wWilm BU,1tAU OfF!~~
703 fEDERAl. OffICE eUii.D~~
SEA!Jll4. WASHINGTON
ASTATISTICAl. STIIDY Of THE EFFECTS Of
WEATHER MODIFICATION ACTIVITIES
IN SOUTHWESTERN WASHINGTON
The Computing Center
Washington State University
A STATISTICAL S'rUDY OF THE EFF~ OF
\lEATHER MODIFICATION ACTI'{ITIES IN S011l'BWESI'FRN WASHINGTON
Prepared for
The Wasbington State Weatber Mod1tication Board
uDder Contract No. 0104
by
The Washington State University Computing Center
Vork Done By:
G. R. Iugru
O. V. Rechard
J. V. Crosby
with the advice ot
T. S. Russell
Report Written By:
G. B. Ingr6.l:ll
O. 101. Bechard
Submitted through the Geo-Hydrologic Research Group
Wasbington State University
TABLE or CON'lEff.rS
I. Introduction..
II. Qualitative Results.
III. Population Distribution and Distribution_Pree
Methods..
IV. Precipitation Distribution . .
V. Tests Based on the Normal Distribution .
1. "t" Tests Comparison of Heans .
2. Analysis of Covariance•••.
3. Regression Analysis.
VI. Ertrelll8_Value Distribution Results .
VII. Summary aDd Conc1usions.
Bibl1ograp~ . . . • • •
9
II
12
15
19
21
I. IIt'l!l.OmrrIOff AJU) GENmAL COlfSIDmA1'IONS
This report containe the results of a study by the Wasb1ngton State University
Computing Center at possible increases in precipitation in Cowlitz County,
Southvestern Washington due to weather modification dtorts in the Lewis River
and White Salmon River loIatersbeds. The area in question is shown in Fig. 1,
with the Levis and White salmon River watersheds labeled as the "Target Area"
and the relll8.inder of Cowlitz County outside the target area labeled 8S the
'~stionable Area."
The general approach to the problem has been to test the hypothesis: the sample
of precipitation values from the years when weather modification efforts were
carried on is frOID the lame population as the sample of values trom the years
without 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 e.f'fected zone but close
enough that the precipitation regimes could be considered similar.
Precipitation records for nearly fifiy stations in western Washington and Oregon
\lere punched into cards, and \lere used in preliminary surveys and analyses.
The followlI18 seven stations were studied intensively: Kalama, Longview, Peterson's
Ranch (Cougar), Ariel (MerWin), Mt. Adams Ranger Station, Seaside and
Aberdeen. The years of record, together with infoI'\ll8.tion about lIIissing data,
for these seven stations are shown in Table 1.
Table 1
Years of Record aDd Months of M.1ssing Data
at Seven Principal Stations
Station Froo To Months for which data is not complete
Aberdeen Sept '17 June '59
Ke1ema Sept '17 June '59 Nov '49, Dec '49, Oct '50, Nov '50,
De, '50·
Longview De, June '59
Mt. ildams R.S. Sept '31 June '59
Peterson's Ranch Sept '31 June '59 Feb '49; Jan '50; May & June '53;
Jan & Feb '55; Jan '59·
Seaside Sept '31 June '59 Oct I Nov & Dec '33·
Ariel_Merwin Sep' '32 June '59 Nov & Dec '32; Jan, Feb, Apr, May,
June J Sept & Oct '33; May & June
'34; Mar, Apr J May, June, Sep't &
"" '35·
ABERDEEN
WASHINGTON
Mon'thly records have been used insofar as 'they were available. From 'the monthly
records at each station, 'the total precipita"tion was obtained, when existing
records permitted, for the wa"ter year: tbose lIIonths from Sep'tember of one
year through June ot the followiI16 year. This eboiee of IIIOnths coincides with
the time period duriI16 which cloud-seeding operations are performed.
Weather modification efforts through cloud-seeding were first carried out in
this area in 'the water year 1950-51. There vere no cloud seeding opera'tions
in 'the year 1951-52, but from 1952·53 through 1958-59, there vere weather modification
efforts in each year. The water years 1950-51 aDd 1952-53 through
1958-59 will be referred to as nseeded years n and all other years as "unseeded
years."
II. QUALITATIVE RESULTS
A scrutiny of the data reveals detinite wet-dry cycles, and suegests that a de_
tailed analysis must take these patterns into account. Thus if seeding were
carried on during s period of years \lhich \lere generally drier over a l.arge
area, one lItight incorrectly conclude that there had been no e1"tect if the 'Pl'evailing
dryness were not considered.
However, it the problelll is -.lore restricted, and the assertion that there has
been!!!2!:! 'Pl'ecipitation during the seeded years is to be test.ed, certain qualitative
exalllinations can be indicative of the truth or falsity of the assertion.
One graphical approach is to plot cumulative water year precipitation against
tillle (in years). If a radical change in the rainfall pattern had occurred, it
'Would be expected that there 'Would be ll. noticeable increase in the slope of ll.
line through these points.
Such plots are giv-en in Figures 2_8, \lith stations in the target, quenioIlll.ble
aad control areas included tor cOlllpe.risons. The co=ent above concerniD8 change
in elope is best illustrated by the points plotted tor Ariel-Mervin. By laying
a straight-edge aloD8 the points, one can imagine ll. good straight line tit
troll yeax 1 to year 10 or ll. Another good straight line tit can be visualized
tor the relllaiD1ng years, but the second line has a noticeably greater slope.
For th1l!l Gtation, the tirst complete year of record is 1936-37 (year 1) so
year 10 corresponds to 1945-46.
For the relllllinins six stations, eX8lllinations of the graphs reveal a greater
slope in the early years of record, and in the final years. J. smaller slope
in the 1940's indicates a relatively dry period during these years. It could
be reJDarked that the difference between the pJ.ot at Ariel_Mer\lin and the other
six plots Illlly be attributable in 'P&rt to the tour years of !lining data at the
former.
If tor each vater year, the month vith the highest precipitation is selected,
these IIlOnths can be COlllJl&red to give s. rough qualitative impression of pre_
cipitation patterns in the seeded aDd unseeded years. These high precipitation
months axe given in Table 2 tor the seven st!ltions.
This table discloses certain intereGting 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 IIlOst cases,
that month \las considerably wetter than the secoDd wettest month during tbe
seeded period. Since this is true for the control stations as well as for
those stations in the target sad questionable areas, it seems to be part of a
general pattern instead of a result attributable exclusively to cloud seeding.
In connection vith this point, it should be noU!d that at six of the seven St8._
tiona, this heavy precipitation ot January 1953 'Was exceeded in December 1933,
MT. ADAMS RANGER STATION
CUMULATIVE PRECIPITATION VS. YEARS
800 f-1-H'--I-+-+-+++++-+-+-1-H'--I--+-+---1
600 f-1-H'--I-+-+-+++++-+-±-!-'H'--I-+-+---1
400 f-1-H'-t-+-+-++++-+-+-+-1-H'-t-+-+~
200 f-1-H--!---+-+-+++++-+-+-1-H'-t-+-+-
OL..JL..L-L--'-.L..-Ll-L-L...L.L...L.l-L--'-...LLJ-l.-.J
YEARS: I 2 :3 4 5 6 7 e 9 10 11""12 13 i4 15 16 /7
o.t: ~ ~ ~
~ i;a ""p ~
.. MISSING DATA IN YEARS 4Z·43.!5Z-S3
FIGURE 2
PETERSON'S RANCH (COUGAR)
CUMULATIVE PRECIPITATION VS. YEARS
26oof-H-I-+-+-+++++ 1-
2400 f-H--J-+-+-+++++-+-+-+-HH-+-+-+-t-++-H
2200f-H-f--+--+--++++++-+-t-HH--+--++-+++-t-i
2000f-H-f--+--+--++++++-+-t-HH--+-t++++-t-i
z 1800 f-H-/--+-+-+-+++++-+-+-HH-l-+-+-+-+-+-H
o B1600 f-H-/--+--+--++++++-+-t-hH-f--+++++-t-i Ii:
iii
If '400f-HH--+--+--+++++++-,-t-H-f--+--++++-t-i
~
~ 1200 f-HH--+--+--+++++-++-t-t-H-f--+--++++-t-i
~ IOOO'f-HH--+-+-+-+-+-+++-+-+-HH--J-+-+-+-+--+--H
800'f-t-HH--+-+-+-+-+++-+-+-+-H-/--+-+--j--+-+-+-l
600f-H--+-+-+-++-H-f--+++++-H-/--++++-t-l
4OOf-H--+-+-+-++-H-I-+-++++-H-I-+-+++-t-1
200 f-HHH-+-+-+-+-+++-+-+-+-H-/--+-+-+-+-+-+-l
°YEARS: I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17
~ ~
~ ~
FIGURE 3
ARIEL-MERWIN
CUMULATIVE PRECIPITATION VS YEARS
1600
1400
0
0
z 1200
0 ~ 0
~IOOO 0
2g: 800
~:::600
Ii
~ 400
200 0
0 I
0
YEARS: I 2 3 4 5 6 7 8 9 10 II 12 13 14 16 17 18 19 20 21 22 23
II: ~ ~
~ .,
~ ~ ~
FIGURE 4
KALAMA
CUMULATIVE PRECIPITATION VS. YEARS
2.
25
2.
23
22
21
20
19
IB
I1.7
15
~ 14
~ 13
>- 12
"10
9
B
7•5•3
2
3l·32 I
L
0
01-
0
0
0
1
0
0
200 400 600 BOO 1000 1200 1400 1600
INCHES OF PRECIPITATION
.. MISSING DATA IN YEARS 49-50,50-51
FIGURE 5
~ONGVIEW
CUMULATIVE PRECIPITATION VS. YEARS
58·59 28
27
2.
25
2.
23
22
21
50-51 20
19
IS
17
~ I.
