ASTATISTICAL STUDY OF THE EFFECTS OF
WEATHER MODIFICATION ACTIVITIES
IN SOUTHWESTERN WASHINGTON
The Computing Center
Washington State Unt\lerslty
A srATISTICAL STUDY OF '1'KS EFF2XiTS OF
WEATHER K:DIlICATION ACTIVITIES IN SOl1I'H\lE8'lmN WA5BINGTON
Prepared for
The Washington Sto.te Weather Modification Board
under Contract No. Ol()4.
by
The Wash1ne:ton State University COlllputine: Center
Work Done By:
G. R. lngru
O. W. Rechard
J. W. Crosby
with the advice of
T. S. Russell
Report Written By:
G. R. Ingram
O. W. Rechard
Submitted through the Geo.Byd.rologic Research Group
Washington State University
TABU OF CONTENTS
I. Introduction.
II. Qualitative Results.
III. Population Distribution and D1etribution_Free
Methods••••
IV. Precipitation Distribution ..
V. 'teats Based on the liorm&l Distribution .
1. "t" Tests Comparison of Means.
2. Anal,ysis ot COV6riance. . •
3. Regression Analysis ••
VI. Extreme.Ve.lue Distribution Results .
VII. Summary and Conclusions.
Bibliography • • . . . .
9
II
12
15
19
21
1. Di'mODlXTION.AND GENERAL CONSID:ERAl'IONS
This report contains the results of a study by the Washington State University
Computing Center of possible increases in precipitation in Covl1tz County,
South\lestern Washington due to weather modification dforts in the Lewis River
and White Salmon River \latersbeds. The area in question is sho\lD. in Fig. 1,
with the Lewis and White Salmon River watersheds labeled as the "Target Area"
and the relllt\inder of Cowlitz County outside the target area labeled as the
~uestionable Area."
The general approach to the problem bas been to test the ~pothesis: the sample
of precipitation values from the years \lhen veatber modification efforts \lere
carried on is from the same population as the sample of values from the years
withcut weather modification efforts. To this end, precipitation records have
been obtained from Weather Bureau publications for stations in the target area
and the questionable area and for stations outside the affected zone but close
enolJ8b. that the precipitation regimes could be considered similar.
Precipitation records for nearly fifty stations in weetern Washington and Oregon
were punched into cards, and were used in preliminary surveys and ana!J'see.
The following seven statione were studied intensively: Kalama, Longview, Peter_
son's Ranch (Cougar). Ariel (Mervin). Mt. MSlDS Ranger Station. Seaside and
Aberdeen. The years of record, together with information about missing data,
for these seven stations are sbovn in Table 1.
Table 1
Years of Record aId Months of Missing Data
at Seven Principal Statione
Station From To Months for which data is not complete
Aberdeen Sept '17 J=e '59
Kalama Sept '17 J=e '59 Nov '49, Dec '49, Oct '50. Nov '50.
De, '50·
Longvie\l De, J=e '59
Mt. Adams R.S. Sept '31 J=e '59
Peterson's Ranch Sept '31 June '59 Feb '109; Jan '50; May &: June '53,
Jan &: Feb '55; Jan '59·
Seaside Sept '31 June '59 Oct. Nov &: Dec '33·
Ariel_Merlo/in Sept '32 Ju~ '59 Nov &: Dec '32; Jan. Feb. Apr, May,
June, sept .,. Oct '33; May & June
'310; Mar. Apr, May. June. Sept'"
Oct '35
ABERDEEN
WASHINGTON
Monthly record s have been used insofar as they were available. FrOlll the IllOnthly
records at each Bt.ation, the total precipitation was obtained, when erlsting
records perllitted, for the vater year: tbose IIlOnths frOlil September of one
year through June of the tolloving year. This cboice of IIIOnths coincides with
the time period. during vhich cloudseeding operations are perforaed.
Weather lIlOd1tication efforts tbrouah cloudseeding were first carried out in
this area in the water year 195051. There were no cloud seeding operations
in the year 1951·52, but from 195253 through 195659, there were weather modification
efforts in each year. The 'Water years 195051 and 195253 through
195859 will be referred to as "seeded years" and all other years as "unseeded
years."
II. QUALITATIVE RESULTS
A scrutiny of the data reveals de!'in1te lo/etdry cycles, and suggests that a detailed
analysis llIust take these patterns into account. Thus 1r seeding were
carried on during a period of years which were generally drier over a large
area, one might incorrectly conclude that there bad been no effect it the pre_
vailing dryness were not considered.
Bowever, if the problem i8 more restricted, and the assertion that there has
been more precipitation during the seeded years is to be tested, certain qualitativeenminations
can be indicative of the truth or falsity of the assertion.
One graphical approach 18 to plot cumulative water year precipitation against
time (in years). If' a radical change in the rainfall pattern had occurred, it
lIould oe expected that there would be a noticeable increase in the slope of a
line through these points.
Such plots are given in Figures 28, with stations in the target. questionable
and control areas included tor comparisons. The cOllll:Dent above concerning change
in slope is best illustrated by the points plotted tor ArielMer.,in. By lay_
ing a straight_edge a.lo!J6 the points, one can imagine a good straight line fit
from year 1 to year 10 or 11. Another good straight line fit can be visuali:ted
tor the remaining years, but the second line has a noticeably greater slope.
For this station, the first complete year ot record is 193631 (year 1) 80
year 10 corresponds to 194546.
Por the rel:'Ain1ng su stations, e:ullllinations of the graphs reveal a greater
slope in the early years of record, am in the final years. A smaller s1.ope
in the 1940's indicates a relatively dry period during these years. It could
be remarked that the dit'ference between the plot at ArielMerwin and the other
su plots may be attributable in part to the four years of missing data at the
former.
It tor each vater year, the month vith the highest precipitation is selected,
these months can be compared to give a rough qualitative impression of' precipitation
patterns in the seeded and unseeded years. These high precipitation
months are given in Table 2 for the seven stations.
This table discloses certain interesting points. For instance, the highest
single month of precipitation during the seeded years occurred in January 1953
at each of' the seven stations. It will be noticed also that in most cases,
that month was considerably wetter than the second wettest month during the
seeded period. Since this is true tor the control stations as well as for
those stations in the target and questionable areas, it seellls to be part of a
general pattern instead of a result attributable exclusively to cloud seeding.
In connection with this point, it should be no""..ed that at au of the seven stations,
this heavy precipitation of January 1953 vas exceeded in December 1933,
Me ADAMS RANGER STATION
CUMULATIVE PRECIPITATION VS. YEARS
800 IHH+++++++++1H++++1
600 IHH++++++++1j,H++++1
400 fH+t++++·Jl+++H+t++l
200 fH+t~++++/+++H+t++l
oLl''...L.LJL.lL...L..L.LJlL...L.l.Ll.....L..J
YEARS: I 2 :3 4 5 6 7 8 9 10 II ~12 13 14 15 16 17
¢. ~ ~ ~
~ ~ ~l? ~
.. MISSING DATA IN YEARS 42  43.52 53
FIGURE 2
8°oIH+++++++tt+IHHPETERSON'S
RANCH (COUGAR)
CUMULATIVE PRECIPITATION VS. YEARS
2800O',,,,,,,,,,,,,n,,,,,,,,,,,,
2600IH++++++++ I
2400 IH+++++++t1~\tH+++++++t1
220°IH+++++++tttIH++++i'++t1
2000IH++++++++++IH++++++++1
1800IH+++++++tt+IHH'I+++++t1
1600IH++++++++++IHH++++++t1
1400IH+++++++++tiHH++++++t1
12ooIH++++++++*+IH++++++++I
1000IH+++++++tt+IHH++++++t1
Hj+++H+++HH+++H/+ t_.
t
600IHt++++++++tIHH++++++t1
400IHt4+++++tt+IfH++++++t1
200IHt++++++tt+IfH+++++++
FIGURE 3
ARIELMERWIN
CUMULATIVE PRECIPITATION VS YEARS
1600
0
1400
0
0
1200
0
1000 0
800
600
0
400
0
200 0
0
0
YEARS: I 2 3 4 5 6 7 8 9 10 II 12 13 14 16 17 Ie 19 20 21 22 23
il: "<lo : "'~"
FIGURE 4
3132
KALAMA
CUMULATIVE PRECIPITATION VS. YEARS
2.
2.
2.
