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K. Ruben Gabriel

Abstract

A recent critique of the Climax cloud seeding experiments has raised many issues, which may cast doubt on the validity of those experiments’ results. An attempt is made here to clarify the importance of these issues in the context of experimentation with data subject to random variability. Issues of the results' validity are separated from issues of their interpretation. It is hoped that this clarification will help focus a response from the Climax experimenters.

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K. Ruben Gabriel

Abstract

A variety of ratio statistics has been used in the design and evaluation of weather modification experiments and their significance has usually been estimated by rerandomization. These ratios, and especially their logarithms, are asymptotically normal with null expectations and variances that can be readily calculated. This paper reviews and generalizes several useful ratio statistics and derives their variances. The variances presented here should make it easier for users of these ratios statistics in large experiments, 100 or more units, to assess significance without going through a large number of rerandomizations. It also shows how these formulas can be used to evaluate power and the required sample sizes. Some illustrations from Israel and from Puglia, Italy, are given.

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K. Ruben Gabriel

Abstract

The biplot is a graphical display of a two-dimensional approximation to a matrix. Its usefulness in the display and analysis of matrices of meteorological data is demonstrated by a detailed exposition of two illustrations based on Israeli rainfall. In the first illustration, the biplot for the sample matrix for monthly rainfall averages is shown to provide a visual display of patterns existing in the data. In the second illustration, data from a rainmaking experiment is the basis for the generation of a biplot which is a graphical approximation to simultaneous tests of a variety of sub-hypotheses in the multivariate analysis of variance (MA.NOVA) one-way layout.

The biplot is useful whenever the two largest characteristic roots of the matrix times its transpose account for most of the variance. When this is the case, relationships and trends in the data are displayed which may be difficult to obtain by common analytic methods.

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K. Ruben Gabriel

Abstract

The methodology of experimentation, randomization, and statistical analysis in weather modification has many parallels in clinical trials, such as the need for randomization, and the question of inclusion or exclusion of units assigned to be treated but not actually treated. There also are considerable differences, mainly in the definition of units, where the obvious choice of a single patient is in contrast with the highly problematic definition of a cloud or storm, and in the ethical aspects. This paper highlights some of these parallels and differences in the hope that looking at one’s own problems in a different context may enhance one’s understanding. It may also reconcile experimenters to their need for statistics: as the Hebrew saying goes, “Tzarat rabim, hatzi nehama” (the misfortune of many is half a consolation).

DEDICATION

It has been my good fortune to have worked with meteorologists who had an appreciation of what statistics could do for them and even seemed to get pleasure from understanding it. Such was Graeme Mather: not only did he seek and heed statistical support for his seminal work in cloud seeding, but he conveyed a sense of enjoying the cooperation and intellectual exchange. When we collaborated, I was challenged to propose and to justify new methods of analysis—as in exploring Nelspruit rainfall by means of biplots and linear models () and in a joint attempt, by e-mail, to apply QQ-plots to the study of detailed differences between the rain distributions of seeded and unseeded storms—and I was gratified to see his intelligent and useful application of these analyses. Graeme not only made his own important contributions but also had a singular gift of making others feel that he understood and appreciated them. It is appropriate to dedicate the following paper to him, not only because I have learned much of what I write about from collaborating with him and other like-minded meteorologists, but also because he was present when I delivered the initial version in Bari, Italy, in 1996 and was generous in expressing his appreciation. I miss him.

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K. Ruben Gabriel

Abstract

The use of confidence intervals for assessing the results of weather modification experiments is demonstrated and is shown to be more informative than tests of significance. Multivariate tests, confidence regions, and simultaneous confidence intervals for multiple effects are discussed. Pooling of the results of several experiments is also described, both for single and for multiple effects. The methods are illustrated on ratio statistics applied to the first two Israeli experiments.

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K. Ruben Gabriel and Demetrios Petrondas

Abstract

Cloud seeding operations are often evaluated by comparing precipitation during operations with records of previous “historical” precipitation. Possible biases that can arise from such comparisons have been discussed elsewhere. This paper uses extensive worldwide precipitation records to examine whether the usual statistical techniques may be validly applied to comparisons of precipitation in successive years, as is done in the above evaluations of cloud seeding. It is concluded that the chance of finding a “significant seeding effect” in the absence of seeding is usually well above the nominal significance level used. We therefore recommend that P-values from such operational/historical comparisons be treated very cautiously, possibly by multiplying them by a suitable factor, e.g., a “5% significant” result of such a comparison should really be regarded as more nearly “10% significant.”

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Abraham Gagin and K. Ruben Gabriel

Abstract

Earlier Published analyses of the second Israeli randomized experiment (1969–75) were restricted to 24-h data; this paper provides more details which are based on continuous time data from recording raingages. The present analyses confirm that when cloud tops were warmer than −21°C, seeding increased the efficiency of precipitation. In the −21° to −11°C window, both amount and duration of rainfall increased by some 50%, but no extra rain events appeared. Extra rain events were apparently initiated by seeding when cloud-top temperatures were warmer (−11°C and above); however, this did not significantly increase the amount of rainfall. No effect of seeding was found when cloud tops were colder than −21°C. It appears that seeding makes the existing process of rain formation more effective and also inducts precipitation formation in some clouds that would not have precipitated naturally.

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K. Ruben Gabriel and Daniel Rosenfeld

Abstract

This paper presents the results of the second Israeli randomized rainfall experiment for both alternative targets (earlier analyses were confined to the north target). It shows that apparently significant positive seeding effects in the north were accompanied by equally strong apparently negative effects in the south. Various statistical breakdowns of the data are tried, but they do not allow an unequivocal conclusion as to whether there were real and opposite effects in the two areas, or the apparent negative effect was a chance occurrence, or both apparent effects were due to chance. A comparison with Israel I is made and possible explanations are given in a companion paper.

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K. Ruben Gabriel and Demetrios Petrondas

Abstract

No abstract available.

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K. Ruben Gabriel and Abraham Gagin

Abstract

This paper reports separate analyses of daytime and nighttime precipitation based on data from recording raingages of the second Israeli randomized experiment. These analyses seemed important because there are a number of hypotheses on the differential effects of AgI seeding during the day and at night, and because about half of the seeding of this experiment was done at night. Our findings are unfortunately equivocal because of the large variability of the date which had to be broken down by categories of modal cloud-top temperatures and 12-b (day/night) periods. The increase of precipitation efficiency that had been noticed (on 24-h data) to occur in the −12° to −21°C window appears to have been larger at night, but the difference is not significant. The increase in the number of rain events for warmer clouds may have been only a daytime effect, but again, the present data are not conclusive.

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