Estimation of vertical water fluxes from temperature time series by the inverse numerical computer program FLUX‐BOT

The application of heat as a hydrological tracer has become a standard method for quantifying water fluxes between groundwater and surface water. The typical application is to estimate vertical water fluxes in the shallow subsurface beneath streams or lakes. For this purpose, time series of temperatures in the surface water and in the sediment are measured and evaluated by a vertical 1D representation of heat transport by advection and conduction. Several analytical solutions exist to calculate the vertical water flux from the measured temperatures. Although analytical solutions can be easily implemented, they are restricted to specific boundary conditions such as a sinusoidal upper temperature boundary. Numerical solutions offer higher flexibility in the selection of the boundary conditions. This, in turn, reduces the effort of data preprocessing, such as the extraction of the diurnal temperature variation from the raw data. Here, we present software to estimate water fluxes based on temperatures—FLUX‐BOT. FLUX‐BOT is a numerical code written in MATLAB that calculates vertical water fluxes in saturated sediments based on the inversion of measured temperature time series observed at multiple depths. FLUX‐BOT applies a centred Crank–Nicolson implicit finite difference scheme to solve the one‐dimensional heat advection–conduction equation. FLUX‐BOT includes functions for the inverse numerical routines, functions for visualizing the results, and a function for performing uncertainty analysis. We present applications of FLUX‐BOT to synthetic and to real temperature data to demonstrate its performance.