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<br />OCTOBER 1980
<br />
<br />JAMES A. HEIMBACH, JR., AND ARLlN B. SUPER
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<br />1177
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<br />experiment can be considered successfully con-
<br />cluded when the treatment effect 0 is detected at a
<br />specified significance level of a, where a is the
<br />probability of a Type I error-the probability of
<br />rejecting a true null hypothesis. In other words,
<br />accepting a seeding effect when, in fact, there is none.
<br />It was assumed that the next phase of HIPLEX
<br />would treat CC's and would employ a random ex-
<br />perimental design with a seed: no-seed ratio of I: 1.
<br />It was further assumed, for planning purposes, that
<br />it would be operationally practical to maintain a
<br />network of 250 raingages, whatever the spacing,
<br />and that operations would be limited to within a
<br />150 km radius of the Skywater 5.4 cm radar a( Miles
<br />City. This simplified the problem of determining the
<br />optimal placement of 250 gages within this specified
<br />area for a random experimental design. Obviously,
<br />use of a different experimental design, different
<br />number of gages, different sized area. etc., might
<br />change the results of this experiment somewhat.
<br />The technique, however, could be applied to widely
<br />differing conditions.
<br />The ultimate measure of success for a precipita-
<br />tion augmentation experiment is the increased
<br />volumetric production of rainfall measured at the
<br />surface. Choosing this as the response variable al-
<br />lowed time-dependent errors to be ignored.
<br />In this paper the term "sampling variance" is
<br />used to denote the variance attributed to the in-
<br />fluence of gage network variations on estimates of
<br />total storm rainfall production. The familiar term
<br />"within-groups" (..storms) variance refers to gage-
<br />to-gage differences in rainfall amounts (plus meas-
<br />urement error). In a uniform network the storms
<br />total is the number of gages N times the average
<br />rainfall measured by the gages. Therefore, the sam-
<br />pling variance is N times the variance of means.
<br />~ince the variance of means is estimated by the
<br />within-storms variance/N, the sampling variance
<br />is, in this case, equivalent to the within-storms
<br />- variance.
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<br />b. Statistical techniques
<br />
<br />The Monte Carlo technique has been used exten-
<br />sively in the design of weather modification experi-
<br />ments. Schickedanz and Decker (1969) used it to
<br />examine the effects of among-storms variance of
<br />Illinois daily rainfall on experimental duration.
<br />Schickedanz and Challgnon ( 1970) applied the
<br />Monte Carlo technique to hail, and Olsen and
<br />Woodley (1975) to rainfall in the Florida Area
<br />Cumulus Experiment. These papers also addressed
<br />the effect of among-storms variance on experi-
<br />mental duration. Silverman (1979)2 applied the
<br />Monte Carlo technique in his study of rainfall sam-
<br />pling variance. In his analysis, the among-storms
<br />variance from actual CC rain swaths in the Miles
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<br />City area \VJ.S compared to the simulated sampling
<br />variance ar:~~ found to be far larger.
<br />In this pc.per among-storms and sampling vari-
<br />ances are left combined. This is a realistic approach
<br />because in an actual experiment the relative mag-
<br />nitudes can only be estimated at best. The degree
<br />of influen{~e of the sampling variance is accessed by
<br />varying the simulated gage network spacing. The
<br />variance due to measurement errors by the raingages
<br />is ignored since it is assumed that it is an insignifi-
<br />cant contribution.
<br />In the techniques described in more detail below,
<br />randomly seeded experimental units (CC's) are
<br />added to develop an increasingly large sample until
<br />a specified a-signifkance is achieved for a particular
<br />treatment effect. This process is repeated to obtain
<br />a distribution of the number of CC' s needed to reach
<br />the a-probability level, thereby allowing the power
<br />of the test, I-~, t0' be specified. ~ is the probability
<br />of a Type II error-the probability of accepting a
<br />false null hypothesis, i.e., rejecting a seeding effect
<br />when one actually exists.
<br />The use of a non parameterized statistical test in
<br />this process eliminates the restraint of requiring a
<br />distribution to be fit to the data base and cumber-
<br />some transforms of the data.
<br />
<br />3. The simulated data base
<br />
<br />a. Definition of convective complexes
<br />
<br />A CC is considered to be a convective system
<br />larger than a field of cumulus congestus but smaller
<br />than a squall line (usually one or a few cumulonim-
<br />bus in close proxiimity). The CC data base used in
<br />this study was obtained by the Skywater 5.4 cm
<br />radar located at Miles City, during May-July 1977.
<br />Volume scans were obtained each 5 min, from
<br />1_120 of tilt, whenever echoes ;;;.20 dBz existed
<br />within 150 km between 1030 and 2400 MDT daily.
<br />Pairs of PPI displays were computer-generated for
<br />each volume scan with each print character -4 km
<br />on a side. One PPI display portrayed the maximum
<br />echo tops and thle other the maximum reflectivity
<br />factors (dBz) from all tilts for each horizontal lo-
<br />cation. These displays were used to manually iden-
<br />tify and track eal;h CC using 10 dBz as the echo
<br />boundary.
<br />To qualify . ': a CC, a radar echo had to exceed
<br />30 dBz, and ":h an altitude of9 km MSL or higher
<br />sometime dli g its lifetime, but not necessarilY
<br />simultaneou~ . The separation between CC's had
<br />no absolute 1. :r limit, but was subject to the inter-
<br />pretation of :: analyst. Sometimes weak echoes
<br />(10-15 dBz: . om adjoining CC's, probably rep-
<br />resenting cir .:: anvils, wouid even touch for a short
<br />period \\)tL e:vidence of merger of the CCs.
<br />Usually. hl. ,'er, individual CC's were separ:ltcd
<br />by many kill, neters for most or all of their lifetimes.
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