~ 15
~ "
13
12
"10 I-f-HH-+-+-+-++++-+-1
91-
sl-f-HH--+-+-+-++++-+-1
7 1--f-H,-+--+-+-+-++++-+-1
• f---CH-o+++--H--++++-H
5 f-
• f---CI---"I--+++-H--++++-H
3 I- o'++-+-HH-+-++-+--H
2/--<>t-H--+--+-+-+-++++-+-1
31-32
200 400 600 800 1000 1200
INCHES OF PRECIPITATION
FIGURE 6
SEASIDE
CUMULATIVE PRECIPITATION Vs. YEARS
58-59 21 H--+-+-+++++++-+--+--H---1--+-++++
26f--HHH-+-+-+++++-+-+--+--H-f-++o
25I-+----+--+-+-++++++-+-+--+--H--+--+-- ~-
~ o~
23I-+--H--+--+-++++++-+-+--+--H--+ ++-+-H
22I-+--H--+--+-++++++-+-+--+--f----+ +--H--+--+-I
21 H--++++-H-+++H--+++ 1--++-H-+--1
20I-+--H--+--+-++++++-+-+--1- -+-+--H--+--+-I
50-51 19f-f-H--+-+-++++++-+-H ++++-+-f-H
49-50 18I-+--H-+--+-++++++-+-+ ++++-+--rH-+
171-+-----1--+--+-++++-+--+-+ +++-+-f-H--+-+-I
16H-++++-H-+++-+- ';-++-H-+++-HH
~ 15I-+----+-+-+-+++++-:o-+-+--rH--+-+-+++--t
~ 14f--HHH-+-++++-t-J-+-+-++++-+--+-+-H
~ 131-+----+-+-+-++++ 1-++++-+-+-rH--+-+-I
121-+---+-+-+-+++ -+++++++-+-+--+--H-+
"H-+++---IH+-+ -t-+++-hH-+-++-H--+--1
101-+----+-+-+-++ t-+--H-+-+-++++-+--+-+-H
4
34-35 '3
32-33* 2f--f--'---\H-+-++++++-+--+--HHH-+-+++--l
31-32 I -oH-+-+-+-++++++-+-+--rH-+-+-+++--t
200 400 600 800 1000 1200 1400 1600 1800 2000
INCHES OF PRECIPITATION
FIGURE 7
ABERDEEN
CUMULATIVE PRECIPITATION VS. YEARS
...... 28 01-
27
26 0 I-
25 0 I-
24 0
23 0
22
21 0
50-51 20 0
"
0
18 0
17 0
16 0
~ I~ 0
~ 14 0
~ 13 0
12 0
" 0
10 0 • 0
8 0
7
6 0
•4
3
32-332 0
31-32 I -0
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
INCHES OF PRECIPITATION
FIGURE 8
Table 2
Max1mum Monthly Prec1p1tation in Water Year
Aberdeen Seaside Kalama Lon6Vie\l
Max Monthly Month Max Monthly Month Max Monthly Montb Max "'.onth1y loklnth
Water Year Preclp. Occurred Prec1p. Occurred Prec1p. Occurred Prec1p. Occurred
Unseeded Years
1931-32 17·92 Do< 15·59 Do< 13·56 Do< 8.26 M"
32·33 19·92 De, 19·71 Jen 15·50 Jen 11.28 Nnv
33-34 35·70 De, 15.08«- Jen 26.59 De, 20·13 Do<
34-35 20·35 Jen 15·15 Jen 17·93 Nnv 11.53 Nnv
35-36 15·22 Jen 15.98 Jan 13.82 Jan 8.00 Jan
36-37 14.84 Fe' 13·95 Do< 13·20 De, 6.72 De,
37-36 26.40 Nov 23.80 Nnv 15·15 Nov 10·39 Do<
38-39 16.62 Jan 15·23 Fe' 9.42 Jan 6.96 Fo'
39-40 18·94 De, 17·35 Do< 17.46 Fe' 10.27 Fe'
40_41 12.20 Oe' 10.68 Oe' 8.00 Nov 5.48 Nov
1941-42 15.48 Do< 16.64 Do< 10.47 Do< 8.26 Do<
42-43 14.16 Do< 16.28 Nov 9.00 Do< 9.47 Nov
43-44 12.62 De, 9·55 0" 6.46 0" 4.40 Oot
44-45 13.36 Jan 11.82 ."" 11·97 "" 5.69 M"
45·46 14.15 Nov 13.71 Fe' 13·39 Jan 9.64 Nov
46-47 12·51 Do< 12.52 Nov 10.62 Do< 10.83 00<
47-48 17.43 Oot 13·35 Oe' 14.67 0" 8.52 Oe'
48-49 14.74 Do< 15·37 Fe' 15·11 Do< 10·95 Do<
49-50 15.28 Fe' 16.54 Fe' 10.87* Jan 8.36 Do<
51~52 12.24 Jeo 14.06 Jan 11.26 De, 7.86 De,
~
1950-51 16.18 Do< 17.78 Do< 12·37* Jen 9. 40 Nov
52-53 30.46 Jen 28.81 Jan 18.00 Jan 13·11 Jan
53-54 20.22 Jan 20.69 Jan 13.65 Jan 11.00 Jen
54-55 14.01 Nov 11.75 De, 10.42 Do< 6.12 Nov
55-56 18.07 Do< 18.38 Jan 13.84 Jen 10.42 Do<
56-57 13·72 0" 12.83 0" 9·39 Mar 6.85 Do<
57-58 15·30 Do< 16.21 Do< 11.42 Do< 10.43 Do<
58-59 16.60 Nov 16.54 Nov 11·99 Jen 10.79 Nov
* Incomplete records for the year
Table 2 (con't.)
Ku:illlUlll Monthly Predpitation in Water Year
Ariel_Mervin Peterson's Ranch M&IlIa RaMer Station
Max Monthly Month "'..AX Monthly l-tonth Max I'.onthly Month
Water Year PreCip. Occurre~ Preclp. Occurred Preclp. Occurred
Unseeded Years
1931-32 . . 25·19 Mar 13.67 D."
32-33 10.21* Mar 26.85 Nov 1l.48 Nov
33-34 25·19'1' De, 57.04 De, 27·37 De,
34-35 15.67* Nov 29·48 Nov l2.75 Nov
35-36 14.45* J~ 27-48 Jen 12.60 J~
36-37 16.00 De, 24.78 Dee 10.58 Feb
37-38 16.36 Nov 33.77 Nov 14.55 De,
38-39 10.42 Feb 21.11 Dec 7.86 Jen
39-40 15.07 Feb 31.11 Feb 14.62 Feb
40-41 8.64 Nov 15·02 J~ 7.76 Jen
1941.42 12·95 De, 23.62 De, 13.61 De,
42-43 15·73 Nov 31.34 Nov 17.40 Nov
43-44 8.63 Cot 1l.40 Cot 5·40 O,t
44-45 11. .;4 M'" 19·44 Mar 7.84 Feb
45-46 14.23 Nov 27.25 Nov 12.21 Nov
46-47 14.32 De, 26.29 Deo 9.69 De,
47-48 1l·35 Co' 24.37 O,t 10.96 Co,
48-49 16.06 Feb 23.26* Nov 11.18 Feb
49-50 13.26 Jen 30.35* Feb 20.18 Jen
51-52 11.42 Cot 23.26 Co' 11.75 Nov
Seeded Years
1950-51 12·91 Nov 25.66 Jao 12.82 Jen
52-53 19.62 Jan 46.14* Jan 23·30 Jen
53-54 15·32 De, 30.69 Jen 16.94 J~
54-55 1l.19 De, 21.61* De, 7.34 Nov
55-56 16.11 Jen 31.04- Jeo 15·09 Jao
56-57 ll·95 De, 22.01 De, 4.39 Dec
57-58 15.98 Dec 31·97 De, 6.71 Dec
58-59 16·87 Nov 35·25* Nov 8.00 Nov
* Incomplete records tor the year.
and the lone exception to this vas Seaside__a control station. At Seaside the
preeipitation for January 1953 vas the heaviest single month on record.
So an ~8JIlination of lllIl.X.1MUlII lDOnthly precipitation shows that seven years ago,
at all the stations, there was a very heavy Illonth. Since this pattern prevailed
over a broad area, and since at each station in the questionable area this
figure is exceeded by one frOlll the non-seeded rears, caution is dictated in
drawing any conclusions.
Another way of comparing monthly precipitation in the tva 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 or a Month in Seeded Years
Oc:t 2 1
Nov 5 3
De< 12 4
Jan 1 1
Feb 16 13
Mar B 4
This table sho\ls, for eX8.Jllple, that at Kalama the highest October precipitation
during the seedill6 period vas tbe second highest October precipitation on rec_
ord \lhUe at Longview the wet"test October on record occurred during a seeded
year.
Turning from a llIOnth_bY_lllOoth exalll1nation of the data, we have also asked bov
the total precipitation for the last five years during which cloud seeding act.ivities
were carried on cOCllperes with the total precipitation for other consecutive
five_year periods. Peterson's Ranch was eliminated from consideration
since missing data made it 1mpossible to evaluate total precipitation for
the last five water rears or indeed for any five consecutive \later years since
1948-49. For four or the remaining six stations it was possible to find a
five-year period in the interval 1931-50 during vhich the total water year precipitation
exceeded the total water year precipltationfbr the period 1954-55
through 1958-59. It seems likely that this could also have been done for ArielMerwin
and Seaside had not missing data forced us to consider the interval
1936-50 in the first case and 1934-50 in the second, thus elilIlinating from
consideration several very wet years. These results are summarized in Table
4 below.
Station
Nt . .MUll B.S.
Ariel_Merwin
l<Al.8ma
Longview
Ilberdeen
Seaside
Table 4
Max. 5-Water Yr.
Total Preeip.
2&.58 in.
352.05 ..
364.97
238.99
478.20 It
376.28 "
Period in which
Max. Occurred
1~5-5O
1~5-50*
1931-36
19'>'-50
1931-36
1934-39**
5-Water Yr. Tot.•
Precip. 1954-59
204.32 in.
