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Horizontal winds in the mesosphere have been measured over Ascension Island (8° S, 14° W) in the tropical mid-Atlantic region throughout the years 2002-2011. The observations were made by a very high frequency (VHF) meteor radar. The observations reveal the presence of atmospheric tides of large amplitude. The observations are analysed to characterise the seasonal and interannual variability of the diurnal and semidiurnal tides. Monthly-mean diurnal tidal amplitudes are found to reach values as large as 48 m s-1 in the meridional component and 41 m s-1 in the zonal. A semiannual seasonal variation is found in diurnal tidal amplitudes with amplitude maxima at the equinoxes and amplitude minima at the solstices. Diurnal tidal meridional vertical wavelengths are generally in the range 24-30 km. The diurnal zonal vertical wavelengths are similar to the meridional, except for the winter months when the zonal vertical wavelengths are much longer, occasionally exceeding 100 km. Semidiurnal amplitudes are observed to be significantly smaller than diurnal amplitudes. Semidiurnal vertical wavelengths range from 20 to more than 100 km. Our observations of tidal amplitudes and phases are compared with the predictions of the extended Canadian Middle Atmosphere Model (eCMAM) and the Whole Atmosphere Community Climate Model (WACCM). Both eCMAM and WACCM reproduce the trend for greater diurnal amplitudes in the meridional component than the zonal. However, eCMAM tends to overestimate meridional amplitudes, while WACCM underestimates both zonal and meridional amplitudes. Vertical wavelength predictions are generally good for both models; however, eCMAM predicts shorter diurnal zonal vertical wavelengths than are observed in winter, while WACCM predicts longer zonal vertical wavelengths than observed for the semidiurnal tide for most months. Semidiurnal amplitude predictions are generally good for both models. It is found that larger-than-average diurnal and semidiurnal tidal amplitudes occur when the stratospheric quasi-biennial oscillation (QBO) at 10 hPa is eastwards, and smaller-than-average amplitudes occur when it is westwards. Correlations between the amplitude perturbations and the El Niño Southern Oscillation are also found. The precise mechanism for these correlations remains unclear.