23 01
22 0 I
21
20
19
18
17
16
" 'o"r "
,;:.J 13 12
"10
9
8
7•
••3
2
I
200 400 600 800 1000 1200 1400 1600
INCHES OF PRECIPITATION
.. MISSING DATA IN YEARS 4950,5051
FIGURE 5
H++++++++++L
IH+++H+IloH++
H++j°llONGVIEW
CUMUlATIVE PRECIPITATION VS. YEARS
5859 28
27
26 I+fH++++++ot+
25
24
23
22
21
5051 20
19 I.
17
'" 16
~ 15
~ 14
13 ftfHf'+++++++1
12 ftfHof+++++++1
"10  r
9  r
•  I o++1++H++J
7 Itr':Itt+++++iI
6
5 fH'+++H++++H
4
3  o+++++fH+++'1
2 H+++H+++ItH
31·32 I ~~+fH+++++++t+
200 400 600 800 1000 1200
INCHES OF PRECIPITATION
FIGURE 6
SEASIDE
CUMULATIVE PRECIPITATION Vs. YEARS
5859 27HH++++++++++IHJ++++o
26++++++++++++II++++0'
25 ~
24H++++++H++++++H+
23 +++H
22H++H+++H++H++ l+H+I
21 ++++++++++++IH 11+++1
20H++++++I+++++ +H+++1
5051 19++++++++++++H +++++HH
4950 18+++++++++++H ++++1++1
I7HH++++++++H
16+++++++++++ ,+++++1++1
w '"HH++++++++!>+J1HJ+++++I
~ 141+++++++++ ++++++++++H
~ 131++++++++ ++++++++1++1
121+++++++0+++1+++++++1
111+++++++ +++++++++++1+
10+++++++
10++++++++1+++++++1
4
343e 3
3233* 2
:3 132 IIo~HJ++++++++++HJ++++I
200 400 600 aoo 1000 1200 1400 1600 1800 2000
INCHES OF PRECIPITATION
FIGURE 7
ABERDEEN
CUMULATIVE PRECIPITATION VS. YEARS
5659 2B or
27 I 0 r
20 ~ r
25 0
2. 0
2' 0
22
21 0
sc:r51 20 0
"
0
18 0
17 0
16 0
~ 15
~ 14 0
>" 0
12 0
II 0
10 0 • 0
8
7
0 0
5•, ~t 3233 2
3132 I 0
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
INCHES OF PRECIPITATION
FIGURE 8
Table 2
Maximum Monthly Precipitation in Water Year
Aberdeen Seaside Kalama Longviel<l
Max Monthly Month Max Monthly Month Max Monthly Month Max l>'.onthly l~onth
Water Year Predp. Occurred Precip. Occurred Fredp. Occurred Fredp. Occurred
Unseeded Years
193132 11·92 De, 15·59 De, 13·56 De, 8.26 Mar
3233 19·92 De' 19·11 Jan 15·50 Jan 11.28 Nov
3334 35·10 Dee 15·08* Jan 26.59 Dee 20.13 Dee
3435 20·35 Jan 15·15 Jaa 17·93 Nov 11.53 Nov
3536 15·22 Jan 15.98 Jan 13.82 Jan 8.88 Jan
3637 14.84 Feb 13·95 Dee 13·20 Dee 8.12 Dec
3738 26.40 Nov 23.80 Nov 15·15 Nov 10·39 Dee
3839 16.62 Jan 15·23 Feb 9.42 Jan 6.96 Feb
3940 18.94 Dee 11.35 De, 17.46 Feb 10.27 Feb
40_41 12.20 00< 10.68 Oat 8.88 Nov 5.48 Nov
194142 15.48 Dee 16.64 Dee 10.47 Dee 8.26 Dee
4243 14.16 Dee 16.28 N= 9.88 Dee 9.47 Uov
4344 12.62 Dee 9·55 Oat 6.46 Oot 4.40 Oat
4445 13.36 Jan 11.82 M~ li·97 M~ 5.69 Me,
4546 14.15 Nov 13.71 Feb 13·39 Jan 9.64 Nov
4647 12·51 Dee 12.52 Nov 10.62 Dee 10.83 Dee
4748 17.43 00< 13·35 Oat 14.67 Oat 8.52 Oat
4849 14.74 Dee 15·37 Feb 15·11 Dee 10·95 Dee
4950 15.28 Feb 16.54 Feb 10.87* Jan 8.36 Dee
5152 12.24 Jan 14.06 Jan 11.26 Dee 7.86 Dee
Seed ed Year s
195051 16.18 Dee 11.78 Dee 12·37* Jan 9·40 Nov
5253 30.46 Jan 28.81 Jan 18.00 Jan 13·11 Jan
5354 20.22 Jen 20.69 Jan 13.65 Jan 11.00 Jan
5455 14.01 Nov 11.75 De, 10.42 Dee 6.12 Nov
5556 18.07 Dee 18.38 Jan 13.84 Jan 10.42 Dee
5657 13.12 Oat 12.83 Oat 9·39 M~ 6.85 Dee
5758 15·30 Dee 16.21 Dee 11.42 Dee 10.43 Dee
5859 16.60 Nov 16.54 Nov 1~_·99 Jan 10.79 Nov
* Incomplete records for the year
Table 2 (con't.)
Maximum Monthly Precipitation in Water Year
ArielMerwin Peterson's Ranch Adams Ra!lJ!jer Station
Max Monthly Month Max Monthly Month Max Monthly Month
Water Year Precip. Occurred PreC1p. Occurred Precip. Occurred
Unseeded Years
193132 . . 25.19 Mar 13.61 De,
3233 10.21* Mar 26.85 Nov 11.48 Nov
3334 25. 19M" De' 57.04 Deo 27·31 Deo
3435 15.61* Nov 29.48 Nov 12·15 Nov
3536 14.45* Jan 21.48 Jan 12.60 Jan
3637 16.00 De, 24.18 Deo 10.58 Feb
3738 16.36 Nov 33·77 Nov 14.55 Deo
3839 10.42 Feb 21.11 Deo 7.86 Jan
3940 15·07 Feb 31.11 Feb 14.62 Feb
40_41 8.64 Nov 15·02 Jan 7.76 Jan
194142 12·95 De, 23.62 De, 13.61 De,
4243 15·73 Nov 31.34 Nov 11.40 Nov
4344 8.63 Oot 13.40 Oot 5·40 O,t
4445 11.54 Mar 19.44 Mar 7.84 Feb
4546 14.23 Nov 21.25 Nov 12.21 Nov
464] 14.32 Deo 26·29 De, 9.69 Deo
4748 13.35 Oot 24.31 O,t 10.96 Oot
4849 16.06 Feb 23.26* Nov 11.18 Feb
4950 13.26 Jan 30·35* Feb 20.18 Jan
5152 11.42 O,t 23.26 Dot 11.75 Nov
~
195051 12·91 Nov 25.66 Jan 12.82 Jan
5253 19.62 Jao 46.14* Jao 23·30 Jan
5354 15·32 Deo 30·69 Jan 16.94 Jan
5455 11.19 Deo 21.61* Deo 7.34 Nov
5556 16.11 Jan 31.04 Jan 15·09 Jan
5657 11.95 Deo 22.01 De, 4.39 Deo
5758 15·98 Deo 31.97 Deo 6.11 De,
58:59 16.81 Nov 35.25* Nov 8.00 Nov
* Incomplete records for the year.
and the lone exception to this was Seaside__a control station. At Seaside the
precipitation tor January 1953 was the heaviest single month on record.
So an eX6.lllination of 1DlUi= monthly precipitation shows thAt seven years ago,
at all the stations, there was a very heavy IIlOnth. Since this pattern prevailed
over a broad area, and since at each station in the questionable area this
figure is exceeded by one from the nonseeded years, caution is dictated in
drawing any conclusions.
Another way of comparing monthly precipitation in the two periods is to ask
how the highest precipitation figure for a given month during the seeded period
at a particular station ranks relative to figures for unseeded years. For
seven stations these results are shown in Table 3.
Table 3
Highest Ranking of a Month in Seeded Years
Kalama Longview Seaside Aberdeen Mt. Adallls Pe:::~~n's :;:i~
Oct 2 1
Nov 5 3
Dec 12 11
Jan 1 1
Feb 16 13
Mar 8 4
This table shows. for e.xample, that at Kalama the highest October precipitation
during the seeding period was the second highest OCtober precipitation on record
while at Longview the wettest October on record occurred during a seeded
year.
'rurning fl'Olll a ll1onth_bY_lIIOnth examination of the data, we have also ask.ed bow
the total precipitation for the last five years during which cloud seeding activities
vere carried on coapares vith the total precipitation for other consecutive
fiveyear periods. Peterson's Ranch was eliminated frOlll consideration
since m18sing data made it 1.IDpossible to evaluate total precipitation for
the last five water years or indeed for any five consecutive vater years since
194849. For four of the remaining six stations it vas possible to find a
fiveyear period in the interval 193150 during which the total water year pre_
cipitation exceeded the total vater year precipitationtbr the period 195455
through 195859. It seems likely that this could also have been done for ArielMerwin
and Seaside had not missing data forced us to consider the interval
193650 in the first case and 193450 in the second, thus eliminating from
consideration several very wet years. These results are summarized in Table
4 below.
Station
Table 4
Ma%. 5....ater Yr. Period in vhich 5Water Yr. 'rot..
Total Prec1p. Max. Occurred Precip. 195459
Mt. Adams R.S.
Ariel_Mervin
Kalama
Longview
Aberdeen
seaside
2611.58 in.
352·05 •
364.97
238.99
478.20 "
376.28 ..
194550
194550*
1931~36
194550
193136
193439"
204.32 in.
380.5'> ..
307·59
222.75
405.73
394.88
* interval considered was 193650 ** interval considered vas 193450
III. POPULATION DIS'DI:IBUTIONS .AND DISTR:I:BUrIOR_FREE METHODS
To carry out the classical statistical tests and in!'erences trom 8 set of
sample values, it is necessary to consider the sample 8S being drawn trom a
population with a certain type of distribution, e.g., the normal distribution.
The type of distribution is frequently s~ested by a knowledge of the physical,
cbelllical, or llleteorological natlU"e of the variable being studied. Then
from 5allIple values it is possible to estimate parameters, e.e;., the mean and
variance, that characterize the particular distribution in que8tiotl. In the
case of precipitation data the population in question is simply the totality
ot all possible values of tbe precipitation aDd in Beetion IV we have examined
three possible assumptions regarding the distribution of this population.
A particular population distribution can be specified by two (related) functions.
One :function is the ~probability detlsity function," IlhicD. is IIOst suggestive
from a graphical viellpoint. The bellshaped normal ClU"ve is a vell_known ex_
ample. The area bounded by the curve between two given values is the probab_
ility at OCCur1"ence of a value between these two 11.alits. 'lhe other function 18
the "cUlllU1ative probability function." Graphically, it is a ClU"ve that rises
from lett to right, and at any point the height of the curve gives the probability
of values less than that point.
Thus, when a distribution type is postulated, and parameters are estimated from
a sample of the population, it 1s possible to make in!'erences or tests wlth
de1'inite probability statements or confidence levels.