380.'" "
307·59
222.75
40'.73
39'>.88
* interval considered vas 1936-50
** interval coosidered was 193~5O
III. POPUL.ATION DISTRIB11I'IONS AND DIS'mIB11I'ION_FREE METHODS
To carry out the classical statistical tests and inferences from a set of
sample values, it is necessary to consider the sample as being drawn from a
population with a certain type or distribution, e.g., the normal distribution.
The type or distribution is frequently suggested by a knowledge of the physical,
chemical, or meteorological nature of the variable being studied. Then
from sample values it is possible to estilll8te parameters, e.g., the mean and
variance, that characterize the pe.rticular distribution in question. In the
case of precipitation data tbe population in question is simply the totality
of all possible values of the precipitation and in Section 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 i8 the "probability density function," which is most 8uuestive
from a graphical viewpoint. The bell_shaped normal curve is a vell.kno\ln example.
The area bounded by tbe curve between two given values 18 the probability
of occurrence of a value between these two limits. The other function :Ls
the "cumulative probability function." Graphically, it is a curve that rises
from left to right, and at any point the height of the curve gives the probab_
ility of values less than that point.
Thus, when a distribution type is postulated, and parameters are estilDated from
a sample of the population, it is possible to make inferences or tests with
definite probability statements or confidence levels.
On the other baed, one IIl&y choose to make no ass\llIlptions about population dis_
tribution and still test fOr differences in location of two populations. A
useful statistic for this purpose 115 the "median" \lhicb fOr a 88.IIlple of size N
or soc:e measurable characteristic is defined to be that value for1b.1ch an
equal IlUI!lOer of &le values fall. above and belovo In the problem at hard,
one woulil like to test the hypothesis that the same population is being sampled
in botb the seeded and unseeded years, without any assUlIIptions about population
distribution. A median test can be made tbat i5 sensitive to d1f1'erenees in
location; 1.e., a shift in median 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 ssmple of n values from unseeded
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 from these expected numbers are statisti2s11y significant, so that
~~:b~=~~ ~~~ [;,r;;~c~3;;]~om~:i:m:u~V:~~a~:; ~~~~~~
by dividing each or the two samples into two groups__those whose value is above
the median of the cOIllbined sample am those whose value is below.
'ben
2 (,(008.) - f(exp. >t
':t - 1: t(exp.)
IoIbere t(obs.) and t(exp.) stand for the observed an::!. expected frequencies respectively
and the summation extends over the four cells of' the contingency
table.
Tabulated values of -:t2 for various probability levels are:
:<:2(.05) .3.84
),:2( .10) • 2.11
~2( .25) _ 1.32
~(.50) c O.~55
Thus. 1£ the ~the818 Is true. we would expect computed values of ~2 to
exceed 3.~ only 5 percent of the time; to exceed 2.71, 10 percent of the tillle.
to exceed 1.32, 25 percent ot the time; and to ueeed .455 ha1.f of the time.
Since one ordinarily wishes to be conservative In rejecting an bypothesls when
it is t:r:'ue, the 5 percent level Is It COiltllOnly used standard.
Tables 5-11 rank tbe water years in increasl!J8 order or the total precipitation
and give :t2 values as computed above tor the seven stations in question.
(Common statistical practice is to reduce by 0.5 the deviations appearing in
t~ ~~~:t~;;~~~ ~:~:bi~:m5:allw~~~~~~~;~a~~v=~)ll. Consequently, the
At Kalama, for example, the record for one of the seeded years is not complete;
tour of the relll4ini~ seeded years fall below the median and three above. The
computed value of:t '" .113 and, comparing this with the tabu1.ated values
listed above, we see that f'rom this test it is not possible, even at the 50
percent level, to reject the hypothesis that the seeded and unseeded years are
aamples f'rOlll the Ba:lle popu1.ation.
While we bave hypothesized tbat tbe same population is being saapled in
the seeded years as well as in the unseeded years, it should be borne in ..ind
that tbe basic assertion being investigated. 19 that prec:1pitation bas increased
durill8 the seeded years. Clearly, then, anywhere the nUlllber of seeded~
faJ.ling below the median is greater than the nUlllber of seeded years above the
median, there is no support for the latter assertion.
~~o~~~~:'c~:~~Je:~u~fo;he~~e:d~6;:i~:c~~e~~tte: :re:i~~~~ ~~ve
reject the hypothesis at the 25 percent level. A similar statement holds at
Aberdeen ....ith 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 afforded by the stations actually in the target area.
Peterson's Ranch (Cougar Ci: since 1953) bas sO::Jevbat veaker records, vith only
tive years ot record during the seeded years. Here, four years are above the
median and only one belovo Hovever, at Mt. Adams Ranger Station, vbere there
are 20 years of complete reccmh in the unseeded years and 8 in the seeded
Table 5 Table 6
KAJ.ua Longview
Water Yr. Preelp. Rank Water Yr. Preeip. Rank
1920.21 87.92 1 1955~56 56.94 1"
32-33 811-.24 2 53-54 50.61 2*
55-56 81.27 3" 32-33 50·13 3
31-32 76.06 4 33-34 50·09 4
34-35 75·71 5 45-46 49.48 5
211.~25 72.00 6 47-48 48.61 6
37-38 71.51 7 50-51 48.24 7"
47-48 71.34 8 49-50 48.16 8
l8-19 70.61 9 46~47 47.89 9
53-54 10·09 10* 34-35 47.74 10
1933-34. 69.85 11 1958-59 46.86 U"
21-28 69·56 12 48-49 44.85 12
26-27 69.29 13 31~32 44.10 13
45-46 67.71 14 42~43 43.06 14
21-22 66.22 15 31-38 42.81 15
11-18 64.78 16 26.27 41.16 16
58-59 62.46 17" 57-58 41.68 17"
22-23 61.03 18 -~~-~ median
46-47 60.99 19 1921-28 41.41 l.8
36-37 60.15 20 52-53 41.~ 19* _____ median 51-52 41.27 20
1952-53 59·79 21" 35-36 40.73 21
35-36 59·ll 22 54-55 39·77 22*
51~52 58.96 23 41-42 39·23 23
48~49 58·58 24 56-57 37.50 24"
54-55 56.30 25"
57-58 56·00 26- 1939·40 36.74 25
30-31 54.56 27 36-37 35·71 26
28-29 54.30 28 30-31 35·50 27
38-39 53.17 29 38-39 34·05 28
39-40 52.86 30 44-45 33.61 29
40-41 32·12 30
1956-57 51.56 31" 28-29 31.34 31
"-45 51.Ja.1 32 29-30 29·31 32
42-43 51.02 33 43-44 28.69 33
Ja.1-42 49-99 34 25-26 28.52 34
40_41 49.99 35
25-26 48.67 36
19-20 48.63 37 ~2 _ .654
29-30 48.05 38
23-24 43.09 39
43-44 38.36 40
'l?- •.173
* Years with seeding aetiVity
Table 7 Table 8
Aberdeen Seas1de
Water Yr. Precip. Rank Water Yr. Prec1p. Rank
1933-34 104.16 1 1955-56 102.98 1
31-32 103·77 2 32-33 99.82 2
55-56 99·72 3* 50-51 92.26 3'
20-21 98·42 4 31-32 89·36 4
34..35 '71.67 5 49-50 87.01 5
32-33 '71.00 6 53-54 66.98 6-
37-38 96·89 7 )4-35 85.16 7
53-54 89.85 5* 37-38 84.75 8
26-27 89.28 9 58-59 83.79 9"
49-50 88.72 10 45-46 81.68 10
42-43 76·92 11
1924-25 87.47 11 52-53 15·01 12*
58-59 87.13 12" 51.52- 13·71 13
21-28 87.03 13
45-46 85·84 14 1938-39 13·10 14 median
50-51 84.82 15*
47-48 84.24 16 1947-48 73.45 15
39-40 81.16 17 57-58 13·09 16-
18-19 79.63 18 39.40 72·91 17
30-31 78.73 19 41-42 71.86 18
52-53 78.28 20* 35-36 69.36 19
38-39 76.22 21 54-55 68.39 20*
----- median 56-57 66.63 21'
1956-57 75.82 22" "-45 66.14 22
35-36 75·00 23 48-49 65.80 23
42-43 73·91 24 36-37 63.31 24
57-58 72.69 25' 46-47 63.22 25
41>-49 72·52 26 40-41 51·91 26
21-22 71.76 27 43-44 57·57 27
51-52 71.41 28
17-18 70·50 29
54-55 70·37 30* ':l;2 •.941
44..45 69.74 31
46-47 69·65 32
1936-31 67.'71 33
41-42 67.56 34
22-23 66.49 35
25-26 64.84 36
28-29 64.02 37
40-41 62·97 38
29-30 61.66 39
43-44 60.41 40
19-20 57.67 41
23-24 55·12 42
'>:.2 •.618
* Years with seeding activity
Table 9 Table 10
Jorie1-Kervin Peterson'l;; Ranch
Water Yr. Preeip. 1lI'"" Water'Ir. Precip. Rank
1955-56 93,'7 1" 1955-56 115·01 1"
58-59 81>."'; 2* 33-31> 149.26 2
'7-48 76·35 3 45-"'; 140.52 3
46-47 70.42 4 32-33 140.35 • 50-51 70.29 5* 50-51 134.54 5*
57-58 70.26 6* 57-58 132.35 6*
49-50 69·81 7 31·32 131.13 7
53-54 69.45 8* 37-38 121.60 8
37-38 68.70 9 47-48 123.94 9
45-46 66.26 10 34-35 122·15 10
48-49 67·51 11 53-54 121·55 11"
1956-57 67.33 12* median 1946-47 120·09 12 median
1954-55 65.30 13* 1951-52 11•. 89 13
51-52 62.59 14 42-43 114.86 14
il.2-43 62.37 15 56-57 l13.l0 15"
36-37 60.77 16 39-40 101.82 16
44-45 60.28 17 "-45 106.19 17
il.1_42 59.86 18 35-36 105·39 18
52-53 59·73 19* 41_42 103.61 19
38-39 52·79 20 31>-39 102.80 20
39-40 52·39 21 3<>-37 99.43 21
40-., 51.41 22 40-41 81>.52 22
43-44 45·30 23 "3-" 15·99 23
?(2 • 1.0514 "X,.2 c 2.27
* Years with seeding activity
Table II
M't. Ad8.lls Ranger St.ation
Water Yr. Precip. R...
