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Joanne Simpson, William L. Woodley, Anthony Olsen, and Jane C. Eden


Randomized dynamic cumulus seeding programs were executed in 1968 and 1970 on isolated clouds and beginning in 1970 on groups of clouds, to promote mergers in a 4000 mi2 target area in south Florida. With the single clouds, 26 seeded and 26 control cases comprise an adequate sample. In the area experiment, 1970 1971 and 1972 produced only 7 random seed, 5 random control, and 5 non-random control cases. The experiments involve a multi-pronged approach to documentation of seeding effects, emphasizing numerical simulation, ground and airborne measurements, and the application of diverse statistical tools, including but not confined to Bayesian analysis, the main subject of this report.

Rain volumeswere calculated with calibrated 10-cm radars, checked and corrected by gage networks. The single cloud rainfalls, both seeded and control, were well fitted by a gamma distribution with the shape parameter invariant under seeding. Preliminary indications with the area data suggest carryover to the multiple cloud experiment, for both the total target rainfall and that of the “floating target” which moves with seeded complexes.

Bayes equation is formulated for the posterior (after data) probability distribution of the seeding factor f defined as the ratio by which dynamic seeding increases the rain. Prior probabilities are mainly diffuse, with results insensitive to their choice. Natural distributions are specified by control sample means (and the appropriate gamma shape parameter). Sensitivity tests show greater dependence on the former, for which the effects of sampling errors are examined. Finally, results are used to estimate the number of cases required to resolve various magnitudes of seeding factor.

Results for the single clouds are virtually conclusive that seeding increased rainfall, by a factor of about 1.7, in good agreement with published results from classical statistics. For the “floating target” indications are strong, but not conclusive, that dynamic seeding had a positive effect, with the expected value about 3. The tentative estimate of total target seeding factor is about 1.7, with too high standard deviation (−σ0.5) and not firm enough depiction of natural variability for confidence.

If the total target seeding factor were in this approximate vicinity, however, two conclusions would follow: 1) continuation of the experiment is readily justified for practical benefit-cost as well as scientific reasons, and 2) about 50 pairs of cases may be required to resolve the result conclusively.

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Joanne Simpson, Jane C. Eden, and Anthony R. Olsen


Combination of numerical simulation, many simultaneous measurements, and a large assortment of statistical tools, employed at all stages, have been found useful in design and evaluation of modification experiments on cumulus clouds. A randomized sample is essential, although non-random controls have supplemented it by providing necessary information on natural distributions.Obstacles to definitive estimates of treatment effects are huge natural variability compounded by the expense and labor involved in obtaining an adequately large data sample. A 26 pair data set from a dynamic seeding experiment on isolated Florida cumuli is used here to illustrate both the problems and the combined approach used to overcome them. In this data set, rain volumes from unmodified single cumuli varied by three orders of magnitude on days screened as suitable. The field phase of the experiment cost above $250,000, requiring instrumented aircraft, calibrated radar, and several radiosondes daily.Numerical simulation of seeded and unseeded cumulus towers defined the key screening variable “seedability,” namely the predicted height difference between seeded and unseeded towers, so that only days on which the physical seeding hypothesis would be expected to work are selected for experimentation. On those days, randomization is between clouds selected by the experimenters as suitable.Classical and Bayesian statistics are used together in the evaluation, with both univariate and multivariate analyses. Various well-known probability density distributions fitted the seeded and unseeded rainfalls. Among the best were gamma, log-normal, beta-K and beta-P. Seed-control differences were examined with nonparametric and parametric tests (some of the latter after data transformation) and effects of random and systematic measurement errors were considered. In all tests, the seed-control rainfall difference was significant at better than 5%. A multiplicative seeding factor of 2–3 was estimated in several ways (allowing for or getting around the bias problem with ratio estimators related to long-tailed distributions).

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