OCTOBER, 1908. MON!I!HLY WEA!l!EEB REVIEW. 327
DENVEB FORECAST DISTBIOT.*
[Wyoming, Colorado, Utah, New Mexico, and Arizona.]
The feature of the month was the heavy precipitation in
western Wyoming, northwestern Colorado, and the eastern
counties of Colorado. In the plains region of Colorado the
rainfall was excessive on the 18th and 19th. Considerable
damage by flood was caused in the southeastern portion of the
State by the overflow of the Arkansas River below the mouth
of the Picketwire. Warnings of the flood were issued on the
morning of the 19th. Temperature averaged lower than usual
thruout the district.-8'. H. Brandenburg, Didrict F'orecaSer.
BAN FRANOISCO FOREOAST D1STBIOT.t
[California and Nevada.]
The month as a whole was one of pleasant weather, with
rather less rain than usual. There were no especially nota-
worthy features.-A. G. Mcddie, Professor and District Fore-
Caster.
[Oregon, Washington, and Idaho.]
Temperature was slightly below the normal, and precipita-
tion, except in a few localities, was in excess of the normal.
Frosts in the western sections, altho not more frequent, were
heavier than usual. There were three storm periods, but the
winds attending them were not severe. The warnings for high
winds were timely and beneficial, and warnings were issued
for all important frosts.--E. A. Beab, &t&t Forecaster.
POBTLAND, OREQ., FOBEUAST D1STBIOT.t
RIVERS AND FLOODS.
The drought conditions that persisted during the first three
weeks of the months over the middle and northern districts
eaut of the Rocky Mountains held the rivers to their abnor-
mally low stages, and the effects of the rains that fell late in
the month were scarcely noticeable. As in September, the
effects of the drought were most noticeable in the Ohio River
where there was no hope of an early resumption of navigation.
At Parkersburg, W. Va., the low-water stage of -0.3 foot was
the lowest on record.
There was a moderate flood in the upper Arkansas River,
beginning on the 19th in southeastern Colorado, and reaching
Wichita, Kens., on the 23d. At the same time there was a
decided rise in the lower Arkansas River and its tributaries,
with flood stages in the Neosho River, and in the Arkansas in
the vicinity of Fort Smith, Ark. At the end of the month the
lower river was still rising, but with no prospect of serious
flood. Warnings were issued wherever possible and they were,
as usual, valuable and timely.
These floods were caused by heavy rsins that extended over
eastern Colorado, Kansas, and Oklahoma, beginning on the
18th in Colorado, and reaching a maximum in Oklahoma and
eastern Kansas from the 20th to the 22d, inclusive. In the
State of Oklahoma, where the rainfall was probably heaviest,
the floods were more pronounced and great darnage was done;
the losses will probably run into millions, but it has thus far
been impossible to obtain detailed estimates. Effort will be
made, however, to secure data for publication in a later edi-
tion of the MONTHLY WEATHER REVIEW.
On the Neosho and lower Arkansas rivers the damage was
small, probably amounting to not more than $26,000.
The heavy rain area extended also into northern Texas, caus-
ing a moderate rise in the upper Trinity River; due notice was
given and no damage resulted.
Heavy rains in South Carolina on the 22d and 28th were
followed by rapid rises in all the rivers of the State; the floods
were moderate. Warnings were issued promptly and no dam-
age of consequence resulted.
The highest and lowest water, mean stage, and monthly
range at 208 river stations are given in Table IV. Hydro-
graphs for typical points on seven principal rivers are shown
on Chart I. The stations selected for charting are Keokuk,
St. Louis, Memphis, Vicksburg, and New Orleans, on the Mis-
sissippi; Cincinnati and Cairo, on the Ohio; Nashville, on the
Cumberland; Johnsonville, on the Tennessee; Kansas City, on
the Missouri; Little Rock, on the Arkansas; and Shreveport,
on the Red.-H. C. Frankenjeld, Professor of Meteorology.
* Morning forecasts made at district center; night forecasts made at Washington, D. C.
-f Morning and night forecasts made at district center.
SPECIAL BRTIOLES, NOTES, AND EXTRAOTS.
DEFLECTING FORCE DUE TO THH EIARTH'S ROTATION.
In connection with Mr. Okada's recent paper' it may be of
interest to show how the deflecting force can be obtained by
aid of the usual two-dimensional expressions for the accelera-
tion resolved along and perpendicular to the radius vector.
If a material point move in any plane curve, and if p and c/.
denote its polar coordinates, then the acceleration along p in-
creasing will Be
By R. A. HAI~RIS. Dated Washington, D. C., September 1.1908.
-
Aoceleration, = 3 - p (g)*, dt'
and that perpendieular to p, + increasing, will be
8# dpd@ Acceleration9 = p - + 2 - -. dt' dt dt
These fundamental expressions are readily obtained either
by considering the velocities resolved with reference to polar
coordinates at two successive instants of time, or by combin-
ing accelerations along the x and y directions, the same having
been first exprest in polar coordinates.
