Uncertainty in thermal time series analysis estimates of streambed water flux

Streambed seepage can be predicted using an analytical solution to the one-dimensional heat transport equation to take advantage of the relationship between streambed thermal properties, seepage flux, and the amplitude ratio and phase shift associated with streambed temperature signals. This paper explores the accuracy of streambed-seepage velocity estimates from this method when uncertainty in input parameters exists. Uncertainty in sensor spacing, thermal diffusivity, and the accuracy of temperature sensors were examined both individually and in combination using Monte Carlo analysis. The analytical solution correctly reproduced known thermal front velocities above 1.25 m d ^-1, using both the amplitude-ratio and phase-shift methods, despite introduced uncertainty in any of the variables. Noise in temperature measurements (because of sensor accuracy) caused erroneous prediction of velocity for gaining stream conditions using both the amplitude ratio and phase shift. Uncertainty in the thermal diffusivity and sensor spacing resulted in incorrect velocity, primarily under gaining conditions, when using the amplitude ratio and near-zero velocity using the phase shift. For a sensor accuracy of 0.15°C, we present combinations of parameters for which the resulting signal amplitude is sufficiently large for use with the Stallman equation.