An innovative solution of diurnal heat transport in streambeds with arbitrary initial condition and implications to the estimation of water flux and thermal diffusivity under transient condition

Abstract

Diurnal heat signal has been widely used to infer the seepage flux and thermal diffusivity in streambeds. The theoretical basis is the one-dimensional (1−D) analytical solution of heat advection-dispersion equation with sinusoidal boundary condition and homogeneous initial condition (Stallman, 1965). However, the assumption of homogeneous initial condition made in Stallman (1965) is physically unrealistic and the assumption of steady flow is often violated when water level changes rapidly (e.g., flooding). To incorporate the realistic initial condition, an innovative solution for 1−D heat transport with sinusoidal boundary condition and arbitrary initial condition is proposed. This solution makes it possible to accurately simulate heat transport with transient flux by sequentially applying the new solution at small time interval. Synthetic temperature signals at different depth of streambeds are generated to study the impact of transient flux to the estimation of water flux and thermal diffusivity. Here are some major findings. Firstly, the calculated flux is sensitive to the flux dynamics. The faster the flux increases or decreases, the less accurate the calculated flux is. Secondly, using temperature time series from deep sensor pair is more likely to cause erroneous estimation of flux because heat signal damps fast with depth. Thirdly, the heat tracer method for estimating water flux is sensitive to the thermal properties of saturated sediments. Large thermal diffusivity leads to high uncertainty for flux estimation.