1955-56 11.62 l'
5OM 51 63.25 2*
49-50 62·69 3
33-34 59·90 4
42-43 56.10 5
53-54 55·59 6>
45-46 52·90 1
47-48 52·11 8
31-32 52.47 9
31-38 52·32 10
1952-53 52·05 11'
34-35 51.18 12
51·52 51·52 13
48-49 50.62 14
~--~- lIledian
1932·33 50.18 15
39-40 46.29 16
46-41 45.60 11
35-36 42.52 18
1~1442 41.85 19
36-31 40.08 20
44-45 39.63 21
40-41 39.41 22
54-55 35.89 23*
58-59 35.89 ", 38-39 32·57 25
57-58 32.20 26>
56-57 28.12 27'
43-44 24.55 28
,:\:2.0
* Years with seeding activity
years, one finds four below the median and four above. Fina.lly, at Ariel_
Kerwin, there are five years above and three below the median.
In addition to the rankings of totals for 10 lIlOnths. rankings for the individUlJ.
months vere made and examinations like that outlined above were conducted.
These rankings are not included in this report dW!; t.o space consideration5, but
the results for tile six heaviest precipitation months are sUlIllIlarized 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 below;
namely December and January. For January, it can be observed that the pattern
is precisely the lSame for all stations except Mt. Adams Ranger Station. For
December tile record for 1950 i8 not complete, but the figures are comparable to
those at the other stat1.ons except for )ott. Adams Ranger Station.
At Longview, the situation Is d1.fferent. In lIl8.klng cOllparisons, it becomes
clear that Aberdeen and Seaside are almost ident"ical with Long'7iew. This can
be contrasted with Ariel_Merwin where for all tIIOntha except October we find a
larger nUillber above the 1:Ied1an than below.
Testing as outlined above, we would find significance for those cases with two
below the median aDd six above. or one below and five above.
Table 12 Table 1)
J<Al.ema Loogviev
No. or No. of No. of No. of
Irs.or Seeded Yrs. Seeded Irs. :irs.of Seeded Yrs. Seeded Yrs.
Mo. Record Below Ned. Above Ned. Mo. Record Below Ned. Above Ned.
Oct '" Oct 3" " N~ 40 Nov 3" 5
Doo 40 Dec 35 ". Jan '2 Jan 35 6
Fcb '2 Fcb 35 3·
M" Mar 35 5
Table l~ Table 15
Aberdeen Seaside
No. of No. of No. of No. of
Yrs.of Seeded Yrs. Seeded :irs. :irs.of Seeded :irs. Seeded :irs.
Mo. Record Below Med. Above Med. Mo. Record Below Med. Above Med.
Oct 42 Oct 21 3·
Nov 42 Nov 27 5
Dec 42 Dec 27 5
Jan 42 Jan 28 6
Feb 42 Feb 28 3
Mar 42 Mar 28 6
* Indicates that the value fox a seeded yeax 18 the median ot the combined
sample.
Table 16 Table 17
Ariel_Merwin Peter son' s Ranch
No. of No. of No. of No. of
Yrs.of Seeded Yrs. Seeded Yrs. Irs.of Seeded Yrs. seeded Yrs.
Mo. Record Below Med. Above Med. Mo. Record Below Med. Above Med.
Oot 25 3* Oot 28
Nov 26 6 Nov 28
Deo 27 5" Deo 28
Jan 26 6 Jan 25
Feb 26 5 Feb 26
"'" 26 5 "'" 28
Table 18
Mt. Adams Ranger Station
No. of No. of
Yrs.of seeded Yrs. Seeded Irs.
Mo. Record Below Med. Above Med.
Oct 28
Nov 28
Dec 28
Jan 28
Feb 28
Mar 28
* Indicates that the value for a seeded year 1s the median of the combined
sample.
IV. PRECIPI"l'MIOH DISI'RIBUrION
As remarked earlier, the classic&l tests depend on assumptions regarding the
form of the population distribution. SUch an aSSUlllPtion sbould be based on
consideration of the physical problem, and for meteorological studies several
possibilities arise.
The suggestion has been made by Tholll (6Jthat the "gamma" distribution be used
in precipitation studies. His suggestion was for precipitation over short
time intervals, e.g., one day.
Another proposal has been set forth by Brakensiek and Fingg D-]which includes
an empirical study of the reasonableness of using the s04called "extreme-value"
distribution for the ratio of precipitation to m'ean precipitation. Their results
are striking, and while one usually deals with the cumulative form of
this distribution, an examination of the density function (4, p. 83J disclosES
that it is a plausible distribution on the same basis as the gamma distribution.
That is, both are ske....ed, the extrellle_value distribution may be boWlded frOM
belo.... as is the gamma, and both are unbounded to the right.
Finally, the very cOlDllOn assumption of normality is frequently llllide. Thom sU&gests
that for precipitation accUlllUlated (Ner a period as long as a year, the
norlll&l distribution is the most reasonable choice. He is doubtful of this
choice for periods of one lIonth.
In view of the existing empirical Just1t'ication for the use of the extre.e-value
distribution, and the history of use of the norlllll.l, it was deeided to use these
in making further tests. It vas felt, however, tbattle g8ll&tl8 distribution
should be examined and compa.red with these tvo for monthly precipitation. Figure
9 is an indication of the results.
As is apparent from the gI'll.ph, the gamma and extreme.value distributions are
in very close agreement. As expected, the normal differs somewhat, and there
are clearly regions where the norlll8.l "fit" is superior and other regions where
it is iD!erior to the others.
On the basis of such examinations it was concluded that no distribution enjoyed
a clear_cut advantage over another. Because of the relative ease of dealil18
with the normal and with the extreme_value populations, the remainder of the
report concerns tests made with one or the other of these two as the underlying
distribution.
1.0 I -'---'-
0.' ~ -::;..-
"" -.
as -&.
0.7
0 I#.
0/
0.• ~' >- .- f-
3Q.s .;0
iii li CUMULATIVE NORMAL
" - -- - CUMULATIVE GAMMA
~ o. {L.
9'-1 . -- - EXTREME - VALUE
0:
Q. Z 0 ACTUAL OBSERVATIONS
03
r 0
, 0
<>2 ,%
0.1f-f-
0 ~;'t
0.' /":1
I 2 3 • 5 • 7 • • 10 " 12 13
"
15 I. 17 I. "
2e
PRECIPITATION (IN INCHES)
KALAMA JANUARY PRECIPITATJON FIT TED TO VARIOUS PROBABILITY DISTRIBUTIONS
FIGURE 9
V. TESTS BASED ON THE NORMAL DISTRIEtrrIQN
L "t" Tests Comparison of Means
One standard method of comparing two 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 distribution-free 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 hypothesis.
Clearly, if the mean for seeded years is lower than the mean for the unseeded
years, 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 we consider as being due to chance in random sampling, or, which
differences are statistically significant. To carry out these test, one sel_
ects a certain probability level as the level of risk in rejecting a 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 two 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 con_
tained in Tables 19-25. 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 has 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, iiovembel',
December, February, March, April and May, the Il:;erage 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 Kalama, 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 t-values With the tabulated t-distribution (2,
p. 38l+J that we would be unable to reject the hypothesis even if we 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) ',Je would be obliged to
reject the hypothesis at the 5 percent level, which suggests that further study
of the January precipitation pattern is in order.
'fable 19 Table 20
<ala.. LoD8Viev
Mean Precip. Mean Precip. Mean Prec1p. Mean Precip.
Mo. UO-seeded Irs. Seeded tu. t Mo. Unseeded Irs. Seeded Yn. t
Sept 2·55 2.11 - .65 Sept 2.13 LIn -1.39
0" 5.85 5·69 _ .11 Oct 4.28 ".67 .....
Nov 8.12 1·91 _ .42 Nov 6.19 6·il.3 .17
De, 10·99 10.68 - .15 De, 7.73 8.06 .23
Jao 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
M" 7."7 7·39 - .07 Mar 4.67 "·99 .48
Ap, 4.41 3.85 - ·55 Apc 2.58 2.15 .27
May 3·21 3.06 - .11 May 2.26 2.19 .12
June 2.5" 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 Tab1.e 22
Aberdeen Seaside
Mean Precip. Mean Precip. Mean Precip. Mean Precip.
Mo. Unseeded Yrs. Seeded Irs. t Mo. Unseeded Yrs. Seeded Irs. t
Sept 3.94 2.85 -1.19 Sept 2·95 2.63 - ....
Oct 8.08 8..... .22 Oct 7·27 8.ll .5"
Nov 10·99 10·15 .11 Nov 10.44 10.06 - .11
Deo 14.93 14.13 - ·09 Dao 12.16 14.21 1.....
Jan 11.53 15·21 1.61 J.o 10.66 15·51 2.17
Feb 10·35 10.06 - .19 Feb 10·09 9.65 .27
Ma, 8.88 9.34 .29 Mar 9·01 9.26 .18
Ap, 5.47 5.72 .20 Ap' 5·20 5.18 .5"
May 3.67 2.36 ·1.75 May 3.5" 2.58 -1.14
Juna 2.5" 2.82 .37 June 2.94 3·32 .46
Total 80.31 82.34 .37 Total 74.40 81.14 1.37
Table 23 Table 24
Ariel_Merwin Peterson's Ranch
Hean Precip. Mean Precip. Mean Precip. Mean Precip.
Mo. Unseeded Yrs. Seeded 'Irs. Mo. Unseeded Irs. Seeded Irs.
