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<br />OCTOBER 1980
<br />
<br />JAMES A. HEIMBACH, JR., AND ARL~N :8. Sl)PER
<br />
<br />1183
<br />
<br />TABLE 3. As in Table 2 except required number of storm': c';:imat~:d using Eq. (4). '
<br />
<br />II
<br />30
<br />.
<br />
<br /> 8 = 25%
<br /> All Large Small
<br /> 103 half half
<br />cr = 0.05 ~ = 0.10 431E 241E 27M
<br /> ~ = 0.25 271E 141E 17/~
<br /> ~ = 0.50 141E 81E 9/~
<br />a = 0.10 ~ = 0.10 331E 191E 21 M
<br /> ~ = 0.25 20lE IlIE l2/~
<br /> ~ = 0.50 91E 51E 5/~
<br />
<br />~
<br />jiI.
<br />iK
<br />
<br /> 8 = jU% 8=100%
<br />All La!ge Small All Large Small
<br />103 h<::f half 103 half half
<br />1I1E 6"7 7M 31E 2/E 2/~
<br />',-
<br />61E 4 C' 5M 21E liE 21~
<br />.~
<br />41E 2:E" 3/~ liE liE 1M
<br />91E 51E SM 31E 2/E 2/~
<br />51E 3.'E 3/~ 2/E liE 1M .'
<br />3/E 2/E 21~ liE lIE 1M
<br />
<br />r
<br />It
<br />s
<br />If:
<br />
<br />lations, then a simple approach outlined by Davis
<br />(1956) is applicable:
<br />
<br />rii
<br />r-
<br />
<br />N = (Zt-a - ZO)2O'2
<br />JL2S2p( 1 - p)
<br />
<br />Here N is the number of seeded plus nonseeded
<br />cases required to detect a o-treatment effect at a-
<br />and l3-probability levels. The standard normal devi-
<br />ates for the specified probability levels are repre-
<br />sented by z. In this simulation the randomization
<br />factor p is 0.5 and the population variance cr is as-
<br />sumed equal to the sample variance S2.
<br />Table 3 summarizes the optimal gage spacing de-
<br />termined through the application of (4). Approxi-
<br />mately twice the number of experimental.seasons
<br />\vere needed to detect a seeding effect of S = 25%
<br />as compared to Table 2, approximately the same
<br />were required for 8 = 50% and half the number of
<br />seasons for 8 = 100%. Extrapolation of Table 2's
<br />indefinite values based on this comparison gives
<br />prohibitively large numbers of required seasons.
<br />Table 3 is redundant in specifying optimal cover-
<br />age for the data sets. The use of (4) does not invoke
<br />the random and multiple selection of CC's. Rather,
<br />the entire sample is always involved through the y
<br />'and s statistics.
<br />
<br />:f~
<br />
<br />~
<br />:r.
<br />l-
<br />It
<br />I,
<br />t:
<br />If
<br />
<br />t-
<br />
<br />~
<br />
<br />.'
<br />.
<br />
<br />~.
<br />
<br />(4)
<br />
<br />dict total CC rain~ll1 accu'E.!1latLQ!L~~tS.J~2{_~!llpli.fi_e.Q
<br />by stratification of the larger and smaller storms.
<br />This--sIgnlt1c-ci'ntly-reduced ihe-n-u~ber of seasons
<br />r~C@Jeo,15~rficul<lljy}qrt'heJarge( halfdftl1e"CC' s. .
<br />For th~ modest treatment effect anticipated. it has
<br />been shown that an unacceptably long experiment
<br />would be needed to achieve acceptable a- and {3-
<br />probability levels. One alternative would be to ease
<br />the a and {3 restrictions; however, the results would
<br />then be suspect. For this reason. it has been recom-
<br />mended that the Miles City HIPLEX raingage net-
<br />work deployment be postponed until covariates are
<br />found which reduce the among-storms variance.
<br />
<br />Acknowledgments. The authors would like to ex-
<br />press their appreciation to Dr. Paul Mielkie, Jr., for
<br />the fruitful discussions on several points in this
<br />experiment and to Ms. Ann Parker for her help in the
<br />analysis. This research was supported by the Office
<br />of Atmospheric Resources Management, Water and
<br />Power Resources Service. U.S. Department of the
<br />Interior, under Contract 14-06-D-7577 with the Mon-
<br />tana Department of Natural Resources and Con-
<br />servation.
<br />
<br />REFERENCES
<br />
<br />Davis, O. L., Ed., 1956: The Design and Analysis .of Industrial
<br />Experiments. Hafner, 636 pp, (see pp. 24-31).
<br />Noether. G. E., \%7: Elements .of Nanparametric Statistics.
<br />Wiley, \04 pp. (see pp. 31-39).
<br />This paper describes the simulated sampling of a Olsen, A. R.. and W. 1.. Woodley, 1975: On the effect of natural
<br />convective complex seeding experiment by rain- rainfall .variability and measurement errors in the detection
<br />gages. Several conclusions can be drawn. The_ .of seedmg effect. .T. Appl. ""feteor., 14.929-938.
<br />, -~- Schlckedanz, P. T.. all1d W. 1.. Decker, 1.969: A Monte Carlo
<br />a~!1g-~~rms ~~..l1atural vanance was much larger technique for designing cloud seeding experiments. J. App/.
<br />than -tties~lJnplingvariance. This generally resulted Meteor.. 8, :::'1-228.
<br />in'iittle variation in the numb'er of CC's required' -, and S. A. C"I:mgnon, 1970: The design and evaluation of
<br />-io--reJectthe null ti'ypotheses below -300 km2 per hail suppres~ ',experiments. Mon. Wea. Rev., .98, 241-,25l.
<br />- . h' h . hI" b -, and F. L. ;. ,1.97\: The deSIgn and evaluation of ram fall
<br />gage,. a~, w. IC. POint. t ,.. samp 109 vanance egan modificatior" 1eriments. J. Appl. Melear., 10,502-;\4.
<br />tp have a slgOlficant mfluence. Thiesson. A. J.. "11: Precipitation averages for large areas.
<br />The usefulness of developing procedures to e~_e..: Man. Wea. I,: ,.. 30, 1082-1084.
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<br />- 7. Discussion
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