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<br />have laboratory-tested models which orchestrate our
<br />understanding of these clouds and predict the outcome
<br />of seeding them. Glaciogenic seeding materials added to
<br />other types of clouds undoubtedly result in additional
<br />ice crystals when these materials are carried to, or are
<br />injected into, supercooled regions. But convective clouds,
<br />which produce most of the world's rainfall, are enor-
<br />mously more complex than are the stratus clouds where
<br />seeding effects are so clear. In my opinion, we do not yet
<br />know enough about large convective clouds to permit us
<br />to build numerical models for quantitative predictions
<br />of rain from them or for qualitative predictions of the
<br />effects of seeding them. Much of our current knowledge
<br />about natural precipitation, and ways in which clouds
<br />are affected by seeding, has come from experiments in
<br />which cloud seeding was coupled with detailed study of
<br />the clouds which made up the experiment. This should
<br />be the thrust of our research for some time to come.
<br />The discussants seem to agree that weather modifica-
<br />tion is an important and challenging subject in mete-
<br />orology, the study of which requires good statistics in all
<br />four stages of experimentation. No one seems to object
<br />to my call for increased involvement by statisticians as
<br />working partners in meteorological projects. However,
<br />Professor Gabriel suggests that a somewhat more inde-
<br />pendent role may be required during the data gathering
<br />and confirmatory analysis phases.
<br />Issues regarding appropriate designs for weather modi":
<br />fication experiments are found in almost every discussion.
<br />Many discussants speak of exploratory and confirmatory
<br />experiments, a distinction that has only recently become
<br />common in meteorological literature in spite of the fact
<br />that it was a topic of discussion at the 1959 Skyline
<br />Conference.
<br />Professor Neyman very usefully calls our attention to
<br />certain features of the natural rainfall distributions, and
<br />to the need for focusing separately on the likelihood of
<br />precipitation, and on the amount of precipitation, in
<br />designing seeding experiments. His points are well taken.
<br />He points out the problem resulting from a few very
<br />large storms or "outliers." Professor Simpson indicates
<br />that most of the evidence for seeding effects in FACE I
<br />came from a few of these "blockbuster" storms. The dis-
<br />cussion by Cook and Holschuh on unit additivity is also
<br />very germane. A similar discussion of these matters can
<br />be found in Flueck (1971).
<br />The matter of Type 1 errors surfaces several times,
<br />either explicitly or implicitly. As I mentioned in my
<br />original article, this issue has prevented an unambiguous
<br />interpretation of Whitetop results. Professor Mielke re-
<br />ports a similar situation in the Climax experiment and in
<br />one of the South Dakota projects. The wide-ranging
<br />differences among these projects (types of clouds, area,
<br />details of seeding, personnel, etc.) make one wonder
<br />whether we are facing a meteorological issue or a sta-
<br />tisticalone (multiple analyses?) or a combination of both.
<br />It is very helpful to have the many remarks about
<br />multiplicity. Perhaps never before has this topic been so
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<br />Journal elf the Americlln Statistical Association, March 1979
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<br />clearly illufilinated in writings which are likely to be seen
<br />and 1Ilsed by meteorologists. I thank each of the discus-
<br />sants, for their views on this topic. Multiplicity arises
<br />both in the context of explora~ry-st!l.ge analysis of ran-
<br />domized experiments and in the 8.nalysis of nonran-
<br />domized data. As far as weather modification is con-
<br />cerned, I veJ;lture Il. guess that it has tripped more toes in
<br />the 8.nalysis of randomized experiments than in the non-
<br />randomized ones. The greater availability of data, and
<br />the Jtact that it i.s randomized, have prompted more
<br />exploratory studies of randomized experiments. In any
<br />event, the message that comes through is that multiple
<br />analyses follow naturally in large, complex experiments,
<br />that significance tests are needed to help assess the pos-
<br />sibility of chance eausation of various results, and that;
<br />except for a very limited number of tests specified before-
<br />hand, the computed levels of significance are not ap-
<br />plicable in the usual way and must be used with care.
<br />Some of these discussions seem to call for additional
<br />details about the Whitetop design and objectives. Most
<br />of this is already f~vailable in Braham (1966) and other
<br />project reports, but I will give a few additional points.
<br />The l&rst document was a proposal dated 15 August 1958,
<br />by n.R. Byers, University of Chicago, to the National
<br />Science Foundation. A few sentences from that proposal
<br />are of special interest:
<br />
<br />The seeding will be carried out on randomly selected days of
<br />convective cloud development. The physical characteristics of
<br />the seeded clouds . .. will be measured . . . and contrasted with
<br />similar measurements made in clouds over a control area.
<br />The Department of Statistics at the University of Chicago will
<br />assist in the design. . . of the experiment,.
<br />n must be realized that... the result may be negative even
<br />though cloud seeding, properly carried out, might have a positive
<br />elffect. For example, in an attempt to create "an effect," one
<br />might cause an overseeded condition to prevail in the seeded
<br />clouds. This might inhibit precipitation formation. However,
<br />even this effect, if it could be positively demonstrated, would be
<br />a contribution to knowledge since at present we do not know
<br />whether adding silver-iodide will correct, a natural shortage or
<br />create an oversupply. .
<br />
<br />In due course a site was selectE~d in south-central
<br />Missouri, and I assumed responsibilities as Principal
<br />Investigator. During the design phase of the project, I
<br />reported to NSF that:
<br />
<br />the objective..; is to identify and isolate physical processes
<br />8I!I8ociated with the production of rain in summer convective
<br />cIlouds, and to study the ways in which these processes are
<br />modified as a consequence of seeding the clouds with silver
<br />iodide.
<br />
<br />The primary measurement tool will be the radar which will be
<br />operated during the entire period of interest on both seeded and
<br />non-seeded days.
<br />
<br />A second means for studying effects will be surface rainfall
<br />measurements collected from a network of recording rain gages.
<br />Inasmuch as all supervisory personnel in the University of
<br />Chicago Project will have access to the dates on which seeding
<br />&ctivities will be carried out, it is believed unwise to carry out
<br />the rain gage analysis within the Project office. It is anticipated
<br />that a qualified independent group will be secured to perform
<br />the analysis of the basic rain gage date. .. (Braham 1960).
<br />
<br />From the beginning of Whitetop, we stressed the necessity
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