The Importance of Thermal Dispersivity in Predicting Water Movement Through Coarse-grained Alluvial Aquifers by Analysis of Seasonal Temperature Signals

Abstract:

In the last decade, there has been a surge in research on the use of time-varying temperature records (e.g. diel temperature) to estimate seepage velocity of water across stream channel boundaries into or out of the hyporheic zone. The hallmark of this research is the use temperature signals measured over length scales of a few meters to determine the properties of interest. Application of the methods at the river reach scale (e.g. tens of meters) using seasonal temperatures signals has not been explored. For instance, research in the Umatilla River basin in north central Oregon USA shows that seasonal temperature records from the hyporheic zone exhibit characteristic phase lagging and amplitude damping that closely matches similar characteristics observed in diel temperature signals typically used to estimate streambed seepage velocity. We demonstrate that at these larger scales, aquifer thermal dynamics are controlled by mechanical dispersion rather than thermal conduction. The trade-off between conduction and dispersion is apparent in plots of the ratio (r) of dispersive to conductive forces verses the thermal Peclet number (Pe). Plotting a range of analytical solutions for r and Pe over a range of hydraulic conductivities and dispersivities allows visual comparison of of their relative position in a spreading-transport domain. We show that when dispersivity and velocity are large, dispersion governs both spreading and transport processes of thermal energy in contrast to conduction. This finding is analogous to well-known findings from solute transport theory that show a trade off from conductive forces to dispersive forces as both scale and velocity increase. Furthermore, we demonstrate that when reasonable values for dispersion are not included in analytical temperature solutions using seasonal temperature records, unrealistic minimal amplitude damping results. Our results suggest that incorporating dispersion into analytical and modeling solutions is key to understanding annual water temperature dynamics in semi-arid streams.