The mean rate of dissipation of turbulent kinetic energy is related to the surface fluxes of momentum and heat through the turbulent kinetic energy budget equation, This relationship may be used to estimate surface fluxes from measurements of the dissipation rates. The success of recent applications of the approach has been limited by uncertainties surrounding the functional relationship between the dimensionless dissipation rates and the atmospheric stability parameter. A pair of field experiments was designed and carried out in the atmospheric surface layer to identify this functional relationship over a broad range of neutral and convective flows, covering greater than 3 orders of magnitude in the stability parameter. Mean dissipation rates were computed using Fourier power spectra, second-order structure functions, and third-order structure functions. Arguments are presented for the superiority of the third-order approach. A three-sublayer conceptual model is invoked to guide the dimensional analysis, and the resulting dissipation rates are shown to scale uniquely in the three sublayers. Near the wall, in the dynamic sublayer, dissipation is significantly less than production, as energy is transported up to the more convective regions, where an equality between dissipation and production is achieved.