AN EY,AjliINATION OF THE EFFECfS OF CLOUD SEEDING
m PHASE I OF THE SANTA BARBARA
CONVECTIVE BAND SEEDING TEST PROGRAM
by
Ral~h A. Bradley, Sushil S. Srivastava,
and Adolf Lanzdorf
FSU Statistics Report No. M467
ONR Technical Report No. 133
June, 1978
Florida State University
Department of Statistics
Tallahassee, Florida 32306
This work was supported by the Office of Naval Research under Contract
No. NOOOl4-76-C-0394. Reproduction in whole or in part is permitted for
any purpose of the United States Government.
Ui~l:L SSHIEO
SECURITY CLASSIFICATION OF THIS PAGE
REPORT DOCU~mNTATION PAGE
I. REPORT NU~iBER 2. GOVT. ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER
FSU Report No. j';j467
ONR Report No. 133
4. TITLE (and subtitle) 5. TYPE OF REPORT &PERIOD COVERED
AN EXAMINATION OF THE EFFECTS OF CLOUD Technical Report
SEEDING IN PHASE I OF THE SN~TA BARBARA 6. PERFORMING ORG. REPORT NUlvIBER
CONVECTIVE BAND SEEDING TEST PROGRAM
FSU Report N467
7. AUTHOR(s) 8. CONTRACT OR GRfu~T NUMBER(s)
Ralph A. Bradley, Sushil S. Srivastava, ONR NOOO14-76-C-0394
and Adolf Lanzdorf
9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELE~lliNT, PROJECT, TASK AREA
The Florida State University &WORK ~~IT NU~ffiERS
Department of Statistics
Tallahassee, Florida 32306
II. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE
Statistics and Probability Program June, 1978
Office of Naval Research Arlington, Virginia 22217 13. NUlvlBER OF PAGES
67
14. MONITORING AGENCY NN~E &ADDRESS (if 15. SECURITY CLASS (of this report)
different from Controlling Office) Unclassified
l5a. DECLASSIFICATION/DOWNGRADING
SCHEDULE
16. DISTRIBUTION STATEMENT lof thlS report)
Approved for public release; distribution unlimited.
17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from report).
18. SUPPLmmNTARY NOTES
19. KEY WORDS
Weather modification, cloud seeding, meteorological covariates, regression analyses,
cloud-seeding effects.
20. ABSTRACT
This report is concerned with an evaluation of the effects of cloud seeding in
Phase I of the Santa Barbara Convective Band Test Seeding Program conducted by North
American Weather Consultants, 1967-71. Earlier reports summarized data on precipitation
over both a Control Area and various Target Areas and provided summary data on meteorological
variables, all by convective band, the chosen experimental unit. In this
report, the meteorological variables are used as covariates to reduce experimental
error with a view to improved precision in the examination of both direct and interactive
effects of cloud seeding. Various analyses are reported with and without the
use of Control Area precipitation as a covariate and with and without weighting for
possibly heterogeneous error variances. A subset of the covariates was effective in
the reduction of experimental error by 60-70%. No effects of cloud seeding were found.
AN EXANINATION OF TIlE EFFECTS OF CLOUD SEEDINC IN PHASE I OF THE
SANTA BARBARA CONVECTIVE BAND SEEDING TEST PROGRAMI
Ralph A. Bradley, Sushil S. Srivastava and Adolf Lanzdorf
Department of Statistics, Florida State University, Tallahassee, Florida
I. INTRODUCTION
This report embodies results of a study of cloud-seeding effects based
on data from Phase I of the Santa Barbara Convective Band Seeding Test Program.
The details of these experiments and data generated from them have been discussed
in reports by Elliott and Thompson (1972), Brown, Thompson, and Elliott (1975),
and Thompson, Brown, and Elliott (1975). A brief description of this experiment
is also contained in an FSU Technical Report by Bradley, Srivastava, and Lanzdorf
(l977a), who considered data summarization. A condensation of the report has
been published (l977b).
Possible seeding effects are studied through the use of covariance analysis,
a statistical methodology which adjusts the response of an experimental unit to
that expected of a standard unit through the use of covariates (or concomitant
variables). In this methodology, a component of variability in the response
variable is removed b:" the introduction of covariates in the model and the re-ma.
ining variation is partitioned into components attributable to the treatment
effect, in this case seeding, and experimental error or residual variability,
usually called the residual component. The main advantage of use of covariates
is to increase precision in the assessment of treatment effects.
lResearch supported by the Office of Naval Research under Contract No.
NOOOl4-76-C-0394. Reproduction in whole or in part is permitted for any purpose
of the United States Government.
- 1 -
- 2 -
Meaningful statistical analyses of randomized experiments require experi-mental
data collected with the utmost care and precision. By their very nature,
weather modification experiments are subject to extremely heterogeneous experi-mental
units. Current uncertainty as to the effects.of cloud seeding, both as
direct effects and as interactive effects with atmospheric and meteorological vari-ables,
suggests that weather modification experimentation is concerned with de-tection
and estimation of small effects in the presence of high natural variability.
It is a tenet of the authors that identification and use of appropriate covariates
for use in covariance analysis provides the best current means to the examinatiort
of the effects of weather modification. With this objective, Gleeson (1977) sum-marized
concomitant variables associated with the Santa Barbara Phase I experi-ment.
Choice of response variable or variables is also a problem ar.d Bradley,
Srivastava and Lanzdorf (1977a) addressed this issue. The present paper reports
on the use of data summarized in these two references in investigation of the
effects of cloud seeding.
The Santa Barbara study attempted to be innovative in several ways. The
experimental unit was a convective band in a winter storm system; questions of
independence of responses to successive experimental uDits arise. The seeding
technique was to use a single ground-based seeding source and seeding was con-tinued
throu hout the eriod of the convective band silver iodide
'1
~\"H'~ .
enerators bein i ited at a roximatel fifteen minute intervals. The amount,
but perhaps not the intensity, of seeding was dependent on the time of passage
of the convective band, a time that we shall see can be very variable for a given
band at locations not widely separated. The choice of the convective band as the
experimental unit leads to other problems. The first is the i.dentification of
beginning and ending times of band passage, not only at the seeding site but also at
many raingage stations. A second is that rainfall at each raingage station
- 3 -
attributable to each experimental unit must be identified from raingage recordings.
The problem of measurement of responses for a given experimental unit is thus
more acute than in many weather modification experiments where a well defined
period, say 24 hours, is often used for the determination of precipitation from
an experimental unit.
Discussion of the available choices of response variables and of covariates
is given in Section II. Section III deals with the details of comprehensive exploratory
analyses undertaken to consider possible response variables, subsets
of covariates, and the form of covariance model to be used to study seeding effects.
The final form of the covariance model and results obtained from its use are discussed
in Section IV. Finally, Section V constitutes a summary with conclusions
reached.
- 4 -
II. THE SANTA BARBARA PHASE I DATA
This section outlines data used for the covariance analyses. North
American Weather Consultants had two projects, one for the Naval Weapons Center
(NWC) at China Lake, California, and the other for the Bureau of Reclamation
at Denver, Colorado. The analysis undertaken for the Bureau of Reclamation used
a larger network of raingage stations than used for the Naval Weapons Center
study. The reports by Elliott and Thompson (1972) and by Thompson, Brown, and
Elliott (1975) discuss data used for the NWC study, while information on the
network of stations for the Bureau of Reclamation study are contained in the
report by Brown, Thompson, and Elliott (1975).
Two alternative measures of precipitation in any given portion of a Target
Area were explored for possible use as response variables in the covariance analyses.
These were (i) the simple mean of raingage measurements for the region and
(ii) the volume of precipitation over the designated region. Four subdivisions
of the Target Area, as defined in the Bureau of Reclamation study by Brown,
Thompson and Elliott (1975), with modifications introduced by Bradley, Srivastava
and Lanzdorf (1977a), were initially considered for the analyses. Later, for
comparison purposes, the Target Area, as defined for the mvc studies, Elliott and
Thompson (1972) and Thompson, Brown and Elliott (1975), was also introduced. This
area has been designated Area (v) in this report. Phase I of the Santa Barbara experiments
also had a Control Area to the west of the ground seeding site where
no seeding effects were expected. Definitions of areas used to measure response
variables and of the Control Area are summarized in Table 1.
- 5 -
Table 1: DEFINITIONS OF RESPONSE AREAS
Area
(i)
(ii)
(iii)
(iv)
(v)
Control 1
Range in Degrees No. of
Latitude Longitude Stations
(34.0, 35.25) (118.0, 120.02) 107
(34.4, 35.0) (119.51, 120.02) 26
(34.0, 35. 0) (118.0, 119.51) 72
(34. 0, 3S.0) (118.0, 120.02) 98
All Stations in NWC Reports to the East
of Seeding Site at longitude, 120.02 61
(34.4, 35.25) (120.02, 120.60) 34
lControl Area for NWC data consisted of all 39 stations west of
Seeding Site at longitude, 120.02°.
Approximate orientations of Areas (i) to (iv) and of the Control Area have been
shown in Figure 1.
Simple means of raingage measurements and volumes of precipitations together
with their variances for Areas (i) to (iv) and for the Control Area have been
reported by Bradley, Srivastava, and Lanzdorf (1977a). Means and variances for
Area (v) (and also for the corresponding Control Area) have been recalculated.
For this area, the response variable, volume, was not used.
The covariates considered to adjust the response variable were taken from a
study by Gleeson (1977). In all, 18 variables measuring synoptic and meteorolo-gical
conditions for Phase I convective bands were evaluated and reported by Gleeson.
Out of these, four variables, (i) date of band passage, (ii) number of radio-sonde
observations used to measure the meteorological variables, (iii) code
indicating station source of the radiosonde observation, and (iv) time of radiosonde
CJ\ •
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34
8
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r---------J, _. ."'11 ~LH•.' eLi ... : ~
FIGURE 1: MAP SHOWING APPROXIMATE DEMARCA1'IONS FOR AREAS (i) TO (iv).
Area within the dotted line!'; i~ Area (i). Area (iv) is the sum of areas (ii) and (iii).
- 7 -
release, were assumed to have no predictive relationship with the response and were
thus not considered as possible covariates. The concomitant variable labelled
"treatment" by Gleeson, giving the number of fusees burnt for each band, was also
not considered, since this information is combined essentially in two other covariates,
Duration of Band Passage, discussed next, and an indicator variable for
seeding or no seeding, included in the analysis. Two variables giving the beginning
and the end times of band passage were combined into one measure called the Duration
of Band Passage. Thus, in all, there were twelve covariates available for use
in the study of seeding effects. These are named Xl' X2, ... , Xl2 and are
listed below:
Xl = Mixing Ratio
X2 = 700 mb wind Speed
X3 = Direction (of 700 mb wind)
X4 = Mean (wind) Speed
Xs = Direction (of average vector wind)
X6 = 500 mb Temperature
X7 = Stability Class
Xs = Showalter Index
X9 = Stability Wind (Speed)
XIO = Direction (of Stability Wind)
Xu = Instability Transport
Xl2 = Duration of Band Passage.
For a more detailed description of these variables, the reader is referred to
Gleeson (1977).
The use of convective bands as experimental units for the Santa 3arbara experiments
is innovative and has several advantages. Nevertheless, it appears that exact
determination of beginning and ending times of band passage at each of the raingage
- 8 -
stations was difficult and introduced an additional source of variation that
affected the precipitation measurements as well as the calculation of band duration
at each station. A cursory examination of the duration data by bands for two
neighboring stations, 5211 and 5212, revealed wide disparities in the time lengths
of precipitations at these stations. The frequency distribution by bands for the
absolute differences in duration times of band passage at these two raingage stations
is given in Table 2. Out of a total of 76 bands for which duration data were
available for both locations, there were 14 bands for which duration at one station
exceeded that at the other by at least 30 minutes. The difference for one band
was actually 90 minutes. While sizable differences in band durations of two neigh-boring
locations are apparently possible, Table 2 does demonstrate the inherent
variability in the available experimental data.
