PROCEEDINGS OF THEFIFTH BERKELEY SYMPOSIUM

VOLUME V

PROCEEDINGS of the FIFTHBERKELEY SYMPOSIUM ONMATHEMATICAL STATISTICS

AND PROBABILITY

Held at the Statistical LaboratoryUniversity of CaliforniaJune 21-July 18,1965

andDecember 27, 1965-January 7, 1966

with the support ofUniversity of California

National Science FoundationNational Institutes of Health

Air Force Office of Scientific ResearchArmy Research Office

Office of Naval Research

VOLUME V

WEATHER MODIFICATION

EDITED BY LUCIEN M. LE CAMAND JERZY NEYMAN

UNIVERSITY OF CALIFORNIA PRESSBERKELEY AND LOS ANGELES

1967

UNIVERSITY OF CALIFORNIA PRESS

BERKELEY AND LOS ANGELES

CALIFORNIA

CAMBRIDGE UNIVERSITY PRESS

LONDON, ENGLAND

COPYRIGHT ( 1967, BY

THE REGENTS OF THE UtNIVERSITY OF CALIFORNIA

The United States Government and its offices, agents, and em-ployees, acting within the scope of their duties, may reproduce,publish, and use this material in whole or in part for governmenitalpurposes without payment of royalties thereon or therefor. Thepublication or republication by the governmenit either separatelyor in a public document of any material in which copyright subsistsshall not be taken to cause any abridgment or annulment of thecopyright or to authorize any use or appropriation of such copy-right material without the consenit of the copyright proprietor.

LIBRARY OF CONGRESS CATALOG CARD NUMBER: 49-8189

PRINTED IN THE UNITED STATES OF AMERICA

CONTENTS OF PROCEEDINGSVOLUMES I, II, III, IV, AND V

Volume I-Theory of Statistics

General TheoryT. W. ANDERSON and S. M. SAMUELS, Some inequalities among binomial and Poisson

probabilities. R. R. BAHADUR, An optimal property of the likelihood ratio statistic.GEORGE A. BARNARD, The use of the likelihood function in statistical practice. D. BASU,Problems relating to the existence of maximal and minimal elements in some families ofstatistics (subfields). YU. K. BELYAEV, On confidence intervals and sets for various sta-tistical models. FRIEDHELM EICKER, Limit theorems for regressions with unequal anddependent errors. R. H. FARRELL, Weak limits of sequences of Bayes procedures in esti-mation theory. R. H. FARRELL, J. KIEFER, and A. WALBRAN, Optimum multivariatedesigns. JAROSLAV HAJEK, On basic concepts of statistics. J. L. HODGES, JR., Efficiencyin normal samples and tolerance of extreme values for some estimates of location. J. L.HODGES, JR. and E. L. LEHMANN, Moments of chi and power of t. WASSILYHOEFFDING, On probabilities of large deviations. PETER J. HUBER, The behavior ofmaximum likelihood estimates under nonstandard conditions. OSCAR KEMPTHORNE,The classical problem of inference-goodness of fit. HIROKICHI KUDO, On partial priorinformation and the property of parametric sufficiency. YU. V. LINNIK, On the elimination ofnuisance parameters in statistical problems. J. MAcQUEEN, Some methods for classificationand analysis of multivariate observations. KAMEO MATUSITA, Classification based on dis-tance in multivariate Gaussian cases. EMANUEL PARZEN, On empirical multiple timeseries analysis. YU. V. PROHOROV, Some characterization problems in statistics. ROYRADNER, A note on maximal points of convex sets in 4.. C. R. RAO, Least squares theoryusing an estimated dispersion matrix and its application to measurement of signals. KAROLYSARKADI, On testing for normality. R. A. WIJSMAN, Cross-sections of orbits and theirapplication to densities of maximal invariants.

Sequential ProceduresPETER J. BICKEL and JOSEPH A. YAHAV, Asymptotically pointwise optimal pro-

cedures in sequential analysis. DAVID BLACKWELL, Positive dynamic programming.Y. S. CHOW and H. ROBBINS, A class of optimal stopping problems. Y. S. CHOW andH. ROBBINS, On values associated with a stochastic sequence. ARYEH DVORETZKY,Existence and properties of certain optimal stopping rules. THOMAS S. FERGUSON, Ondiscrete evasion games with a two-move information lag. M. V. JOHNS, JR., Two-actioncompound decision problems. JERZY LOS, Horizon in dynamic programs.