Sept 2·97 2.25 - ·92 Sept 4.52 3.06 -1.19
Oot 6.67 7.14 .30 Oot 11.45 12·97 .53
Nov 9·31 10.27 .47 Nov 17.62 18.76 .28
Deo 11.73 13·15 ·79 Deo 21.78 24.06 .62
Jan 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
A" 4.03 4.27 .22 A" 7.46 8.53 .58
Moy 3.05 3·15 .12 May 4.81> 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.lllS Ranger Sutton
Mean Precip. Mean Precip.
Mo. Unseeded Irs. Seeded Irs. t
Sept 1.26 loll - .36
Oot 3.94 4.78 ·59
Nov 7.42 6.58 - .44
De, 9.94 8.62 - .62
Jan 7.80 10.76 1.33
Feb 6.86 4.76 -1.47
Mer 4.81 4.98 .19 A" 2.22 2.78 .77
May 1.71 1.53 .29
J=e 1.33 1.02 .60
Total 47.29 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 ;:rears. 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 ·...ould 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 i3tatioos in January, it is clearly
indicated that a longer study of this month is desirable. Again it should be
remarked that we could not, on the basis of this test, attribute the significance
to any partic1.Uar factor.
In connection with this observation, we compare results of those in the ques_
tionable area with results at control stations; namely, Seaside and Aberdeen.
SUlllmariz,ing brief'ly, at Seaside, for eight months of the year the average is
either lo·...er 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 Peter_
son'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 ve 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 hypo_
thesis for them. The t-value for January is significant at the 10 percent level.
For only two months did the unseeded_years' averages exceed the seeded at ArielMerwin.
For five of the months that show an increase, the difference is so
small that we would be unable to reject the !l3pothesis of equal means even at
the 30 percent level, and for one other month 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 significant difference
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 yeax results. We proceed now to a fm-ther
analysis of January and water year precipitation.
11
2. Analysis of Covariance
Because of the unusual January precipitation pattern indicated by the t_test,
these data were subjected to an ~sis ~ covariance. This technique COl!!biDes
the analysis of variance (a method or testlr18 for sign11'lcant d11'ferences
between means of two groups) lIitb regression methods to yield a somewhat more
dlscrinlinatlng analys15 than furnished by either individually.
The basic intent of this analysis, then, Is to test for slgn1!lcant d1fferences
in the questionable area, Yh1le considering the general precipitation pattern
as exemplified by the precipitation at a control station. Here again the assumptions
are the same as those made earlier for the t-test.
The results can be summarized 1:Iy saying that when precipitation at Seaside was
considered 8S the control, there was no sign11'icant dif'ference between mean
January precipitation for the seeded and l.W.seeded years at either Kalame. or
LorJgV"iev even at the 25 percent level. Statisticians usual4' pre:!er to work
with the 5 percent level, so this 18 a rather liberal choice of probability
level. The same test disclosed sWlar results at Wind River, south or the
target area.
With Seaside as a control, the conclusion at Ariel-Merwin and Nt. Ad8.llls Ranger
Station was the same; name4', the lJ3pothesis or equal means cannot be rejected
even at the 25 percent level. For Peterson's Ranch we would be unable to reject
at the 10 percent level.
When Aberdeen was used as the control station, the conclusion WIlS ux:hansed for
Kalama, but at LorJgV"iew the hypothesis of no difference in means would be rejected
at the 10 percent level. At Mt. Adams Ranger Station, we woUld be unable
to reject at the 25 percent level, while at Ariel-Merwin we would reject at the
10 percent level, and for P1:!ter80n' S Ranch, we would reject at the 5 percent
level. .
An additional teature of the ana4'sis of covariance is that it enables a comparison
of averages tor the two periods when precipitation is "adjusted" (by
regression lllethods) for the precipitation at the control station. These adjusted
means are presented in Tables 26 aDd 27.
The mean precipitation for the seeded years at Seaside was considera'b~ higher
than that for the l.W.seeded years. We are not aurprlsed, therefore, to see only
slight dU:!erences in the adjusted means at Longv1ew and KalalQa. The adjusted
mean for the seeded years i8 actUAlly lower than for unseeded years at both
Kalama and Lonsv1ev.
At Mt. Adams Ranser Station, the adjusted mean for the seeded years is again
lower than that for the unseeded years. Ariel-Merwin shows an adjusted mean
tor seeded years that is about an inch larger than the adjusted lIlean for unseeded
years, while the difference between adjusted means at Peterson's Ranch is in
excess 01' 3.5 inches, with the seeded years hAv1ns the larger value.
When Aberdeen vas used as the control station, adjusted means for January pre_
cipitation in the seeded years was greater at every station. These va.l.ues are
shown in Table 27.
12
What Is involved in this apparent divergence Is a met.eorologlceJ. problem: from
considerations of' physical factors, which of' the two control atations would be
expected to give the better rdlection of precipitation in the questionable
area?
Table 26
Mean JallUllrY Precipitation Adjusted tor
Precipitation at Seaside
Station Unaeeded Yrs. Seeded Yrs.
Kalama 9.30 9.11
Longview 6.03 5· 71
Ariel-Mervin 9.19 10.2)
Peterson's Ranch 11.56 21.20
Mt. MaillS R.S. 8.93 1.92
TaMe 27
Mean January Preclp"ltatlon Adjusted for
Precipitation at Aberdeen
Station Unseeded Yrs. Seeded Yrs.
Kalama 9·01 9·84
Longview 5.73 6.44
Ariel-Merwin 8.76 1l.24
Peterson's Ranch 17.07 22.13
Nt. MalliS R.S. 8.""9 9·01
3. Regression Analys16
A final evaluation of the ef'teet or weather modification efforts, using a parent
normal distribution, was made \11th regression methods.
The pertinent graphs are shown in Figs. 10-19. Some explanation of the graphs
is advisable. In each case, the straight 11ne is the best-fitting least-squares
line for the unseeded years of record, with the number of years, n, indicated
on each graph. The curved lines above and below the regression line are confidence
curves. and may be interpreted as follows:
,j7~ /
~ ~
WATER YEAR PRECIPITION (SUM FOR 10 MONTHS) }' !,/ V
KALAMA (Yl VS. SEASIOE (X) '~' /
,/ " {~05-'6
60 717~-;V
, " V
. t-(~I /y~
Y-2.51+0.857X /",-~
70 - n" 18 /.""75 nO ...
, -0.820 /1- '1 '1 53-" _ 7.?~:;;.",-.v
Y- ,..-;" /rO-56-59
A: ~~/
60 ,. ,~, I 52-53 , /f'';10",,(57I-5. /f,1>,~-15'-55
50 )......1'4:7/::rL7''1"> '6-57 _.._50"1. CONFIDENCE INTERVAL "At'_...~, w-9S'7'. CONFIDENCE INTERVAL L' / INCOMPLETE RECORDS AT STATiON .09 FOR YEAR 50-51
.0 '-T' , :Yi' 3°30 40 50 60 70! 80 90 100 110
X
FIGURE 10
WATER YEAR PRECIPITATION (SUM FOR 10 MONTHS)
LONGVIEW(Yl Vs. SEASIDE (Xl
70
60
Y=12.32+.392X )/G5S-56
n "1.9 ./ 1,,.Lj.,,
, ".679 ,/1/',
50 55- ~L1 I
58---9:r:1:"~, ~ 0'-5-1 'I _ I .... c ::::> 1 __- - -~~', =--
y- 54-J!!.c-~- .--'1'- --
40 ~ _, "-' --r
~_':----I _... ,. /r/ 52-53 I"T I _-r 'A~
.. ~.. / t 56-57
~/!,//
50 I ~-
~...............y ........ 1 "'1 ---.- 50"'0 CONFIDENCE INTERVAL 1 ...v --- 95% CONFIOENCE INTERVAL
20 r 30 40 50 60 70 t 80 90 100 110
X
FIGURE II
90
V-5S- S6
WATER YEAR PRECIPITATION (SUM FOR 10 MONTHS) ,k /
AREAL- MERWIN ) VS. SEASIOE(X) 0< - 7'
1 ' V 80 )+,/f/~,'' V
70
,17-58",y' ~.... /1" 0/5~-;~... !.--"
54-55 i:+/'b.A-:-?r
56-57-<> /1 ' /'" ,V £3-54
v- ------I---r~t--,~--
60 ,....--.,;'....:)/-:'1 ,~--- ----- 1----t::--::: ---y' 52-53 ~4.~/ ,
.-.,- ~ , y~26.58+0.496X
50 .- __ ¥ n~15 V ./ .. - c- r=O.521
V -" --- ' !L
40 --- , /
/ .~. - 50",0 CONFIDENCE INTERVAL
- - - 95'"10 CONFIDENCE INTERVAL
/ 30
40 50 60 70 ~ 80 90 '00 110
FIGURE 12
I j[
WATER YEAR PRECIPITATION (SUM FOR 10 MONTHS) ,4; PETERSON'S RANCH-COUGAR (Y) VS. SEASIDE (X)
150 ,{z/b!
/-q-"L
~ • 14.96 + 1.323 X 140 n = 17 I/+~
r = 0.846
o,.-o~ '-fl-/
0 /1/ :L~o-V/
130 %,,71-/ P-/<-f--
'Y://f71
~O /~~,r-',.3-54
):VJ~
y 0·-\"0 '~/
;Lt~.