Table 2: FREQUENCY DISTRIBUTION OF ABSOLUTE DIFFERENCES OF DURATIONS
(IN MINUTES) BETWEEN LOCATIONS S211 AND S212
Absolute Diff. (Minutes) 0-10 11-20 21-30 31-40 41-50 51-60 61+ Totals
Unseeded Bands 20 12 3 2 1 - 1 39
Seeded Bands 16 7 4 3 2 5 - 37
Total 36 19 7 5 3 5 1 76
- 9 -
III. EXPLORATORY ANALYSES
In the post facto analysis of experimental data, decisions on the choice
of a statistical model are often data dependent. This is particularly true when
regression or covariance models are used. For the Santa Barbara Phase I data,
Gleeson (1977) developed possible independent variables or covariates. Prelimin-ary
investigation of their utilities is reported in this section. These investi-gat
ions use the precipitation responses of the experiment and they are used again
in Section IV where more details are given on final analyses after choices of
possible models. In subsequent work, the investigators should be able to confirm
model choices with Santa Barbara Phase II data. Area (v) was not used in exploratory
analyses.
A good covariance model is one which uses a small number of covariates and
still explains a major portion of variation in the response variable. Extensive
exploratory analyses were undertaken to determine which subset of the covariates
listed in Section II would explain major variation in the response variable. These
analyses were also used to determine (i) whether volume of precipitation in desig-nated
target areas would be a better response variable than the corresponding
Mean of Raingage measurements, (ii) whether the covariance model should be weighted
or unweighted, and (iii) whether it would be useful to include the Control Area
precipitation measure as a covariate. While Control Area precipitation would seem
to be a most promising covariate intuitively, it could remove the effects of cloud
seeding if Control Area contamination from seeding had occurred.
Let Y represent the response variable for the Target Area, simple mean of
raingage measurements or volume of precipitation, as the case may be. Let Xc
represent the corresponding measure of precipitation in the Control Area and let
Z be the seeding variable assuming values 0 or 1 as the band is unseeded or
seeded. Further, let X., i = 1, ... ,12, be the covariates listed in Section II,
I
- 10 -
and let I. = x.z, j = 1,2, ... ,12, represent interactions of t;lose covariates
J J
with seeding. The four models that were used for exploratory analyses were:
12
y = aO + 2 a. x. + oZ + E, ( 1)
i=l 1. 1.
12 12
Y = 80 + 2 s. x. + 2 y. I. + oZ + E, (2)
i=l 1. 1. j =1 J J
12
Y = aO + aX + 2 a.X. + oZ + E, ( 3) c i=l 1. 1.
and
12 12
y = So + f3X + I B. X. + I y.1. + oZ + E. (4) c i=l 1. 1. j =1 J J
In i\Jodels (1) and (3), the twelve covariates of Section II are used, together
with Control Area precipitation in [,lodel (3), to explain and reduce variation in
the response variable. The indicator variable Z for seeding can then be examined
for effect after such adj ustment. In lvlodels (2) and (4), the same covariates are
used but additional terms in the models are introduced in order to consider pos-sible
interactive effects of seeding with the meteorological covariates. This was
done since the effects of seeding may be dependent on desirable meterological con-ditions
as measured by the covariates.
Each model was fitted to the response data for Target Areas (i)-(iv) of
Table 1. The two responses, Target Area [·:jean Precipitation and Target Area Volume
of Precipitation, were taken from Tables A-12 and A-II of Bradley, Srivastava
and Lanzdorf (1977a) respectively. Control Area responses were given in the same
tables. Note that these responses were proviued together with estimates of their
variances, variances that are somewhat heterogeneous. Accordingly, since the
- 11 -
models were to be fitted by the method of least squares, the question of whether
to use unweighted or weighted least squares had to be addressed. In unweighted
least squares, parameters of the right-hand members of [~odels (1)-(4) were esti-mated
by minimization of
where f (u) represents the appropriate right-hand model member, u representing
a
the corresponding independent variables. In weighted least squares, the quantity
minimized was
NI
w [Y - f (u)]2,
a=l a a a
where w represents the reciprocal of the variance of the response, Y. In a a
both situations, N represents the number of experimental units (convective bands)
used. In all, 32 regression or model fitting runs were made.
In these initial regressions, the SPSS regression program was used and this
is a . step-up" or forward elimination procedure. Independent variables are intro-duced
into the equation or model one at a time. The first independent variable
introduced is the one explaining the highest proportion of variation in response
Y, the next is the one accounting for the highest proportion of residual variation
after use of the first independent variable and so on. The single most important
index emerging from each regression analysis is the coefficient of determination R2 ,
the square of the multiple correlation coefficient. Values of R2 are given in
Tables A-I and A-2 for the 32 runs when the response variable was the Target Area
mean of raingage measurements and when it was the Target Area volume of precipitation
respectively. Note that the values of R2 reported result from the 'step-up" pro-cedure
and somewhat differing subsets of independent variables have been used.
- 12 -
The first thing that emerges from a perusal of Tables A-I and A-2 is that
the inclusion of X amongst the covariates significantly increases the value
c
Thus, it appears that X is an important covariate.
c
The possibility
that this covariate may be contaminated, that is, may have been influenced by
seeding will be examined later. Further, these tables show that for all models
in which X is included, use of the simple mean of raingage measurements results
c
in considerably higher values of R2 than when volume is used as the response
variable. For models without X) mean precipitation continues to yield higher
c
values of R2 than volume in the unweighted cases, but not in the weighted cases.
Bradley, Srivastava and Lanzdorf (1977a) in their Table 6 showed that mean pre-cipitation
and precipitation volume were highly correlated (correlations in
excess of 0.97) for all specifed target regions. Thus, they should exhibit very
sindlar performances in analyses in this report.
The effect of weighting can be seen also from Tables A-I and A-2 through
comparison of paired columns. If R2 is chosen as a criterion, weighting does
not appear to be helpful. deighted models always have lower values of R2 than
the unweighted ones when the response variable used is mean precipitation and
Xc is included. This is essentially the case also when volumes are useu and
X is included. If X is not includeJ as a covariate, the situation is the c c
same with response variable, mean precipitation. However, with the use of volumes,
no definitive conclusions can be reached; weighted models have higher values of
R2 for model fitting in Areas (i) and (ii) and have lower values of R2 for
model fitting in Areas (iii) and (iv).
Comparisons of weighted models with unweighted ones were examined also by
a detailed analysis of residuals obtained from fitting the various models. Resi-duals
from weighted models had more extreme values; their distributions were
right-skewed and leptokurtic more frequently. On the other hand, residuals from
- 13 -
ul1\veightedmodels had distributions still somewhat right-skewed but more synunetric
and the numbers of residuals outside the two standard deviation range were rather
comparable to what one would expect for san~les from normal populations.
The inclusion of interaction terms (in r·jode Is (2) and (4)) over and above
the basic covariates (in Models (1) and (3)) does increase the values of "."Z.
as must be the case. However, these increases are relatively small, usually not
significant. Interaction terms seem to play even smaller roles in models with
Xc than in those without Xc.
To sum up, if RZ is used as the criterion, models with X are better c
than those without X, since the former have considerably higher values of RZ
c
than the latter. In these cases, it is clear also that mean precipitation is a
response variable more responsive to the independent variables than volume.
Finally, weighting does not seem to be effective, although it has appeal theoreti-cally.
Interations do not play an appreciable role in models with simple means
and X
c
The problem of selecting a subset of covariates which would best describe
the response variable without an appreciable sacrifice in the value of RZ was
handled through an examination of (i) a matrix of correlation coefficients, and
(ii) the rankings of covariates entering the estimated regression equations.
Some subjectivity is involved necessarily in the final choice of covariates.
The correlation coefficients between pairs of variables measuring mean pre-cipitation
Y in the total target area, Area (i), the mean precipitation in
Control Area Xc' and twelve covariates, Xl' X2, ... , X12 , are given in Appendix
Table A-3. A good covariate is usually one which (a) has large absolute corre-lation
with the response variable and (b) is simultaneously not heavily corre-lated
with any other covariate. The latter criterion helps reduce, even eliminate,
problems of multicollinearity in regression analyses. Further, any covariate
- 14 -
which is affected by seeding wi+1 have a large correlation coefficient with
z. It is seen from Table A-3 that none of the covariates (including x ) has such
c
a high correlation and X may be used as a covariate.
c
If the sample correlation coefficient between two variables (X, Y) is denoted
by reX, Y), Appendix Tabb A-3 shows that somewhat large correlation coefficients
are (i) r(X3, Xs) = 0.90, (ii) r(X4, Xg) = 0.94, and (iii) r(XS' X10) = 0.96.
One covariate from each of the above pairs might be deleted in order to avoid
possible problems of multicollinearity and in order to achieve parsimony. Note
that three covariates, X2, X4, and Xg, all measure wind speed and have sizeable
correlations. (See definitions of covariates on Page 7). The corresponding
measures of wind direction are X3' XS' and X10 ' again with large correlations.
The deletion of covariates X4 and Xs is indicated.
Appendix Table A-4 gives the order in which various covariates entered the
regression equation in the case of unweighted ~odels (1) without X and when
c
the response variable used was mean precipitation. This table also shows the
proportion of variation in Y explained by the introduction of the first eight
covariates. It is seen that almost as much variation ln Y can be explained
by only eight covariates and as by the inclusion of all covariates.
The pair of covariates, X4 and XS' recon~ended for deletion, do not
appear in Table A-4. In addition, Xg, the third wind speed, and X10 ' the third
measure of wind direction, are not among the sets of first eight covariates in
Table A-4. Information on wind speed and wind direction is being carried by
covariates X2 and X3 appearing in Table A-4. Further, the covariate Xl'
mixing ratio, is known from meteorological considerations not to be an important
covariate. It has low rankings among the covariates in Table A-4. Five covariates
Xl' X4, XS' Xg, and XIO will be deleted in our final analyses.
- 15 -
As a result of the preliminary analyses of this section, seven covariates
will be used in examination of the effects of seeding in the next section. These
covariates are:
X2 - 700 rnb Wind Speed,
X3 - 700 rnb Wind Direction,
X
6
- 500 mb Temperature,
X7 - Stability Class,
Xs - Showalter Index,
XII - Instability Transport,
Xl2 - Duration of Band Passage.
In addition, X, Control Area Precipitation, will be used. The preliminary c
analyses suggest that unweighted analyses be used with inclusion of X . c
For
completeness, we shall, in fact, use the seven covariates listed and do weighted
and unweighted analyses with and without inclusion of x . c
Analyses will be done
using both mean precipitation and precipitation volume as dependent variables
and interactions will be both included and excluded.
- 16 -
IV. THE EFFECTS OF CLOUD SEEDING
In this section, we report on regression analyses completed with a view to
examinations of both the direct effects of cloud seeding and the possible interactive
effects of cloud seeding with the seven covariates listed on Page 15. Models (1)-(4)
of Page 10 were used except that the number of covariates and interactions have
been reduced from 12 to 7. Analyses with Target Mean Precipitation as the dependent
variable Y were done for all five Target Areas, the last consisting of
the set of stations used in the Naval Weapons Center study; when Xc was included,
it was taken to be the Control Area Mean Precipitation. Analyses with Target
Precipitation Volume were done for Target Areas (i)-(iv) only and when Xc was
included in a model, it was taken to be the Control Area Precipitation Volume.
While the exploratory analyses suggested that Precipitation Mean is the better
independent variable and that weighting is not beneficial, we report on analyses
both with and without weighting and with either dependent variable. We report
also on analyses with and without inclusion of X as an independent variable c
even though the exploratory analyses indicated its efficiency and suggested that
it is free of contamination from seeding effects.
