Spectral scaling of heat fluxes in streambed sediments

Advancing our predictive capabilities of heat fluxes in streams and rivers is important because of the effects on ecology and the general use of heat fluxes as analogues for solute transport. Along these lines, we derived a closed-form solution that relates the in-stream temperature spectra to the responding temperature spectra at various depths in the sediment through a physical scaling factor including the effective thermal diffusivity and the Darcy flow velocity. This analysis considers the range of frequencies in temperature fluctuations that occur due to diurnal and meteorological variation both in the long and short term. This approach provides insight regarding the key frequencies for analysing temperature responses at different depths within the sediment and also provides a simple and accurate method that offers quantitative insight into heat transport and surface water interactions with groundwater. We demonstrate for Sva Brook, Sweden, how the values of effective thermal diffusivities can be estimated based on the observed in-stream and sediment temperature time series and explain the temporal scaling of the heat transport as a function of a dimensionless frequency number. We find that the lower limit of periods of significance for the analysis increases with depth, and we recommend further research regarding appropriate frequency windows.