" 7 /;1/ I
/A,~~)
10 /4A/~~A
/~/~Y-
/I V I' 9(~~/i/71;1
INCOMPLETE RECORDS AT H717-}'-! STATION 15 FOA YEARS
52-53.54-55,58-59 m4' ----50 '70 CONFIDENCE INTERVAL It ,1 ---95 '70 CONFIDENCE INTERVAL /7 Ii
40 50 60 70 I 60 90 100
X
FIGURE 13
55-~ Y 70r-==-'-=='-===:':::-:-c-'-:-:::-'-::-:-:-:-:--::--,-1c-:---L_+--+-+-y-+---+-+-I WATER YEAR PRECIPITATION: MT. ADAMS RS (Y) ,
VS, SEASIDE (X) /' I
50-r'",'I'----j7rl/-+-I---1
Y "1/
60 I----'-----L.--L-+--l-+--+---+--+-+-I--co'r-Y ~o7.80+0,522X 5~-54-Y 1//1/).---
n o l9 I ,4->,'1 ''''','-,-+_-+_+_+----1
, • 0,658 ,\,,-5,,- ~/Y"':-' '1 I
50 I /1/ //-::1 ,-' -0----;
~ )~-:'/ ;.---
y - _'14:~7~. ,/'-X~~' --V'<:f':--'+-T+-I_+-+-I_-+--I
40 -:--' ,4:::::"i:/' J-_'-+--I-+--I-+--+-+-+----1I-+--I
I __"I' 1 / VTJ I
f---+-+--+-",.r+/1'4~ . 54-55 e 58-5
~'I /' • 57-58 .
3Of----1--+'Y'<Of--/,17V- I
/ ~' • 56-57 I
20f--t-+-+--t-+-II--+_+--I-+_L--l_-L_L-L_-L_L-j
- ---- 50"70 CONFIDENCE INTERVAL
--- 95"70 CONFIDENCE INTERVAL
40 50 60 ~ 70 80 90 100 110
FIGURE 14
WATER YEAR PRECIPITATiON (SUM FOR 10 MONTHS) 1 ~
KALAMA (Yl VS. ABEOEEN (X) , '1:>4
80
~5-5V+
,~/J,' .l:::
~-b
70
~:;i2S+0724X ~:~ /1/1'
r =0.851 '" I.....:.~ 54 MU
60 ...--rdV' ....5!-59
/i:: >y0~52 54-55--;..~ 53
I - .. I
\'- ". V"':¥S7-S8
50
./1/:;::) '/ 0 56L57
'----;1-, ¥
YJ:~ (/ /-~
~¥ .....r ~ INCOMPLETE RECORDS AT ~ STATION 09 FOR YEAR 50-51
40 <.I- V I "'f ----- 50"lo CONFIDENCE INTERVAL
./ ~ - -- 95"lo CONFIDENCE INTERVAL
30
40 50 60 70 ~ 80 90 100 110
FIGURE 15
70
WATER YEAR PRECIPITATION (SUM FOR 10 MONTHS)
LONGVIEW(Y) VS. ABERDEEN(X)
60
"'-'\0
X Y=9.412 +0.391 X
S8- Sf rSi ,J<.J........- .0 n =26
r =0.741 I-S~ 0 I ---:1'YI ~'_ 1-=
y~ ~~-y 54.5~ \, I . l,..,': ... ..! ... ..J.--
40 ' ~~ ---i- '-f,--:k:'i' 'I _" _":,,,~~'" 56-57
.J..~V
'0
...r~ - -- ---1'1 ---'-SO% CONFIDENCE INTERVAL
--- .........;-' --- 95% CONFIDENCE INTERVAL
20
'0 40 SO 80 70 t 80 90 'DO 110
X
FIGURE 16
90
'55-5
WATER YEAR PRECIPITATION: ARIEL-MERWIN (Y) I .L, /
'" '"'"~'" '" r"tt 80 / V ./
/1/ cd /V
Y· 24.08+ 0.503X 50-01 Y 1/7( V
70 n '" 15 57-58 0 -=t-:'"!:::.~ ~,~
r :: 0.596 IS6-5h ::=1"...... I ~~54
V- -54-5r5 ~~A _ ./"-1 T T -1- ... I L---
60 .---- _.d;::;:.._v--::l -~ I
I l./t-/y/Y 52-53
~ J4-
50
...--( I/VJ/
/VJ.-/t'l-
1/ 7' -
40 /1
A ~---- 50 "10 CONFIDENCE INTERVAL r -- 95 "10 CONFIDENCE INTERVAL
1
40 50 60 70 8 90 100 110
FIGURE 17
0--
55-56
170
WATER YEAR PRECIPITATION
PETERSON'S RANCH (V) VS. ABERDEEN IX)
160
'9" 23.IO+1.145X / 150 n =18
r =0.850 V
140 ,Z~
0S0-sv/Vj
057-58
130 I 4/- G/ 6,L
Y ,¥l1~r-
120 ~~-/ -
S6-~ ~:¥
I '1' 110 V17~ 71 4 / I ,'> 100 ~
90 I 'JZI ~ :/-----50% CONFIDENCE 'N7ERVAe
/ ---95% CONFIDENCE INTERVAL
1/ ,{
50 60 70 t 80 90 100
X
FIGURE 18
I I I I 155-56
70
WATER YEAR PRECIPITATION: MT. ADAMS RS. (Xl VS. ABERDEEN (Yl I
60
j50-T ~
~
53-5~ ./j' ", I
7 0
' ...{;:::"+-~
Y<10.67+.456X 52j53. ~~P,)..-/-I 1
50 n=20 .. 14 ~~
, <680 ,~/~-5f --= y- .....-/'J- _-:::----1-.--;'-
~IY--r:-' ,-T--)~/
40 ____r'-'-y-,4-/
L../I/.....~ 54-t 0StS9
V V 717'
"./ GI 57-58
30 ____ ~ • 56-57
20
----- 50"'0 CONFIDENCE INTERVAL
--- 95'70 CONFIDENCE INTERVAL
40 50 60 70 eo! 90 100 110
FIGURE 19
13
Consider Fig. 10, Kalama (Y) VB. Seaside (x) as an example. Tr.e regression
line 16 based on 18 years ot record. The oute:- pe.1r at curves give a 95 percent
confidence interval tor means of further 6Wllples. That Is, if' we took
other S8lIIples of size 18 with X, the precipitation at seasIde, fixed .for eacb
sample. and then plotted the 'POints (x/i) where Y is the Illean precipitation at
Kal.ama tar the sample, 'fie would expect that on tM average, 95 percent or such
points would tall between these curves. The inner pe,ir ot curves represent
50 percent confidence intervals at each ve.1ue or X. 'rhus, tor repeated samples
of size 18, we would expect the plotted points to fall outside this region as
treq,uently as inside the region. For a single observation, such as we have
plotted on 'the graphs, the confidence 1ntervala would, or cour se. be wider.
These wider intervals are not plotted, since statistical theory dictates that
a neysample ",ould have to be taken for each such individual prediction.
With this in miOO we examine the graphs, and observe that for Kalama vs. seaside
only one point is above the regression line, and this by a sllI.!l.ll margin, well
within the 50 percent confidence limits for the mean ~ a sample of size 18.
We note in passitl8 that two observations out of six fall below the 95 percent
curve.
For the graph of Longview vs. Seaside, we fiOO five points falling within or
on the 50 percent intervals. Two additional ones fall within the 95 percent
limits, while one is outside the 95 percent limit. It must be emphasized
again that one point above the 95 percent limit or two below, as was the case
at Kalama, is not surprising lIhen we consider that these curves imply probabll~ty
statements about the means of samples of size 19 and 18 respectively.
A cOlllparison Is afforded by 7igs. 11-19, wl'th graphs of Ariel (MerWin), Peterson's
Ranch (Cougar 68), and Nt• .Adams Ranger Station vs. seaside. For Peterson's
Ranch the::.-e are only 5 complete years of record in the seeded period.
Three points are above the upper 95 percent confidence curve, one below the
lower, and one betlleen the 50 percent curves. At Ariel, there are four points
above, and one very slightly below the upper 95 percent confidence curve, wbile
two are v!thin 50 percent limits, and one below the lower 50 percent curve, but
vi tbin the 95 percent curve.
The graph for Mt. Adama Ranger Station va. Seaside reflects other analyses in
shoving a greater variability at Nt. Ad8llls Ranger Station. There we find three
points above the upper 95 percent confidence curve, one Just above the upper
50 percent curve, and four ~ll 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 nUlllber of hours cloud-seeding
generators vere operated in a given yeax. While this problem is beyond the
scope of this report, it is noted that in the water year 1950.51, the number
of hours of operation was rather small, yet tbis point was above the upper
curve. On the other hand, the year 1957.58 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 sketc~
information, but a cOlOprehensive examination of weather modification activities
that includes this factor could provide valuable information.
With Aberdeen used as the independent station, the resUlts at Mt. Adams Ranger
Station are strikingly similar as can be seen from Fig. 19. At Peterson's Ranch,
(Fig. 18) resUlts are comparable also, with tbree points above the upper 95
percent curve, and tyO between the two curves at that level. Ariel (Fig. 11)
14
also sbo'ol8 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 va. Aberdeen, we find results cOIlIp!lrable with
those at seaside; namely, two points within the 50 percent confidence region,
three more on or within the 95 percent band, and t\/O below the lower 95 percent
curve.
At Longview. however, two points fall within the 95 percent regioD, and the re_
maining 81% are above the upper 95 percent curve. While this Is not r~kable
frOlll a statistical vle\lpolrrt, it Is certainly different frOID the picture when
Seaside \/8S the control station. This again raises the question posed after
eUl.llllnatlon of the adjusted means in the analysis of covariance.
15
VI. EX'l'REME-VALUB DISTRIBI11'ION RESULTS
The unusual January precipitation motivated an analysis of this date. assuming
that monthly precipitation conformed to the so-called "extreme-value" distribution.
As pointed out earHer, the January 1953 precipitation was large at
every station considered.
Before examining results, the point should be Ill8de that In the present context,
the l'i8l11e "e:z;treme-ve.lue distribution" Is a misnomer. In this approach, we are
not dealing with a set of max1JJlUJll values of January precipitation as the name
Cllght suagest. Rathe; ve are considering all the January precipitation valuel:l
as a 68.lIIple drawn frOlll a population \;h1ch has this distribution form. The
apparent succeS5 of this technique 18 due to the properties which this function
shares with the ga:nma distribution, aDd which are based on physical considerations.
The lllOst straight-forward metboa or dealing with this distribution involves
estiaaating the cUlllulative probability function. For tle problelll at hand, the
variable chosen was the ratio or precipitation to mean precipitation, with es_
timates made frOll! unseeded years' records. This choice of variable permits a
lDore ready comparison of results than would precipitation alone, tor the latter
may have considerably different ranges at two stations.