Appendix Tables A-S and A-6 give values of the coefficient of determination
R2 for the new analyses with the number of covariates reduced to 7. The regression
analyses done assume that the models have been determined beforehand and do
not involve "step up" routines. These tables are directly comparable to Tables
A-I and A-2. We see that the reduced models lead to only small reduction in
values of R2, reductions consistently of approximate size 0.02. These tables
tend to confirm the wisdom of reducing the number of covariates. It is possible
that the number of covariates could be reduced further but sufficient data are
available for use of these models. The covariates have been effective in the
- 17 -
control of experimental error. Variation in the response variable Y has been
reduced by 60-70% as measured by 100 R2 and residual variation, or experimental
error, is correspondingly smaller, thus increasing sensitivity in examination
of the effects of seeding.
Detailed examination of Tables A-5 and A-6 leads to the same conclusions
relative to choice of models as obtained in Section III. This was to be expected
since the same basic data are used in both sections. Note that Table A-5 has
an additional row for Target Area (v) and that values of R2 here are good,
x is included in the models. c
The estimated regression coefficients, estimated values of the parameters
particularly when the Control Area Precipitation
in Models (1)-(4) with 7 covariates or with 7 covariates and 7 interactions, are
given in Tables A-7 to A-22. Let us take an example to illustrate use of these
tables. Model (4) now has the specific form,
When Y is Target Area Precipitation Mean and X is Control Area Precipitation c
Mean and an unweighted analysis is used for Target Area (iii), estimates of the
parameters above may be taken from Table A-lO and the estimated regression equa-tion
is
Y = 0.0568 + 0.6125 Xc + 0.0020 X2 - 0.0010 X3 - 0.0052 X6 - 0.0248 X7
- 0.0008 Xs - 0.0002 XII + 0.0012 Xl2 + 0.0077 12 - 0.0002 13 - 0.0049 16
- 0.0478 17 - 0.0172 18 + 0.0002 III + 0.0001 112 - 0.2174 Z.
- 18 -
Other estimated regression equations may be read directly from the Appendix
tables or their estimated regression coefficients examined in the tables.
In Tables A-7 to A-22, the statistical significances of individual esti-mated
regression coefficients have been examined and asterisks indicate levels
of significance. The statistical test used is a test of the individual regression
coefficient, the null hypothesis being HO: B. = a for specified i against
1
the alternative, H : a S. ;t O.
1
The tests have been made to indicate in a sense
the importance of terms in the models. Interpretation requires caution. The
estimated regression coefficients are correlated. The inclusion or exclusion
of an additional independent variable, for example x , c affects the estimates
of all of the other regression coefficients. The various analyses involve the
same basic data set or subsets of it and are then heavily dependent and tend to
give similar results.
Interpretation of individual regression coefficients is fraught with peril
and has led to many erroneous conclusions in interpretation of regression analy-sis.
The notion that a marginal change in rainfall will result from a unit
increase in an independent variable, sayan increase in wind velocity, is a
doubtful concept because the specified independent variable may be such that a
unit change in that variable must induce changes in other variables. We attempt
only some broad summaries of the coefficients in Tables A-7 to A-22. The more
important covariates are X12 , Duration of Band Passage, X2, 700 mb Wind Speed,
X3, 700 mb Wind Direction, and possibly X7' Stability Class. The importance of
these covariates is diminished by introduction of x , Control Area Precipitation,
c
particularly in regard to X3 and ~ and sometimes X2. It seems clear that
and X
c
are the best predictors of Y, Target Area Precipitatio~ and this
is intuitively reasonable since increases in both Duration and Control Area
Precipitation should be positively correlated with Target Area Precipitation.
- 19 -
It has been argued that the major effect of cloud seeding may be to increase
the duration time of precipitation and we comment on this in the next section.
The effect of weighting is to reduce the apparent importance of X
Z
' X
3
and XII
as covariates while Xc remains the important independent variable. The intro-duct
ion of interaction terms also tends to reduce the apparent importance
of the covariates, particularly X3 and XII' Results for the response variables,
Target Area Precipitation Mean and Target Area Precipitation Volume, are very
similar and the two responses have been shown to be highly correlated.
None of the regression coefficients associated with the seeding variable
Z is significantly different from zero. Accordingly, no real interpretation is
possible. The regression coefficient tends to be positive when interactions
are absent and they tend to be negative except for Target Area (ii) when interactions
are included in the model. There is little indication that interaction
terms are in~ortant and, if there is any suggestion present, it would relate
to 12 and lIZ' the interactions of seeding with 700 mb Wind Speed and Duration
of Band Passages respectively. We believe that any decisions on the effects
of cloud seeding are best based on the analysis of variance tables discussed
immediately below.
Appendix Tables A-23 to A-38 show the analysis of variance tables corresponding
to Tables A-7 to A-22 and in the same sequence. One of the models,
models (1)-(4) is selected. The first source of variation is listed as llcovariatesil
X is not included and c
In the two situations, 7 or 8
in each table; these are the 7 covariates specified if
the 7 covariates plus Xc if Xc is included.
degrees of freedom respectively are shown for this source of variation. If
interaction terms are present in the model, the second listed source of variation
is Interaction with 7 degrees of freedom. The third source of variation (second
if interaction terms not included) is Seeding with 1 degree of freedom and the
- 20 -
final source labelled nResidual l
·. measures variation about the fitted regression
model. The Residual Sum of Squares is the sum of squared deviations of observed
responses Y from corresponding values of Y predicted from the estimated
model. The order in which entries are calculated in the analysis of variance
table is important. The sum of squares for covariates is obtained by first
fitting a model with only constant and covariate terms; it represents the
amount of variation in the response variable Y explained by the covariates
alone. The sum of squares for Interaction (when included) represents the additional
amount of variation in the response variable explained by the inter-·
action terms in the model in cOlfiparison with the first model containing only
constant and covariate terms. Finally, the sum of squares for Seeding measures
the additional variation in response (additional over constant, covariate, and
interaction terms) explained by inclusion of the Seeding variable Z in the
model. The effect of the analysis is to adjust responses Y for mean values
of the covariates and interactions, divide the sample of adjusted responses
into two groups, one for seeding and one for no-seeding, and compare these two
adjusted samples for effect of seeding. Values of R2 tabulated in Tables A-S
and A-6 may be recovered from these tables -- to compute R2 , take the sum of
all sums of squares in a table section except that for Residual and divide by
the sum of all sums of squares (including Residual) in the table section.
Interpretation of the analyses of variance in the various table sections
of Tables A-23 to A-33 is easy. For every analysis of variance, Covariates are
significant at the O.OI-level of significance showing that they are effective
in reducing response variation and in improving the precision of tests for
Interactions and Seeding. For every analysis of variance, the test for Seeding
is not significant at the O.OS-level of significances. Further, nearly every
value of F for Seeding is less than unity, a fact that might be of concern if
- 21 -
it were not for the dependence of the various analyses because of use of the
same data set or subsets of the data set. The tests of Interaction are somewhat
more difficult to assess. No Interactions are significant for the unweighted
analyses with either the response variable, Target Area Precipitation Mean or
Target Area Precipitation Volume. The weighted analyses do show significance
of Interactions in several situations, sometimes for Target Area (iii) and sometimes
for Target Areas (i) and (ii); no clear pattern is discernable and we have
indicated in Section III that unweighted analyses seem preferable.
We may conclude this section by noting that there is no evidence of a real
direct effect of cloud seeding on Target Area Precipitation, either in enhancement
of precipitation or in retardation of precipitation. We conclude also that
there is little evidence of an interactive effect of cloud seeding with the
covariates available. If an interactive effect had been clearly evident, it
might have suggested that seeding could be more effective under certain meteorological
conditions measured by one or more of the covariates than under other
conditions.
- 22 -
V. OTHER ANALYSES
Elliott and Thompson (1972) in their Abstract and in their Section 6 suggest
that an effect of cloud seeding may be to increase X12 , Duration of Band Passage,
and hence total precipitation attributable to a band. They state:
tlAn analysis of four years of data on the duration of bands seeded
from the ground site compared to those bands not seeded strongly suggests
that a definite relationship exists between increased total precipitation
in seeded bands and the increased total duration of seeded
bands. "
We agree that band duration is highly correlated with Mean Precipitation for
the band; see Table A-3 -- the correlation is 0.61. It has already been noted that
X12 is perhaps the best covariate in our analyses. We do not agree that cloud
seeding has an effect in Target Area Precipitation nor do we agree that cloud
seeding increases band duration. In order to investigate this issue, we used
X12 as a response variable (in place of Y) and the remaining eleven of the
twelve covariates as covariates in models like those specified as (1) and (2).
The "step-upii procedure was used and values of R2 calculated simi lar to those
of Table A-S were of the order of 0.18 and 0.28 when interactions were not included
and were included respectively. Analysis of variance showed no direct or inter-active
effects of seeding on band duration. We believe that mean precipitation
and band duration are correlated as seems intuitively likely and that neither are
directly affected by cloud seeding.
Neyman (1977, 1976, 1975) has been concerned with the far-away (distances
between 90 and 180 miles) of local cloud seeding and theories as to the mechanism
involved. In the Grossversuch III experiment in Switzerland, the far-away,
down-wind effects were an apparent increase in precipitation when seeding took
place in the presence of a warm stability layer. In studies of cloud seeding
over the Santa Catalina ~buntains in Arizona, there were apparent decreases in
- 23 -
precipitation at substantial distances down-wind and large apparent increases
in far-away areas "on the right" of the day's wind direction. In the light of
these findings, we attempted to investigate the situation with the Phase I Santa
Barbara data.
Our initial choice of Target Areas (i)-(iv) was made with a thought of investigation
of areas geographically different but with good raingage coverage;
Target Areas (ii) and (iii), differing in distance from the seeding site, were
of particular interest. To attempt to study down-wind effects more specifically,
precipitation data on the North-East corner of the Target Area should be considered
because wind Jirection was quite stable for the various convective bands
chosen as experimental units. The desired target area, basically stations in
Kearn County, is the area between latitude 35.0° and 35.25° and longitude 118.0°
and 119.51°. However, the number of raingage stations with non-missing observations
in the area is too small for meaningful analysis. An extended corner region
consisting of all raingage stations North of 35.0° latitude and East of the seeding
site (longitude 120.02°) was used. Covariance analysis similar to those reported
above were carried out using Target Area Precipitation Mean as the response
variable. There was no indication of seeding effect and other details of the
analysis did not provide any information different from that reported in detail
on Target Areas (i)-(v).
Serfling (1977) provided some simple investigations of the effects of cloud
seeding with the Santa Barbara Phase I data. He used covariate information to
classify non-seeded and seeded experimental units (convective bands) by Stability
Category and Temperature Category (by 500 mb temperature), our covariates X6
and X7. He tried first to compare seeded and non-seeded bands within table
cells on the basis of the ratios, Mean Target Area Precipitation to ~~an Control
Area Precipitation; but abandoned this approach because of the high variability
- 24 -
of these ratios. He then formed ratios from the average (over bands in the cell)
of Mean Target Area Precipitations divided by the average of Mean Control Area
Precipitations, the ratios calculated separately for seeded and non-seeded bands.
This approach suggested effects due to seeding for bands in the UL (unstable,
low convective instability base) stability class and the Medium (500 mb temperature
between -17.S o C and -22.S 0 C) temperature class and for bands in the UL stability
class and the Warm (above l7.S o C) temperature class. In our analyses, X6 and
X7 do not seem to have any special role nor do they appear to interact with
seeding. In the analyses by Serfling, the data used were derived from Elliott
and Thompson (1972) and constitute only a subset of the data used in this report.
Scott (1978) has addressed the issue of data summarization using a multivariate
approach. He sought to find components of variation among Target Area
raingage observations that would yield data reduction and possibly interpretable
components. He was successful in this and, in a subsequent report, will consider
use of one or more of these components as the response variable in regression or
covariate analyses similar to those of this report.
