On the Design and Evaluation of Cumulus Modification Experiments

Abstract

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).