The estilll8te of the cumulative probability function is obtained from a ranking
of the data. Thus, if there Iolere 19 years of record, the largest pIP ratio
would correspond to a probability or 19/20 ,. 0.95. The second le.rgest ratio
corresponds to a probability or 18/20 =0 0.90, etc.
Figs. 20 through 26 present graphical results for the stations at Kalama, LoIl6view,
Seaside, Aberdeen, Ariel-Merwin, Peterson's Ranch and Kt. J\d8lllS Ranger
Station. The straight line is the estimate of the cUlllulative function: for
a particular value or pIP, the correspo!¥l.ina value or F(PfP), as deterlllined by
tbis line, is the probability or occurrence of a precipitation value less than
or equal to P. Possibly a more mear.1ngtul interpretation of the borizont81
scale can be made from the "Return Period" scale at the top of each graph.
This is related to the other scale in the following way: if F represents the
cumulative probability, then Return Period .: l/(l_F). Thus se.yins the probab_
ility is 0.95 that precipitation values are below a 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 variat!!," y, is related to 1<'(PjP)by
a double logarithmic transformation, with the origin taken at the mode of the
distribution.
In addition to the estilll6.te or the cumulative function, the graphs give an
iDdication of "goodness of fit." The dotted lines represent the "control band,"
and are located one "reduced standard error" on e1tber side of the theoret1cal
line. (See Gumbel DJ Chapter 6.) Accord1ng to theory, approXimately two-thUds
of the observed po1nts sbould fall within tbis control band. An examlllll.tion
of the graphs sbows that this percentage is exceeded in every case, 80 clearly
the "fit" 1s good.
;;;~.;".
KAMALA EXTREME PROBABILITY PAPER JANUARY PRECIPITATION
l..2..L:.1.lill I ~:~~.09+2.62PIp
poS.46
JII"'~:+;tt-:-'"# !-S
Fl?r!
~
·.LI
-F-~.
"?-!Li
~/;
~
...,.F
;
117+
I
'~ +1,
m
,tH·4slfl~..
1.:::::r::I:I!"
~"''''
~ I I ' , '--i i ,Ii"
,.2.-&
~~'
I-
.J;" ~,.'" ,,'.'" ';~" ~t, ,~r "~'" '~'" ~,:"~:':.~~~':':~,,, ',','" '.~'" '."" '.~'" ',')" '.~'" '."" 'J}
U$lX»CM·WI·DC FiGURE~/20
i ~"'
'o" rz~
15 g: ~ h" e"' . • >-
o ::i
IIII
I1I1
III
I II
'on
- T
F-
\
- t
-,
-I-
- ~
Pip"''''
~
ABERDEEN
n.21 ml'i
~:~27;4+2,76l}p
EXTREME PROBABI L1TY PAPER JANUARY PRECIPITATION
,
PTTi
Ii;
;
,.,'~
,-!f.ff1Ti '·4
"mT~"':'.':;'-,-4-l.::."" i !' ::l~ .:~.: ~: .'::' : :' P','
';: : ,--r-;- :,1'-
-f'!-
~I ' r- ~.:~ =p
~,,:,.
i.. G-'"
,I I' 'I'.
"
~I-,
;tf-;
Ft'l,i
III! I': II ,I ! I' ~,' ~11~;j~ ;~,~ ,~.!! .~.! !:7;I!~T"~~~':~t~! ,'~IULLiLlll'L~I!111111! 11111111 ~
~ U U ~ U ~ u ~ U ~ U u u
F1GURE"'2'3
~p"_'" PETERSON's RANCH
\/iOY.Ge'!.)"
n '" 21
y =-~
~. 15.44
~
tWrm
+tttT
~:
f+
tI.ltIZPAlI'nGmOfc:rJloOG:llCZ wtAnlDllUUAU
EXTREME PROBABILITY PAPER
,...
-i-;;!._..!-
rtF
JANUARY PRECIPITATION
mt±Eml±H±l:l±!±±l±±±Et±:±j~F('j,)
I," ,,'~',:., , ,~,:'~ "'~" ~r. ,~r ',,~,,,,~,,,~i,::~;'~::~:~~, ~, ,~,' ,'~L" ,'••~, ,'.': ,~, ••,,~',.~,~', "o" ,~~.'.
FIGURE 25
.;~~:'~II"
MT. ADAMS RS. EXTREME PROBABILITY PAPER JANUARY PRECIPITATION
·53+-+--
m
n
n:< 21 I
Y< -1.50+2.025~
P< 7.85 I
7."li
''';.2'''';"--
" ,
I 'H~~~ :'1:
I I J,.
I' ,."
II .' '10
'.1," ,I
.1." ,~,'." ,~~:~ , ,:~" ~r, ,~r, ,,~,",~" I ;,~':,~~';<;'::~,~ ":~, I ",~" I ',': I ",'." I 'l," ",~" I 'l," "l.t.
USCOWM.WI.t>C: 1t~(XJ(;LD ~~"/~rr
FIGURE 26
16
On each graph are given the nUlllber of years of record (from unseeded years)
used in making the estimate, the equation ot the straight line in terms or the
reduced variate, 1, and the lIe&n preclp11;atlon tor the historical period.
HaVing plotted the cUlml1.ative distribution t'Wlctlons trom the data on January
precipitation during the unseeded years we now proceed, as before, to compare
January precipitation f'igures for the seeded years with the predictions that
might be made on the basis of these distributions. For this purpose, we bave
cOmputed the ratio of January precipitation tor each year of the seeded period
to the !!lean 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
Kalama, such a month vould have a return period o:f' approximately 33 years, while
at Longvle1i the return period is about 90 years. At Ariel-Merwin it is rougb.ly
45 years. At Nt. Adams Ranger Station ore would expect this heavy a month ODCe
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 1'igures give a vivid impression 01' bow unusual the precipitation was in
this particular month, and suggest that such a rare occurrence would indeed. be
upsett1.ng in such a s1.lllple test tor differences between iJle8Ua as the "t"-test.
At a majority 01' the stations, the second highest January of the seeded period
occu:-red in 1954, with return periods ranging trom 13 years (at Aberdeen) to
33 years at Longview.
At Kalama, all other precipitation ratios had a return period under 10 years.
At Longview, two years were as cited above, and the other values had a return
period of 13 years or less with three over 9 years and three under 4 years.
Ariel_Merwin showed three precipitation values with a return period greater
than 15 years (including the 1953 value cited above), and five with a return
period under 10 years. At Mt. Ad8llls Ranger Station, three bad return periods
ot 13 or over, and five bad return periods under 8 years, with four of these
under 3 years. Peterson's RaDch had three precipitation values with return
periods greater thaD 15 years, and three with return periods under 10 years.
(Data lere not available 1'or January of 1955 nor 1959 at the latter StatiOD.)
For tile control station at Atlerdeen, we find only tvo years with return periods
in eJtcess 01' 10 years, while su are below 6 years. At Seaside, three are over
12 years, and five are under 1 years.
Certain trends are apparent from the graphs. For eJt8Clple, the years 1955 and
1951 were the tvo low values in every case where data were available. (The
1955 data were missing at Peterson's Ranch.) Thus, while 1953 was 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 S8lIIple of size 8, we ",ould have
two years with January precipitation as 10", as that of 1955 and 19571 Using
the cUlllU1ative distribution we have obtained, and assuming sample values are
independent, ore say the probabll1'ty is approJtimately 0.13. So 11' repeated
samples of size 8 could be taken, we would expect on the average only one in
seven or eight of such B8.IIIples to contain tvo values this low.
17
As a further indicat.ion of the type ~ statement one can make on the basis of
the estimated distribution, and again uslI18 Longview as the trial station, we
ask: wMt Is the probability that in a sample of s1:.e 8, one January precipitation
would have a return period as h1ah as 90 years? From the probability
level this 111lpl1es for January precipitation at Longview, and assuming independent
68l1lple values, ve COilpute a probability of appraz:iJlatel.y .09.
The good fit of the ertrellle value dirlribution to January precipitations suggested
a similar approach to water year totals. These results are given in
Pigures 27 tbrough 33. Rere again it is seen that the fit 15 very good in
every case.
Look.11'l8 fust at Kalama, ve find the higbest water year total, in 1955-56, had
a return period of roughly 12 years. All other figures bad a return period
under five years. Incidentally, the total precipitation tor the vater year
1955-56 was the highest in tbe seeded period at every station considered. At
Longview, the highe8t water year total had a return period or 22 or 23 years.
Three others had return periods between 5 and 10 years, while four had periods
under 3 year s.
Pursuing the comparison, it caD be seen that there is a noticeable similarity
between l.cngview and Seaside. At the latter, the water year total for 1955-56
had a return period of 25 years while three other water year totals had return
periods between 4.5 and 10 years. (These three years were the same ones tha't
had return periods between 5 and 10 years at Longview.) The four other water
year totals had. return periods less than 3 years.
The pattern at Aberdeen can be cOUIpared with that at Kalallla. The total preci~
itation for ten lIlOnths in 1955-56 showed a return period of 11 years, while
the rello!l.in1ng totals bad return periods of 5 years or less.
The graphs ror Mt. Ad8llls Ranger Station, Ariel-Merwin and Peterson'" Ranch are
somewhat dif'rerent. At Mt. Adallls Ranger Station t.he tot.al for 1955-56 has a
return period or about 30 years, and tha.t for 1950-51 bas a return period or
about II years. The remaining tot.als show return periods or 5 years or less,
with two years being very low. We might ask the same type of question posed
earlier about January precipitation at Longview; namely, what is the probability
that, in a SlilIIple of' size 8 at Mt. Adams Ranger Station, there will be two
water totals as low as those or 1956-51 and 1951-58r Using the probabilities
obtained frolll our population distribution estilll8te, and assuming that the sa.
values are independent, we cOlllpUte a probability of .02.