Next suppose this plane to be tangent to a sphere, the mov-
ing point marking, or coinciding with, the point of contact for
the short interval considered. Let 1; e, and Q, denote the polar
coordinates of this point (e being north polar distance and Q
east longitude from a meridian fixt in space), and let the origin
1 Monthly Weather Review, May, 1908, XXXVI, p. 147.
of its plane coordinates (p, +) be taken at the point where the
axis of the sphere from which e is reckoned pierces the tan-
gent plane; then
p = r tane, dp= r de;
Now suppose the velocity along the path to be uniform for
the short time considered.
COS e - - %* Acceleration8 = - r sin gr cos e -" (ddt)l rain0
COS e 'V+ 'vg d e d p Acceleration+= 2 r cos e - - =2 - dt dt r sin 0
where, of course, the velocities are absolute velocities in space.
On the earth, which rotates from west to east with an an-
gular velocity k,, we have
vg = v,
v+ = r k, sin e + v,
where v, and v, denote velocities relative to the earth's surface.
Hence, accelerationg of particle moving with reference to
the earth's surface - acceleration0 of particle at rest upon the
earth's surface = - 2k,v, cos 8.
Similarly, Acceleration+ = 2k,q cos e. Hence, the material point is capable of exerting deflecting
forces such that
OCTOBER, 1908
symmetrical, tho the principles of vortes action prevail with
more or less perturbation. It is our first study to obtain the
symmetrical vortes with all its velocities, angles, and pres-
sures; we can then find the forces which produce the actual
vortex, thru a aeries of differences obtained by subtracting
the symmetrical system from the observed data. Thus the
progressive northwestward motion of the typhoon makes the
wind-angles greater southwest of the center than to the north-
west. This angular difference is eliminated as follows: At the
northern, eastern, southern, and western points of each isobar
construct the appropriate wind vector (the heavy dotted arrows
of fig. 12) as accurately as possible from the wind observations
taken in the region and plotted on the composite diagram,
fig. 12. Then take the mean velocity and the mean aIigle on
each isobar, i. e., the mean values of the four average vectors
of each isobar. I n the present study the angle 30° has been
assumed thruout this horizontal section, whence i = - 30'
and az = 60°, the angular height at which the general vortex
is truncated by the sea-level plane, whatever its actual height
in meters may be.
TABLE 52.-iUeteorobgiaal datd of tlw De Wit& typhoon, Auguet 13, 1.901.
Hour.
3p.m. g a m . 3P.Ul. g a m .
3p.m. 9a.m. 3 p.m. Dam.
3 p m . !lam 3p.m. 9a.m.
10p.m. 1Oa.m. 1Opm. S a m .
1op.m. 1oa.111. I0p.m 5 a m .
1Op.m. 10a.m.
lop.m. 6a.m.
I0p.m. 10s m. 10p.m. 5 a.m.
1Op.m. 10a.m. 10p.m. 5 a.m.
10p.m. 10a.m. lop.m. 5a.m.
10p.m. l o a m .
Southward force = ,2k1v, cos i3.
Eastward force =-2k,w8 cos e.
Hence, Total force = ~~,I J .C O S 8.
(from south via east) is
The tangent of the direction of the action of this force
B.
--
Nin. i57.2 75LY
7 x 8
753.1 748.3 743.6 738.8
753.9 751.1 747.5 742.2
750.4 742.6 732.7 736.8
744.9
736.3 734.4
751.7 147.6
.......
73a 7
7 e .5 140.5
750.2 746.3 142.7 742.1
547.3 739.8 738.6 739.7
710.6 125.5 737.2 744.7
741.0 742.5
while the tangent of the direction of the moving particle is,
of course,
t.
OC. 28.9 26.7
26.1
28.0
30.0 82.3 26.7
31.6 28.3 51.4 aO.3
The force, therefore, acts at right angles to the instantaneous
path of the particle, and so is a deflecting force. (Cf, Coast
and Geodetic Survey Reports, 1900, p. 571; 1904, p. 332.)
Rela- tivehu iuidity.
Percent 87 80
95
85 86
91 73
80 83 94 96
--
,............
STUDIES ON THE VORTIUES OF THE ATMOSPHERE OF THE EKRTH.
1V.-THE DEWITTE .TYPHOON, AUGUST 1-3, 1901.
By Prof. FBANK H. BIOELOW. Dated Washington, D. C., March 16. 1908
TEE METEOROLOQICAL DATA.
I n order to illustrate the structure of a hurricane as anal-
yzed by the theory of the dumb-bell-shaped vortex, I have
chosen the DeWitte typhoon which occurred in the China Sea
August 1-6, 1901. This hurricane is specially valuable for
our studies, because the observations at observatories on the
coast of China and on the outlying islands afford an unusually
large amount of suitably published data. A paper by Rev.
