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

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 m²/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.