Calculational results for a wavelength of 11 /rm are shown in Fig. 8. Because of the large particle diameters in the rain distributions, Qex and Qa rapidly converge to values of 2 and 1, respectively, as we integrate from a, to a2. For R > 0.1 mm/h, therefore, the present results are effectively independent of wavelength for wavelengths in the infrared, and depend only upon the explicit details of the particle distribution. Observational measurements, however, show distinct differences between the total attenuation coefficient for different wavelengths, partly due to differences in molecular absorption. Few measurements of the attenuation of laser radiation due to rain have been performed; Chu and Hogg (29) made observations at 0.63, 3.5, and 10.6 gm during periods of rainfall largely free of accompanying fog. They observed greater attenuation at 10.6 gm than at the shorter wavelengths, and we have plotted their data in Fig. 8. The curve labelled is a least-squares fit to their experimental data and represents total attenuation due to all processes. The curve labelled is the estimated extinction coefficient, found by subtracting the molecular absorption and clear-air background aerosol attenuation from Because the relative humidity during the summer showers reported by Chu and Hogg approaches 100%, the molecular absorption coefficient was calculated at 10.6 /zrn using the code laser and the tropical summer atmospheric model. We notice that the corrected extinction curve thus obtained is in good agreement with theoretical predictions using the continuous rainfall particle distribution. Wilson and Penzias (46) found values of ^/R in the range 2.3-2.8 x 10 2 km-1 mm ' h for/? < 50 mm/h, in good agreement with our theoretical predictions without any correction. Obviously, the range of and /?„ observed at a particular rainfall rate is due to variations in the particle distributions. Snow. Little theoretical or observational data of laser propagation in snow exists. Observational measurements taken by Chu and Hogg (29), Wilson and Penzias (46), Soklov (47), and Nakajima et al. (48) show severe attenuation for moderate precipitation rates, and preliminary measurements indicate that the attenuation at 10.6 gon is significantly greater than at 0.63 and 3.5 gun. We have estimated the value of /3n and /3a as functions of the snowfall rate R using two models. In the equivalent liquid-drop model, Sekhon and Srivastava (49) found that the particle distribution of melted snow crystals is given by Here, D is the liquid drop diameter (mm) and R is the melted snowfall rate (mm/h). In the second model, called the aggregate snowflake model, we use the actual particle size distribution which can also be represented in the Marshall-Palmer functional form. To obtain the snowflake diameter, the relationship between particle masses in the liquid and ice-crystal forms is used: where p is the density, D is the particle diameter, and the subscripts L and i denote liquid and ice forms, respectively. Passarelli (50) found that 3, from which we obtain
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