Louis Froc, 5. J.,' and some notes by Rev. Jose AlguB, S. J.,a
give the isobars, wind directions and velocities at midnight
of August 2, 1901. In Table 52 will be found other data es-
tracted from the China Coast Meteorological Register and the
Monthly Report of the Central Meteorological Observatory of
Japan. The isobars of August 2,lO a. m., 10 p. m.,August 3,5 a. m., are
reproduced in Chart IX, figs. 9, 10, and 11, respectively. The
isobars of August 2,lO p. m., fig. 10, have been made the basis of
the computation, because the typhoon was then at its greatest
intensity, the barometer at the center having fallen td about 690
millimeters. Chart IS, fig. 12, shows upon an adopted system
of isobars constructed from the vortex data, the wind direction
and velocity located according to circumstances within the
diagram so as to give a composite view of the vectors on all
sides of the axis and a t the proper distances from it. The
temperatures, fig. 13, and the relative humidity, fig. 14, have
been plotted in a similar manner. An inspection of the tem-
perature and relative humidity diagrams, shows that in t h k
case there is no important difference between the western and
the eastern quadrants, such as is always found in ordinary
cyclones as distinguished from hurricanes. The relative hu-
midity, however, seems to be somewhat higher in the south-
west quadrant than in the others, due probably to the excess
of the tendency to precipitation in that region. It is very
evident that no temperature differences esist in the sea-level
horizontal section of the hurricane, such as can account for
ita energy thru rotations generated by two masses at diEer-
ent temperatures lying side by side on the same level. It is
probable that these temperature differences esist in higher
levels where a cold sheet overlays a warm sheet, the surface
of separation being horizontal rather than vertical.
It is our purpose to construct the average vortex which
underlies the actual hurricane with all its divergencies due to
local conditions. The vortices in the atmosphere are seldom
Annals Zi-ka-we1 Obser- vatory.
CONSTRUCTION OF THE AVERAGE HURRICANE VORTEX.
1The DeWitte Typhoon, August 1-6, 1901.
'The Cyclones of the Far East. Manila Observatory. p. 31.
24.8
25.2
25.1 aG.1 24.1 26.9
2 a o 29.5 28.8 28.G
28.1
25.9
26.2
27.4
26.0 27.4 27.3
26.0
27.0 28.7
25.6 26.5 26.8 26.6
27.9 28.0 27.4 26.6
28.8
5 .8
Station.
99 86
91 93 98 97
85 76 87 91
80
100 67
76 92 74
87
loo 91 WI
83 91
90
83
80 76
80 85
71
93
Gutzlaff.. .. .. ,. .
Sharp Peak . . . . . .
Ainoy.. . . . . .. . . . .
Taihuku . . . . . . . . .
Lati- I Longi-
26.7 119.40
!!A27 I 118.6
I
!
I
Taichu.. . . . . . . . . . .
i
Hokoto . . . . . . . . . . . 23.33
I
Tainau . . . . .. .. . . . 52.59
I i
Taito ..... . .. .... . 22.45
Ishigakijinia. .. .. . i 24.20
Nabs . . . . . . . . . . . .
Oshiuia . .. . . . . . . .
26.13
38.23
__
For the rn-_,n is
19.40
119.34
110.12
121.8
1%. 7
$127. 41
129.30
--
Dab.
Aug.
2 3
Aug. 1 2 2 3
Aug. 1 2 2
e
2
2 3
a 2 3
2 2
8
2 2 3
2
2 3
Aug. 1 2
2 3
Aug. 1 2 2 8
Aug. 1 2 2 3
Aug. 1
Aug. 1
Aug. 1
Aug. 1
Aug. 1
-
bars of thl
lows: Scale off the distance o
Wind.
-
K p . 8.
7 11
25
11 7 7 26
9 7 9 16
4 21 27 17
4 16 6 15
10
16 12 17
6 12 10 17
4 8 21 17
17
n 37 26
21 24 10 9
4 14 10 7
......
-
vortex the procedure is a
-
Dir. ese.
e m
ese. ......
ne. una.
SEW.
now.
se. wsw.
W.
sw.
nw. nw. nw.
SW.
11.
ow.
SW.
n.
nw.
nw. wsw.
OW.
n W.
W.
nw.
W.
SW.
MW.
sw.
nw.
n. n. s.
1.
e. em. se.
Re.
e. ae. se. ese.
-
fol-
the isobars-from the center on
the north, east, south, and west lines and take the-mean of
these four as the observed radius, m, of the appropriate vortex
tube. Look out the log m of the successive radii and take
the successive differences, log p=log q,-log m,,,,. Finally,
take the mean, log p+,. and reconstruct the computed log m, by
'Extracted from the China Coast Meteorological Register and the Monthly Report of Central Meteorological Observatory of Japtan.
-- -