On the other hand, one JDay choose to llI8ke no assumptions about population distribution
and still test for differences in location of two population!>. A
useful statistic for this plU"pose is the "median" which for a sample of size N
of some measurable characteristic 1s defined to be that value for which an
equal number of sample values fall above and belovo In the problem at hand,
one would like to test the hypothesis that the same population is being sampled
in both the seeded aDd unseeded years, without any assumptions about population
distribution. A llledian test can be 1llIl.de that is sensitive to differences in
location; Le., a sh1!'t in lIIedian values for the two periods, but not particularly
sensitive to differences in shapes of the two distributions.
The idea of the test is this: if we have a sample of n values from un seeded
years, and m values from seeded years, and the hypothesis is true, we would
expect apprOXimately n/2 unseeded years and approximately m/2 seeded years to
exceed the median of the combined sample. It is possible to test whether the
deviations frolll these expected nUlllbers are statisti2ally 6ignif'icant, so that
the 1J3pothesis should be rejected, by computiDB a'l;. value and c~paring this
with tabulated values [5, pp. 390395]. The COlDputed value of ~ 16 obtained
by dividing each of the two samples into two groups__ those whose value is above
the Illedian of the COlDbined sample and those whose value i6 below.
Then
2 [t(obs.)  f(exp. )t
':t .. .E f(e:x;p.)
where f(obs.) and f(exp.) stand for the observed and e:x;pected frequencies respectively
and the summation extends over the four cells of the contingency
table.
Tabulated values of 'l:,2 for various probability levels are:
:\;2(.05)·3.84
;(;2(.10) '" 2.11
~2(.25) .. 1.32
.)(2( .50) • 0,'55
Thus! if the hypothesis is true! we would e;ll;pect computed values of ;t:2 to
exceed 3.84. only 5 percent of the time; to exceed 2.11, 10 percent of the time;
to exceed 1.32, 25 percent of the time; and to exceed .455 half of the time.
Since one ordinarily wishes to be conservative in rejecting an hypothesis when
it is true! the 5 percent level is a commonly used standard.
Tables 511 rank the water years in increasing order of the total precipitation
and give ~2 values as computed above for the seven stations in question.
(Common statistical practice is to reduce by 0.5 the deviations appearins in
the numerator of the above formula when f(exp.) is small. Consequently, the
'{2 values appearing in Tables 511 are conservative.)
At Kalama, for example! the record for one of the seeded years is not complete;
four of the retll8.inin~ seeded years fall below the median and three above. The
computed value of ~ • .173 and, comparing this with the tabulated values
listed above, we see that from this test it is not possible! even at the 50
percent level! to reject the bypothesis that the seeded and unseeded years are
samples from the same population.
While we have bypothesi:z;ed that the same population is being sampled in
the seeded years as well as in the unseeded years, it should be borne in mind
that the basic assertion being investigated is that precipitation has increased
during the seeded years. Clearly, then! anywhere the number of seeded~
falling below the median is greater than the number of seeded years above the
median, there is no support for the latter assertion.
:;o~~~:'c~~~~Je:~u~o;h~~e:d~6;:i~~~c~u:;e~:tte: :;:i:a:~ ;~ve
reject the hypothesis at the 25 percent level. A silllilar statement holds at
Aberdeen with 42 years of record and Seaside with 21 years. In neither case
would we be able to reject the hypothesis at the 25 percent level.
A further comparison is aff'orded by the stations actually in the target area.
Peterson's Ranch (Co\.l8ar 6E since 1953) has somewhat weaker records! with only
five years of record during the seeded years. Here! four years are above the
median and only one below. However! at Mt. Adams Ranger Station, where there
are 20 years of complete records in the unseeded years and 8 in the seeded
Table 5 Table 6
Kalama Longview
Water Yr. Precip. Rank Water Yr. Precip. Rank
1920~21 81.92 1 195556 56.94 I'
3233 811.24 2 5354 50.61 2*
5556 81.21 3' 3233 50.13 3
3132 16.06 4 3334 50·09 4
3435 75·11 5 4546 49.48 5
2425 12.00 6 4748 48.61 6
3738 71·51 7 5051 48.24 7'
4148 11.34 8 4950 48.16 8
1819 10.81 9 4641 47.89 9
5354 10·09 10* 3435 41.14 10
193334 69·85 11 195859 46.86 11'
2128 69.56 12 4849 44.85 12
2621 69.29 13 3132 44.10 13
4546 61.11 14 4243 43.06 ·14
21_22 66.22 '5 3138 42.81 15
1118 64.78 16 2621 41.16 16
5859 62.46 17' 5758 41.68 17'
2223 61.03 18  median
4641 60·99 19 192128 41.41 18
3637 60.15 20 5253 41.44 19*
____ median 5152 41.21 20
195253 59·79 21' 3536 40.73 21
3536 59·11 22 5455 39·11 22*
5152 58.98 23 41_42 39·23 23
4849 58.58 24 5657 31·50 24'
5455 56.30 25'
5158 56.00 26 193940 36.14 25
3031 54.56 27 3637 35·11 26
2829 54.30 28 3031 35·50 27
3839 53·77 29 3839 34.05 28
3940 52.86 30 4445 33.61 29
40_41 32.12 30
195651 51.56 31' 2829 31.34 31
4445 51.41 32 2930 29·31 32
4243 51.02 33 4344 28.69 33
4142 49.99 34 2526 28·52 34
40_41 49·99 35
2526 48.67 36
1920 48.63 37 '):.2 = .654
2930 48.05 38
2324 43.09 39
4344 38.36 40
'i ..173
* Years with seeding activity
Table 7 Table 8
Aberdeen Seaside
Water Yr. Precip. Rank Water Yr. Precip. Rank.
193334 104.76 1 195556 102.98 1
31~32 103·77 2 3233 99.82 2
5556 99·72 3* 5051 92.26 3"
20_21 98.42 4 3132 89.36 4
3435 97.67 5 49~50 87.01 5
3233 97·00 6 5354 86.98 6"
3738 96·69 7 3435 85·16 7
5354 89.85 8* 3738 84.75 8
2627 69·28 9 5859 83.79 9*
4950 88.72 10 4546 81.68 10
4243 76.<;'2 11
1924~25 87.47 11 5253 75·01 12*
5859 87.13 12* 5152 73·71 13
2728 87.03 13
4546 85.84 14 193839 73·70 '14 median
5051 84.82 15*
4748 84.24 16 194748 73.45 15
3940 81.16 17 5758 73·09 16<
1819 79.63 18 3940 72·91 17
3031 78.73 19 41_42 71.86 18
5253 78.28 20* 3536 69.36 19
3839 76.22 21 5455 68.39 20*
 median 5657 66.63 21"
195657 75.82 22* 41>45 66.14 22
3536 75·00 23 4849 65.80 23
4243 73·91 24 3637 63.31 24
5758 72·69 25" 4647 63.22 25
4849 72·52 26 4041 57·91 26
21_22 71.76 27 4344 57·57 27
51~52 71.41 28
1718 70·50 29
5455 70·37 30* ~2 ••941
4445 69.74 31
4647 69.65 32
193637 67.97 33
41_42 67.56 34
2223 66.49 35
2526 64.84 36
2829 64.02 37
40_41 62.97 38
2930 61.66 39
4344 60.41 40
1920 57.67 41
2324 55·12 42
'>...2 ...618
* Years with seeding activity
Table 9 Table 10
Ariel_Mervin Peterson's Ranch
Water Yr. Precip. ~ water Yr. Precip. Rank
195556 93.47 1" 195556 175·01 1"
5859 8'<.46 2* 3334 149.26 2
47"" 76.35 3 4546 140.52 3
4641 10.42 4 3233 J.4o.35 4
5051 70.29 5* 5051 134.54 5"
5758 70.28 6 5758 132.35 6
4950 69.81 7 3132 131·73 7
5354 69.45 8* 3738 127.80 8
3738 68.70 9 4748 123.94 9
4546 68.26 10 3435 122·75 10
4849 67.51 11 5354 121·55 11"
195657 67.33 l2* median 194647 1.20·09 1.2 median
195455 65.30 13* 195152 114.89 13
5152 62.59 14 421,3 114.88 14
4243 62.37 15 5657 113·10 15"
3637 60.77 16 3940 101.82 16
4445 60.28 17 ......5 106.19 17
4142 59.86 18 3536 105·39 18
5253 59·73 19* 41_42 103.67 19
3839 52·79 20 3839 102.80 20
3940 52·39 21 3637 99·43 21
40_41 51.41 22 4041 8'<.52 22
4344 45.30 23 43" 75·99 23
':(2.1.0514 'X,.2 = 2.27
* Years with seeding activity
Table II
Nt. Mams Ranger Station
Water Yr. Precip. Rank
195556 71.62 1"
5051 63.25 2*
"950 62·69 3
3334 59·90 42"3 56.10 "5
535" 55·59 6*
"546 52·90 7
"7li8 52·77 8
3132 52."7 9
3738 52·32 10
195253 52·05 U"
3"35 51.18 12
5152 51.52 13
48"9 SO.62 ,"  median
193233 50.18 15
39"" "6.29 16
46"7 45.60 17
3536 42.52 18
194142 41.85 19
3637 "".08 20
.......5 39.63 21
""1>1 39.41 22
5455 35.89 2)*
5859 35.89 "'" 3839 32·57 25
5758 32·20 26*
5657 28.72 27"
"3"" 24.55 28
~2. 0
* Years with seeding activity
years, one finds four below the median and four above. Finally, at ArielMerwin,
there are five years above and three below the median.
In addition to the rankings of totals for 10 months, rankings for the individUl.l
months vere made and examinations like that outlined above were conducted.