Information TheoryTOSIO KITAGAWA, Information science and its connection with statistics. ALFRED

RENYI, On some basic problems of statistics from the point of view of information theory.MILLU ROSENBLATT-ROTH, Approximations in information theory. J. WOLFOWITZ,Approximation with a fidelity criterion.

Nonparametric ProceduresPETER J. BICKEL, Some contributions to the theory of order statistics. RALPH A.

BRADLEY, Topics in rank-order statistics. Z. GOVINDARAJULU, L. LE CAM, and M.V

Vi CONTENTS OF PROCEEDINGS

RAGHAVACHARI, Generalizations of theorems of Chernoff and Savage on the asymptoticnormality of test statistics. PRANAB KUMAR SEN, On a class of two-sample bivariatenonparametric tests. I. VINCZE, On some questions connected with two-sample tests ofSmirnov type.

Volume II-Part I-Theory of ProbabilityProbability on Algebraic Structures

SIMEON M. BERMAN, Sign-invariant random elements in topological groups. R.GANGOLLI, Abstract harmonic analysis and L6vy's Brownian motion of several parameters.LEONARD GROSS, Abstract Wiener spaces. EDITH MOURIER, Random elements inlinear spaces. CZESLAW RYLL-NARDZEWSKI, On fixed points of semigroups of endo-morphisms of linear spaces. A. and C. IONESCU TULCEA, On the existence of a lifting com-muting with the left translations of an arbitrary locally compact group.

Distributions in Functional SpacesHERMANN DINGES, Random shifts of stationary processes. TAKEYUKI HIDA and

NOBUYUKI IKEDA, Analysis on Hilbert space with reproducing kernel arising from multipleWiener integral. KIYOSI ITO, Generalized uniform complex measures in the Hilbertian metricspace with their application to the Feynman integral. A. V. SKOROHOD, On the densitiesof probability measures in functional spaces. LESTER E. DUBINS and DAVID A. FREED-MAN, Random distribution functions.

Stochastic Processes and PredictionHARALD CRAMER, A contribution to the multiplicity theory of stochastic processes.

R. M. DUDLEY, On prediction theory for nonstationary sequences. K. URBANIK, Someprediction problems for strictly stationary processes. A. M. YAGLOM, Outline of some topicsin linear extrapolation of stationary random processes.

MartingalesM. BRELOT, Capacity and balayage for decreasing sets. LESTER E. DUBINS and

GIDEON SCHWARZ, On extremal martingale distributions. STEVEN OREY, F-processes.VOLKER STRASSEN, Almost sure behavior of sums of independent random variablesand martingales.

Special ProblemsD. A. DARLING, Some limit theorems associated with multinomial trials. GERARD

DEBREU, Integration of correspondences. WILLIAM FELLER, On regular variation andlocal limit theorems. MILOSLAV JIRINA, General branching processes with continuoustime parameter. EUGENE LUKACS, On the arithmetical properties of certain entire charac-teristic functions. HERMAN RUBIN, Supports of convolutions of identical distributions.E. SPARRE ANDERSEN, An algebraic treatment of fluctuations of sums of random vari-ables. LAJOS TAKACS, On combinatorial methods in the theory of stochastic processes.

Volume II, Part fl-Theory of ProbabilityMarkov Processes

R. M. BLUMENTHAL and R. K. GETOOR, Accessible terminal times. LEOBREIMAN, First exit times from a square root boundary. E. B. DYNKIN, General lateralconditions for some diffusion processes. H. KESTEN, The Martin boundary of recurrentrandom walks on countable groups. MINORU MOTOO, Application of additive functionals tothe boundary problem of Markov processes (Levy's system of U-processes). TADASHI UENO,

CONTENTS OF PROCEEDINGS Vii

A survey on the Markov process on the boundary of multidimensional diffusion. HIROSHIKUNITA and TAKESI WATANABE, Some theorems concerning resolvents over locally com-pact spaces. DAVID G. KENDALL, On Markov groups. JANE M. 0. SPEAKMAN, Someproblems relating to Markov groups. DAVID WILLIAMS, Uniform ergodicity in Markovchains. J. G. BASTERFIELD, On quasi-compact pseudo-resolvents. JANE M. 0. SPEAK-MAN, A note on Markov semigroups which are compact for some but not all t > 0. DANIELRAY, Some local properties of Markov processes. DONALD ORNSTEIN, A limit theorem forindependent random variables. CHARLES STONE, On local and ratio limit theorems. JOHNLAMPERTI, Limiting distributions for branching processes. SAMUEL KARLIN and JAMESMcGREGOR, Uniqueness of stationary measures for branching processes and applications.WALTER L. SMITH, Some peculiar semi-Markov processes. WALTER L. SMITH, A theo-rem on functions of characteristic functions and its application to some renewal theoretic ran-dom walk problems. F. SPITZER, Renewal theorems for Markov chains.

