Quantifying the effect of in-stream rock clasts on the retardation of heat along a stream

With the introduction of Distributed Temperature Sensing (DTS) into the field of hydrology, temperature has
become a powerful tracer in both space and time. However, the interpretation of the observed temperature
signal is often not straightforward due to its non-conservative behavior. The objective of this research is to
explore and quantify the retardation of heat along a small first order stream, with the long-term objective of
identifying different runoff mechanisms by using heat as a tracer.
We carried out two tracer experiments. A small water storage basin was emptied into the stream over time
periods of 50 and 18 min increasing stream discharge roughly by a factor of two. Salt was added as a tracer in
both experiments. In the second experiment the temperature of the added water was additionally cooled to
about 0 °C by adding snow into the storage basin. The electrical conductivity was measured at three points
along the 565 m long stream, while the temperature was measured with a resolution of 2 m and 3 min using
the DTS system. During the second experiment, we observed a significant time lag between the salt
breakthrough curves (BTC) and the heat BTCs. We routed the water with a hydraulic model, which we
coupled with a 1-D advection-dispersion model, and in case of heat we also coupled it with an energy
balance. We used the salt BTCs to calibrate the transient storage zones, after which we applied the energy
balance to simulate the heat BTCs.
Although heat exchange with the streambed delays the advection of heat, it could not fully explain the retarded
BTC we observed. We hypothesize that the retardation of heat is caused by its storage in the many rock clasts
present in the stream and positioned on top of the streambed.
To allow for water-rock clast interaction, we included the fraction of rock clasts in the storage term of the
advection–dispersion equation. In this approach we only have to add one additional parameter to account for
the fraction of rock clasts in the cross-sectional area of the stream. By applying a fraction of 35% we were able to
simulate the retarded heat BTC correctly. Although the fraction of rock clasts in the stream will change with
different water levels, it is a straightforward approach, which enables us to couple the hydraulic model directly
with the advection–dispersion model, while ensuring that the retardation of heat is simulated correctly.