Effect of atmospheric turbulence on the spot size of a radio-acoustic sounding system: A calculation revisited


  • Richard J. Lataitis,

  • Steven F. Clifford


A theory developed almost 20 years ago suggests that atmospheric turbulence does not significantly alter the average spot size of the radar return from a radio acoustic sounding system (RASS). This theory predicts that the primary effect of turbulence is a reduction of the on-axis intensity and the formation of extended tails in the spot profile, with little or no broadening of the central core of the spot. For a narrow-beam radar, the width of the central core was found to be proportional to the diameter of the radar transmitting antenna. We demonstrate that this conclusion is based on an erroneous numerical evaluation of a fourfold integral that rigorously describes the spot profile. We use an alternate formulation to show that the spot profile can be expressed as a convolution of the radar antenna illumination function and a function whose width depends on the strength of turbulence. This convolution is governed by the ratio W/P0, where W is the horizontal dimension of the radar beam and p0 is the characteristic transverse scale of the turbulence-induced acoustic wavefront distortions, both evaluated at the range R of interest. In weak turbulence (i.e., when Wp0) the spot profile approximates the antenna illumination function. In strong turbulence (i.e., when p0W) the spot profile is significantly broadened and has a diameter proportional to λR/p0, where λ is the radar wavelength. The spot broadening is consistent with recent theoretical and experimental work. The approximate spot profile as a function of turbulence strength for a variety of circularly symmetric antenna illumination functions is examined.