Ergodic TheoryROBERT J. AUMANN, Random measure preserving transformations. J. R. BLUM,

H. D. BRUNK, and D. L. HANSON, Roots of the one-sided N-shift. R. V. CHACON, Ageometric construction of measure preserving transformations. ARSHAG B. HAJIAN andYUJI ITO, Conservative positive contractions in L'. KONRAD JACOBS, On Poincar6's recur-rence theorem. SHIZUO KAKUTANI, Ergodic theory of shift transformations. ULRICHKRENGEL, Classification of states for operators. KLAUS KRICKEBERG, Strong mixingproperties of Markov chains with infinite invariant measure. CALVIN C. MOORE, In-variant measures on product spaces. JACQUES NEVEU, Existence of bounded invariantmeasures in ergodic theory. M. ROSENBLATT, Transition probability operators.

Volume III-Physical SciencesAstronomy

E. M. BURBIDGE and G. R. BURBIDGE, Evolution of galaxies. W. H. McCREA,Age distribution of galaxies. THORNTON PAGE, Masses of galaxies: singles and membersof multiple systems. BEVERLY T. LYNDS, Space distribution of small dark nebulae. W. C.LIVINGSTON, On correlations between brightness,,velocity, and magnetic fields in the solarphotosphere.

PhysicsR. L. DOBRUSHIN, Existence of phase transitions in models of a lattice gas. J. M.

HAMMERSLEY, Harnesses. HERBERT SOLOMON, Random packing density.

Spectral AnalysisM. S. BARTLETT, The spectral analysis of line processes. BENOIT MANDELBROT,

Sporadic random functions and conditional spectral analysis: self-similar examples and limits.

Control ProcessesJOHN BATHER and HERMAN CHERNOFF, Sequential decisions in the control of

a spaceship. RICHARD BELLMAN, On the construction of a mathematical theory of theidentification of systems. P. WHITTLE, The deterministic stochastic transition in controlprocesses and the use of maximum and integral transforms.

ReliabilityR. E. BARLOW and A. W. MARSHALL, Bounds on interval probabilities for restricted

families of distributions. YU. K. BELYAEV, B. V. GNEDENKO, and A. D. SOLOVIEV,On some stochastic problems of reliability theory. Z. W. BIRNBAIJM and J. D. ESARY, Some

CONTENTS OF PROCEEDINGS vii

A survey on the Markov process on the boundary of multidimensional diffusion. HIROSHIKUNITA and TAKESI WATANABE, Some theorems concerning resolvents over locally com-pact spaces. DAVID G. KENDALL, On Markov groups. JANE M. 0. SPEAKMAN, Someproblems relating to Markov groups. DAVID WILLIAMS, Uniform ergodicity in Markovchains. J. G. BASTERFIELD, On quasi-compact pseudo-resolvents. JANE M. 0. SPEAK-MAN, A note on Markov semigroups which are compact for some but not all t > 0. DANIELRAY, Some local properties of Markov processes. DONALD ORNSTEIN, A limit theorem forindependent random variables. CHARLES STONE, On local and ratio limit theorems. JOHNLAMPERTI, Limiting distributions for branching processes. SAMUEL KARLIN and JAMESMcGREGOR, Uniqueness of stationary measures for branching processes and applications.WALTER L. SMITH, Some peculiar semi-Markov processes. WALTER L. SMITH, A theo-rem on functions of characteristic functions and its application to some renewal theoretic ran-dom walk problems. F. SPITZER, Renewal theorems for Markov chains.

Ergodic TheoryROBERT J. AUMANN, Random measure preserving transformations. J. R. BLUM,

H. D. BRUNK, and D. L. HANSON, Roots of the one-sided N-shift. R. V. CHACON, Ageometric construction of measure preserving transformations. ARSHAG B. HAJIAN andYUJI ITO, Conservative positive contractions in L1. KONRAD JACOBS, On Poincar6's recur-rence theorem. SHIZUO KAKUTANI, Ergodic theory of shift transformations. ULRICHKRENGEL, Classification of states for operators. KLAUS KRICKEBERG, Strong mixingproperties of Markov chains with infinite invariant measure. CALVIN C. MOORE, In-variant measures on product spaces. JACQUES NEVEU, Existence of bounded invariantmeasures in ergodic theory. M. ROSENBLATT, Transition probability operators.

