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Anthony R. Olsen

Abstract

Statistical procedures for analyzing the results of randomized weather modification experiments are presented in a format designed to emphasize their underlying assumptions. A parallel development of Bayesian and classical statistical techniques is given to demonstrate that both methodologies can be used under the assumed experimental conditions and that the difficulties in applying either are comparable.

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Anthony R. Olsen and William L. Woodley

Abstract

Natural rain variability and measurement errors are obstacles to the determination of the seeding effect in convective cloud seeding experiments. The relative importance of these problems in Florida is evaluated in this paper. Its major thrust is embodied in a computer simulation of area cloud seeding experiments for two areas (570 km2 and 1.3 × 104 km2) using field measurements as input. The effect of natural rain variability is studied as it relates to the power functions of selected statistical tests for seeding effect. Measurement errors for gage and radar systems are introduced by modifying the underlying distribution of area mean rainfall.For the two Florida areas, natural rain variability is by far the major obstacle to the determination of a seeding effect. Errors are of lesser importance for the system of rain measurement used in Florida, which involves radar-rain estimates adjusted by gages. With a less accurate system of rain measurement, errors would assume greater relative importance. It is concluded that to detect a particular seeding effect with a minimum number of cases, the importance of natural rain variability must be decreased through either stratification of the experimental days or through meteorological predictors. The measurement system used by the Experimental Meteorology Laboratory is adequate for the evaluation of its seeding experiments and little will be gained through the expenditure of time and effort to improve it further.

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William L. Woodley, Anthony R. Olsen, Alan Herndon, and Victor Wiggert

Abstract

Gage and radar methods of convective rain measurement are compared in the context of the continuing multiple cloud seeding experiment of the Experimental Meteorology Laboratory. An optimal system, combining the best features of both, is recommended.The nature of the Florida convective rainfall to be measured is documented using measurements from a dense raingage mesonet (about 3 km2 per gage over 570 km2) that was operated for a total of 93 days in 1971 and 1973, and the gaging requirements for detection and measurement of 24 h rainfalls in the mesonet are determined using the full complement of gages as the standard. For the measurement of areal convective rainfall greater than 0.25 mm within a factor of 2 on 90, 70 and 50% of the days, gage densities of 31, 91 and 208 km2 per gage, respectively, are required.Radar performance in estimating convective rainfall over south Florida is determined using two collocated, calibrated 10 cm radars (UM/10-cm of the University of Miami and WSR-57 of the National Hurricane Center). In all cases, the radar estimates of rainfall are compared with the rainfall as determined by raingages (densities 3 to 8 km2 per gage) in cluster arrays. The relative performances of the two radars are compared.In 1973, WSR-57 radar-derived rainfalls were computed by hand as in 1972 and by computer using taped radar observations. On a daily basis, 80% of the radar estimates were within a factor of 2 of the cluster standard. The combined accuracy of the WSR-57 radar in 1972 and 1973 in estimating convective rainfall approximated that which one would obtain with a gage density of 65 km2 per gage over an area the size of the mesonet.The daily representation of rainfall by the radar improves if one adjusts it using gages. In the mean, adjustment produced a statistically significant 15% improvement (<1% level with two-tailed “t” test) in radar accuracy. The adjusted radar measurements then had an approximate gage density equivalence of 25 km2 per gage.The gaging requirements for the estmation of area mean rainfall for an area the size of the EML target (1.3 × 104 km2) is inferred using the digitized radar observations. To meet a specification that the area-mean rainfall be measured to within a factor of 2 of the true value 99% of the time requires 143 km2 per gage, compared to a requirement of at least 13 km2 per gage for the mesonet.An optimum method of rain measurement is suggested. For the measurement of the rainfall from individual showers anywhere, the gage-adjusted radar is far superior to gages alone. For measurement in a fixed area the size of the mesonet, gages are superior to the radar. To measure rainfall over the EML target either gages alone, or a radar adjusted by gages, can accomplish the task. About 90 evenly spaced gages in the EML target should provide area rain measurements within a factor of 2 of the true value 99% of the time. The radar estimates adjusted by gages should be as accurate as those provided by the network of 90 gages. The final choice as to the measurement system will probably be determined by other considerations such as budget, personnel and terrain over which the measurements are to be made.

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

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).

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