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PAUL T. SCHICKEDANZ and STANLEY A. CHANGNON JR.

Abstract

A statistical methodology involving the analysis of three basic types of historical hail data on an areal approach is presented for the planning and evaluation of hail suppression experiments in Illinois. The methodology was used to generate nomograms relating the number of years required to detect significant results to 1) type I error, 2) type II error, and 3) power of the test for various statistical tests and experimental designs. These nomograms were constructed for various area sizes and geographical locations within the State.

Results indicate that, for an Illinois experiment, insurance crop-loss data are the optimum hail measurement if the study area has more than 60 percent insurance coverage. The optimum experimental design is the random-historical design in which all potential storms are seeded on a particular day, and 80 percent of the forecasted hail days are chosen at random to be “seeded days.” The recommended statistical analysis is the sequential analytical approach. If, however, conditions for the sequential analytical approach are not fulfilled by the data sample, the nonsequential approach utilizing a one-sample test with the historical record as the control (random-historical design) should be employed.

For a significance level of 0.05 and a beta error of 0.3, the average detection time in an area of approximately 1,500 sq mi would be 11 yr for a 20 percent reduction in the number of acres damaged, 2 yr for a 40 percent reduction, and 1 yr for a 60 and 80 percent reduction. If the nonsequential analyses were required, the number of years would be 25, 5, and 1, respectively.

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STANLEY A. CHANGNON JR. and PAUL T. SCHICKEDANZ

Abstract

Historical hail-day records of U.S. Weather Bureau first-order stations and cooperative substations are the only long, objective records of hail occurrence available throughout the United States. Although hail-day data are limited in areal density and are not necessarily the most desired measure of seeding effects, they are the only data available to obtain a measure of the areal-temporal variability of hail for most areas of the United States. Consequently, hail-day data from Illinois have been employed in a pilot project to determine the time required to obtain statistically significant changes in hail-day frequencies over various sized areas. Four statistical designs were investigated using the historical hail-day data for five areas in Illinois. The results show that the optimum design for hail-day data is the continuous seeding (seeding on all days likely to have hail) over an area. The optimum test is the sequential test involving the Poisson and Negative Binomial distributions. Detection of a 20-percent reduction in summer hail days would require, on the average, a continuous seeding program ranging from 13 to 37 yr, depending on the level of precision desired, and the size and location of the seeded area. Major reductions, those in excess of 60 percent, would require experiments of only 1- to 3-yr length.

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