Volume III-Physical SciencesAstronomy

E. M. BURBIDGE and G. R. BURBIDGE, Evolution of galaxies. W. H. McCREA,Age distribution of galaxies. THORNTON PAGE, Masses of galaxies: singles and membersof multiple systems. BEVERLY T. LYNDS, Space distribution of small dark nebulae. W. C.LIVINGSTON, On correlations between brightness,,velocity, and magnetic fields in the solarphotosphere.

PhysicsR. L. DOBRUSHIN, Existence of phase transitions in models of a lattice gas. J. M.

HAMMERSLEY, Harnesses. HERBERT SOLOMON, Random packing density.

Spectral AnalysisM. S. BARTLETT, The spectral analysis of line processes. BENOIT MANDELBROT,

Sporadic random functions and conditional spectral analysis: self-similar examples and limits.

Control ProcessesJOHN BATHER and HERMAN CHERNOFF, Sequential decisions in the control of

a spaceship. RICHARD BELLMAN, On the construction of a mathematical theory of theidentification of systems. P. WHITTLE, The deterministic stochastic transition in controlprocesses and the use of maximum and integral transforms.

ReliabilityR. E. BARLOW and A. W. MARSHALL, Bounds on interval probabilities for restricted

families of distributions. YU. K. BELYAEV, B. V. GNEDENKO, and A. D. SOLOVIEV,On some stochastic problems of reliability theory. Z. W. BIRNBAUM and J. D. ESARY, Some

CONTENTS OF PROCEEDINGS iX

S. PURI, A class of stochastic models of response after infection in the absence of defensemechanism. J. GANI, Models for antibody attachment to virus and bacteriophage.

Cellular PhenomenaHERBERT E. KUBITSCHEK, Cell generation times: ancestral and internal controls.

H. RUBIN, Cell growth as a function of cell density. WALTER R. STAHL, Measures oforganization in a model of cellular self-reproduction based on Turing machines. D. G.BURNETT-HALL and W. A. O'N. WAUGH, Sensitivity of a birth process to changesin the generation time distribution.

CarcinogenesisDAVID LINDER and STANLEY M. GARTLER, Problem of single cell versus multicell

origin of a tumor. WOLFGANG J. BtVHLER, Single cell against multicell hypotheses of tumorformation. T. TIMOTHY CROCKER and BERYL J. NIELSEN, Chemical carcinogensand respiratory epithelium. K. B. DEOME, The mouse mammary tumor system. DAVIDW. WEISS, Immunology of spontaneous tumors. M. B. SHIMKIN, R. WIEDER, D. MARZI,N. GUBAREFF, and V. SUNTZEFF, Lung tumors in mice receiving different schedules ofurethane. M. WHITE, A. GRENDON, and H. B. JONES, Effects of urethane dose andtime pattern on tumor formation. JERZY NEYMAN and ELIZABETH L. SCOTT, Sta-tistical aspect of the problem of carcinogenesis.

ExperimentationF. YATES, A fresh look at the basic principles of the design and analysis of experiments.

P. ARMITAGE, Some developments in the theory and practice of sequential medical trials.HERMAN CHERNOFF, Sequential models for clinical trials. JEROME CORNFIELDand SAMUEL W. GREENHOUSE, On certain aspects of sequential clinical trials. BRADLEYEFRON, The two sample problem with censored data. MARVIN A. SCHNEIDERMAN,Mouse to man: statistical problems in bringing a drug to clinical trial.

Decision Theory in Medical DiagnosisLEONARD RUBIN, MORRIS F. COLLEN, and GEORGE E. GOLDMAN, Frequency

decision theoretical approach to automated medical diagnosis. CHARLES D. FLAGLE, Adecision theoretical comparison of three procedures of screening for a single disease. LEEB. LUSTED, Logical analysis in medical diagnosis. J. T. CHU, Some decision making meth-ods applicable to the medical sciences.

Volume V-Weather Modification

Physical BackgroundM. NEIBURGER, Physical factors in precipitation processes and their influence on the

effectiveness of cloud seeding.