- 25 -
VI. SurvlJ'VlARY AND CONCLUSIONS
This teclmical report is the culmination of a major effort in reanalysis of
data from Phase I of the Santa Barbara Convective Band Seeding Test Program.
Two ideas have been inherent in the approach. The first was that improved precision
in examination of cloud-seeding effects should result from the use of
meteorological covariates in appropriate analyses. Only in this way does it
seem likely that extremely heterogeneous experimental observations can be brought
under good experimental control. Gleeson (1977) su~narized the meteorological
data associated with the experimental units in the Phase I experimentation.
The second idea was that improvement in summarization of raingage observations
in a specified geographical area might result from the use of fitted response
surfaces in calculation of precipitation volume, the usual alternative being
calculation of area means over the raingages. Bradley, Srivastava and Lanzdorf
(l977a, 1977b) reported on the use of response surfaces for raingage data summarization.
Twelve possible covariates were identified for use. Exploratory analyses
led to reduction of this number to seven. An additional independent variable,
Control Area Precipitation, was sometimes used. From the array of covariates
available, Duration of Band Passage, 700 mb Wind Speed, 700 rnb Wind Direction,
and possibly Stability Class seemeu most use£ul. The best single predictor of
Target Area Precipitation is Control Area Precipitation. Concern that both
Control Area Precipitation and Duration of Band Passage might be affected by
seeding seemed unfounded. The use of covariateswas very effective in the reduction
of experimental error and it is judged that use of covariates is important
in the design and analysis of future weather modification experiments. Further,
- 26 -
future meteorological research should examine the possibility of identification
of new or additional covariates that may be even more helpful.
Bradley, Srivastava and Lanzdorf (l977a) noted that precipitation volume
was highly correlated with precipitation mean for designated target areas.
Because of that high correlation and the fact that analyses in this report with
Target Area Precipitation Volume as the dependent or response variable do not
yield any new insights in the data analysis, it is concluded that the additional
effort to compute precipitation vollli~es was not worthwhile. We do believe that
it was an idea that needed trial and hence justified.
Examination of the direct effects of cloud seeding and of possible differential
effects of cloud seeding through interaction with covariates yielded no
indication that cloud seeding was effective.
Our conclusion that there is no evidence that cloud seeding was effective
in the Phase I Santa Barbara experimentation is at variance with conclusions
reached in reports of North American Weather Consultants. Neither their analyses
nor those reported here are free from criticism. In our analyses, we have
treated the independent variables, including the meteorological covariates, as
known without error when they are clearly subj ect to error. We have assumed that
the response variable has an appropriately Normal or Gaussian distribution
with homogeneous error variances and these assumptions are not fully tenable.
We have treated convective bands as independent experimental units and we have
some concern about this when several convective bands are part of the same storm
system. In the NAWC analyses, data by raingage station is evaluated over the
set of convective bands. These separate analyses are surely not independent
both because of correlated responses over raingage stations, particularly those
close together, and because common standardization based on control area precipitation
was used. We propose to investigate further the use of data by raingage
st~tion and the NAWC analyses and comment in more detail in a subsequent report.
- 27 -
Summary conclusions are as follows:
1. The analyses of this report give no indication that cloud seeding had
either a direct effect or an interactive effect on precipitation in designated
target areas.
2. The use of meteorological covariates was effective in reducing the
experimental error, the measure necessary for evaluation of the effectiveness
of cloud seeding.
3. The most effective meteorological variables for use as covariates were
Duration of Passage, 700 mb Wind Speed, 700 mb Wind Duration, and possibly
Stability Class.
4. The use of a Control Area on which precipitation is measured and for
which possible contamination by seeding is precluded provides a most effective
independent variable for control of experimental error.
S. The use of response surface methods for summarization of raingage data
for a specified geographical area was not superior to use of a simple average
of the raingage measurements.
In comment on the design of the experiments, we have noted the value of
the Control Area. For future improvement of similar experiments, possible additional
meteorological covariates should be considered and attention given
tOas precise measurement of all such covariates as possible. This is likely
to involve more radiosonde measurements, perhaps more widely dispersed geographically.
The response to all experimental units is based on a network of raingages. In
many studies, a twenty-four hour period for the raingage recording is defined
although Neyman, in references cited, has raised questions of adjustment of this
period for distance from the seeding site. In the Santa Barbara study, it was
necessary to determine the period of convective band passage at each raingage
- 28 -
in order to record precipitation attributable to that band. It appears that
this was difficult and that the times of band passage were very variable. It
may be that this problem created a major source of data heterogeneity.
- 29 -
REFERENCES
Bradley, Ralph A., Srivastava, Sushil S., and Lanzdorf, Adolf (1977a): Data
Summarization in a Weather Modification Experiment: I. A Response
Surface Approach, FSU Statistics Report No. M4l7, ONR Technical Report
No. 117, Florida State University, Department of Statistics, Tallahassee,
Florida.
Bradley, Ralph A., Srivastava, Sushil S., and Lanzdorf, Adolf (1977b): Summarization
of Precipitation Data for a Weather Modification Experiment,
Proc. Fifth Conf. on Prob. and Statist., Amer. Met. Soc., Boston, Mass.
Brown, Keith J., Thompson, John R., and Elliott, Robert D. (1975): Large Scale
Effects of Cloud Seeding, Final Report 1970-74 Seasons, Aerometric
Research Inc., Santa Barbara Municipal Airport} Goleta, California.
Elliott, Robert D., and Thompson, John R. (1972): Santa Barbara Convective
Band Seeding Test Program 1970-71 Season and 1967-71 Summary, Naval
Weapons Center, China Lake, California.
Gleeson, Thomas A. (1977): Data Sun~arization in a Weather ~bdification Experiment:
II. Concomitant Variables, FSU Statistics Report No. M4l9,
ONR Technical Report No. 118, Florida State University, Department of
Statistics, Tallahassee, Florida.
Neyman, Jerzy (1975): Problems of Design and of Evaluation of Rain Making
Experiments, in A Survey of Statistical Design and Linear Models,
J. N. Srivastava, Editor, North-Holland Publishing Company.
Neyman, Jerzy (1976): Experimentation with Weather Control and Statistical
Problems Generated by It, Stat. Lab., Univ. of Cal., Berkeley (Inaugural
Address, S~nposium on Applications of Statistics, Wright State
University, June 14, 1976).
Neyman, Jerzy (1977): A Statistician's View on Weather Modification Technology,
Stat. Lab., Univ. of Cal., Berkeley (mimeo).
Scott, Elton (1978): Data Summarization in a Weather Modification Experiment:
III. A ~~ltivariate Analysis, FSU Statistics Report No. M442, ONR
Technical Report No. 127, Florida State University, Department of
Statistics, Tallahassee, Florida.
Serfling, R. J. (1977): Toward a Nonparametric Covariance Analysis of a Weather
Modification Experiment, FSU Statistics Report No. M428, ONR Technical
Report No. 122, Florida State University, Department of Statistics,
Tallahassee, Florida.
Thompson, John R., Brown, Keith J., and Elliott, Robert D. (1975): Santa Barbara
Convective Band Seeding Test Program, Final Report, Naval Weapons
Center, China Lake, California.
- 30 -
OTHER TECHNICAL REPORTS ON THIS CONTRACT
Report Numbers
/f~388, ONR-110 Hanson, Morgan, Bach, Charles L. and Cooley, Edward A.,
Bibliography of Statistical and Meteorological Methodology
in Weather Modification, September, 1976.
M409, ONR-111 Bradley, Ralph A. &Srivastava, S.S., Correlation In
Polynomial Regression, March, 1977.
M410, ONR-112 Bach, Charles L., An Interpretive History of 30-years
(1945-1975) of Weather Modification, March, 1977.
M417, ONR-117 Bradley, Ralph A., Srivastava, S.S. and Lanzdorf, Adolf,
Summarization of Precipitation Data In a Weather ~bdification
Experiment: I. A Response Surface Approach, June, 1977.
M419, ONR-118 Gleeson, T.A., Data Summarization In a Weather Modification
Experiment: II. Concomitant Variables, June, 1977.
M420, ONR-119 Hanson, Morgan A., Rank Tests in Iveather t!lodification Experiments,
June, 1977.
M428, ONR-122 Serfling, R.J., Toward a Nonparametric Covariance Analysis
of a Weather ~~dification Experiment, August, 1977.
M440, ONR-126 Hanson, Morgan A., Barker, Lawrence E., and Hunter, Charles H.,
Bibliography of Statistical and ~~teoro1ogical Methodology in
Weather Hodification, II, October, 1977.
M442, ONR-127 Scott, Elton, Data Summarization in a Weather r>lodification:
III. A Multivariate Analysis, June, 1978.
M467,ONR-133 Bradley, Ralph A., Srivastava, Sushi1 5., and Lanzdorf, Adolf,
An Examination of the Effects of Cloud Seeding in Phase I of
the Santa Barbara Convective Band Seeding Test Program, June,
1978.
APPENDIX TABLES
- 31 -
- 32 -
Table A-I: COEFFICIENT OF DETERMINATION (R2) FOR REGRESSIONS WITH PRECIPITATION
MEANS WITHOUT AND WITH CONTROL AREA MEAN AS ONE OF THE
COVARIATES
MODELS WITHOUT CONTROL MEA.~ 1 MODELS WITH CONTROL ~lliAN
Target Area Unweighted Weighted Unweighted Weighted
(1) (2) (1) (2) ( 3) (4) (3) (4)
(i) 0.622 0.675 0.563 0.634 0.727 0.779 0.700 0.741
(ii) 0.600 0.686 0.655 0.707 0.804 0.850 0.796 0.826
(iii) 0.603 0.652 0.490 0.579 0.664 0.722 0.588 0.671
(iv) 0.628 0.680 0.564 0.639 0.727 0.779 0.695 0.740
lModel numbers are defined on Page 10.
Table A-2: COEFFICIENT OF DETERMINATION (R2) FOR REGRESSIONS WITH PRECIPITATION
VOLU~ffiS WITHOUT AND WITH CONTROL AREA VOL~ffi AS ONE OF THE
COVARIATES
MODELS WITHOUT CONTROL VOLUME l ~~DELS WITH CONTROL VOLill\ffi
Target Area Unweighted Weighted Unweighted Weighted
(1) (2) (1) (2) (3) (4) (3) (4)
(i) 0.592 0.646 0.632 0.704 0.667 0.719 0.660 0.729
(ii) 0.605 0.689 0.695 0.757 0.712 0.769 0.730 0.796
(iii) 0.589 0.639 0.542 0.628 0.642 0.696 0.564 0.643
(iv) 0.612 0.664 0.599 0.669 0.677 0.728 0.622 0.692
lModel numbers are defined on Page 10.
Table A-3: CORRELATION COEFFICIENTS N~ONG ~lliN~ PRECIPITATION, COVARIATES 1 , AND SEEDING:
AREA (i)
y xc Xl X
2
X
3
X
4
X5 X6 X7 X<,
u
X
9 X10 Xll X
12
X 0.74
c
X 0.02 1 -0.01
X2 0.38 0.26 0.10
X3 -0.32 -0.20 0.13 -0.00 ~
~
X4
0.37 0.22 0.20 0.76 -0.15
Xs -0.32 -0.20 0.06 0.07 0.90 -0.08
X6 -0.12 -0.01 0.64 0.28 0.22 0.26 0.14
X7 -0.10 0.03 -0.06 0.24 0.04 0.04 O.OS 0.23
Xs -0.04 0.12 -0.31 0.20 0.11 0.11 0.06 0.32 0.35
X 0.38 0.20 0.17 0.73 -0.25 0.94 -0.22 0.22 0.04 0.09
9
X10
-0.29 -0.17 0.05 0.05 0.87 -0.06 0.96 0.10 0.01 0.04 -0.19
Xl! -0.16 -0.12 0.16 0.04 0.02 0.10 0.01 0.14 0.18 -0.14 0.09 -0.04
Xu 0.61 0.64 -0.09 0.16 -0.17 0.16 -0.24 -0.05 0.10 0.18 0.19 -0.24 -0.01
Z 0.16 0.08 0.04 0.02 -0.10 0.13 -0.09 -0.07 -0.05 -0.17 0.10 -0.09 0.10 0.16
lCovariates are defined on Page 7.
