Radiance uctuations from Upper Atmosphere Research Satellite Microwave Limb Sounder (UARS MLS) re ect atmospheric temperature oscillations of short ( ยฟ 30 km) horizontal and long (ยฟ10 km) vertical wavelengths at 38-80 km altitudes. These radiance uctuations often show wave-like structures with clear phase coherence among di erent altitudes. This paper applies a spectral analysis to MLS limb-tracking radiances and obtains a seasonal climatology of horizontal wavenumber spectra at scales of 50 -800 km for 6 altitudes (38, 43, 48, 53, 61 and 80 km) and 8 latitudes (from 70 โข S to 70 โข N). Most of the power spectra exhibit a slope close to -2 but some can be as steep as -3 in wave active regions. The spectral power density is strongly season-and-latitude dependent in the stratosphere, which is thought largely due to the modulation of the background winds on the vertical wavenumber spectrum. The spectral amplitudes grow exponentially with height between 38 and 50 km but the growth rate becomes small or close to zero near and above 50 km. The growth rates at 38-53 km altitudes are scale-dependent showing less e cient vertical propagation for larger-scale waves. The near-zero growth in the lower mesosphere is thought mainly due to wave saturation=breaking at these altitudes.