Large Randomized ExperimentsLOUIS J. BATTAN and A. RICHARD KASSANDER, JR., Summary of results of a

randomized cloud seeding project in Arizona. J. BERNIER, On the design and evaluationof cloud seeding experiments performed by Electricit6 de France. WAYNE L. DECKERand PAUL T. SCHICKEDANZ, The evaluation of rainfall records from a five year cloudseeding experiment in Missouri. DONALD L. EBERLY and LEWIS H. ROBINSON, Designand evaluation of randomized wintertime cloud seeding at high elevation. K. R. GABRIEL,The Israeli artificial rainfall stimulation experiment. Statistical evaluation for the period 1961-65. LEWIS 0. GRANT and PAUL W. MIELKE, JR., A randomized cloud seeding experiment

X CONTENTS OF PROCEEDINGS

at Climax, Colorado, 1960-65. E. PEREZ SILICEO, A brief description of an experiment onartificial stimulation of rain in the Necaxa watershed, Mexico. PAUL SCHMID, On"Grossversuch III," a randomized hail suppression experiment in Switzerland. E. J. SMITH,Cloud seeding experiments in Australia.

Relevant Climatological StudiesS. A. CHANGNON, JR. and F. A. HUFF, The effect of natural rainfall variability in verifi-

cation of rain modification experiments. THOMAS J. HENDERSON, Tracking silver iodidenuclei under orographic influence.

Nonrandomized OperationsGLENN W. BRIER, THOMAS H. CARPENTER, and DWIGHT B. KLINE, Some

problems in evaluating cloud seeding effects over extensive areas. HANS GERHARDMtULLER, Weather modification experiments in Bavaria.

Methodological DiscussionARNOLD COURT, Randomized cloud seeding in the United States. L. G. DAVIS and

C. L. HOSLER, The design, execution and evaluation of a weather modification experiment.ARCHIE M. KAHAN, The Bureau of Reclamation's Atmospheric Water Resources ResearchProgram. VUJICA M. YEVDJEVICH, Evaluation of weather modification as expressed instream flow response. JERZY NEYMAN and ELIZABETH L. SCOTT, Some outstandingproblems relating to rain modification. JERZY NEYMAN and ELIZABETH L. SCOTT,Appendix. Planning an experiment with cloud seeding. JERZY NEYMAN and ELIZABETHL. SCOTT, Note on the Weather Bureau ACN Project. J. M. WELLS and M. A. WELLS,Note on Project SCUD. JERZY NEYMAN and ELIZABETH L. SCOTT, Note on tech-niques of evaluation of single rain stimulation experiments. ROBERT B. DAVIES andPREM S. PURI, Some techniques of summary evaluations of several independent experi-ments. BARRY R. JAMES, On Pitman efficiency of some tests of scale for the Gammadistribution. FRANK YATES, Discussion of reports on cloud seeding experiments.

Observational DataA collection of data from cloud seeding experiments in five countries.

PREFACETHE PURPOSE OF THE Berkeley Statistical Symposia, held every five years, isto stimulate research through lectures by carefully selected speakers and throughprolonged personal contacts of scholars brought together from distant centers.Accordingly, particular Symposia last from four to seven weeks. On occasion,and this was the case with the Fifth Symposium, they are conducted in two parts,one in June-July, emphasizing theory, and the other in December-January,emphasizing applications. The winter part of the Fifth Symposium was heldin conjunction with the 132nd Annual Meeting of the American Association forthe Advancement of Science.The Proceedings of the Symposia are intended to present a comprehensive

cross-section of contemporary thinking on problems of probability and statisticsand on selected fields of application. The rapid growth of research in statisticsand especially in probability makes it increasingly difficult to achieve a completecoverage of the field, but sincere efforts are made to invite to the Symposiarepresentatives of all the existing schools of thought, each individual havingcomplete freedom of expression.The organization of the theoretical part of the Fifth Berkeley Symposium was

carried out, and the contributors were selected, with the participation of anAdvisory Committee composed of Professors J. L. Doob, S. Karlin, and H.Robbins, delegated for this purpose by the American Mathematical Society andby the Institute of Mathematical Statistics. In addition, we had the assistanceof Professor D. L. Burkholder, the Editor of the Annals of Mathematical Sta-tistics. The interest of the American Mathematical Society and of the Instituteof Mathematical Statistics and their help are deeply appreciated.While a broad coverage of contemporary work in the theory of probability

and statistics is difficult, the field of applications of these disciplines is currentlyso wide that the program of a single symposium can include no more than afew particular domains. The domains covered at the Fifth Symposium wereselected on two principles. First, some applied problems appeared as subjects ofstudies by outstanding probabilists and statisticians invited to the Symposiumon account of their work in theory. Second, an effort was made to delineate afew fields of substantive studies that appear particularly promising for proba-bilistic and statistical treatment. One of the most fruitful fields of this categoryis undoubtedly biology and problems of health. Here we profited greatly by theadvice of Drs. LaMont Cole, Jerome Cornfield, F. N. David, Louis Hellman,Samuel Greenhouse, Hardin Jones, Samuel Karlin, David Krech, Lincoln Moses,Curt Stern, Michael B. Shimkin, and Cornelius Tobias. Quite a few of thesecolleagues are connected with the broad research activity of the National Insti-tutes of Health and helped to bring to our attention many novel and importantsubfields of research.

