Signal power for radio acoustic sounding of temperature: The effects of horizontal winds, turbulence, and vertical temperature gradients

Abstract

A simple expression for the expected average signal power of a radio acoustic sounding system (RASS) comprising a monostatic pulsed Doppler radar and a continuous‐wave broadbeam acoustic source is developed. The effects of horizontal winds, atmospheric turbulence, and vertical temperature gradients are included. Under ideal conditions (i.e., in the absence of winds, turbulence, and gradients) the received signal power is a maximum and, for a broadband acoustic source, is predicted to be proportional to the radar range resolution and inversely proportional to the acoustic bandwidth and square of the range R. Turbulence‐induced distortion of the acoustic wave fronts yields the expected R−26/5 range dependence, provided winds are light. This result is based on the assumption that the turbulence strength does not vary with range. For the more realistic case of turbulence concentrated primarily within the boundary layer (R ≲ 1 km) a much weaker range dependence at longer ranges is predicted. A flattening of the acoustic wave fronts by temperature gradients typical of unstable midday conditions results in an R−6 range dependence, provided winds are light. Turbulence effects are predicted to dominate at shorter ranges (R ≲ 8 km) and gradient effects at longer ranges. The expected compensation of power loss associated with the wind‐induced lateral displacement of the acoustic wave fronts by the turbulence‐ and gradient‐induced broadening of the displaced RASS focal spot is also predicted.

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

“…Equation (1) applies to a uniform, circularly symmetric radar beam pattern function and an acoustic beam that is much wider than the radar beam. The function Dw[R#, R], where R is the sounding range and # = [sin 2 01 + sin 2 02 -2 sin 01 sin 02 cos (4)1 -qb2)] 1/2 is called the wave structure function [Lutomirski and Yura, 1971] and describes the effect of turbulence on the acoustic wave [e.g., Kon, 1984;Lataitis, 1992]. For homogeneous, isotropic turbulence described by the Kolmogorov spatial spectrum In the absence of turbulence, P0 --> o•.…”

“…Turbulence produces both amplitude and phase perturbations across the acoustic wave-front. These perturbations can be included by multiplying the partially reflected field by a complex phase term [e.g., Kon, 1984;Lataitis, 1992]. The total reflected field at range R can then be propagated back to the ground, and the average spot intensity profile computed.…”

“…We note that the parameter a is related to the parameter H of Clifford et al [1978] through H oc ot 5/3. Lataitis [1992] provided that we replace Pt in the development of Lataitis [1992]…”

“…Recent theoretical work contradicts the predictions of Clifford et al [1978]. In particular, Lataitis [1992] and Bauer [1992] predict a RASS spot that broadens as the turbulence strength increases. These derivations involve different types of approximations, but all three developments can be shown to be internally consistent.…”

“…The broadening of the spot profile due to turbulence has not, however, been studied extensively. The result of Lataitis [1992] corresponds to a Gaussian antenna illumination function and an approximate form for the turbulence term that enters into the analysis. The development of Clifford et al [1978] corresponds to a uniform beam pattern (i.e., a uniform angular illumination function with no sidelobes) and an exact expression for the turbulence term.…”