These rankings are not included in this report due to space considerations, but
the results for the six heaviest precipitation months are summarized in Tables
12_18.
Certain features of the table are striking. We note that at Kalama for only
two of the six months are there more seeded years above the median than belolol;
namely December and January. For January, it can be observed that the pattern
is precisely the same for all stations except Mt • .Adams Ranger Station. For
December the record for 1950 is not complete, but the figures are comparable to
those at the other stations except for Mt • .Adams Ranger Station.
At Longviev, the situation is different. In making comparisons, it becomes
clear that Aberdeen and Seaside are almost identical with Longvie1ol. This can
be contrasted 10Iith ArielMerwin where for all months except October we find a
larger number above the median than below.
Testing as outlined above, we ....ould find significance for those cases ....ith two
below the median and six above, or one below and five above.
Table 12 Table 13
KAlama Lo~iew
No. of Ro. of No. of No. of
Yrs.of Seeded Yrs. Seeded Yrs. Yrs.of Seeded Yrs. Seeded Yrs.
Mo. Record Below Ked. Above Med. Mo. Record Below Ked. Above Meel.
Oct 'n Oct 3' • Nov 40 Nov 3' 5
Deo 40 Deo 35 'v
Jan .2 Jon 35 6
Fab .2 F.b 35 3*
Mar .2 Mar 35 5
Table 14 Table 15
.Aberdeen Seaside
Ho. of Ho. of lio. of No. of
Yrs.of Seeded Yrs. Seeded hs. Yrs.o! Seeded Yrs. Seeded Yrs. M,. Record Belo." Med. Above JoI..ed. Mo. Reeord Below Ked. Above Med.
Oct "" Oct 27 3*
Nov .2 Nov 27 5
Da, '2 De, 27 5
Jan .2 Jan 28 6
Fa' .2 F.b 2/! 3
Mar '2 Mar 28 6
* IDdicates that the value tor a seeded year is the median of the cOlllbined
68l11Ple.
Table 16 Table 17
Ariel~Merwin Peterson's Ranch
No. of No. of No. of No. of
Yrs.of Seeded Yrs. Seeded Yrs. Yrs.of Seeded Yrs. Seeded Yrs.
Mo. Record Below Med. Above Med. Mo. Record Belo'W Med. Above Med.
Oct 2, 3* Oot 28
Nov 26 6 Nov 28
Doc 27 5* De, 28
Jan 26 6 Jan 2'
F.b 26 , F.b 26
M~ 26 , 28
Table 18
Mt. Adams Ranger Station
No. of No. of
Yrs.of Seeded Yrs. Seeded Yrs.
Me. Record Below Med. Above Med.
Oct 28
Nov 28
Dec 28
Jan 28
Feb 2288
'* Indicates that the value for a seeded year is the median of the combined
sample.
IV. mECIPITATION DISTRIBUrION
As remarked earlier, the classical tests depend on assumptions regardil18 the
torm ot the population distribution. Such an assumption should be based on
consideration ot the physical problem, am tor lIleteorologlcal studies severa.!
posslbll1ties ar16e.
Tbe SU88estion has been made by Tholl r6Jtbat the "ga:ulS" dlstribution be used
in precipitation studies. 81s sl188estion was for precipitation over short
time intervals, e.g., one day.
Another proposal bas been set forth by Brakensiek and Fingg ~]....hich includes
an empirical study ot the reasonableness of using the socalled "extreme_value"
distribution for the ratio of precipitation to mean precipitation. Their results
are striking, and while one usually deals ....ith the cumulative form of
this diatribution, an eX8ltlination of the density function (4, p. 83] discloses
that it is a plausible distribution on the same basis as the galllDla distribution.
'fr.at ls, both are ske....ed, the enreaMlvalue distribution may be bounded frOlll
belov as is the ga.a, aDd both are wibounded to the right.
Finally, the very cOlDlDOn assumption of norlll8l1ty is frequently lIl8de. ThollI suegests
that for precipitation accUlllU1ated over a period as long as a year, the
normal distribution is the most reasonable choice. He is doubtful of this
choice tor periods of one month.
In view of the existing empirical Justification for the use of the extreme_value
distribution, and the history of use of the normal, it ....as decided to use these
in making further tests. It vss telt, he.ever, that 1he. gamma distribution
should be eumined and COlllpared with these tvo for 1II0nthl.y precipitation. Figure
9 is an imication of the results.
As is apparent frOllll the graph, the gamma and extremevalue distributions are
in very close agreement. As expected, the normal differs SOIlevhat, aDd there
are clearly regions vhere the normal "tit" is superior and other regions vhere
it is interior to the others.
On the basiS of such examinations it was concluded that no distribution enjoyed
a clearcut advantage over another. Because of the relative ease of dealing
with the normal and with the extremevalue populations, the remainder of the
report concerns tests lIl8.de with one or the other of these t ....o as the underlying
distribution.
I.
0.' ~ ;:;..:
~ .
08 1,J!.;;1
07
0 #
0../
0 .• 
.>... 
:3 0.5 OJ ~;} CUMULATIVE NORMAL
"    CUMULATIVE GAMMA
~ o. ~.
~. a:   EXTREME  VALUE
0 Z. 0 ACTUAL OBSERVATIONS
Q.3
'/ 0
, 0
02 ,Z
0.1 o p/ '"
O.S f .~/
I 2 3 4 S • 7 8 • '0 11 "2 13 14 15 I • 17 '8
"
2
PRECIPITAT ION (IN INCHES)
KALAMA JANUARY PRECIPITATION FIT TED TO VARIOUS PROBABILITY DISTRIBUTIONS
FIGURE 9
V. TESTS BASED ON THE NORMAL DISTRIBUl'IOIi
1. "t" Tests Comparison of Means
One standard method of comparing t·,10 populations is to compare the means (av_
erage value) of samples drawn from each. This can be done on a monthly basis
as well as an annual basis. We note that this is analogous to the median test
in the distributionfree method used, but with stronger assumptions, we can
draw stronger conclusions.
Since it is contended that precipitation has been heavier during the seeded
years, we will hypothesize that the means of the two periods are equal, and
then investigate the data to see if there is reason for rejecting this hypo_
thesis.
Clearly, if the mean for seeded years is lower than the mean for the unseeded
yea1's, the data will not support the original contention. The question that
the ensuing tests attempt to answer is: how much of a difference between the
two means can 'ole consider as being due to chance in random sampling, or, which
differences are statistically significant. To carry out these test, one selects
a certain probability level as the level of risk in rejecting e. true hypo_
thesis.
The first such test applied was Student's "t"_test. In addition to the nor_
mality assumption, it must also be assumed that the tlOO populations have equal
variances. That is to say that the two distributions are equally spread about
the mean. This assumption was checked, using Bartlett's test for homogeneity
of variances.
The results of the t_test for the seven stations chosen for intensive examin_
ation for the 10 months of the water year and the total water years are contained
in Tables 1925. In examining these results, it should be stressed that
this test does!!£! consider the general trend of precipitation over a wide area~
it simply indicates whether or not there bas been a significant difference in
average rainfall in the two periods. Thus in a cycle of wet years one might
mistakenly conclude that weather modification efforts were responsible for the
change, or conclude the reverse in a cycle of dry years when neither conclusion
is correct.
The results for Kalama show that for the months of September, October, November,
December, February, March, April and May, the average precipitation in the
seeded period was less than that of the unseeded period. The difference is
never statistically significant, however, and we find no reason to reject the
hypothesis for these eight months.
Also at Kalallla, we find that for January, June, and the total water year, the
situation is reversed. For the month of June, and for the total water year,
we find in comparing computed tvaluel; with the tabulated tdistribution (2,
p. 384J that we would be unable to reject the hypothesis even if '.;e were willing
to operate at the 30 percent level. That is, if we would take the risk of reJecting
a true hypothesis three times in ten, we could still not reject for
these time periods. However for the month of January, we 'Jould be obliged to
reject the hypothesis at the 5 percent level, which suggests that further study
of the January precipitation pattern is in order.
Table 19 Table 20
Kalama. Longvie....
Mean Prec1p. Mean Prec1p. Mean Prec1p. Mean Precip.
Mo. Unseed ed Yr s. Seeded Yrs. t Mo. Unseeded Yrs. Seeded Yrs. t
Sept 2·55 2.17  .65 Sept 2.13 1.47 1.39
Oct 5.85 5.69 _ .11 Oct 4.28 4.67 .44
Nov 8.72 7·91 _ .42 Nov 6.19 6.43 .17
D" 10·99 10.68  .15 De, 7.73 8.06 .23
Jan 8.42 11.29 1.81 Jao 5·15 7.89 2.47
Feb 7·05 6.73  .25 Feb 5·09 4.42  .73
Mar 7.47 7.39  .07 Mar 4.67 4.99 .48
Apr 4.41 3.85  ·55 Apr 2.58 2·75 .27
May 3·21 3.06 .17 May 2.26 2.19  .12
June 2.54 2·95 ·52 June 1.89 2·51 1.05
Total 61.14 62.50 .27 Total 41.95 45.38 1.24
Table 21 Table 22
Aberdeen Seaside
Mean Precip. MeaD Prec1p. Mean Precip. Mean Precip.
