[7] Different methods of determining atmospheric turbulence parameters have been discussed [*Hocking*, 1985; *Nastrom et al.*, 1986; *Rao et al.*, 1997, 2001; *Satheesan and Murthy*, 2002; *Ghosh et al.*, 2003]. There are three methods for determining turbulence parameters using radar spectral parameters, namely, (1) power, (2) spectral width, and (3) variance methods. Actually, there are two methods that make use of observed spectral width, namely, spectral width method 1 and spectral width method 2. In spectral width method 1, Brunt-Vaisala frequency *N* is required for estimation the turbulence parameters, which are normally derived from the in situ measurements of temperature. In spectral width method 2, only the antenna characteristics are used and no temperature measurements are required. Estimation of turbulence parameters using spectral width method 2 may not be possible to find accurately at the height where wind shear is high [*Cohn*, 1995]. *Hocking* [1996] and *Nastrom and Eaton* [1997a] reported that the spectral width method 2 is appropriate only in the lower atmosphere below 5 km, whereas width method 1 is more appropriate at higher altitudes. So, in the present study, spectral width method 1 is used for estimating turbulence parameters like (1) eddy dissipation rate (ɛ), (2) eddy diffusivity (*K*_{h}), (3) buoyancy scale size (*L*_{B}), and (4) the minimum scale size (*l*_{0}). The spectral width method makes use of the observed radar received signal half spectral width to determine ɛ [*Cunnold*, 1975; *Sato and Woodman*, 1982; *Hocking*, 1983, 1985; *Fukao et al.*, 1994; *Jain et al.*, 1995; *Nastrom and Eaton*, 1997a, 1997b; *Rao et al.*, 1997, 2001; *Ghosh et al.*, 2003]. It is to be noted that, spectral width is estimated using oblique beam instead of vertical beam as MST radar (53 MHz) vertical beam is very sensitive to specular reflections. Thus, the spectral width is estimated from the oblique beam as oblique beam is largely free from Fresnel scattering/reflection [*Rotteger and Larsen*, 1990]. The effect of specular reflections is free beyond 10° oblique beam [*Gage and Balsley*, 1980]. However, the observed radar signal spectral width (*σ*_{1/2obs}) in the oblique beam consist of real spectral width (*σ*_{1/2}) due to backscattering from refractive index irregularities associated with atmospheric turbulence along with (1) beam broadening due to finite beam volume (*σ*_{1/2beam}), (2) broadening due to wind shear (*σ*_{1/2shear}), and (3) also contamination due to transience effect (*σ*_{1/2transit}) [*Atlas et al.*, 1969; *Sato and Woodman*, 1982; *Hocking*, 1983, 1985, 1986, 1996; *Hocking and Lawry*, 1989; *Fukao et al.*, 1994; *Jain et al.*, 1995; *Rao et al.*, 1997; *Nastrom and Eaton*, 1997a, 1997b; *Ghosh et al.*, 2003]. Another effect by which spectral width may be contaminated is due to the gravity waves (*σ*_{1/2wave}) [*Murphy et al.*, 1994; *Nastrom and Eaton*, 1997a]. That is the measured signal spectral width *σ*_{1/2obs} may be contaminated by nonturbulent factors and thus, the broadening corrected spectral width *σ*_{1/2} is given by:

The contribution of the spectral width due to beam and shear broadening are given by [*Hocking*, 1983, 1985, 1986; *Ghosh et al.*, 2003]:

where *U*_{h} and ∣∣ are the horizontal wind speed and vertical shear of horizontal wind respectively with height (*z*). For Gadanki MST radar, the half power half width (*δ*_{1/2}) of the two way radar beam (1.1°) is 0.0019 rad. Before calculating the wind shear, the wind data are also averaged over ∼30 min to remove the high-frequency fluctuation.

[8] It is to be noted that in the present analysis the number of incoherent integration of the spectrum is unity (see Table 1), and the beam dwell time is estimated to be 16 s. Thus, the spectral width contamination due to transience effect (*σ*_{1/2transit}) is minimal and can be neglected for the present analysis. However, the effects of gravity wave on spectral broadening is estimated by using hourly mean standard deviation of vertical velocity (mode 2 experiment) as described by *Nastrom and Eaton* [1997a]. The estimated (*σ*_{1/2wave})^{2} is again reduced by a factor 3/4 to account for a circular shape of MST radar beam pattern instead of square [*Nastrom and Eaton*, 1997a]. In the present analysis, (*σ*_{1/2wave})^{2} is found to be relatively very small compared to the other correction factors and thus, the effect of gravity wave is neglected. The details of the spectral width correction can also be found elsewhere [e.g., *Hocking*, 1983, 1985, 1986; *Murphy et al.*, 1994; *Nastrom and Eaton*, 1997a; *Ghosh et al.*, 2003, and references therein].

#### 3.2. Vertical Eddy Diffusivity

[10] The vertical eddy diffusivity *K*_{h} is defined by the kinematic heat flux and vertical gradient of the mean potential temperature, i.e.,

where *w* is the vertical velocity, θ is potential temperature, and the over bar and the prime denote the mean field and the perturbations, respectively.

[11] From the consideration of energy budget of the turbulence and the definition of the static stability parameter (*N*^{2}) it can be shown [*Fukao et al.*, 1994] that

where *R*_{f} is the flux Richardson number. It should be noted that the above expression gives a local value of K_{h} for locally homogeneous turbulence (say for each radar volume cell).

[12] *Lilly et al.* [1974] used a value of 0.25 for *R*_{f} and obtained *β* = 1/3 = 0.33. This value of *β* is also consistent with the generalized formulation as given by *Weinstock* [1981] where the dominant turbulence scale is slightly smaller than the buoyancy scale. Equations (4), (5), and (6) yield

#### 3.3. Scale Size of Turbulence

[13] The inner scale and buoyancy scale size are important for the discussion of turbulence. The inner scale size of turbulence *l*_{0} is estimated using the relationship

where *η* is the Kolmogorov microscale.

and

where *υ*, ɛ and *ρ* are the kinematic viscosity, eddy dissipation rate and the atmospheric density, respectively. Atmospheric density for determination of *η* and *l*_{0} is taken from the model by *Sasi and Sen Gupta* [1986], which is a representative model for Indian tropical region.

[14] The buoyancy scale *L*_{B} determines the transition scale lengths between the inertial and buoyancy range and the same is given by [*Weinstock*, 1978; *Hocking*, 1985; *Jain et al.*, 1995]

It should be mentioned here that equation (8) is applicable only to shear generated turbulence in statically stable atmosphere. For convective turbulence, *N*^{2} < 0 and therefore above equation would not be meaningful.