xi

xii PREFACE

In the field of astroniomy we are deeply inldebted to D)rs. 'N. 1U. Mayall,lRudolph iAlinkowski, and Thorntont L. IPage.For advice in the field of meteorology we are grateful to Drs. Earl I)roessler,

James Hughes, Dwight B. Kline, Morris Neiburger, Jerome Spar, Edward 1P.Todd, and 1. H. Wyckoff. Special thanks are due to Dr. Kennieth B. Spengler,Secretary of the American Meteorological Society.

Following the established tradition, V"olume I of the present Proceedings isgiven to the theory of statistics. Volume II is devoted to the theory of proba-bility. Because of the large amount of material, about 1000 pages in print, thisvolume had to be divided into two parts formed through a somewhat arbitraryclassification of papers. Volume III includes papers related to physical sciences:astronomy, theory of control, physics, and the theory of reliability. Volume IV,on biology and problems of health, includes papers on information and brainiphenomenia, on chance mechanisms in live organisms, on epidemiology, ongenetics, on medical diagnosis, on clinical trials, on carcinogelnesis and cellularpheniomenia, on demography, and on ecology. Some of these subdomains arealready subjects of well developed statistical treatment. Others appear to offeriniteresting and important possibilities.Compared to the 1'roceedings of the earlier Symposia, Volume V, being en-

tirely given to the problem of artificial weather modification, is an inniovationi.With the classification adopted for the first four volumes, weather modificationwould fit Volume III. It is assigned a special volume because of the specificity ofthe domain and because of its separateniess from all the other fields dealt within Volume III. Also, the novelty of the problem of weather modification, con-sidered by itself and as a field for statistical research, indicated the desirabilityof producing a comprehensive coverage of the more extensive experiments.Finally, it appears probable that the readership of the material being publishedill Volume V will be essentially different from that expected to be interested inV'olume III.The fifth Symposium would not have been possible witlhout very substantial

finaincial support from various sources. Hearty thaniks are due to Dr. ClarkKerr, Presidenit of the UTniversity of California, for a special grant made severalyears in advance of the Symposium. Without this grant, no planninig anid noinitial steps for the organization of the Symposium would have been possible.This initial triggerinig grant of the Uniiversity of Californiia was later supple-mented by the subsidy of the University Editorial Committee, without whichthe publication of the Proceedings, to be sold at a reasonable price, woul(d havebeeni a very difficult problem. To a very considerable extent, the theoreticalpart of the Symposium anid the part concernied with physical scienices, werefiianiced by The lrogram in Mathematics of the National Science Fouindationi,by the Air Force Office of Scieintific Research, by the Army Research Office, andby the Office of Naval Research. The large program on biology and problems ofhealth was made possible by a grant of the National Institutes of Health. The

PREFACE Xiii

program on weather modification was organized using a grant of the AtmosphericSciences Section of the National Science Foundation. Finally, we wish to recordspecial help from the Office of Naval Research, in the form of air transportationfor a number of foreign participants in the Symposium.

It is our pleasure to acknowledge gratefully the generosity of the governmentalinstitutions enumerated. The vitality of our Symposia and the growth of theProceedings, from 500 pages in 1945 to about 3,000 in 1965, seem to indicatethat the funds provided are being spent to fill a real need.The problems connected with the publication of such an amount of technical

material are very substantial, especially since some of the material was originallywritten in languages other than English and required translation. All effortswere made toward speedy publication at a reasonable price, and we are pleasedto acknowledge the excellent cooperation and assistance we received from theUniversity of California Press.For the translation of manuscripts, we are indebted to Drs. Amiel Feinstein,

Morris Friedman, and Mrs. C. Stein. We are also indebted to several of ourcolleagues in the Department for work connected with the preparation of manu-scripts for the printer. Special thanks are due to Professors E. L. Scott, M.Loeve, E. W. Barankin, to Drs. Carlos-Barbosa Dantas, W. Buihler, NoraSmiriga, Grace Yang, to Mr. Steve Stigler, and Mrs. M. Darland. We arepleased to acknowledge the technical help of Mrs. Sharlee Guise and Mrs-Carol Rule Roth.For taking care of the many complexities of editing technical manuscripts we