Mo. Unseeded Yrs. Seeded Yrs. t Mo. Unseeded Yrs. Seeded Yrs. t
Sept 3.94 2.85 1.19 Sept 2·95 2.63 .42
Oct 8.08 8.44 .22 Oct 7·27 8.13 .54
Nov 10·99 10.75 .11 Nov 10.44 10.06  .17
De, 14.93 14.73  .09 De, 12.16 14.21 1.44
Jan 11·53 15·27 1.61 Jan 10.66 15·51 2.17
Feb 10.35 10.06 .19 Feb 10·09 9.65  .27
Mar 8.88 9·34 .29 Mar 9·01 9·26 .18
Apr 5.47 5·72 .20 Apr 5·20 5.78 .54
May 3.67 2.36 1.75 May 3.54 2.58 1.14
June 2.54 2.82 ·37 June 2.94 3.32 .46
Total 80.37 82.34 ·37 Total 74.40 81.14 1.37
Table 23 Table 24
ArielMer\lin Peterson's Ranch
Hean Precip. Mean Precip. Hean Precip. Hean Precip.
Mo. Unseeded Irs. Seeded Ira. Mo. Unseeded Ira. Seeded Irs.
"pt 2·97 2.25 • ·92 "pt 4.52 3.06 1.19
Oct 6.67 7.14 .30 Oct 11.45 12·97 ·53
Nov 9·31 10.27 .47 Nov 17.62 18.76 .28
De, 1l.73 13·15 ·79 De, 21.78 24.06 .62
Jen 7.94 12.76 2.75 Jan 15·32 28.28 3·29
Feb 8.05 8.01 ~ .03 Feb 14.90 15·32 .15
"" 6.60 8.26 1. 43 "" 13·90 14.35 .19
Ap, 4.03 4.27 .22 Ap' 7.46 8.53 .58
May 3·05 3·15 .12 May 4.84 3 ..16 1.38
J=e 3·07 3·30 .25 J=e 3·92 4.31 .29
Total 61.92 72.54 2·57 Total 115·11 135·32 1.98
Table 25
Nt. Ad8.lll8 Ranger Station
Mean Precip. Mean Precip.
Mo. Unseeded Irs. Seeded Irs. ,
"pt 1.26 loll . .36
Oct 3.94 4.78 ·59
Nov 7.42 6·58 .44
Dec 9.94 8.62 .62
Jan 7.80 10.16 1·33
Feb 6.86 4.76 1.11.7
"" 4.8J. 4.98 .19
Ap, 2.22 2.18 ·77
May 1.11 1.53  .29
J=e 1.33 1.02 .60
Total 41.29 46.90  .08
10
At longview, the months of September, February and May show smaller average
values in the seeded years than in the unseeded years. The months of October,
November, December, March and April have larger averages in the seeded years,
but with such slight increases that even at the 30 percent level we would be
unable to reject the hypothesis. For the remaining periods, we would reject
the hypothesis for January at the 2.5 percent level, but at the 10 percent level
would be unable to :reject for the water year, and would reject for June at the
20 percent level.
In view of the significance at each of these stations in January, it 1s clearly
indicated that a longer study of this month 1s desirable. Again it should be
remarked that we could not, on the basis of this test, attribute the signifiemee
to any particular factor.
In connection with this observation, we compare results of those in the questionable
area with results at control stations; namely, Seaside and Aberdeen.
Summarizing briefly, at Seaside, for eight months of the year the average is
either lower in the seeded years, or so slightly larger that we would be unable
to reject at the 25 percent level. For the month of December and for the
water year, we would reject at the 10 percent level. while for January, we
would reject at the 2.5 percent level. At Aberdeen for January we would reject
at the 10 percent level, but not at 5 percent. For all other months and the
water year, either the average is lower in the seeded years, or we would be
unable to reject at the 25 percent level.
As a final comparison, we note the results of the same test applied to PetersonI
s Ranch (Cougar 6E since 1953). While only the months of September and May
show a smaller average during the seeded years for all other months except
January we would be unable to reject, at even the 25 percent level. For the
total water year we would reject at 2.5 percent, while the t_value for January
is significant at the 1 percent level.
An examination of results at Mt. Adams Ranger Station shows that six months and
the water year total had a lower average during the seeded years than during
the unseeded years. Three months had slightly higher averages during the seeded
period, but even at the 20 percent level we would be unable to reject the hypothesis
for them. The tvalue for January is signif'icant at the 10 percent level.
For only two months did the unseededyears' averages exceed the seeded at ArielMerwin.
For five of the lllonths that show an increase, the dif'ference is so
small that we would be unable to reject the hypothesis of equal means even at
the 30 percent level, and for one other lllonth we would be unable to reject at
the 20 percent level. For the month of March we would reject at the 10 percent
level, while for January and for the total water year, we would reject at the
5 percent level.
From these comparisons one obtains the impression that the signii"icant dii"fer_
ence in average January precipitations prevails over a considerable area. Since
January is usually one of the heaviest precipitation months, we expect it to
have a fairly large effect on the water year results. We proceed now to a fUX'ther
analysis of January and water year precipitation.
11
2. Analysis of Covariance
Because or the unusual January precipitation pattern indicated by the ttest,
ttleBe data vere subjected to an analysis or covariance. This technique COIllbines
the analysis of variance (a lIlethod or testing !or significant differences
between lIlellDS of two groups) ....ith regression IQethod,s to yield II. some....hat IlIOre
dlscrllllinating analysis than furnished by either individually.
'l'be basic intent or this analysis, then, Is to t.est tor significant differences
In the questionable area, while considering the general precipitation pattern
as e%eIDpl.1fied by the precipItation at II. control station. Here again tbe IlSSUlllPtioDa
are the BaIIle as those lI&de earlier tor the ttest.
The resuJ.ts CllD be sl.Clm8.rlzed by saying that wilen precipitation at Seaside vas
considered as the control, there vas DO significant difference between mean
January precipitation tor the seeded and unseeded years at either Kalama or
Longviev even at the 25 percent level. Statisticians usually prefer to work
with the 5 percent level, so this is a rather liberal choice of probability
level. The swr.e test disclosed l:Iimllar results at Wind River, south of the
target area.
With Seaside as a control, the conclusion at Ariel_Mer1olin and Mt. Adams Ranger
Station 10Ias the same; namely, the hypothesis of equal means cannot be rejected
even at the 25 percent level. Por Pet.erson's Ranch we \/ould be unable to reject
at the 10 percent level.
When Aberdeen \las used as the control station, the conclusion was ur:hanged tor
Kalama, but at wngview the hypothesis of' no difference in means would be re_
jected at the 10 percent level. At Mt. Ad8.:lls Ranger Station, we would be unable
to reject at the 25 percent level, while at ArielMerwin we would reject at the
10 percent level, and for :Peterson's Ranch, ore would reject at the 5 percent
level.
An additional reature of the analysis of covariance is that it enables a cocpari60n
of averages for the tvo perioos when precipitation is "adjusted" (by
regrellSion methods) for the precipitation at the control station. These adjusted
.eans are presented in Tables 26 and 27.
The Illelln precipitation tor the seeded years at Seaside 10Ias considerably hiaher
than that for the unseeded years. We are not surprised, therefore, to see only
slight differences in the adjusted means at U;)ngview and Kala.!!Ia. The adjusted
mean for the seeded years 18 actually lower than for unseeded years at both
Kalama and. Lo~iew.
At Mt. Adams Ranger Station, the adjusted mean tor the seeded years is again
lover than that for the unseeded years. ArielMerwin shows an adjusted mean
for seeded years that 16 about an inch larger than the adjusted mean for unseeded
years, while the difference bet10leen adjusted means at Peterson's Ranch is in
excess ot 3.5 inches, 10Iith the seeded years having the larger value.
When Aberdeen \las used as the control station, adjusted means for Janua=y precipitation
in the seeded years 10Ias greater at every station. These values are
shown in Table 21.
12
What is involved in this apparent divergence 1s a meteorological problem: from
considerations of p~slcal factors, which of the two control stations would be
expected to give the better reflection of precipitation in the questionable
area?
Table 26
Mean January Precipitation Adjusted for
Precipitation at Seaside
Station Unseeded Yrs. Seeded Yrs.
Kalama 9.30 9.11
Longview 6.03 5.71
ArielMerwin 9.19 10.23
Peterson's Ranch 17.56 21.20
Mt. Adams R.S. 8.93 '7.92
Table 27
Mean January Precipitation Adjusted for
Precipitation at Aberdeen
Station Unseeded Yrs. Seeded Yrs.
Kalama 9.01 9.84
Longview 5.73 6.44
Ariel_Merwin 8.76 11.24
Peterson's Ranch 17.07 22.73
Mt. Adaws R.S. 8.49 9.07
3. Regression Analysis
A final evaluation of the effect of weather modification efforts, using a parent
normal distribution, was made with regression methods.
