Radio Science

Mean Vertical Gradient of Potential Refractive Index in Turbulent Mixing and Radar Detection of CAT


  • Hans Ottersten


Radar backscattering from the turbulent clear atmosphere is determined by the small-scale variability in the radio refractive index and is therefore related to the mean gradient of potential refractive index and to the degree of turbulence. Consequently, the mean gradient of potential refractve index is considered in works concerned with radar detection of CAT (clear air turbulence). This note clarifies the role of potential quantities and their vertical gradients in quantitative discussions of the generation of small-scale atmospheric inhomogeneities by turbulent mixing. If potential quantities are referred to a standard pressure of 1000 mb, as is common, the mean vertical gradient of potential refractive index cannot be used directly to evaluate the small-scale refractive-index variability resulting from adiabatic mixing. It is convenient to define a generalized potential refractive index, and a generalized potential temperature as potential quantities referred to the mean pressure at the level under consideration. The refractive-index inhomogeneities produced by turbulent mixing are directly related to the mean vertical gradient of generalized potential refractive index (generalized potential temperature if specific humidity is negligible). The terminology already adopted in several works on radar detection of CAT is preserved if it is emphasized that the potential quantities employed are generalized. Errors of several decibels may result if the ordinary potential quantities referred to 1000 mb are used mistakenly to determine the smale-scale refractive-index variability.