An analytical model of multi-layered heat transport to estimate vertical streambed fluxes and sediment thermal properties

Using heat as a tracer to estimate the vertical streambed fluxes (VSFs) and sediment thermal properties, the choice of mathematical models of heat transport is critical for the accuracy of estimated values. In this study, a new analytical model of heat transport in a multi-layered streambed is developed with arbitrary boundary conditions, arbitrary initial conditions, a velocity-dependent effective thermal diffusivity, and time-variant VSFs, which is named the MLT model. A finite-difference solution and field experimental data are employed to test the MLT model. The particle swarm optimization (PSO) algorithm is employed to estimate VSFs and streambed sediment thermal properties. Results show that the MLT model releases the limitation included in the one-layered streambed models in parameter estimation that the observation locations have to be within a sub-layer of the streambed. The MLT model coupled with the PSO method can accurately estimate the VSFs and thermal properties of each layer in a multi-layered streambed system using only one observation point, and the location of the observation point has no impact on the accuracy of parameter estimation when using the MLT model. The Morris global sensitivity analysis reveals that heat transport in the layered streambed system is most sensitive to VSFs, and followed by the effective thermal diffusivity of the upper streambed layer, the effective thermal diffusivity of the lower streambed layer, and the thickness of the upper streambed layer. The field application shows that the MLT model outperforms the previous models in terms of interpreting field data, and the location of interfaces between streambed layers could be estimated by the MLT model.