The pertinent graphs are shown in Figs. 1019. Some explanation of the graphs
is adVisable. In each case, the straight line is the bestfitting leastsquares
line for the unseeded years of record, with the number of years, n, indicated
on each grallh. The curved lines above and below the regression line are con_
fidence c\U'ves, and may be interpreted as follows:
171 /
90 /t/1 WATER YEAR PRECIPITION (SUM FOR 10 MONTHS) }, /A
KALAMA(Yl VS. SEASIDE (X) 'V'
/, ~....("I
80 7b.i ;, <>"5556
'~{ ,J '+'~
Y·2.51+0.857X /'T~ /' 70 f n = [8 /.7'5 ~O ,
, ·0.820 /j, 'I '1 53

54
_ 7.f:'I:L:.V
y ... ::..., //YO585~
60 47~~'T
/.. /' I 5253 .../f';;"0/6.0;7I 58 /1",1>}~(15455
50 j.....A '47"I ..,..q. 5657 I ;/::,.rL _____50'10 CONFIDENCE INTERVAL
~ _.....q, )"1'/' 95% CONFIDENCE INTERVAL L INCOMPLETE RECORDS AT STATION .09 FOR YEAR 5051
40 '17 ' /'q;,Lf',
/V/1
30 30 40 50 60 70! eo 90 100 HO
X
FIGURE 10
WATER YEAR PRECIPITATION (SUM FOR 10 MONTHS)
LONGVIEW (Y) Vs. SEASIDE (X)
70 f,,,,r,.,,r,ftt+t+ffI
60 Y'12;32+.392X '~556
n '19 ~.."'ir+I!I
, '.679 ,/I/r..:::::P'
53 'VI .......I~ I 5Of,,,+ttt++5._+,.':r":>:::::r ,~ I I
"';X/ V~51 ~
ftt,ff+t+="._..r:;;c,~".e>r:±='~~=+++t+1
y _ 54';'~"'1:>< ~ .::t= _..:
40 ~I <~:/ 5253+11+++++1
1t+,11+ l~~;C/5;~57
.!_;:o'_V'V' trt+ttj+ttjJ
30 I __ ~'t+II+_...L.JLL_''_L_''1
~ ......... y'" I "'~I  50% CONFIDENCE INTERVAL
ft+1t:. V I 95% CONFIDENCE INTERVAL
Y
2030 40 !50 60 70 t BO 90 100 110
X
FIGURE "
90
V55~56
WATER YEAR PRECIPITATION (SUM FOR 10 MONTHS) 1.. /
AREAL MERWIN yl VS. SEASIDE (X) <f _••0 '
I ,/ V
80 i Al" 'H "V A ,/
5758 ' ./1' I
70 o'b4~~l·;~.r~'Y 5455 ... _
58·57<> "/14'St;://=J, '354
V _'" ,./1'
 1""1 I ~  I
60 ,'.::.c,!",_::J ,~
l~~Y 5253 4 ,"', _ :;:;r151 ' Y'26 58+0.496X
50 ______ y " , ¥ ",,5   "0.521
/' / VI,...
,/ ,
40
,/ /
/  ~  50"0 CONFIDENCE INTERVAL
   95'7.. CONFIDENCE INTERVAL
/ 30
40 50 60 70 ~ 80 90 100 110
FIGURE 12
I j[
WATER YEAR PRECIPITATION (SUM FOR 10 MONTHS) ,4; PETERSON'S RANCHCOUGAR (Y) VS. SEASIOE (X)
150 ,)tz~,"yL
Y= 14.96 + 1.323 X 140 n = 17 +~L
r = 0.846 Il 4/ L
5'rb~ /I,/~~ov/
130 i7r,~ t7 'Lf
'y/t7! 120 /,(~/ \3'54 ;(VJi: y 06\" /,' '/
A~~
" i' ,;)1/ /
,A'?,:bL
10 4A';,~A
//'1t' '" ~IY/ /l V I 9(~~/t1't/
INCOMPLETE RECORDS AT rbi7tj STATION 15 FOR YEARS
5253, 54 55, 5859 1%+4  50 "1,. CONFIDENCE iNTERVAL It 'I
95 "10 CONFIDENCE INTERVAL ;7 Ii
7 '
40 50 60 70 ! 80 90 100
X
FIGURE 13
70
555~
WATER YEAR PRECIPITATION: MT. ADAMS R.5. tY) 14 vs. SEASIDE (X) !L
5051, /1 y
60 !/ "1/
y. 780+0.522X 5354¥'[:/'f/"""y
0'19 ~'::I 1
, • 0.658 r 53, T ,::Y"" I I
r ~ 50 ~~..c;;;:;,,  ,:1 J..'
'i'
_....1,~J,1 _~  T:~ I
40 r(l<p;fi Y1l'41~'  J I I 0 5455 • 5859
30
/' ~/e]L::/ . 05758 I 5657 I
20
 500;0 CONFIDENCE INTERVAL
 95'"10 CONFIDENCE INTERVAL
40 50 60 ~ 70 80 90 100 110
FIGURE 14
I I I I I I
WATER YEAR PRECIPITATION (SUM FOR 10 MONTHS) 1 I.
KALAMA (Y) VS. A8EDEEN (X) , T,6 555V/ 80 'o/J":1k" ;t07V
y ~ 5.225+0.724X ¥'±~'1 ,/1"
70 n =33 _,,/'0 "
r =0.851 / . L,7 3 54
MUI
60
A'~/ "5~59
Wf0~52545~_' ' Y I' 5
'i I pi V ..... "I ""::::5758
50
.,/{d' '~ 0 56~57
';'<, ¥
YJ/~(~' h ..... , INCOMPLETE RECORDS AT
¥~ STATION 09 FOR YEAR 5051
40 <.J_
V I ""1  50'70 CONFIDENCE INTERVAL /" k   95"70 CONFIDENCE INTERVAL
'0 40 50 60 70 80 90 100 110
X
FIGURE 15
70
WATER YEAR PRECIPITATION (SUM FOR 10 MONTHS)
LONGVIEW(Y) VS. ABERDEEN(X}
60 5r5,,"
y =9.412 +0.391 X 58'5973'5~ J<j~
50 n =26 50'5~~'...:::::.J
r =0.741 i 1'" I ,j~I
_Yf: ,_ '....=
y~ 5r~ 5253[ 7'~~.y
54S5.,! 0 I . !./.... ~ _~
40 J..1:_?, 'ri I
__~~'57
30
~v

V /',1 ...50% CONFIDENCE INTERVAL
~. 95% CONFIDENCE INTERVAL
20
30 40 50 60 70 t 80 90 100 110
X
FIGURE 16
FIGURE 17
'555
90
WATER YEAR PRECIPITATION: ARIELMERWIN (Y) I ,L / Vs. ABEROEEN (Xl ,
80
r9,~ ./
/1/ d .J./
y. 24.08+ 0503X 5O5~l
70 n =15 57S8e  ~b .... 1 ....
\'.
r • 0.596 1565,~~/ I ,l~54
54j55T,•.7"""'t:A , ' ,1' v I l __e
60 ~ d;:::;; v1 ~ I 1./'~/T· 52"
~ ~.
.( I ••VI,
50 /1/'T~
J, ,,4
1/ "7 .
40 ,4
A f 50"70 CONFIDENCE INTERVAL r   95"70 CONFIDENCE INTERVAL
I
40 50 60 70 80 90 '00 110
   
0
5556
170
WATER YEAR PRECIPITATION
PETERSON'S RANCH (Y) VS. ABEROEEN{X)
'60
'9 =23.10+I.l45X / 150 n =18
r =0.850 V
140 I(Jr;L
0~5rs~
057S8
130 I ~t <:J/ bL
y~ ,~~~r
120 56 ?t~/  AC ~:¥
I 'I' 110 r/JZ[ /~>q
100  90 I 'JZI ~ /150% CONFIDENCE ,NTERVAL i 95% CONFIDENCE INTERVAL 1/ Ii
50 60 70 t 80 90 100
X
FIGURE 18
5556
70
WATER YEAR PRECIPITATION' MT. AOAMS RS. (X) VS. ABERDEEN (Y) I
i SO

51' ,71
60 ,I ,~
5354 /' _' I I
7b~"+.~
9, 10.67 +.456X 52;53. ~::':::::r".,~"1 t
50 "'20 ' __ ~....::+= ..
v ".680 _~ ,' I ..; ,_J ,::;'1,.....;"'
~Y'T."1
40 I.,.(:',d:'" )
_rY'')/I I
~I/ ~ 5455 .5859 '7 : V ;>/ 41 5756
30 ~
__ • 5657
20
 50'10 CONFIOENCE INTERVAL
 95"10 CONFIDENCE INTERVAL
40 50 60 70 80t 90 100 110
FIGURE 19
13
Consider Fig. 10, Kal.am& (Y) VB. Seaside (X) 88 an example. The ::oegresslon
l1ne 18 based OD 18 years of record. The outer pair or curves give a 95 percent
confidence interval tor means of further samples. That 15, 1f we took
other 8IllIples or size 18 \11th X, the precipitation at Seaside, rued for each
sample, aDd then plotted the points {I,Y} where r Is tbe mean lll"eclpitattoD at
Kalama. for the sample, we would upect that on the average, 95 percent of such
points would fall between these curves. The inner pair of curves represent
50 percent confidence intervals at each value of X. Thus, for repeated samples
of size 18, ve vould expect the plotted points to fall outside this region as
frequently 85 inside the region. For a single observation, such as we have
plotted on the graphs, the confidence intervals llOuld, of course, be vider.
These vider intervals are not plotted, since statistical theory dictates that
a nevsample vauld have to be taken for eacb sucb individual prediction.
With this in lIlind we exallline the graphs, and observe that for Kalama vs. seaside
only one point is above the regression line, and th1B by a small lIl8.rgin, well
within the 50 percent confidence limits for the mean of a sample of size 18.
We note in passing that two observations out of s1:l: fall below the 95 percent
curve.
For the graph of Longview vs. Seaside, we find five points falling within or
on the 50 percent intervals. T\lo additional ones tall within the 95 percent
limits, while one is outside the 95 percent limit. It Illust be emphasized
again that one point above the 95 percent limit or two below, as was the case
at Kalama, is not surpt'ising when we consider that these curves imply probabl1~ty
statements about the means of samples of size 19 and 18 respectively.
A cOlllparison is afforded by Figs. 1719, with graphs of Ariel (Merwin), Peterson's
Rancb (Cougar 6E), aDd Mt. Mams Ranger Station vs. seaside. For Peter.
son's Rancb thee are only 5 cOlllplete years or record in the seeded period. .
Three points are above the upper 95 percent confidence curve, one below the
lower, and one between the 50 percent curves. At Ariel, there are four points
above, and one very slightly below the upper 95 percent confidence curve. while
tva are within 50 percent 11mits, and one below the lower 50 percent curve, but
within the 95 percent curve.
