Although usage of the inverse solution of the one-dimensional advection-diffusion equation for estimating streambed fluid fluxes, bed elevation changes, or bed thermal diffusivity have historically assumed the need for sinusoidal or at least nominally sinusoidal surface boundary temperature fluctuations, it is technically not a requirement. It has similarly been assumed that gradients in temperature in the bed would cause errors in parameter estimates. A published mathematical derivation (Luce et al., 2017) demonstrates that this is not true, but laboratory experiments and numerical modeling were done to support the illustration of the consequences of the derivation. These data are supplied here.

Reference:
Luce, C. H., Tonina, D., Applebee, R., & DeWeese, T. (2017). Was that assumption necessary? Reconsidering boundary conditions for analytical solutions to estimate streambed fluxes. Water Resources Research. doi: 10.1002/2017WR020618