are deeply indebted to Miss Susan Jenkins whose patience and skill deservesuperlative praise. Thanks are also due to Mrs. Virginia Thompson for hergreatly appreciated assistance in the same process.To Mr. August Frug6, the Director of the University of California Press, we

extend heartfelt thanks for financial, technical, and moral support in publishingso much difficult material. Special thanks are due also to Joel Walters, Editorof the University of California Press. In spite of all our efforts, we found ourselvesunable to keep up with the schedule of publication proposed by the Press, butwe must thank them for helping us to keep the delays at a minimum and forproducing a publication in accordance with the usual excellent standards of theUniversity of California Press.Many thanks are due to our Administrative Assistant, Miss M. Genelly for

taking care of many financial and organizational difficulties. For transportation,housing, and other logistic problems connected with the organization of themeeting itself, very valuable assistance was received from the staff of theLaboratory and in particular from Miss June Haynes and Mrs. J. Lovasich.As was the case on many earlier similar occasions, for supervising and taking

care of the innumerable intricacies of local organization we are deeply indebtedto our colleague Professor Elizabeth L. Scott. It is a pleasure to express hereour deepest appreciation.

XiV PREFACE

Last but not least we wish to thanlk the Department of Statistics of theUniversity of California, Berkeley, and all our colleagues therein, for theirsympathetic attitude and help. Particular thanks are due to David Blackwell.

During the winter part of the Fifth Symposium, the Statistical Laboratorylost one of its organizers as well as one of its most active members. Our colleagueand cordial friend, Professor Evelyn Fix died of a heart attack on December 30,only a few hours after she acted as one of the hostesses at the banquet of theSymposium. Sit ei terra levis!

LUCIEN LE CAM JERZY NEYMANDirector, Statistical Laboratory

July, 1967

PREFACE TO VOLUME V

The idea of organizing a special Weather Modification Section of the FifthSymposium, and of publishing a separate volume of the Proceedings, specificallygiven to weather control problems, occurred to us in the fall of 1964 as a resultof studying the seven voluminous annual reports on the Swiss experimentGrossversuch III. Even though the primary purpose of this experiment washail prevention, the reports contain a wealth of data on rainfall and on othercollateral factors. The analysis we performed indicated not only the presenceof real effects of seeding on rainfall, but also the puzzling circumstance that insome not clearly defined conditions these effects are positive and in some otherconditions they are likely to be negative. Since over the last two decades anumber of randomized cloud seeding experiments have been carried out, itappeared timely to organize a systematic review of as many of them as prac-ticable. Jointly they may reveal an intelligible pattern of the effects of cloudseeding, even though in separate experiments these effects seem inconclusiveor contradictory.Weather control is a new field of experimentation with peculiarities not

encountered in other fields which stimulated the development of experimentaldesigns and of statistical techniques that are now available. Our hope is thatthe Weather Modification Section of the Symposium and the present volumewill serve as a stimulus for novel statistical research, theoretical as well asempirical, which will be beneficial both to statistics and to applied meteorology.It was a pleasure to find that the above ideas met with the approval of theWeather Modification Program of the National Science Foundation whosefinancial help is gratefully acknowledged.As we see it, the inspiration of fresh statistical research, and also an advance

in the understanding of the complex reactions of the weather to external stimuli,

PREFACE XV

depend very much oIn ready availability of observational data which couldserve for verification of various tentative hypotheses that may be formulated.Thus, an effort was made to assemble a substantial collection of experimentalresults on rainfall and on some collateral factors. This collection is published atthe end of the volume.To our knowledge, the present review of weather control studies is the fifth

to be published. The first review, which was brought to our attention by Dr.George Steck of Sandia Corporation, appeared more than 70 years ago. Therelevant article, written by M. W. Harrington under the title "Weather making,ancient and modern," is contained in the Smithsonian Report, 1894, pp. 249-270.The paper makes a distinction between scientific methods of rain making andthose based on superstition. It appears that already at that time some of the"scientific" methods had been patented. The paper is interesting and at timesamusing reading.The second published summary of weather modification studies seems to be

the controversial Final Report of the Advisory Committee on Weather Control,Vol. 1 and 2, Washington, D. C., 1957. This was followed by two reports of thePanel on Weather and Climate Modification of the National Academy ofSciences-National Research Council, the Preliminary Report of 1964 (NAS-NRC Publication 1236), and the two volume Final Report of 1966 (NAS-NRCPublication 1350). Even though contemporaneous and concerned with the samegeneral domain, the two volumes of the Final Report of the Panel have little incommon with the present volume of the Proceedings. There is no duplication.

