P . 6 Estimations of Model Parameters for Gravity Wave Spectra Observed by Mst

The general theory of MST radar observations of gravity wave spectra is developed in this paper. This effort extends the previous results to include anisotropy and Doppler effects for the spectra, aswellastheconsequencesforthemultibeamconfiguration. The relationships between theobservedoneortwo-dimensionalspectrafortheline-of-sight velocityinthegravitywave spectraare derived.Expressionsforcrossspectra,as wellascovariancesbetweenvelocities observedon different beams,arecomputed. Using theseresults, studiesarecardedouttoshow how model parametersforgravitywave spectracan be estimatedfrom theobservedquantities. Model parametersincludethe variance,power-law indices,anisotropyparameters,Doppler parameters, mean scalesizes, etc.Caseswithdifferentumbersofbeams willbeinvestigated. INTRODUCTION Recently, MST radars have been used by many investigators to study the spectra of velocity fluctuations in the middle atmosphere [Balsley and Carter, 1982; Meek et al., 1985; Scheffler and Liu, 1985; Scheffler and Liu, 1986; Smith et al., 1985; Franke et al, 1988, VanZandt, 1985]. Attempts have been made by these authors to interpret the observed spectra in terms of internal gravity waves. Based on the Garrett-Munk model spectrum for ocean waves, VanZandt [1985] proposed a similar model spectrum for atmospheric waves. Features of the model spectrum have been compared to observed spectra [Smith et al., 1985; Franke et al., 1988]. Inthispaper,we generalize themodel spectrumfortheatmospheretoincludedifferent types of asymmetry in the model. We then derive relations between radar observed quantities and the model parameters. Based on these relations, we propose several observational configurations and data processing schemes in order to determine, experimentally, some of the parameters in the model spectrum. MODEL GRAVITY WAVE SPECTRUM For a general GM type spectrum for gravity waves the following form is assumed: E(0,kz.O) ) = Eo Az(kz,CO)B(¢o) F(0,c0 ) (1) Eo is the energy density constant; kz* is the vertical wave number bandwidth; p and t are the frequency and wave number power law indices, respectively. The corresponding three algebraic model functions are defined as tO kze )(t-1)kz*t-I Az(kz,tO) = 1 + _-_ _zl _,v) (kz,+lkzl) t (2a) B(c0)= p-I lea -P for_ <1o)1< COb,and B(c0)= 0 elsewhere (2b) o}il-P_ C0bl-P https://ntrs.nasa.gov/search.jsp?R=19890020553 2017-09-13T02:00:36+00:00Z