- 34 -
Table A-4: COVARIATES IN ORDER OF INCLUSION IN STEP-UP
REGRESSIONS FOR vDDEL (1), ~~~EIG~TED, RESPONSE
VARIABLE MEAN PRECIPITATION.
Order Area (i) Area (ii) Area (iii) Area (iv)
1 X12 X12 X12 X12
2 X2 X2 X2 X2
3 X7 X X7 X 3 7
4 X X7 X
3
X3 3
5 Xu Xl! X6 Xl!
6 Xg X," X X" 0 1 0
7 X6 Xl Xl! v
"6
8 Xl X6
X_ XI ::>
0.614
0.622
0.595
0.600
0.597
0.603
0.621
0.628
W'2 is the coefficient of determination with the first eight
covariates only and R2 is taken from Table A-I.
- 35 -
Table A-5: COEFFICIENT OF DETERMINATION (R2) FOR REGRESSIONS WITH
PRECIPITATION MEANS WITHOm AND WITH CONTROL AREA MEAN
AS ONE OF THE COVARIATES
~DDELS WITHOUT CONTROL ~ffiANl MODELS WITH CONTROL MEAN
Target Area Unweighted Weighted Unweighted Weighted
( 1) (2) (1) (2) (3) (4) (3) ( 4)
(i) 0.597 0.621 0.503 0.560 0.712 0.750 0.682 0.699
(ii) 0.578 0.608 0.573 0.630 0.789 0.815 0.783 0.790
(iii) 0.578 0.606 0.304 0.482 0.646 0.691 0.518 0.593
(iv) 0.604 0.629 0.505 0.562 0.712 0.751 0.677 0.693
(v) 0.575 0.593 0.571 0.625 0.773 0.800 0.747 0.765
Table A-6: COEFFICIENT OF DETER~lINATION (R2) FOR REGRESSIONS lnTH
PRECIPITATION VOLU~ffiS WITHOUT AND WITH CONTROL AREA VOLUME
AS ONE OF THE COVARIATES
MODELS WITHOm CONTROL VOLUME 1 MODELS WITH CONTROL VOLUME
Target Area Unweighted Weighted Unweighted Weighted
( 1) (2) (1) (2) (3) (4) (3) (4)
(i) 0.556 0.585 0.550 0.616 0.630 0.662 0.627 0.677
(E) 0.582 0.600 0.630 0.686 0.692 0.713 0.696 0.754
(iii) 0.555 0.586 0.475 0.543 0.605 0.642 0.533 0.590
(iv) 0.580 0.606 0.529 0.587 0.644 0.676 0.592 0.637
lModel numbers are defined on Page 10. Models here have only the seven
covariates listed on Page 15 instead of the original twelve on Page 7, together
with corresponding interactions with Seeding when appropriate.
- 36 -
Table A-7: REGRESSION COEFFICIENTS FOR UNhfEIGHTED lI-iODEL (1),
RESPONSE VARIABLE ~ffiAN, X NOT INCLUDED
c
INDEPENDENT
VARIABLES
(i) (ii)
TARGET AREA
(iii) (iv) (v)
Constant 0.0892 0.2562 0.0377 0.0946 0.2334
X2 0.0082** 0.0096** 0.0085** 0.0088** 0.0079**
X3
-0.0015** -0.0019** -0.0015** -0.0016** -0.0016**
\ -0.0038 0.0014 -0.0062 -0.0041 0.0003
X7 -0.0544* -0.0571 -0.0613* -0.0590* -0.0518
X8 -0.0100 -0.0126 -0.0093 -0.0105 -0.0109*
Xu -0.0002* -0.0002* -0.0001 -0.0002* -0.0002*
X12 0.0025** 0.0030** 0.0025** 0.0030** 0.0024**
Z 0.0105 0.0224 0.0058 0.0101 0.0114
* Significant at level a = 0.05,
** Significant at level a =0.01.
- 37 -
Table A-8: REGRESSION COEFFICIEirrS FOR UN~mIGHTED ,iODEL (2), RESPONSE
VARIABLE ~ffiAN, X NOT INCLUDED
c
INDEPENDENT
VARIABLES (i) (ii)
TARGET AREA
(iii) (iv) (v)
Constant 0.1536 0.2342 0.1527 0.1738 0.2608
X2
0.0061* 0.0084** 0.0057* 0.0065* 0.0069**
X3
-0.0015 -0.0016 -0.0016 -0.0016 -0.0015
X6 -0.0050 -0.0021 -0.0065 -0.0053 -0.0012
X7
-0.0689 -0.0911 -0.0631 -0.0737 -0.0793
X8
-0.0016 -0.0052 -0.0006 -0.0017 -0.0044
XlI -0.0002 -0.0001 -0.0002 -0.0002 -0.0001
X12
0.0020** 0.0022** 0.0021** 0.0021** 0.0020**
12 0.0034 0.0018 0.0045 0.0037 0.0016
13
0.0001 -0.0003 0.0003 0.0002 -0.0000
16
0.0019 0.0068 -0.0002 0.0016 0.0027
17
0.0358 0.0757 0.0221 0.0372 0.0574
18
-0.0189 -0.0179 -0.0202 -0.0198 -0.0146
III -0.0000 -0.0002 0.0001 -0.0000 -0.0001
112
0.0009 0.0014 0.0008 0.0009 0.0008
Z -0.1650 0.0054 -0.2755 -0.2018 -0.0875
* Significant at level ~ = 0.05,
** Significant at level ~ = 0.01.
.. ..... ; -
Table A--9: REGRESS IOi': COEFFICIENTS FOR UNIJEIGHTED f-10DEL (3),
RESPONSE VARIABLE ~ffiAN, X INCLUDED c
INDEPENDENT
VARIABLES
(i) (ii)
TARGET AREA
(iii) (iv) (v)
Constant 0.0186 0.1401 -0.0190 0.0220 0.1376
X 0.6267** 1.0295** 0.5029** 0.6438** 0.8383**
c
X2 0.0065** 0.0067** 0.0071 ** 0.0070** 0.0054**
X3 -0.0012* -0.0013** -0.0013* -0.0013** -0.0012**
X6 -0.0043 0.0005 -0.0066 -0.0047 -0.0006
X7 -0.0483* -0.0472* -0.0564* -0.0528* -0.0410*
Xs -0.0088 -0.0108* -0.0088 -0.0093 -0.0095*
Xu -0.0001 -0.0001 -0.0001 -0.0001 -0.0001
X12 0.0012** 0.0009** 0.0015** 0.0013** 0.0008**
Z 0.0156 0.0308 0.0098 0.0153 0.0178
* Significant at level a = 0.05,
** Significant at level a - 0.01.
- 39 -
Table A-10: REGRESSION COEFFICIENTS FOR UNWEIGHTED MODEL (4),
RESPONSE VARIABLE ~lliAN, X INCLUDED
c
INDEPENDENT
VARIABLES (i) (ii)
TARGET AREA
(iii) (iv) (v)
Constant 0.0396 0.0592 0.0568 0.0566 0.1249
X 0.7280** 1.1178** 0.6125** O. 7489** 0.9309**
c
X2 O. 0017 0.0016 0.0020 0.0020 0.0012
X3 -0.0007 -0.0005 -0.0010 -0.0008 -0.0007
X6 -0.0034 0.0004 -0.0052 -0.0036 0.0006
X7
-0.0174 -0.0121 -0.0248 -0.0208 -0.0128
X8 -0.0018 -0.0056 -0.0008 -0.0020 -0.0048
'\ XlI -0.0002* -0.0001 -0.0002* -0.0002* -0.0001*
X12 0.0010* 0.0006 0.0012* 0.0010* 0.0006
12
0.0072** 0.0077** 0.0077** 0.0077** 0.0064**
I -0.0005 -0.0013 -0.0002 -0.0005 -0.0008
3
16 -0.0036 -0.0017 -0.0049 -0.0041 -0.0042
17
-0.0473 -0.0519 -0.0478 -0.0482 -0.0441
18 -0.0154 -0.0125 -0.0172 -0.0161 -0.0104
III 0.0002 0.0000 0.0002 0.0002 0.0001
112
0.0001 0.0002 0.0001 0.0001 -0.0001
Z -0.0961 0.1115 -0.2174 -0.1309 -0.0214
* Significant at level a = 0.05,
** Significant at level a = 0.01.
- 40 -
Table A-ll: REGRESSION COEFFICIENTS FOR WEIGHTED ivlODEL (1),
RESPONSE VARIABLE ~ffifu~, X NOT INCLUDED
c
INDEPENDENT
VARIABLES (i) (ii)
TARGET AREA
(iii) (iv) (v)
Constant -0.0259 0.0021 -0.1650* -0.0132 -0.0026
X2 0.0004 0.0003 -0.0007 0.0005 0.0005
X3 -0.0001 -0.0001 0.0003 -0.0001 -0.0001
X6 -0.0022 -0.0002 -0.0058** -0.0022 -0.0009
X7 -0.0064 0.0056 -0.0109 -0.0076 -0.0038
Xs -0.0042* -0.0086** -0.0000 -0.0048* -0.0039*
XlI -0.0000 -0.0000 0.0000 -0.0000 -0.0000
Xl2 0.0010** 0.0014** 0.0005** 0.0011** O. 0011 **
Z -0.0012 0.0089 -0.0076 -0.0017 0.0032
* Significant at level a = 0.05,
** Significant at level a = 0.01.
- 41 -
Table A-12: REGRESSION COEFFICIENTS FOR WEIGHTED MODEL (2),
RESPONSE VARIABLE ~ffiAN, X NOT INCLUDED c
INDEPENDENT
VARIABLES (i) (ii)
TARGET AREA
(iii) (iv) (v)
