WMOD00440

• Title: HIPLEX-1: Statistical Evaluation
• Date: 4/4/1984
• Weather Modification - Doc Type: Report

Reprinted from JOURNAL OF CLIMATE AND ApPLIED METEOROLOGY, Vol. 23, No, 4, April 1984
American Meteorological Society
Printed in U.S.A.

HIPLEX-l: Statistical Evaluation

PAUL W. MIELKE, JR.I AND KENNETH J. BERRy2
Department of Statistics. Colorado State University. Fort Collins, CO 80523

ARNETT S. DENNIS

I'

,

Division of Atmospheric Resources Research, U,s. Bureau of Reclamation, Denver. CO 80225

PAUL L. SMITH AND JAMES R. MILLER, JR.
Institute of At:nospheric Sciences. South Dakota School of Mines and Technology, Rapid City. SD 57701

BERNARD A. SILVERMAN

Division of Atmospheric Resources Research, U,S. Bureau of Reclamation, Denver, CO 80225
(Manuscript received 22 December 1982; in final form 25 October 1983)

ABSTRACT

Results of statistical analyses for HIPLEX-l, a randomized cloud seeding experiment, are presented, The
analyses are based principally on multi-response permutation procedures (MRPP) as specified'before the
HIPLEX-I experiment was initiated. Even though the sample sizes are very small, due in part to the premature
termination of this experiment, the three primary response variables measured in the first five minutes following
treatment indicate pronounced differences in the development of ice crystals between nonseeded and seeded
events. However, the response variables measured more than five minutes after treatment generally do not
indicate obvious differences in the subsequent development of precipitation between nonseeded and seeded
events, This lack ot: difference is a possible consequence of I) lack of a seeding effect, 2) inadequacies in the
physical hypothesis, or 3) the small sample sizes. Consequently, only the initial steps in the HIPLEX-I physical
hypothesis could be confirmed in this evaluation of the experiment.

1. Introduction

The primary statistical results and interpretations
of HIPLEX-l, a randomized summertime cumulus
cloud seeding experiment, are presented in this paper.
Elsewhere in this issue, the experimental design, phys-
ical hypothesis, and response variables are described
in detail by Smith et al. (1984) and the physical in-
terpretations are considered by Cooper and Lawson
(1984). The purpose of this paper is to evaluate sta-
tistically the chain of events prescribed by the physical
hypothesis.
The statistical procedures are described in Section
2 and preliminary sample size estimates are explained
in Section 3. Section 4 presents the empirical results
of this study, and discussion and conclusions are given
in Section 5.

2. Statistical procedures

The statistical analyses in this paper are based on
multiresponse permutation procedures (MRPP). While

I Also Department of Atmospheric Science.
2 Also Department of Sociology.

@ 1984 American Meteorological Society

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complete descriptions and theoretical topics related to
MRPP are given elsewhere (Brockwell et al., 1982;
Mielke, 1978, 1979; Mielke et al., 1976, 1981a,b, 1982;
O'Reilly and Mielke, 1980), a brief description is given
here. Let
Q = {WIo . . . , WN}

be a finite population of N objects (e.g., cumulus
clouds), let

Xl = (XII, . . . , XrI)

denote r commensurate response measurementS for
object WI (I = 1,. . . , N) of a point in the r-dimensional
Euclidean data space, let

f:..I,J = [L (XkI - XkJ )2J 1/2
k=1

be the Euclidean distance between points associated
with objects WI and WJ in r-space, and let SI, . . . , Sg
denote an exhaustive partitioning of the N objects
comprising Q into g disjoint groups. In cloud seeding
experiments like HIPLEX-l, there will usually be two
groups (seeded and nonseeded experimental units) so
that g = 2. The choice of Euclidean distance yields an