Lucien M. LeCam Jerzy Neyman Elizabeth L. Scott

CONTENTSPhysical BackgroundM. NEIBURGER-Physical Factors in Precipitation Proc-

esses and Their Influence on the Effectiveness of CloudSeeding . . . . . . . . . . . . . . 1

Large Randomized Experiments

Louis J. BATTAN and A. RICHARD KASSANDER, JR.-Sum-mary of Results of a Randomized Cloud Seeding Projectin Arizona . . . . . . . . . . . . . 29

J. BERNIER-On the Design and Evaluation of CloudSeeding Experiments Performed by Electricite de France 35

WAYNE L. DECKER and PAUL T. SCHICKEDANz-TheEvaluatio'n of Rainfall Records from a Five Year CloudSeeding Experiment in Missouri . . . . . . . 55

DONALD L. EBERLY and LEWIS H. ROBINSON-Design andEvaluation of Randomized Wintertime Cloud Seedingat High Elevation . . . . . . . . . . . 65

K. R. GABRIEL-The Israeli Artificial Rainfall StimulationExperiment. Statistical Evaluation for the Period1961-65 ... . . . . . . . . . . . 91

LEWIS 0. GRANT and PAUL W. MIELKE, JR.-A Random-ized Cloud Seeding Experiment at Climax, Colorado,1960-65 ... . . . . . . . . . . . 115

E. PEREZ SILICEo-A Brief Description of an Experimenton Artificial Stimulation of Rain in the Necaxa Water-shed, Mexico . . . . . . . . . . . . . 133

PAUL SCHMID-On "Grossversuch III," a RandomizedHail Suppression Experiment in Switzerland . . . 141

E. J. SMITH-Cloud Seeding Experiments in Australia . 161

Relevant Climatological Studies

S. A. CHANGNON, JR. and F. A. HUFF-The Effect ofxvii

Xviii CONTENTS

Natural Rainfall Variability in Verification of RainModification Experiments . . . . . . . . . 177

THOMAS J. HENDERSON-Tracking Silver Iodide NucleiUnder Orographic Influence . . . . . . . . 199

Nonrandomized Operations

GLENN W. BRIER, THOMAS H. CARPENTER, and DWIGHTB. KLINE-Some Problems in Evaluating Cloud SeedingEffects Over Extensive Areas . . . . . . . . 209

HANS GERHARD MtLLER-Weather Modification Experi-ments in Bavaria . . . . . . . . . . . 223

Methodological Discussion

ARNOLD COURT-Randomized Cloud Seeding in the UnitedStates. . . . . . . . . . . . . . . 237

L. G. DAVIS and C. L. HOSLER-The Design, Executionand Evaluation of a Weather Modification Experiment 253

ARCHIE M. KAHAN-The Bureau of Reclamation's Atmos-pheric Water Resources Research Program . . . . 271

VUJICA M. YEVDJEVICH-Evaluation of Weather Modifi-cation as Expressed in Streamflow Response. . . . 283

JERZY NEYMAN and ELIZABETH L. ScoTrT-Some Outstand-ing Problems Relating to Rain Modification. . . . 293

JERZY NEYMAN and ELIZABETH L. ScoTT-Appendix. Plan-ning an Experiment with Cloud Seeding . . . . . 327

JERZY NEYMAN and ELIZABETH L. SCOTT-Note on theWeather Bureau ACN Project. . . . . . . . 351

J. M. WELLS and M. A. WELLS-Note on Project SCUD 357JERZY NEYMAN and ELIZABETH L. SCoTT-Note on Tech-

niques of Evaluation of Single Rain Stimulation Experi-ments. . . . . . . . . . . . . . . 371

ROBERT B. DAVIES and PREM S. PURI-Some Techniquesof Summary Evaluations of Several Independent Experi-ments. . . . . . . . . . . . . . . 385

CONTENTS XiX

BARRY R. JAMES-On Pitman Efficiency of Some Tests ofScale for the Gamma Distribution. . . . . . . 389

FRANK YATES-Discussion of Reports on Cloud SeedingExperiments . . . . . . . . . . . . . 395

Observational Data

A Collection of Data from Cloud Seeding Experiments inFive CountriesIntroduction . . . . . . . . . . . . . 399

I. Arizona Experiments . . . . . . . . . 400II. Australian Experiment (with Explanatory Note by

E. J. Smith) . . . . . . . . . . . 407III. An Experiment in France, 1963-64 . . . . . 424IV. Israeli Experiment, 1961-65 . . . . . . . 426V. Swiss Hail Prevention Experiment "Grossversuch

III," 1957-63 . . . . . . . . . . . 449