The graph for Mt. Adallls Ranger Station vs. Seaeide reflects other analyses in
showing a greater variability at Nt. Adams Ranger Station. There we find three
points above the upper 95 percent confidence curve, one just above the upper
50 percent curve, and four well below the lower 95 percent curve. The years
that fall outside the 95 percent confidence region suggest another interesting
problem, that of precipitation in relation to the number of hours cloud_Be~ing
generators were operated in a given year. While this problem is beyond the
scope: of this report. it 18 noted that in the water year 195051, the number
of hours of operation was rather small, yet this point was above the upper
curve. On the other hand, the year 195758 surpassed all previous years in
the total hours of operation. but the point for this year is below the lower
95 percent curve. Certainly no conclusions should be reached on such sketchy
information, but a comprehensive examination of weather modification actiVities
that includes this factor could provide valuable infor~tion.
With .(I)erdeen used as the independen't station, the results at Mt . .Adams Ranger
Station are strikingly s1lllilar as can be seen froo Pig. 19. At Peterson's Ranch,
(Fig. 18) results are comparable also. wi'th three points above the upper 95
percent curve. and two between the two curves at that level. Ariel (Fig. 17)
,.
also shows obvious similarity: five points above the highest curve, two in tIE
95 percent confidence region, and one in the 50 percent region,
Examining Fig. 15 for Kalama Ya. Aberdeen, we rind results comparable vith
those at Seaside; namely, two points within the 50 percent confl"ence region,
three IDOre on or \lithia the 95 percent band, and tvo belo\l the lover 95 percent
eurve.
At Longview, however, two points fall within the 95 percent region, and the re_
maining six are above the upper 95 percent curve. While this Is Dot remark8ble
troll II. statistical viewpoint, it Is certainly diftereDt frOlll the picture when
seaside vas the control station. This aall.ln raises the question posed after
e%llminatlon or the adjusted means In the analysis ot covariance.
15
VI. EXTREME_VALUE DIS'mIBU'I'ION RESULTS
The unusual January precipitation motivated an analysis of this data 8s8umlt16
that monthly precipitation conformed to the socalled "extreme_value" distri_
bution. As pointed out earlier, the January 1953 precipitation was large at
every station considered.
Before exal:l1nlng results, the point should be lMlde that 1n the present context,
the name "enreme_value distribution" Is a lIisnomer. In this approach, ve are
not dealing; with a set or maximum values of January precipitation 8S the name
lI1ight suggest. Rathe; we are considering all the January precipitation values
as a sample drawn from a population which has this distribution forlll. The
apparent success or this technique Is due to the properties ",hleb this function
shares with the gamrr.a distribution. and which are based on physical considerations.
The Illost straightforward IOOthod of dealing with this distribution involves
estill8.ting tbe cUlllulative probability function. For tl:e problem at band, the
variable chosen Io/as the ratio of precipitation t.o mean precipitation, Io/ith estimates
me.de trom unseeded years' records. This choice of variable permits a
more ready comparison ot results than 'oIould precipitation alone, tor the le.tter
lDay have considerably different ranges at t'olO stations.
The estimate ot tbe cumulative probability function is obtained from a ranking
ot the data. Thus, it there ..ere 19 years of record, the largest PIP ratio
would correspond to a probability of 19/20 .. 0.95. The second largest ratio
corresponds to a probability of 18/20 .. 0.90, etc.
Figs. 20 through 26 present graphical rer;ults tor the stations at Kalama, Longvie....
, Seaside, Aberdeen, ArielMerlo/in, Peterson's Ranch and Mt. Adams Ranger
Station. The straight line is the estimate of the cumulative function: for
a particular value of pfP, the corresponding value of F(PfP), as determined by
this line, is the probability of occurrence ot a precipitation value less than
or equal to P. Possibly a more mear.ingt'ul interpretation of the horizontal
scale can be made from the "Return Period" scale at the top of each graph.
This is related to the other scale in the follolo/ing ....ay: if F represents the
cUfllulative. probability, then Return Period '" l/(l.F). Thus saying the probabiUty
is 0.95 that precipitation values are 001010/ e. fixed value P is equivalent
to saying that on the average we would expect values of precipitation greater
than P once every 25 years. The "reduced variate," y, is related to F(PfP)by
a double logarithmic transformation, Io/ith the origin taken at the mode of the
distribution.
In addition to the estimate of the cumulative function, the graphs give an
indication of "goodness of fit." The dotted lines represent the "control band,"
and are located one "reduced standard error" on either side of the theoretical
11ne. (see GUSllbelWChapter 6.) According to theory, approJtilll8teIy twothirds
ot the observed points should fall Io/ithin this control band. An examination
of the graphs shows that this percentage is exceeded in every case, so clearly
the "fit" is good.
I ! !
~III II
! I I I I I I I I I I I II I I I I I I I Ii
§
~.
ARIELMERWIN
n =19
~:8'i~I+2.33~ I
, mm
piI1il ,
1III ,r>
I:.. ',I I
.
:,' .11 1'1 I
I ,~,
I;: I:,jl
" II'
EXTREME PROBABILITY PAPER JANUARY PRECIPITATION
;i"t..Fi:tl
FlGURE"24
k.~4J
~p"."' PETERSON's RANCH
~90ype~}I.1
n·21
y .2.03+2.561}~
~, 15.44
\l'llD'Nm«lHTOI~wv.rnnlMlllV.U
EXTREME PROBABILITY PAPER JANUARY PRECIPITATION
it
:u f
,..
to
'7~
FI"~
J," , ,'~::" ,,~,,:: ")~, ,~r, ,~J~, "~' ,,':',,:;~':)~~~':J,,~, ,~" ,,~.'.' " .,~, ,',',' ,~"", ,~"J.,~""" , ,~~:.
IISCO_·WlDC FIGURE~/25
'}pHOKI
MT. ADAMS RS. EXTREME PROBABIliTY PAPER JANUARY PRECIPITATION
":orri
,·f TTTi·rt,
OOtto .. to ~~Ily(......r..,:j"'"
.}.' I , .u' ,I ~!.' ! , .~$' , ! , ~ ! , , '~,~ , , '/~' ! ! '},' ! , '~~c~~ i:~i:r~ 11.' I . '$', ! ! !).' ! ! '.~.! , , ','.' , , ',~' , , ',~' ! , ! ,:,' ! , ! ).t.
FIGURE 26
16
On each graph are given the number or years or record (from Wlseeded: years)
used. in making the estilllllte, the equation of tbe straight ~lne in terllls of tM
reduced variate, :/, and the mean precipitation tor the historical period.
Havins plotted the cumulative distribution functions from the data on January
preeipltation during the unseeded years we DOV proc~J as 'before, to cOlIIpal'e
January precipitation figures tOT the seeded years with the predictions tbat
might be made on the basis or these distributions. For this purpose, we have
COlipUted the ratio ot January precipitation tor each year or the seeded period
to the mean January precipitation of the unseeded years. Each arrow points to
the straight line at the computed ratio.
We note that as indicated. earlier, January 1953 was an unusual year. Thus for
KalalQ9., such a Month would have a return period of apprOJ:lmately 33 years, while
at L::Ill8'"lev the return period Is about 90 years. At ArielMerwin it is roughly
45 years. At Mt. Adams Ranger Station we would expect thill heavy a month once
in 120 years, while the figure is 140 years at Aberdeen. Finally, the return
periods at Peterson's Ranch and seaside are virtually identical at 180 years!
These figures give a vivid impression of how unusual the precipitation was in
this particular month, and suggest that such a rare occurrence would indeed be
upsetting in such a simple test for differences between llJeans as the "t"_test.
At a roe.jority o£ the stations, the second highest January of the seeded period
occurred in 1954, loIith return periods ranging from 13 years (at Aberdeen) to
33 years at Longvielol.
At Kal.alla, all other precipitation ratios had a return period under 10 years.
At Lon,gvielol, two years loIere as cited above, aDd the other values bad a return
period of 13 years or less with three over 9 years and three UDder 4 years.
ArielKerwin shoved three pre<;ipitation values with a return period greater
than 15 years (including the 1953 value cited above), aDd five with a return
period under 10 years. At Ht. Ad8.llls Ranger Station, three had return periods
of 13 or over, and five had return periods UDder 8 years, with four of' tbese
under 3 years. Peterson's Ranch bad three precipitatIon values wIth return
periods greater than 15 years, and three loIith return periods under 10 years.
(Data ~re not available for January of 1955 nor 1959 at the latter station.)
For tbe control statIon at Aberdeen, we find only two years wIth return periods
in excess of 10 years, while six are below 6 years. At seadde, three e.re over
12 years, aDd five are under 1 years.
Certain trends are apparent from the graphs. For eX8.lllple, the years 1955 and
1951 were the tvo low values in every case where data were available. (The
1955 data vere missing at Peterson's Ranch.) Thus, while 1953 vas highly unusual,
the two years with low January precipitation could be considered mildly
unusual.
To clarify the latter statement, we might choose Longview as an example, and
InqUire; what is the probability that, in a salDple of size 8, we 'IIould have
two years with January precipitation as 10101 as that of 1955 and 19511 UsIng
the cumulative distributIon we have obtaIned, and a6Sumi~ sample values are
independent, we say the probability Is approximately 0.13. So if' repeated
samples of size 8 could be taken, we would expect on the average only one in
seven or eight of' such 88Ilples to contain two values this low.
17
As a f'urther indication or tbe type of lrt.atement ODe can l:l8ke on the basis of
the estimated distribution, and again using Longviev &s the trial station, we
ask: what 18 the probab1l1ty that in a sample of size 8. one January precipitation
yould have a return period as h1gh as 90 years? FrOlll the probability
level this illlplies tor January preclpite:tion at Longview, and &ssum1ns inde_
pendent S8IlIple values, we COl:Ipute a probability ot approximately .09.