Constant -0.0369 0.0466 -0.1458 -0.0223 -0.0092
~ -0.0001 0.0002 -0.0008 -0.0000 0.0002
X3
0.0000 -0.0001 0.0004 -0.0000 0.0000
X6 -0.0031 0.0000 -0.0048* -0.0032 -0.0010
X7 -0.0118 0.0157 -0.0179 -0.0132 -0.0109
X8 -0.0024 -0.0081** 0.0012 -0.0028 -0.0029
Xll
0.0000 0.0000 0.0000 0.0000 0.0000
X12
0.0007** 0.0009** 0.0005* 0.0007** 0.0007*
12 0.0010 0.0011 0.0020 0.0010 0.0008
13 -0.0004 -0.0002 -0.0009* -0.0004 -0.0004
16
0.0026 0.0013 0.0021 0.0028 0.0014
17
0.0099 -0.0223 0.0188 0.0109 0.0113
18 -0.0034 0.0033 -0.0034 -0.0042 -0.0025
III -0.0001 -0.0001 -0.0000 -0.0001 -0.0001
112
0.0008** 0.0012** 0.0005 0.0008** 0.0009*
Z 0.0766 0.0132 0.1643 0.0745 0.0525
* Significant at level a =0.05,
** Significant at level a = 0.01.
- 42 -
Table A-13: REGRESSION COEFFICIENTS FOR WEIGHTED MODEL (3),
RESPONSE VARIABLE MEAN, Xc INCLUDED
INDEPENDENT
VARIABLES (i) (ii)
TARGET AREA
(iii) (iv) (v)
Constant 0.0677 0.1138 -0.0182 0.0811 0.0792
Xc 0.5512** 0.8227** 0.4630** 0.5702** 0.6441**
X2 -0.0002 0.0000 -0.0007 -0.0001 0.0001
X3 -0.0004 -0.0005* -0.0001 -0.0004 -0.0003
X6 -0.0016 -0.0003 -0.0033** -0.0016 -0.0003
X7 -0.0164* -0.0111 -0.0188* -0.0115* -0.0138
X8 -0.0010 -0.0023 0.0013 -0.0014 -0.0007
Xu -0.0000 -0.0000 0.0000 -0.0000 -0.0000
X12
0.0003 0.0004* -0.0000 0.0003* 0.0003*
Z 0.0005 0.0011 -0.0040 -0.0002 0.0027
* Significant at level a = 0.05,
** Significant at level a = 0.01.
- 43 -
Table A-14: REGRESSION COEFFICIENTS FOR WEIQiTED ~DDEL (4),
RESPONSE VARIABLE ~ffiN~, X INCLUDED
c
INDEPENDENT
VARIABLES (i) (ii)
TARGET AREA
(iii) (i v) (v)
Constant 0.0263 0.0730 -0.0510 0.0416 0.0209
X 0.5653** 0.8122** 0.4221** 0.5813** 0.6473**
c
X2 -0.0007 -0.0005 -0. 0011 -0.0007 -0.0003
X3 -0.0001 -0.0002 0.0001 -0.0002 -0.0000
X6 -0.0017 0.0005 -0.0032 -0.0018 -0.0000
X7 -0.0186 -0.0093 -0.0218 -0.0198 -0.01S7
Xs 0.0003 -0.0021 0.0021 0.0001 0.0002
Xu -0.0000 -0.0000 0.0000 -0.0000 -0.0000
Xl2 0.0003 0.0004 0.0003 0.0004 0.0003
12 0.0009 0.0011 0.0015 0.0010 0.0008
13 -0.0004 -0.0004 -0.0007 -0.0004 -0.0006
16 -0.0003 -0.0010 0.0003 -0.0000 -0.0005
17 0.0056 -0.0071 0.0144 0.0067 0.0084
18 -0.0037 0.0016 -0.0054 -0.0046 -0.0020
III 0.0000 -0.0000 0.0001 0.0000 0.0000
112 -0.0000 0.0002 -0.0001 -0.0000 0.0001
Z 0.0753 0.0524 0.1233 0.0749 0.0912
* Significant at level a = 0.05,
** Significant at level a = 0.01.
- 44 -
Table A-IS: REGRESSION COEFFICIENTS FOR UNWEIGHTED ~DDEL (1),
RESPONSE VARIABLE VOLUi"JE, X NOT INCLUDED
c
INDEPENDENT
VARIABLES (i)
TARGET AREA
(ii) (iii) (iv)
Constant 0.0980 0.0908 0.0478 0.1386
X2 0.0134** 0.0031** 0.0097** 0.0128**
X3
-0.0024* -0.0006** -0.0018* -0.0024**
X6 -0.0065 0.0006 -0.0068 -0.0062
X7 -0.0689 -0.0182* -0.0619 -0.0801
X8 -0.0205 -0.0034 -0.0120 -0.0154
Xll -0.0003* -0.0001** -0.0002* -0.0003*
Xl2 0.0046** 0.0007** 0.0029** 0.0036**
Z 0.0119 0.0076 0.0041 0.0117
* Significant at level a = 0.05,
** Significant at level a = 0.01.
- 45 -
Table A-16: REGRESSION COEFFICIENTS FOR UNWEIGHTED lvlODEL (2),
RESPONSE VARIABLE VOLU~ffi, X NOT INCLUDED
c
INDEPENDENT
VARIABLES (i)
TARGET AREA
(ii) (iii) (iv)
Constant 0.0859 0.0509 0.1162 0.1669
X2 0.0094* 0.0029** 0.0064* 0.0093*
X3 -0.0018 -0.0004 -0.0016 -0.0020
X6 -0.0111 -0.0004 -0.0081 -0.0085
X7 -0.1141 -0.0260 -0.0789 -0.1050
X8 -0.0056 -0.0012 -0.0009 -0.0020
Xu -0.0004 -0.0000 -0.0002* -0.0003
X12
0.0037** 0.0006** 0.0024** 0.0030**
12 0.0063 0.0003 O. 0053 0.0056
13 -0.0006 -0.0002 -0.0001 -0.0003
16 0.0076 0.0022 0.0013 0.0035
17
0.1013 0.0153 0.0424 0.0577
IS -0.0321 -0.0053 -0.0236 -0.0289
III 0.0000 -0.0000 0.0001 0.0000
112
0.0017 0.0002 0.0009 0.0012
Z -0.1056 0.0797 -0.2191 -0.1392
* Significant at level a = 0.05,
** Significant at level a = 0.01.
- 46 -
Table A-17: REGRESSION COEFFICIENTS FOR UNWEIGHTED MODEL (3),
RESPONSE VARIABLE VOLUIviE, X INCLUDED c
INDEPENDENT
VARIABLES (i)
TARGET AREA
(ii) (iii) (iv)
Constant -0.1262 0.0408 -0.0734 -0.0327
X 1. 3599** 0.3035** 0.7356** 1. 0390**
c
X2 0.0104** 0.0025** 0.0081** 0.0106**
X3 -0.0017 -0.0004** -0.0014* -0.0018*
X6 -0.0101 -0.0002 -0.0087 -0.0089
X7 -0.0381 -0.0114 -0.0452 -0.0566
X8 -0.0186 -0.0030 -0.0109 -0.0139
XlI -0.0003* -0.0001** -0.0002 -0.0002*
X12 0.0036** 0.0005** 0.0023** 0.0028**
Z 0.0192 0.0092 0.0081 0.0173
* Significant at level a =0.05,
** Significant at level a =0.01.
- 47 -
Table A-18: REGRESSION COEFFICIENTS FOR UNWEIGHTED MODEL (4),
RESPONSE VARIABLE VOLUME, X INCLUDED
c
INDEPENDENT
VARIABLES (i)
TARGET AREA
(ii) (iii) (iv)
Constant -0.1304 0.0033 -0.0052 -0.0021
X 1. 4359** 0.3161** 0.8060 u 1.1222**
c
X2 0.0034 0.0016* 0.0031 0.0047
X3 -0.0009 -0.0002 -0.0011 -0.0013
X6 -0.0134 -0.0009 -0.0094 -0.0103
X7 -0.0398 -0.0097 -0.0372 -0.0469
X8 -0.0043 -0.0010 -0.0002 -0.0012
Xu -0.0003 -0.0000 -0.0002 -0.0003*
X12 0.0027** 0.0004* 0.0018** 0.0022**
12
0.0108 0.0013 0.0078* 0.0091*
13
-0.0009 -0.0003 -0.0003 -0.0006
16 0.0034 0.0013 -0.0010 0.0002
17 0.0302 -0.0004 0.0025 0.0021
IS -0.0314 -0.0051 -0.0232 -0.0283
III 0.0000 -0.0000 0.0001 0.0001
112 0.0014 0.0002 0.0008 0.0009
Z -0.1422 0.0716 -0.2396 -0.1678
* Significant at level a = 0.05,
** Significant at level a =0.01.
- 48 -
Table A-19: REGRESSION COEFFICIENTS FOR WEIGHTED ~DDEL (1),
RESPONSE VARIABLE VOLU~~, X NOT INCLUDED c
INDEPENDENT
VARIABLES (i)
TARGET AREA
(ii) (iii) (iv)
Constant -0.1244 -0.0412 -0.0523 -0.0943
X2 0.0003 -0.0002 0.0007 0.0009
X3 0.0000 0.0001 -0.0001 -0.0001
X6 -0.0055 -0.0010 -0.0037 -0.0046
X7 -0.0190 -0.0001 -0.0228 -0.0236
Xs -0.0042 -0.0004 -0.0023 -0.0030
Xu 0.0000 0.0000 0.0000 0.0000
X12 0.0023** 0.0003** 0.0013** 0.0017**
Z 0.0116 0.0076 0.0052 0.0099
** Significant at level a = 0.01.
- 49 -
Table A-20: REGRESSION COEFFICIE~lS FOR WEIGHTED MODEL (2),
RESPONSE VARIABLE VOLUME, X NOT INCLUDED
c
INDEPENDENT
VARIABLES (i)
TARGET AREA
(ii) (iii) (iv)
Constant -0.0780 -0.0715* -0.0773 -0.1320
X2 -0.0014 -0.0002 0.0008 0.0003
X3
0.0002 0.0003** 0.0001 0.0003
X6 -0.0053 -0.0008 -0.0038 -0.0044
X7 -0.0310 0.0013 -0.0328 -0.0338
Xg -0.0015 -0.0004 -0.0005 -0. OOll
Xu 0.0001 0.0000 0.0000 0.0000
Xl2 0.0017** 0.0002** 0.0011** 0.0014**
12 0.0036 0.0007 0.0014 0.0016
13 -0.0008 -0.0003* -0.0007 -0.0009
16 0.0004 -0.0004 -0.0002 -0.0007
17 0.0327 0.0008 0.0322 0.0326
18 -0.0064 -0.0010 -0.0074 -0.0082
III -0.0000 -0.0000 0.0000 0.0000
112 0.0014* 0.0004** 0.0006 0.0009
Z -0.0028 0.0436 0.0624 0.0996
* Significant at level a = 0.05,
** Significant at level a = 0.01.
- 50 -
Table A-21: REGRESSION COEFFICIENTS FOR WEIGHTED MODEL (3),
RESPONSE VARIABLE VOLUlVIE, X INCLUDED c
INDEPENDENT
VARIABLES (i)
TARGET AREA
(ii) (iii) (iv)
Constant -0.0597 -0.0438 -0.0240 -0.0590
X 1.0076** 0.1817** 0.5166** 0.6792**
c
X2 -0.0002 -0.0002 0.0004 0.0006
X3 -0.0002 0.0001 -0.0002 -0.0002
X6 -0.0064 -0.0013* -0.0041 -0.0051
X7 -0.0222 -0.0005 -0.0247* -0.0262
Xs -0.0018 -0.0000 -0.0009 -0.0012
Xl! -0.0000 0.0000 0.0000 0.0000
Xl2
0.0016** 0.0002** 0.0010** 0.0013**
Z -0.0048 0.0006 -0.0030 -0.0010
* Significant at level a =0.05,
** Significant at level a = 0.01.
- 51 -
Table A-22: REGRESSION COEFFICIENTS FOR WEIGHTED MODEL (4),
RESPONSE VARIABLE VOLU~ffi, Xc INCLUDED
INDEPENDENT
VARIABLES (i)
TARGET AREA
(ii) (iii) (iv)
Constant 0.0388 -0.0407 -0.0068 -0.0346
X 0.9379** 0.1980** 0.4942** 0.6486**
c
X2 -0.0022 -0.0004 -0.0004 -0.0004
X3
-0.0002 0.0002 -0.0001 -0.0000
\ -0.0043 -0.0006 0.0033 -0.0037
X7
-0.0233 0.0017 -0.0291 -0.0288
X8
0.0003 0.0001 0.0006 0.0004
X
ll
-0.0000 0.0000 -0.0000 -0.0000
X12
0.0012** 0.0002* 0.0009** 0.0011**
12
0.0040 0.0009* 0.0016 0.0020
13
-0.0004 -0.0001 -0.0004 -0.0005
16
-0.0046 -0.0019 -0.0026 -0.0041
17
0.0152 0.0034 0.0243 0.0216
IS -0.0045 -0.0011 -0.0065 -0.0068
III 0.0001 -0.0000 0.0001 0.0001
112
0.0010 0.0004** 0.0004 0.0006
Z -0.1875 -0.0624 -0.0592 -0.0703
* Significant at level a = 0.05,
** Significant at level a = 0.01.
- 52 -
Table A-23: ANALYSIS OF VARIANCE FOR Ul·mEIGHTED dODEL (1),
RESPONSE VARIABLE ivlEAN, X NOT IiKLUDED
c
TARGET
AREA
(i)
(ii)
(iii)
(iv)
(v)
SOURCE OF
VARIATION
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDIi~G
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDI:'JG
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
d.f.
