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<br />_., .~-~-_.~".."-----~~.._.-
<br />
<br />76
<br />
<br />.
<br />
<br />which mea.ns seeded yesterday and also seeded today,
<br />with the category NN, not-seeded project day yesterday
<br />and the same today. Thirty-seven pairs of days were SS
<br />- (only 35 if the noncriteria days are discarded), aD(~ 22
<br />pairs were NN. The percentage increase in precipitation
<br />is +297 percent (only +205 percent when noncriteria
<br />days are discarded) during the to-hour period from
<br />midnight to 10 A.M. of today, which is the 10 hours im-
<br />mediately following yesterday, and thus may contain the
<br />aftereffect of what happened yesterday. This to-hour
<br />period is also the 10 hours preceding today's start of
<br />seeding period. Our problem here is to attempt to dis-
<br />entangle which of the two possible causes-aftereffect or
<br />before-seeding-provides the more plausible explanation
<br />of the observed effect during the 10 hours. The 297 per-
<br />cent increase indicates a very large aftereffect of yester-
<br />day's seeding, if this is the correct explanation, or a very
<br />large before-seeding effect for today, if this is the correct
<br />explanation for whatever reason.
<br />One category, even though it has a two-tail significance
<br />probability of 0.055, does not provide the solution. In
<br />the second block of the table, all those pairwise categories
<br />where yesterday was seeded are compared with the cor-
<br />responding category where yesterday was a not-seeded
<br />project day'. If the percentage effect is entirely an after-
<br />effect of what happened yesterday, we would expect all
<br />the percentage effects to have the same sign, all positive
<br />or all negative, except for chance fluctuations (which may
<br />be considerable since the sample sizes are not large). How-
<br />ever, if the percentage effect is entirely a before-seeding
<br />effect of today, we would expect all the percentage effects
<br />to be zero except for chance fluctuations. The 'observed
<br />percentage effects do not provide a clear solution; the
<br />signs of the eff.ects do vary and some are quite large, al-
<br />though none is significantly different from zero.
<br />In the third block are comparisons between all those.
<br />pairwise categories where today was seeded with the cor-
<br />responding category where today was a not-seeded project
<br />day. If the percentage effect is entirely an aftereffect of
<br />what happened yesterday, the first three lines in the third
<br />block should show zero effect (since what happened
<br />yesterday is the same in this block) except for chance
<br />fluctuations. The last line's effect should be'near zerO--:-
<br />what happened yesterday may not be perfectly balanced.
<br />On the other hand, if the entire explanati~n is a before-
<br />seeding effect of today, all the percentage effects would
<br />be in the same direction. Again, the observed percentage
<br />increases in this block do !;lot provide a clear solution.
<br />The effects are far from zero, although not significantly
<br />so, but the signs are not all in the same direction.
<br />We would expect to sharpen <?ur search if we restricted
<br />attention to the pairwise categories where today was an
<br />E-day (or some other type of Braham-day), and made a
<br />series of analyses pairwise, each similar to that in Table 2
<br />of Braham's article. The drawback is that the sample
<br />sizes become very small, roughly half of those in our
<br />table. We made these computations for E-days, examining
<br />the precipitation in the target area. The results differ
<br />
<br />I
<br />. J.
<br />',;., !."I _ . .... '"h,~. .... ,... ..~.
<br />
<br />~~._~
<br />
<br />-
<br />
<br />Journal of the American Statistical Association, March 1979
<br />
<br />from those in the table, which corresponds to the target
<br />area also but for all project days. Comparing SS pairs
<br />with NN pairs, there isa negative effect of seeding which
<br />is not significant. In the second block, the large positive
<br />effect for SN compared to NN pairs becomes negative
<br />when only E-days are considered. On the other hand, the
<br />last block for E-day computations shows some positive
<br />and some negative effects. All in all, we do not see a
<br />ready conclusion from the analysis. Roughly, there may
<br />be evidence of seeding aftereffects; there does not seem
<br />to be strong evidence of before-seeding effects when we
<br />examine precipitation in categories of days which are
<br />paired on the yesterday, today classification.
<br />We join with Braham in urging more cooperation be-
<br />tween meteorologists and statisticians. We also urge that
<br />there be more statisticians involved in meteorology and
<br />cloud physics. Some commercial cloud seeders have very
<br />little statistical training, and this occasionally leads them
<br />to misuse statistical techniques. For example, though it is
<br />known that making a square-root transformation, then
<br />doing a regression analysis, and transforming back will
<br />provide estimates of the increase in precipitation biased
<br />by a factor of two, we have seen analyses using cube-root
<br />and even fourth-root transformations! Some weather
<br />resel:Lrchers use similar statistical devices, and others
<br />have difficulties reporting their results. It appears that
<br />more training, and probably more scrutiny, would. be .
<br />desirable.
<br />
<br />REFERENCES
<br />
<br />Brahll.m, Roscoe R,., Jr.' (1966), "Final Report of Project White-
<br />top," PartB 1 and 2, mimeographed publication, Department of
<br />Geophysical Sciences, University of Chicago.
<br />-- (1977), personal communication to J. Neyman.
<br />--, and Flueck, John A. (1970), "Some Results of the Whitetop
<br />EX]periment," in Procudings of the Second NatUmal Conference On
<br />Weather Modification of the American Meteorological SocWy, Santa
<br />B&irbara, California. -
<br />Flueck, John A. (1971), "Final Report of Project Whitetop: Part
<br />V--8tatistical Analyses of the Ground Level Precipitation Data,"
<br />Department of Geophysical Sciences, University of Chicago.
<br />LoV8.l1ich, Jeanne L., Neyman, Jerzy, Scott, Elizabeth L., and Wells,
<br />Me.rcella A. (1971a), "Further Studies of the Whitetop Cloud.
<br />SeEding Experiment," Proceedings of the NatUmal Academy of
<br />Sciences, 68, 147-151.
<br />--, Neyman, Jerzy, Scott, Elizabeth L., and Wells, Marcella A.
<br />(lgI11b), "Hypothetical Explanatioll5 of the Negative Apparent
<br />Effects of Cloud Seeding in the Whitetop Experiment," Procudings
<br />of the NatUmal Academy of Sciences, 68, 2643-2646.
<br />Neyman, Jerzy, Osborn, Herbert B., Scott, Elizabeth L., and Wells,
<br />. Me.rcella A. (1972), "Re--Evaluation of the Arizona Cloud-Seeding
<br />. EX]periment," Prof:eedings of the NatUmal Academy of Science8, 69;
<br />134S-1352. .
<br />--, and Scott, Elizabeth L. (1967a), "Note on Techniques of
<br />EVI~luation of Single Rain Stimulation Experiments," in Pro-
<br />ceedings of the Fifth Berkeky Symposium on Mathematical Stati8tic8
<br />amt Probability, V, Berkeley: University of California Press, 371-
<br />384.
<br />--, and Scott, Elizabeth L. (1967b), "Some Outstanding Prob-
<br />lems Relating to Rain Modification," in Proceedings of the Fifth
<br />Ber'keky Symposium on Mathematical Statistics and Probability,
<br />. V, .Berkeley: University of California Press, 293-326.
<br />--, and Scott, Elizabeth L. (1973), "Some Current Problems of
<br />Rain Stimulation Research," in Proceedings of the Intern4tUmal
<br />SII1.rlp08ium on Uncertainties in Hydr'ologic and Water Resource
<br />Systems, Volume III, eds. L. Duckstein and C.C. Kisiel, Uni-
<br />vel'lgity of Arizona, 'fucson, 1167-1244. . .
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