The good fit ot the extreme value distribution to January preclplta.tioDs suggested
a similar approach to water year totals. These results are given in
Figures 27 through 33. Here again it 15 seen that the fit Is very good in
every case.
Looking first at Kalama, we find the highest water year total, in 195556, had
a return period of roughly 12 years. All other figures bad a return period
under five years. Incidentally, the total precipitation for the water year
195556 vas the highest in the seeded period at every station considered. At
Longviev, the highest vater year total bad a return period of 22 or 23 yearl:l.
Three others bad return periods betveen 5 and 10 yearl:l, ....hile four bad periods
under 3 years.
PursUing the comparison, it can be seen that there is a noticeable similarity
betveen Longview and Seaside. At the latter, the water year total for 195556
had a return period of 25 years ....hile three other water year totals bad return
periods betveen 4.5 and 10 years. (These three years were the same ones that
had return periods bet....een 5 and 10 years at Longvie..... ) The four other water
year totals had return periods less than 3 years.
The pattern at Aberdeen can be compared ....ith that at Ka.la.ma. The total precipitation
for ten months in 1955~56 showed a return period of 11 years, while
the remaining totals had return periods of 5 years or less.
The graphs for Mt. Adams Ranger Station, Arie1Mer....in and Peterson's Ranch are
somewhat d1:fferent. At Mt. Adams Ranger Station the tota.lt'or 195556 has a
return period of about 30 years, and that for 195051 bas a return period of
about 11 years. The remaining totals show return periods of 5 years or less,
with tlKl years being very low. We might ask the 88Ule type of question posed
earlier about January precipitation at LongV"iew; namely, what is the probability
that, in a samp1e of size 8 at Mt. Adams Ranger Station, there \/ill be two
water totals as 10'11' as those of 195651 and 1951581 Using the probabilities
obtained 1'1'011I our population distribution estilD8te, and. assuming that the samIie
vaJ.ues are independent, we COlDPUte a probability of .02.
ArielMerwin's graph shows one total (195556) with a return period of approximately
70 years and 195859 with a period of about 22 years. We note that
here the latter year appears higher than it does on any of the graphs for other
stations. The remaining six water year totals had return periods of 5 years
or less.
Finally, the return period for the water year total in 195556 at Peterson's
Ranch lias about 40 years. The other four water years for which records are
available have return periods of 5.5 years or leaa.
At Longview and Kalama, an additional estimate of the cumulative function was
lIl8de, using the combined s~ed and unseeded ,.ears as the SWlIple. ThAt is,
regarding years from the two pttiods as being drawn from the same population,
~::~:.:".. KALAMA EXTREME PROBABILITY PAPER WATER YEAR TOTALS
•• C • r .. .
_.,~:," ',~'" ',;'" T;~ir(~:'~l" ',','" '.','" ',','" ,,'.'" ',j' " ',~' II ','.' II '.','.
.,:,.,
ii"i
"O"Tl ,
: ,I , " '.
I I' ~" , "~
,l'.J ,ll,j
!\ " .:"
\ ·.il'
1\1' !I
_,!,' I I ~J~' , I ~!,: '
UICOMM·",aOC
"t.
m!:&
f;!;>' j~
, ,
II y;;
, ,
;
Bl',!"E,
III'l,
Ft"~
'f
'.".J
~
~
0: .'".. >
.0...:.. ! ..:L:~~. 3! . _.
> 0: \:.
5~
I~ ;
I~ ~
\;. ~'?
0
~ '<0
<or i ""
o ,I!:

!. ~~ llJ
~ 0: > 10.·
~o:
W •
i~ ~~
"
 i
Q ~
~~ G:
.... D "W
:~ ro.~~llLl1f.lllliWilllillWJl]]:rrm:o!ttttrJttJ]
II
,
 l
1
I !
~ :uu1 lLU++I1m+ 1AAt+HHttHttHttHiilnttlnt1JOJ
... I
a:
''>""
a: I
i'"
z
'~"
a:
.o'".n
++
illl
'}pliO'" ARIELMERWIN EXTREME PROBABILITY PAPER WATER YEAR TOTALS
i9
d
T"i
;:+1";:['
!T"n
b'
,7
~
~
iftI
,f 1
555
r
:r.::'
.., >O~.., .., ~IO >0 10 P'lIO....:.TY[...~..:j
_}~' , I .J~ I ' 1'.),1 , , .ls' , , ,!! ,,! ,'} !,I,!,! , I 'I~I I 1 'T~' ! I ',~" ';.' I' }S" 1 '},I I ! r.~, , , !.~' , , ';.,r 1 1 tl.' 1 I I,~' I ' I J.~
FIGlrRE'''?X
1.1.. ~
rTTTTTTTTTITlTTlllIlTm11nTlTTT1TTTTTllnTITrmTI]JTI I [[]JIllWW,!Ui+tlHmHtKttHl,ittltttttlttmiI
I
I
I
!


•
1+, __ 1_ 1
I
~f ~ :E  ~IIIII~I::j::mttm~WIII ,
L .. ,J , t
i
en i
oJ gI
I i
a: "w
>
a:
w
I
~
18
\ole estllI1!lted the cumulative distribution from t.hese S8.lIIples. If there vere a
marked dlfference between 'the two periods, one would expect IlIal'ked divergence
of the two straightlines and possibly an increase in the width of the control
band.
These two 8daltional estimates are shovn by the dotted lines slightly below tbe
first estimate trolD F ...95 to tile right, ",1tb a few reference dots at the lett
of the graph. fhe dotted lines slightly below the upper control band, near
F _ .97, give the revised estilllate or that band. There are also sbort dotted
Hnes at F ...85, slightly below the upper control line. In each case, lower
control lines vere practically identical.
;~a~U:r~Pd:V~:t=~~/1;,t~t~i;b~;~;~a;:dt~l::~i~eina:h:e~~:~~y 8::;18.
The control band was slightly narrower, aDd the new estimate of the cumulative
distribution was quite close to the earlier one.
19
VII. SUMMARY AND CONCWSIOlfS
To s\1JIlllIB.l'17;e, precipitation data has been examined for stations in the questionable
area, in the target area, and at control stations. Comparisons have been
made betveen these areas, and various statistical techniques applied to the data.
From these analyses, ve find that for Cowlitz County outside the target area,
as exemplified by Kalama and Longview. there 16 little or no evidence to support
the conclusion that precipitation in the seeded years bas been significantly
higher than in the Wlseeded years. 'l'his Is the case on either a Ilontbly basis
or a total wateryear basis.
We reviev and 8UD:1l118.rize the considerations that point to tb1s conclusion as
follovs:
Plots of cumulative precipitation against years disclose no marked
cbanae in slope.
B. At both statiODS there was a consecutive fiveyear total in the Wl_
seeded period higher than that of the last five consecutive seeded
years.
C. Qualitative comparisons show that an unusually high precipitation
figure for January 1953 has been exceeded by SOllle llIOnth in the unseeded
years at all stations except the control station, Seaside.
D. In a ranki~ of cocbined S&lIlples (from seeded and unseeded years)
the highest rank for each heavy precipitation llIOnth duri~ the
seeded period was tabulated. It appears that Longview and Kalama
do not rank higher than control stations.
E. Distributionfree tests were etIIployed so that conclusions could be
reached without aS8Ullptions about precipitation distribution form.
2. For the six heaviest precipitation months, only January
shows significance at these two stations, but this result
hold s at control stations also.
F. Three tests were used assuming a "normal" distribution for the precipitation.
1. "tN_tests also indicate that January is the only 1llOnth
where there are significant d1f1'erences between the two
periods.
20
2. Analy5e5 of covariance applied to January precipitation
S'Uggest tbat Iluch of the increase In precipitation can be
explal~ 8S part of a pattern that preva1led at control
st.e.tl0DS a1so.
3. Regreeelon lines and coD!ldence curves for Longview and
Kalama va. Seaside show excellent agreement betveen ques_
tionable and control areas. A somewhat dUferent scatter_
ing with Aberdeen as a control raises a meteorological
question.
G. Extreme_value distribution methods ""ere applied to both January and
total vater_year precipitation.
L The impression of a rare occurrence in January 1953 15
fortified by the estilll8.tes that precipitation In that
month bas a return period 815 high as 180 years at a
control station, but considerably shorter at Kalama.
aDd Longview.
2. Aside trOlll this uncOllllDOD month, return periods are not
remarkable.
3. A combined sample, using both seeded and uoseeded years to
estilll8.te the cumulative function, leads to results very
similar to those obtained from unseeded data alone. The
standard deviation of the precipitation ratio is slightly
less, and the control band is narrowed. Thus, probability
statements made on the basis of the unseeded years would
be almost identical w1th those made on the basis of the
combined sample.
21
Bibliography
1. Brakensiek, D. L. and Zill68, A. \1'., Application of the E%tretlle Value Statistical.
Distribution to Annual Precipitation and crop Yields, Agricultural
Researcb Service 4113, 1951.
2. DlIOu, W. J. and Massey, F. J./ Introduction to Statistical AnalySiS, 2nd
Edition. McGrawHill Book Co., 1957.
3. Gumbel, E. J., Statistics of Extremes, Columbia Unlver"lty Press, New
York, 1958.
4. Liebleln, J'J A New Method or Analyzing Extreme Value Data, National Advisory
COllllDlttee tor Aeronautics, Technical No'te 3053, Washington, 1954.
5. Mood, A. M' J Introduction to the Theory of StatisticS, McGrawBill Book
Co., 1950.
6. Too., H. C. S., A Statistical Method or Evaluating Augmentation of Preelplta'tion
by Cloud seeding", U. S. AdvisorY COIDIIllttee on Weather Control
Final Report, Vol. 12, 'fechn:1cal Report No. 1.