwater in a permafrost region using heat tracing methods

“…The streambed vertical fluxes are calculated by the extracted 5 daily sinusoidal component of temperature (Rau et al, 2015). The one-dimensional heat convection conduction equation is (Eq.…”

“…However, temperature gradient measurements beneath the streambed combined with an analytical or numerical heat transfer model can only estimate point groundwater discharge (Rau et al, 2015). The application of distributed temperature sensors along river reaches can identify large spatial variations, significantly increasing the spatial and temporal scale of temperature observations (Hatch et al, 2010;Krause et al, 2012;Selker et al, 2006), but this method cannot provide estimations of 30…”

“…Lautz (2012) and Rau et al (2015) have 25 shown that the quantification using heat tracing methods based on the assumption of harmonic temperature data can lead to potentially flawed flux estimates. Thus, we focused only on the direction and variation of the thermal front velocity (v), rather than calculating the Darcy velocity (q) and effective thermal diffusivity.…”

“…the nature of the flood hydrograph as well as return flow to bank storage), complicates the system's thermal response. Thus, the use of heat tracing methods based on the assumption of harmonic temperature data will lead to potentially flawed flux estimates (Rau et al, 2015).…”

“…Since common signal-processing methods introduce erroneous temporal spreading of advective velocities and significant anomalies (Rau et al, 2015), we developed a semi-automated computer program for deriving amplitudes and phases from the 30 temperature data to delineate the noise signal in the temperature-time signal. The program selects the peak temperature and The Cryosphere Discuss., https://doi.org /10.5194/tc-2017-176 Manuscript under review for journal The Cryosphere Discussion started: 5 September 2017 c Author(s) 2017.…”