7
1
97
7
1
97
7
1
97
7
1
97
7
1
97
SUi·) OF
SQUARES
3.797
0.003
2.565
5.370
0.012
3.933
3.989
0.001
2.912
4.312
0.002
2.826
3.652
0.003
2.700
[.IEAN
SQUARE
0.542
0.003
0.026
0.767
0.012
0.041
0.570
0.001
0.030
0.616
0.002
0.029
0.522
0.003
0.028
F
20.516**
0.099
18.917**
0.304
18.982**
0.027
21.145**
0.085
18.747**
0.114
** Significant at level a = 0.01.
- 53 -
Table A-24: fu~ALYSIS OF VARIANCE FOR UNWEIGHTED ~IODEL (2),
RESPONSE VARIABLE MEAN, X NOT INCLUDED c
TARGET
AREA
SOURCE OF
VARIATION d.f. SUM OF
SQUARES
MEAN
SQUARE F
(i) COVARIATES 7 3.797 0.542 20.255**
INTERACTIONS 7 0.152 0.022 0.813
SEEDING 1 0.005 0.005 0.177
RESIDUAL 90 2.410 0.027
(ii) COVARIATES 7 5.370 0.767 18.884**
INTERACTIONS 7 0.289 0.041 1.018
SEEDING 1 0.000 0.000 0.003
RESIDUAL 90 3.656 0.041
(iii) COVARIATES 7 3.989 0.570 18.875**
INTERACTIONs 7 0.183 0.026 0.864
SEEDING 1 0.013 0.013 0.437
RESIDUAL 90 2.717 0.030
(iv) COVARIATES 7 4.312 0.616 20.936**
INTERACTIONS 7 0.174 0.025 0.843
SEEDING 1 0.007 0.007 0.241
RESIDUAL 90 2.647 0.029
(v) COVARIATES 7 3.652 0.522 18.166**
INTERACTIONS 7 0.117 0.017 0.581
SEEDING 1 0.001 0.001 0.463
RESIDUAL 90 2.585 0.029
** Significant at level a = 0.01.
- 54 -
Table A-25: AJ'JALYSIS OF VARIANCE FOR UNWEIGHTED MODEL (3),
RESPONSE VARIABLE ~ffiAN, Xc INCLUDED
TARGET
AREA
(i)
(ii)
(iii)
(iv)
(v)
SOURCE OF
VARIATION
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
d.f.
8
1
96
8
1
96
8
1
96
8
1
96
8
1
96
SUM OF
SQUARES
4.524
0.006
1.835
7.328
0.023
1. 963
4.457
0.002
2.442
5.079
0.006
2.055
4.904
0.008
1.443
MEAN
SQUARE
0.565
0.006
0.019
0.916
0.023
0.020
0.557
0.002
0.025
0.635
0.006
0.021
0.613
0.008
0.015
F
29.590**
0.313
44.795**
1.135
21.910**
0.093
29.651**
0.268
40.756**
0.515
** Significant at level a =0.01.
- 55 -
Table A-26: fu~ALYSIS OF VARIANCE FOR UNWEIGHTED ~DDEL (4),
RESPONSE VARIABLE 1-iEAN, X INCLUDED
c
TARGET
AREA
SOURCE OF
VARIATION d.f. SUM OF
SQUARES
MEAN
SQUARE F
(i) COVARIATES 8 4.524 0.565 31.679**
INTERACTIONS 7 0.250 0.036 2.005
SEEDING 1 0.002 0.002 0.090
RESIDUAL 89 1.588 0.013
(ii) COVARIATES 8 7.328 0.916 47.415**
INTERACTIONS 7 0.265 0.033 1.962
SEEDING 1 0.001 0.001 0.065
RESIDUAL 89 1.719 0.019
(iii) COVARIATES 8 4.457 0.557 23.225**
INTERACTIONS 7 0.301 0.043 1.790
SEEDING 1 0.008 0.003 0.342
RESIDUAL 89 2.135 0.024
(iv) COVARIATES 8 5.079 0.635 31.742**
INTERACTIONS 7 0.280 0.040 2.003
SEEDING 1 0.003 0.003 0.149
RESIDUAL ~9 1. 7130 0.020
(v) COVARIATES 8 4.904 0.613 42.895 **
INTERACTIONS 7 0.179 0.026 1. 783
SEEDING 1 0.000 0.000 0.006
RESIDUAL 89 1.272 0.014
** Significant at level a = 0.01.
- 56 -
Table A-27: ANALYSIS OF VARI~~CE FOR WEIGHTED ~DDEL (1),
RESPONSE VARIABLE MEAN, X NOT INCLUDED c
TARGET
AREA
(i)
(ii)
(iii)
(iv)
(v)
SOURCE OF
VARIATION
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
d.f.
7
1
97
7
1
97
7
1
97
7
1
97
7
1
97
SUM OF
SQUARES
4291. 334
1.297
7498.504
1948.323
14.713
3300.412
3423.019
64.338
8751. 882
4775.197
2.216
8100.884
1946.746
3.749
3713.761
ivJEAN
SQUARE
613.048
1.297
77.304
278.332
14.713
34.025
489.003
64.338
90.226
682.171
2.216
83.514
278.107
3.749
38.286
F
7.930**
0.017
8.180**
0.432
5.420**
0.713
8.168**
0.027
7.264**
0.098
** Significant at level ~ =0.01.
- 57 -
Table A-28: ANALYSIS OF VARIANCE FOR WEIQ1TED MODEL (2),
RESPONSE VARIABLE MEAN, X NOT INCLUDED c
TARGET
AREA
SOURCE OF
VARIATION d.f. SUM OF
SQUARES
tvIEAi'J
SQUARE F
(i) COVARIATES 7 4291.334 613.048 8.313**
INTERACT IONS 7 843.950 120.564 1.635
SEEDING 1 18.745 18.745 0.254
RESIDUAL 90 6637.105 73.746
(ii) COVARIATES 7 1948.323 278.332 8.763**
INTERACfIONS 7 456.332 65.190 2.052
SEEDING 1 0.159 0.159 0.005
RESIDUAL 90 2858.635 31.763
(iii) COVARIATES 7 3423.019 489.003 6.760**
INTERACTIONS 7 2203.996 314.857 4.353**
SEEDING 1 101.798 101.798 1.407
RESIDUAL 90 6510.426 72.338
(iv) COVARIATES 7 4775.197 682.171 8.551**
INTERACf IONS 7 906.325 129.475 1.623
SEEDING 1 16.831 16.831 0.211
RESIDUAL 90 7179.945 79.777
(v) COVARIATES 7 1946.746 278.107 7.696**
INTERACTIONS 7 460.620 65.803 1.821
SEEDING 1 4.479 4.479 0.124
RESIDUAL 90 3252.411 36.138
** Significant at level ~ =0.01.
- 58 -
Table A-29: ANALYSIS OF VARIANCE FOR WEIGHTED MODEL (3),
RESPONSE VARIABLE fvlEAi'IJ, X INCLUDED c
TARGET
AREA
(i)
(ii)
(iii)
SOURCE OF
VARIATION
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
d.f.
8
1
96
8
1
96
8
1
96
SUM OF
SQUARES
6996.201
0.209
4794.724
3408.444
0.224
1676.780
6157.756
17.626
6063.856
MEAN
SQUARE
874.525
0.209
49.945
426.055
0.224
17.466
769.720
17.626
63.165
F
17.510**
0.004
24.393**
0.013
12.186**
0.279
(iv) COVARIATES 8 7581. 870 947.734 17.178**
SEEDING 1 0.026 0.026 0.000
RESIDUAL 96 5296.401 55.171
<
(v) COVARIATES 8 3473.790 434.224 19.054**
SEEDING 1 2.678 2.678 0.118
RESIDUAL 96 2187.787 22.789
** Significant at level a =0.01.
- 59 -
Table A-30: ANALYSIS OF VARIANCE FOR WEIGHTED MODEL (4),
RESPONSE VARIABLE MEAN, Xc INCLUDED
TARGET
AREA
SOURCE OF
VARIATION d.f. SUM OF
SQUARES
MEAN
SQUARE F
(i) COVARIATES 8 6996.201 874.525 17.149**
INTERACTIONS 7 238.319 34.046 0.668
SEEDING 1 18.115 18.115 0.355
RESIDUAL 89 4538.499 50.994
(ii) COVARIATES 8 3586.444 448.305 24.537**
INTERACTIONS 7 48.379 6.911 0.378
SEEDING 1 2.518 2.518 0.138
RESIDUAL 89 1626.107 18.271
(iii) COVARIATES 8 6157.756 769.720 13.375**
INTERACTIONS 7 902.684 128.955 2.241*
SEEDING 1 57.033 57.033 0.991
RESIDUAL 89 5121. 766 57.548
(iv) COVARIATES 8 7581.870 947.734 16.796**
INTERACTIONS 7 257.547 36.792 0.652
SEEDING 1 17.005 17.005 0.301
RESIDUAL 89 5021. 875 56.426
(v) COVARIATES 8 3473.790 434.224 18.955**
INTERACTIONS 7 138.205 19.744 0.862
SEEDING 1 13.482 13.482 0.589
RESIDUAL 89 2038.778 22.908
* Significant at level a = 0.05,
** Significant at level a = 0.01.
- 60 -
Table A-31: ANALYSIS OF VARIANCE FOR UNWEIGHTED MODEL (1),
RESPONSE VARIABLE VOLUME, X NOT INCLUDED
c
TARGET
AREA
(i)
(ii)
(iii)
(iv)
SOURCE OF
VARIATION
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
d.f.
7
1
97
7
1
97
7
1
97
7
1
97
SUlvj OF
SQUARES
12.152
0.003
9.688
0.423
0.001
0.305
5.258
0.000
4.218
8.599
0.003
6.220
MEAN
SQUARE
1.736
0.003
0.100
0.060
0.001
0.003
0.751
0.000
0.043
1. 228
0.003
0.064
F
17.380**
0.035
19.255**
0.446
17.271**
0.010
19.158**
0.052
** Significant at level a = 0.01.
- 61 -
Table A-32: fu~ALYSIS OF VARIANCE FOR UNWEIGHTED ~~DEL (2),
RESPONSE VARIABLE VOLUME, X NOT INCLUDED
c
TARGET
AREA
SOURCE OF
VARIATION d.f. SUM OF
SQUARES
MEAN
SQUARE F
(i) COVARIATES 7 12.152 1. 736 17.223**
INTERACTIONS 7 0.619 0.088 0.877
SEEDING 1 0.002 0.002 0.019
RESIDUAL 90 9.071 0.101
(ii) COVARIATES 7 0.423 0.060 18.661**
INTERAer IONS 7 0.013 0.002 0.574
SEEDING 1 0.001 0.001 0.340
RESIDUAL 90 0.292 0.003
(iii) COVARIATES 7 5.258 0.751 17.223**
INTERACTIONS 7 0.286 0.041 0.936
SEEDING 1 0.008 0.008 0.191
RESIDUAL 90 3.925 0.044
(iv) COVARIATES 7 8.599 1.228 18.943**
INTERACTIONS 7 0.384 0.055 0.845
SEEDING 1 0.003 0.003 0.052
RESIDUAL 90 5.836 0.065
** Significant at level a = 0.01.
- 62 -
Table A-33: ANALYSIS OF VARIANCE FOR UNWEIQiTED MODEL (3),
RESPONSE VARIABLE VOLU~lli, X INCLUDED c
TARGET
AREA
(i)
(ii)
(iii)
(iv)
SOURCE OF
VARIATION
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
d.f.
