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Taylors' frozen turbulence hypothesis suggests that all turbulent eddies are advected by the mean streamwise velocity, without changes in their properties. This hypothesis has been widely invoked to compute Reynolds averaging using temporal turbulence data measured at a single point in space. However, in the atmospheric surface layer, the exact relationship between convection velocity and wave number k has not been fully revealed since previous observations were limited by either their spatial resolution or by the sampling length. Using Distributed Temperature Sensing (DTS), acquiring turbulent temperature fluctuations at high temporal and spatial frequencies, we computed convection velocities across wave numbers using a phase spectrum method. We found that convection velocity decreases as k(-1/3) at the higher wave numbers of the inertial subrange instead of being independent of wave number as suggested by Taylor's hypothesis. We further corroborated this result using large eddy simulations. Applying Taylor's hypothesis thus systematically underestimates turbulent spectrum in the inertial subrange. A correction is proposed for point-based eddy-covariance measurements, which can improve surface energy budget closure and estimates of CO2 fluxes.