Heat flux between river water and riverbed contributes significantly t
o river water heat content and river temperature, especially in shallo
w rivers. A numerical model of heat conduction in a riverbed was verif
ied with detailed temperatures measurements in a riverbed. Three diffe
rent methods, the heat budget method, the gradient method, and an inve
rse method, were used alternatively for the estimation of the riverbed
heat flux. Propagation of uncertainty in the riverbed temperature mod
el was studied using a vector state space perturbation method. Output
uncertainty was estimated by random perturbations of the effective the
rmal conductivity from the main value. The coefficient of variation of
effective thermal conductivity was 0.1. Temperatures and heat fluxes
in the riverbed were affected by the uncertain thermal conductivity.