BDFLUX: A new bounded domain model for quantifying vertical fluxes in streambeds using heat as a tracer

The use of heat as a tracer has become a widely used approach to estimate vertical streambed fluxes (VSFs). We present BDFLUX, a new bounded domain model that can be used as a rapid-screening tool to quantify VSFs and thermal properties of streambed sediments by analyzing on-site temperature–time series. BDFLUX uses a closed-form analytical solution that takes thermal advection and thermal conduction into account. BDFLUX, unlike other one-dimensional closed-form analytical solutions, does not assume a semi-infinite half-space. The initial and boundary conditions are described by arbitrary functions that can be directly determined by fitting the measured temperature–time series in the streambed at various depths. The particle swarm optimization (PSO) method and Markov Chain Monte Carlo (MCMC) method are used to estimate VSFs using temperature–time series observed at three depths. BDFLUX is validated using synthetic temperature–time series, demonstrating that it can perform well when the top and bottom boundary conditions are determined directly by the measured data. The capabilities of BDFLUX are further evaluated using laboratory and field data. The simulation results show that BDFLUX performed well in terms of interpreting laboratory experiments and field data, with a root mean square error as low as 0.059. The simulation of laboratory experiments shows that the MCMC method has a lower computational efficiency than PSO method. The magnitude of nonvertical flow components at a field site were quantified by analyzing the results of estimated VSFs in different vertical subdomains. Overall, BDFLUX improves one-dimensional heat analytical models in terms of assessing the magnitude of the nonvertical flow component in heterogeneous streambed sediments.