Ariel-Mervin's graph shows one total (1955-56) with a return period of approxilll8tely
10 years and 1958-59 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 fr:n- the water year total in 1955-56 at Peterson's
Ranch wall about 40 years. The other four water years for which records are
available have return periods of 5.5 years or less.
At Longview and Ka1.ll.ma, an addi'tional estilll8.te of the cumulative f'unction was
made J using the cOlllbined seeded and unseeded years as the sample. That is J
regarding years from tbe two periods as being drawn from the same population,
,,-..,)
'},; LONGVIEW EXTREME PROBABILITY PAPER WATER YEAR TOTALS
"t"-
+ '*l-I·-,
,H
fTTf
fTT
II:
Til
mM ~
-:-1
T
T"fTT'1"
'iIFi+
p:!
'H
!. ~,:, ,,,'. ..':, ,·,r~· "~ "'~'" t:~;:,~;=~,:t, ",','" 'L'" ',','" ',~'" ',',' ',~" ',,'" ',~~
FIGURE 28
p)"-"' SEASIDE EXTREME PROBABILITY PAPER WATER YEAR TOTALS
i¥+t,.:.,
~
if1::1:H
~ T""
":,,, :#,;~>
5i\c~,
-- '+-+1J:;::'.
•
""L'"
'F" '," "i1"':" .;. "
'11"10111 ", 'I'
,: -;::;: -+.1:;,:'
·1 ' •
. '. I.: ,I
, ';' ,j" ' ,
ITT' ;-; "ill+-J=k'.
,:~.J.;.4+i
!TTl . I
+t-+i ilj
.-f-t
+'
H-;-t
TTT"!'
-f+1t'
-!
"III"'lii-!!!ijl]i' h
.!." ~':," .'..•~ .~~, ~t",~, ,~,~:',~:':.~~':;':':~",,',,, !.' ".' "',',"",)"'.'." ".'."".'.:
FIGURE#'29
I
i tt+-H+fttt+++t-t+1i+++I+++H-li+t+.J+.l.-l+W+W-.J+.l.-W-U+W-J
g~ f I i 1-tttttttttttttt+++++++++++++++ffi-t+J-t+J+Wi-W--W-+-1--I--W
...
0: i
J--
"...,
P,p ARIEL-MERWIN EXTREME PROBABILITY PAPER WATER YEAR TOTALS
SiT-S'
~ -1-t-l--1.
14-t.;-
,-i-,
-+
>'> >0 ioo to ~to to .., ""oue~lTv[...,...;;...,~j
_,'.' I ~,~!! I .).' " ~".. ' ,! .,~! I,~!' I '/, ! I !,~' I! ',~'! '~ I I ' ..... I I.~ I ',.," I !,~' I! '4~' I I 'L' I I ',~,!!' I)~
FIGlJ"RE"'?X
~~~~~II" MT. ADAMS R5.
t, '0'
: _i 11.J. I'" .! J /.!
rn''-42.904+5.46 Pip m~*
p' 47.28 '"
mtTl'
H-H+!ff1+H+t+
EXTREME PROBA.BILITY PAPER
t'
WATER YEAR TOTALS
'7
tt+t
E!Fffl1
.4
"Tf'TT
ITflT'iT
iT<
~,f:
, ,
1'".1
'lliilii.l•i.,..',,"i .~ tft++t:1
T#i
~
;~
;o~r--r-:
, --.-'
#L++~
EE
-R=t-t-
H
TI:'
t++
L...t'
.~
',,+te'
n-!
f=
L ";''''';''~ ~f ·':-"~:"""~::~;;'i:;=~'t~,::,', ',',"" ,',', '}, ".',"".:,"'L~
lISCOIolM.WB·DC FIGURE 33
18
we estielated the c\Jlllulatlve distribution trolll these sampUs. If there vere a
lIlarked d1£ference bet~en the tvo periods, one would expect I118rked divergence
of the two straight_lines and possibly an increase In the width ot the control
band.
These two 8ddltlonal estimates are shovn by the dotted lines slightly belolol the
rust estll:15.te from P ...95 to the right, ....ltb a :few reference dots at the Idt
of the graph. The dotted lines slightly below the upper control bam, near
F •.97, give tbe revised estimate at that band. There are also abort dotted
Unes at F ••65, slightly below the upper control line. In each case. lOller
control lines \l'ere practlca.lly identica1.
;~a~~~Pd;ei:t=~i~if,t~t~i;b~;~:~a;~t:~1:~~1na:h:e~~:~e:Y5::;le.
The control band vas slightly narrover I and the ne\l estimate of the cUJIlulatlve
distribution 10188 quite close to the earlier one.
19
VII. SUMMARY AND CONCWSIONS
To sUlDIlJal'ize, precipitation data bas been eX8lllined for stations 1n the questionable
area, 1n the target area, and at control stations. COlllparlsons have been
made between theee areas, and various statistical techniques applied to the data.
FrOlll these analyses. we find that tOr Cowlitz County outside the target area,
as exemplified by Kalaaa aDd longylew, there 1s little or no evidence to support
the conclusion that pree1pitatiOD in the seeded years has been slgn11'icantly
higher than 1n the unseeded years. This is the case on either a monthly basis
or a total vater-year basis.
We review and summarize the considerations that point to this conclusion &s
follows:
A. Plots of cumulative precipitation aaainst years disclose no IlI8.rked
change in dope.
B. At both stations there vas a consecutive five-year total in the UD_
seeded period higher than that or the last five consecutive seeded
years.
C. Qualitative cOlllp8risons show that an unusually high precipitation
figure fC1r January 1953 has been exceeded by some lIIonth in the UD_
seeded years at all statioos except the control station, Seaside.
D. In a ranking of cOlllbined salllples (from seeded and unseeded years)
the highest rank for each heavy precipitation lDCnth during the
seeded period was tabulAted. It appears t.bat Longv1.ew and Kale.ma
do not rank higher than control stations.
E. Distribut.ion_tree teat.s were eaployed so that conclusions could be
reached vitbcut assumptions about precipitat.1on dist.ribution torlll.
2. For the six heaviest precipitation months, only January
shows significance at. these t.vo stations, but this result
holds at control stations also.
F. Three testa were used assuming a "nor_l" distribution for the precipitation.
1. "t"_tests also indicate that January is the only llIOnth
wllere there are significant d1:N'erences between tile two
periods.
20
2. Analyses of covariance applied to January precipitation
suggest that lIluch of the increase in precipitation can be
explained 8S part of a pattern that prevalled at control
statiODS &160.
3. Regression lines and coDt'ldence curves for Longy1.ev and
Kalama VB. Seaside show excellent agreement between ques_
tionable and control areas. A somewhat different scatter_
1118 with Aberdeen as a control raises 8. meteorological
question.
G. E::I:treme-value IUatributlon metbods vere applied to both January and
toUlJ. vater-year precipitation.
1. The impression of a rare occurrence in January 1953 18
fortified by the estimates that precipitation in that
lIlonth has a return period as high as 180 years at a
control station, but considerably shorter at Kalama
and Longview.
2. Aside from this uncommon IIIOnth. return periods are not
relll6Xkable.
3. A combined sample, udng both seeded and unseeded years to
estimate the cumulative tunction, leads to results very
similar to those obtained trom unseeded data alone. The
standard deviation of the precipitation ratio 18 slightly
less, and the control band ill narrowed. Thus, probability
statellents made on the basis or the unseeded years would
be almost identical with those made on the basis of the
combined sample.
21
31bl.1ograpby
1. Brakenslek, D. L. and Zingg, A. V., Application of the Erlrene Value Stathtical
Distribution to Annual Precipitation and Crop Yields, Agricultural
Research SerVice 1il-1.3, 1957.
2. Dixon, W. J. and Massey, F. J., Introduction to Statistical .Analysis, 2nd
Edition. McGraw-Hill Book Co., 1957.
3. Gumbel, E. J., Statistics ot Extremes, Colurobla University Press, New
York, 1958.
4.. Lleblein, J., A Nelol Method or Analyzing Extreme Value Data, National Advisory
Committee tor Aeronautics, TechnicCll Note 3053, Washington, 1954.
5. Mood, A. M., Introduction to the Theory or Statistics, McGraw-Hill Book.
Co., 1950.
6. 'l'hoIlI, B. C. S., "A Stat1atlcal Method or Evaluating Augmentation of Precipitation
by Cloud Seedln~(J U. S• .Advisory Committee on Weather Control
Final Report, Vol. 1-2, l'ecbnical Report No. 1.
STATE OF WASHINGI'ON WEATHER MODIFICATION BOARD
Chairm.an - Earl Coe, Director of Department of Conservation
Members - Dr. Phil E. Chureh - Eltecutive Officer. Department of Meteorology
University of Washington
Dr. S. Tow stephenson - Dean of Faculty, Washington State
University
Julian Steinbergen - Yakima Horticulturist
Judge B. B. Horrigan. Ret. - Pasco wheat grower
AGalDA FOR JANUARY 2a, 1960 MEETING
A. Presentation of precipitation analysis in southwest Washil18ton by
members of the Division of Industrial Research. Washington State
Institute of Technology. Washington State University.
B. Formulate & reply to the Director of the National Science Foundation
outli.n:ing a proposal for a research project to be conducted in this
state.
1. Determine and define a more adequate lllllthod of informing the p.1blic
of a 1'1l1ng for a weather modification permit in an area.
2. Define a procedure for receiving an accurate, current report from al1
operations.
3. Consider requiring a copy of the contract between operator and client.
4. Consider a proposal submitted by the W. R. D. C. loIhereby permits would
issue on a calendar-year' basis.
5. Disposition of application for permit subDitted by Water Resources
Develop:lel1t Corporation to conduct a weather modification project in
the analyzed area, subject to items 1 through 4 above.
1. Renewal of licenses for Water Resources Developnent Corporation and
North America Weather Consultants.
2. Renewal of W. R. D. C. permit on operation for Ellreka nat Water
Developnent Corporation.