Summary
Middle-atmosphere gravity wave spectra of energy against vertical wavenumber are usually assumed to have a log-log slope of -3, based on a number of studies over many years and geographical locations, as well as from theoretical work. A series of simulation runs was performed in order to investigate the criteria required for the satisfactory recovery of the input gravity wave spectrum from lidar data, in the face of the typical signal-to-noise ratios and also from effects due to the waves themselves. The simulations involved taking a model atmospheric density profile, converting to equivalent lidar photon counts by scaling by the inverse square of height and adding photon shot noise corresponding to the photon counts for a given height. To this basic ‘lidar profile’ a number of waves with characteristics typical of middle atmosphere gravity waves were added: the amplitude of the waves were set to be proportional to m1.5 or m1, hence yielding wave populations with energy per unit mass dependencies (proportional to the amplitude squared) of either m3 or m2. The wave frequencies were chosen at random from the interval w=f to w=N, but from a population with an w5/ 3 distribution. Sets of simulations were performed with either 20 or 200 such waves added to the basic lidar profile, for three different values of signal-to-noise ratios. These synthetic ‘added wave’ density profiles were then treated in the same way as real lidar data is analysed, in order to produce profiles of relative density fluctuations as input into harmonic analysis routines. The resulting slopes measured from the calculated power spectra showed, in general, that the analysis procedures used were able to recover the input spectral slope, but often with an error of order of ±0.5 or ±1.0 (i.e. 3.0±0.5, or 3.0±1.0), for an individual simulated data set of effective length comparable to a typical night’s data. The mean of ten such simulations recovered the input slope reasonably well for the cases