FIELD EXPERIMENTS ON DIFFUSION OF SPORE-CLOUDS Several experiments have now been reported that give data from which it is possible to test the applicability of eddy diffusion theories to diffusion of the spore-cloud in a horizontal direction.
Stepanov (1935) used artificial sources of spores that were liberated at a point in the open air. He trapped the spores on glass slides, coated with glycerine jelly, placed on the ground at various distances from the source and in various directions relative to the wind. At the end of the experiment cover-glasses were placed on the slides, and the number of single spores per unit area was counted (spore clusters were disregarded).
In Experiment i (28 July 1933), on a lawn near the Middle Neva River, Elagin Island, Leningrad, approximately 1.2 x log spores of Tilletia caries were disseminated into the air through gauze, at a height of about 8o to cm. above the ground. According to anemometer readings the wind varied from 0.5 to 4•0 metres per sec., but sometimes fell to a complete calm; its direction was also variable. Two glass slides were placed at each trapping position, the numbers of spores trapped being shown in Table V.
Experiment 2 (5 September 1933) was made at the same place as the previous one. This time a mixture of spores of Tilletia caries and Bovista plumbea was disseminated through a small sieve at a height of about 150 cm. Scattering of the spores occupied 15 minutes, after which 3o to 35 minutes were (perhaps unnecessarily) allowed to elapse for the deposi tion of the spores. During this period the wind mostly varied from 2.3 to 3•0 metres per sec., but was sometimes calm. As shown in Table VI, three slides were placed at each trapping position. Approximately 1.8 x log spores of Tilletia were used but those of Bovista were unfortunately not estimated.
Stepanov's results led him to an empirical law of spore dispersal which was expressed as: y = C a/sx, where `y' = the distance at which the spores were trapped, x = the number of spores deposited per unit area of trap surface, s = area of trap surface, and `C' and `a' are parameters dependent on the conditions of the experiment. The number of spores deposited is thus regarded as varying inversely as the first power of the distance from an origin of co-ordinates that is not coincident with the source.
It will be shown later that Stepanov's formula, which is the first fruits of the experimental approach to the problem, needs modification if it is to describe spore dispersal over a wide range of conditions (Gregory, 1945). First it will be necessary to re-examine Stepanov's results in the light of present knowledge of eddy diffusion.
Stepanov's observational data enable us to test whether the standard deviation, a, of the spores from their mean position agrees with Sutton's form: = or with the older diffusion theories where a2 = 2Kt. The data also allow us to estimate the parameters ni and C, which can then be compared with values obtained by meteorologists for similar conditions. Examination of Tables V and VI shows that the spores at any one distance do not lie in a smooth normal frequency distribution, but are significantly clumped. This is probably because the duration of the dis persal operation was insufficient to smooth out the action of a few large scale eddies.
The standard deviations of spores lying at each distance from the source have been calculated for Table VII, where for convenience the deviations from the mean position at each distance were measured along the arc with the point source as centre. The standard deviation at each distance was calculated from the usual formula, a = A/[(x — — i)]. This is not strictly legitimate, because the trapped spores are a systematic instead of a random sample of the population and should be regarded as estimates of the ordinate of a normal frequency curve. However, the formula clearly gives a useful approximation—which would have been better if the traps had extended farther laterally and if data for some of the intermediate radii had not been missing.
Both experiments were done in the same place, and with comparable wind velocities, and when values for log a are plotted against log x the points are found to lie reasonably close to a straight line. The slope of this line is not unity, as it would have been with the older diffusion theories, but corresponds with Sutton's formula for Q, where C = o•64 (metre)*, and m = P76. Sutton's work was apparently unknown to Stepanov when these experiments were done, and so the data could not at the time be analysed in terms of eddy diffusion. However, the agreement between experiment and theory provides evidence that spore dispersal in air is mainly controlled by eddy diffusion of the type postulated by Sutton (see Table VII). The values for C and m obtained from Stepanov's experiments agree well with those found in spore dispersal tests by other workers (Table VIII), and with comparable data obtained by Richardson (192o) for dispersal of smoke from a point source over distances of tens of metres, where C = o•6 (metre)*, and in = 1•75.
E. E. Wilson & Baker (1946) liberated Lycopodinln spores at 7.5 ft. above ground-level and caught them, not on glass slides on the ground as Stepanov had done but, because they were interested in diseases of fruit trees, on vertical sticky slides placed on three vertical posts at 1.5, 3•0, and 5.1 metres down-wind from the source, and at thirteen heights above ground at each distance; seven tests were done at wind speeds ranging from P7 to 7.2 metres per sec. Other tests measured the horizontal dispersion. Nilson & Baker calculated the standard deviation of the spores deposited at each distance in each test, and from their values for a we can now esti mate the parameters for Sutton's equation. In a few individual experi ments their values obtained for in lay outside the limits of 1.24 and postulated by Sutton. But their mean value is ill = P74—thus agreeing well with Sutton's theory (in = 1.75) and with Stepanov's experimental value (in = r76). 'Though their values for agree well with Sutton's findings, those for are much higher, but agree with those of Gregory, Longhurst & Sreeramulu (unpublished).