Abstract

Atmospheric precipitation, similar to turbulence (and together with it), causes significant intensity fluctuations $\left({\sigma }_3^2\right)$. They also result in characteristic peculiarities of the intensity fluctuation spectrum [W(f)]. The measurements were carried out along the 130–1310-m path. The He–Ne laser generated at λ = 0.6328 μm. The beam diffraction parameter $\Omega ={k\alpha }_0^2/L\left(k=2\pi /\lambda \right)$ is the wavenumber, α₀ is the effective beam radius). The measurements were made in collimated, divergent, and focused beams. The receiver’s diameter was 0.1 mm. It was noticed that, in precipitation (snowfall, rain) regardless of the laser beam parameters, the turbulence properties are mainly observed in the low-frequency region and those of precipitation in the high-frequency region. In weak precipitation the spectrum had two maxima, and at heavy precipitation it had its hydrometeoric maximum at frequency f_r in the range of several kilohertz. In heavy rains in the region of low frequencies f < f_r the spectrum was described by the dependence W(f) ~ f with satisfactory accuracy. In rain at f > f_r the spectrum decreased as W(f) ~ f^−α. In snowfall at f > f_r the following dependence was observed: W(f) ~ l^−βf. The theoretical conclusion f_r ~ V/d, where V is the terminal rate and d is the mean particle size, was quantitatively verified. On the 130-m path the experimental values of the normalized variance $\left({\sigma }_3^2\right)$ are described by the dependence ${\sigma }_3^2=A+N\tau$, where τ is the optical depth of precipitation. The coefficient N in the divergent beam depends on the particle sizes and increases from 0.3 to 0.8 when increasing the maximum size of particles from 0.1 to 3 cm, respectively. The estimates of turbulence ${\sigma }_T^2$ and snowfall ${\sigma }_c^2$ contributions to the measured variance ${\sigma }_3^2$ were made assuming that they are additive (i.e., ${\sigma }_3^2={\sigma }_T^2+{\sigma }_c^2$). When the maximum diameter of the snowfall particles was <5 mm and τ = 0.4–0.5, the empirical dependence ${\sigma }_c^2=-0.07+0.37\text{log}\Omega$ for Ω values of 0.3–30 was obtained. Measurements of the scattered radiation in the snowfall (Ω = 54, L = 130 m) were carried out at the receiver’s angular distance 10⁻⁴ rad from the beam axis; ${\sigma }_3^2$ at τ > 0.2 was saturated at the leve of ~0.85. Here W(f) had its maximum in the region of a few kilohertz. We concluded that the high-frequency region of the intensity fluctuation spectrum in the divergent laser beam had the largest information content. A focused beam was preferable for studying the turbulence in precipitation.

© 1988 Optical Society of America

Laser beam propagation through the turbulent atmosphere with precipitation

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