8
1
96
8
1
96
8
1
96
8
1
96
SUM OF
SQUARES
13.755
0.009
8.079
0.503
0.002
0.224
5.727
0.002
3.747
9.534
0.007
5.280
t4EAN
SQUARE
1.719
0.009
0.084
0.063
0.002
0.002
0.716
0.002
0.039
1.192
0.007
0.055
F
20.430**
0.107
26.850**
0.885
18.343**
0.041
21. 669**
0.133
** Significant at level ~ =0.01.
- 63 -
Table A-34: ANALYSIS OF VARIANCE FOR UNWEIGHTED MODEL (4)
RESPONSE VA1:':IABLE VOLUME) X INCLUDED c
TARGET
AREA
SOURCE OF
VARIATION d.f. SUM OF
SQUARES
MEAN
SQUARE F
(i) COVARIATES 8 13.755 1. 719 20.751**
INTERACTIONS 7 0.710 0.101 1. 224
SEEDING 1 0.004 0.004 0.042
RESIDUAL 89 7.374 0.083
(ii) COVARIATES 8 0.503 0.063 26.623**
INTERACTIONS 7 0.016 0.002 0.966
SEEDING 1 0.001 0.001 0.377
RESIDUAL 89 0.210 0.002
.r)'.1..1) COVARIATES 8 5.727 0.716 18.796**
INTERACTIONS 7 0.349 0.050 1.309
SEEDING 1 0.010 0.010 0.262
RESIDUAL 89 3.390 0.038
(iv) COVARIATES 8 9.534 1.192 22.099**
INTERACTIONS 7 0.483 0.069 1.279
SEEDING 1 0.005 0.005 0.091
RESIDUAL 89 4.800 0.054
** Significant at level ~ =0.01.
- 64 -
Table A-35: ANALYSIS OF VARIfu~CE FOR WEIGHTED MODEL (1),
RESPONSE VARIABLE VOLU~ffi, X NOT INCLUDED c
TARGET
AREA
(i)
(ii)
(iii)
(iv)
SOURCE OF
VARIATION
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
d.f.
7
1
97
7
1
97
7
1
97
7
1
97
SUM OF
SQUARES
1515.002
8.663
2547.653
1639.170
130.367
3647.915
2112.801
6.478
4313.635
3733.598
25.031
6679.535
MEAN
SQUARE
216.429
8.663
26.264
234.167
130.367
37.607
301.829
6.478
44.470
533.371
25.031
68.861
F
8.240**
0.330
6.227**
3.467
6.787**
0.146
7.746**
0.364
** Significant at level a = 0.01.
- 65 -
Table A-36: ANALYSIS OF VARIANCE FOR WEIGHTED MODEL (2),
RESPONSE VARIABLE VOLUME, Xc NOT INCLUDED
TARGET
AREA
SOURCE OF
VARIATION d.f. SUM OF
SQUARES
tvlEAN
SQUARE F
(i) COVARIATES 7 1515.002 216.429 8.980**
INTERACTIONS 7 387.235 55.319 2.295*
SEEDING 1 0.002 0.002 0.000
RESIDUAL 90 2169.080 24.101
(ii) COVARIATES 7 1639.170 234.167 6.809**
INTERACTIONS 7 666.244 95.178 2.768*
SEEDING 1 16.899 16.899 0.491
RESIDUAL 90 3095.139 34.390
(iii) COVARIATES 7 2112.801 301.829 7.239**
INTERACTIONS 7 564.143 80.592 1.933
SEEDING 1 3.492 3.492 0.084
RESIDUAL 90 3752.478 41.694
(iv) COVARIATES 7 3733.598 533.371 8.186**
INTERACTIONS 7 831.530 118.790 1. 823
SEEDING 1 9.245 9.245 0.142
RESIDUAL 90 5863.791 65.153
* Significant at level a =0.05,
** Significant at level a = 0.01.
- 66 -
Table A-37: A~ALYSIS OF VARIANCE FOR WEIGHTED MODEL (3),
RESPONSE VARIABLE VOLU~ffi, X INCLUDED
c
TARGET
AREA
(i)
(ii)
(iii)
(iv)
SOURCE OF
VARIATION
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
COVARIATES
SEEDING
RESIDUAL
d.f.
8
1
96
8
1
96
8
1
96
8
1
96
SUM OF
SQUARES
1962.353
1.454
2107.511
2420.586
0.599
2996.267
2594.838
2.049
3836.027
4647.229
0.259
5790.676
MEAN
SQUARE
245.294
1.454
21. 953
302.573
0.599
31.211
324.355
2.049
39.959
580.904
0.259
60.320
F
11.174**
0.066
9.694**
0.019
8.117**
0.051
9.630**
0.004
** Significant at level a =0.01.
- 67 -
Table A-38: ANALYSIS OF VARIANCE FOR WEIGHTED ~~DEL (4),
RESPONSE VARIABLE VOL~ffi, Xc INCLUDED
TARGET
AREA
SOURCE OF
VARIATION d. f. SUM OF
SQUARES
MEAN
SQUARE F
(i) COVARIATES 8 1962.353 245.294 11. 937**
INTERACT IONS 7 272.990 38.999 1.898
SEEDING 1 7.082 7.082 0.345
RESIDUAL 89 1828.893 20.549
(ii) COVARIATES 8 2420.586 302.573 11. 091**
INTERACTIONS 7 538.722 76.960 2.821**
SEEDING 1 30.035 30.035 1.101
RESIDUAL 89 2428.109 27.282
(iii) COVARIATES 8 2594.838 324.355 8.570
INTERACTIONS 7 466.494 66.642 1. 761
SEEDING 1 3.031 3.031 0.080
RESIDUAL 89 3368.551 37.849
(iv) COVARIATES
INTERACTIONS
SEEDING
RESIDUAL
8
7
1
89
4647.229 580.904 10.034**
634.111 90.587 1.565
4.437 4.437 0.077
5152.387 57.892
** Significant at level a = 0.01.
ERRATA TO
FSU STATISTICS REPORT NO. M467, ONR TECHNICAL REPORT No. 133
Ralph A. Bradley, Sushil S. Srivastava, and Adolf Lanzdorf,
An Examination of the Effects of Cloud Seeding in Phase! of
the Santa Barbara Convective Band Seeding Test Program, June,
1978, Department of Statistics, Florida State University,
Tallahassee, Florida. 32306.
An error in interpretation of computer output in weighted regression
analyses led to errors in values of the coefficient of determination R
2
reported in Tables A-I, A-2, A-5, and A-6 under column headings for weighted
regressions in the above referenced technical report. Corrected table
sections are appended.
Analyses for Target Area (v) defined in Table I were done for compari-sons
with those of the Naval Weapons Center study. A footnote to that
table indicates that the Control Area for the NWC study consisted of 39
stations. Fewer stations were used in the report because of truncation of
the Control Area as defined in the table. Analyses for Target Area (v)
have been done to use all 39 stations and minor changes occur in Tables A-5,
A-9, A-lO, A-13, A-14, A-25, A-26, A-29, and A-30. Corrections to these
tables are appended also.
A listing error occurred in Table A-29 for Target Area (ii) and this
is corrected below.
None of the changes alters· interpretation of analyses in the report,
but it is important that results of analyses be reported accurately.
The reader is referred to a subsequentpaperl for some additional
insights and analyses.
Ralph A. Bradley
January 31, 1979
lRalph A. Bradley, Sushi! S. Srivastava, and Adolf Lanzdorf (1979), Some Approaches
to Statistical Analysis of a Weather Modification Experiment, Prepared for communications
in Statistics A, Preprinted ~n Proc. Workshop on Statist. Design and Analysis
of Weather MOd. Expts., FSU Statistics Report No. M49U, ONR Technical Report No.
135, nepartment of Statistics, Florida State University, Tallahassee, Florida 32306.
2
CORRECTED TABLE SECTIONS
Tables A-I, A-2: COEFFICIENTS OF DETERMINATION (R2) FOR REGRESSIONS WITH
P~{L;CIPI'TATIC)N MEAl'S (A-I) OR VOLUMES (A-2) WITH AND
WITHOUT CONTROL AREA ~ffiAN (A-I) OR VOLUME (A-2) AS ONE
OF THE COVARIATES
TABLE A-I ,1..1."..'\.D,~nLT1f""":" A-2
'Seigilted ;-iodels ~~~'e~L g:1te-l "i'iodeis
Target :!itil:Jelt ;/ith "Jiti,o".ll': ;.hth
Area
Con-:':rol I'le::m ·=J·.!..~:......ol Volune
(1) (2) (3) (4) (1) (2) (3) (4)
(i) 0.441 0.511 0.616 0.668 0.489 0.590 0.528 0.624
(ii) 0.493 0.569 0.681 0.745 0.445 0.559 0.509 0.628
(iii) 0.399 0.538 0.541 0.643 0.415 0.524 0.443 0.544
(iv) 0.446 0.520 0.614 0.670 0.455 0.550 0.486 0.582
Table A-5: COEFFICIENTS OF DETERMINATION (R2) FOR REGRESSIONS WITH PRECIPITATION
MEANS WITH CONTROL AREA ~ffiAN AS ONE OF THE COVARIATES
i:oJelslit11 CcntToi liean
UnweigxLe,-~ Weighted
Models Without Control Mean
Target Weighted
Area
(1) (2)
(v) 0.344 0.426
(3)
0.778
(4)
0.805
(3)
0.603
(4 )
0.627
3
Tables A-5, A-6: COEFFICIENTS OF DETERMINATION (R
2
) FOR REGRESSIONS WITH
PRECIPITATION ~ffiANS (A-5) OR VOLUMES (A-6) WITH AND
WITHOUT CONTROL AREA MEAN (A-5) OR VOLUME (A-6) AS ONE
OF THE COVARIATES
TABLE A-5 TABLE A-6
Weighted Hoclels l'lei gi1ted '!"iodels
Target lJitllOut l;Tith ;Jitllout With
Area
Control Mean COi1trol Volume
(1) (2) (3) (4) (1) (2) (3) (4)
(i) 0.364 0.437 0.593 0.615 0.374 0.467 0.482 0.551
(ii) 0.373 0.457 0.681 0.691 0.327 0.429 0.447 0.552
(iii) 0.285 0.468 0.505 0.582 0.329 0.417 0.404 0.476
(iv) 0.371 0.442 0.589 0.610 0.360 0.438 0.445 0.506
4
Tables A-9, A-lO, A-13, A-14: CORRECTIONS TO REGRESSION COEFFICIENTS FOR
TARGET AREA (v), Xc INCLUDED
Table and Model
INDEPENDENT
VARIABLES
Unweighted
A-9, (3) A-lO, (4)
Weighted
A-13, (3) A-14, (4)
Constant
y
"C
X
2
X3
X6
X7
Xs
Xll
X12
12
13
1
6
1
7
IS
III
112
z
0.1460
0.8180**
0.0049**
-0.0012**
-0.0016
-0.0404*
-0.0083*
-0.0001
0.0008**
0.0155
0.1231
0.9091**
0.0006
-0.0007
-0.0006
-0.0130
-0.0034
-0.0001*
0.0007
0.0066**
-O.OOOS
-0.0041
-0.0929
-0.0104
0.0001
-0.0002
-0.0212
0.0747
0.5S94**
0.0001
0.0004
-0.0012
-0.0134
-0.0005
-0.0000
0.0004*
0.0009
0.0297
0.5927**
-0.0005
-0.0001
-0.0006
-0.0177
0.0003
-0.0000
0.0004
0.0009
-0.0005
-0 .0011
0.0076
-0.0016
0.0000
0.0001
0.0653
*Signifacant at level a = 0.05,
**Significant at level a = 0.01.
5