Letters to the Editor
s ~ u n dmethod in our calculations (VAN DEN DUNGEN
ct d. 1950).
2 . The flux of west niomentuni across the earth's
surface
is an asccnding one where easterlies dominate
By F. H. van den DUNGEN,
(low latitudes) and a descending one where westerJ. F. COX and J. van MIEGHEM
lies dominate (middle latitudes). In the mean, as
Uiriversity of Brrrsrcls
easterlies are better developed in the northern than
Novcniber 6t13 I 9 5 o
in the southern hemisphere, the ascending flux of
the low latitudes is not compensated in the northern
I . It is generally accepted that available aerological
information concerning the distribution, in space hemisphere by the descending flux of the middle
and time, of the Zonal component of the atmospheric latitudes. A part of the ascending flux of the tropical
circulation, is not yet complete enough to permit a regions of the northern hemisphere passes across the
1949) and is compensated in the
reliable calculation of the angular niorncntum of the equator (WIDGER,
middle latitudes of the southern hemisphere, where
atmosphere.
If it is renienibcred that the zonal circulation more intense westerlies bring a descending flux of
varies strongly with longitude (NAMIAS
and CLAYP, west momentum, more considerable than in the
1g4g), even probably more strongly in the northern northern hemisphcre.
Assuming that for the entire surface of the earth,
than in the southern hemisphere, it will appear that
a calculation based on the information availablc at a uniform rate throughout the year, a complete
about the distribution of the zonal velocity in one compensation of the ascending and descending west
momentum happens, w e obtain (VAN DEN DUNGEN
or two meridional cross sections only, does not seein
ct al. 1950) a scheme of the fluctuations of the earth's
very satisfactory.
W. H. MUNKand R. L. MILLER(1950) have rotation in good accordance with the published
calculated the angular nionientum of the southern valpes (Stoyko, Finch, Uhink).
When numerkal tables of the kind calculated by
atmosphere using winter and summer cross sections
along the 150"E meridian, as established by F. V. P. STARRand his collaborators and related to the
LOEWEand U. RADOK(1950 a). These cross sections southern hemisphere are available, the assumption
show that the wind speed in thc centcr of the west- about yearly compensation may be tested. It seems
erly jet exceeds 120 nii/h (at 25 S), in winter, and probable that a coniplete yearly compensation at
uniform rate does not occur and this niay open the
50 mi/h (at 40" S) in summer.
More conip!ete and recent information show way for a meteorological explanation of apparently
(LOSWE and RADOK, 1950 b) that the summer erratic changes. In that connection it must be resouthern "jet stream" would in fact be much more membered that the reduction of the clock rates
intense, exceeding IOO nii/h in the center. The disrcinains intricate and that future work niay prosimilarity or assymmetry of the westerlies in the two vide furthcr valuable information in that field.
hemispheres is, in summer, much more marked
3. Column (4)of Table z in W. H. Munk and
than previously assunied.
I<. L. Miller cited paper needs, in our opinion, to
We arc of the opinion that the annual variation be carefully examined. Let A p represent the variaof the momentum transfer between the earth and the tion from January to July of the mean pressure p
atmosphere offcrs a better basis for calculating thc (on the ground) not reduced to sea level, along a
annual variation of thc angular momentum of the parallel of latitudep; obviously, the total niass of the
atmosphere.
atmosphere remaining constant, it is necessary that
This transfer results from the friction between thc
earth surface and the atmosphere (including the
-, x
7
pressure effect due to mountains).
Utilising tables calculated by V. P. STARRand his
collaborators (1949) on the basis of numerous surface information, we believe to have followcd a
Variations in the Earth's Angular Velocity
Resulting from Fluctuations in Atmospheric
and Oceanic Circulation
~~
3 20
L E T T E R S TO T H E EDITOR
In other words, the mean value of the A p in thc
northern hemisphere must be equal and opposite
in sign to the mean value of the A p in the southern
hemisphere. Dividing the surface of the spherical
globe into zones of 5 " and 10' latitude, let us
denote by [ A p ] the mean values of A p for every of
these zones.
Equation ( I ) shows that the ( A p ] brought into a
(sinpl, [ A p ] ) diagram must appear such (stairs
curve) that the algebraic sum of the areas comprised
between it and the "sin
a x i s be zero.
It is easy to check that the [ A p ] values tabulated
by W. H. Munk and R. L. Miller do not fulfill
this condition. As a special case, one finds with
those values
v''
I4
80"
0.85 mb for the northern
- 2 . 1 ~
hcmispherc ;
nib for the southern
hemisphere;
LOEWE, F. and RADOK, U., r y ~ oa: A iiieridional
aerological cross scction in thc South-West Pacific.
J. Meteor., 7, I , pp. 58-6s.
-- - 1950 b : Sotne amendments to "A nieridional
aerological cross scction in the South-West Pacific.
J . M e t e o r . , 7. 4, pp. 305-306.
MUNK,W. H. and MILLER,R. L., 1950: Variation in
the Earth's angular velocity resulting from fluctuations in atmospheric and oceanic circulation. Tel/145, 2, 2. pp. 93-101.
NAMIAS,J. and CLAPP,P. F., 1 ~ 4 9 :Confluence thcory of thc high tropospheric jet stream. J. Meteor.,
6, 5 . PP. 330-336.
STARR,V. P.. 1 9 4 y : Investigation of the General Circulation of the Atmosphere. M.I.T., Repert no 4 .
V A N DEN DUNGEN,
F. H., Cox, J. F., V A N MIEGHEM,
J., i949: Sur les fluctuations de piriodc annuelle
de la rotation dc la T e r m Acnd. r. de Belgiqrrr.
Bull Cl. dcs S c . . se Ser., 35, 7, pp. 642-655.
.
.. 1950: Sur les fluctuations saisonnihes dc
la rotation du globc terrestre. Acad. r. de Bdgique.
Brill. Cl. des Sc., ge Sir., 36. 5, pp. 388-402.
WIDGER,W. K., 1949: A study of the flow of angular momentum in thc atniospherc. J . Meteor.,
6, 5 . pp. 291-299.
it follows that
IA
p:
[:A p
80" N
Reply
G -0.67
80"
nib,
s
J"
l3y W . H. M U N K and R. L. MILLER
Srripys Iitstifririorr cf Ocrnrtograplry
La Jolla, November I s f h , 1950
representing the niran value of A p bcI . The cffkct of thc wind circulation on the earth's
tween latitudes pl and pz. rotation can be computed either from (a) changes in
the angular momentum of the atmosphere as a
It seems quite unlikely that this mean negativc
whole, or (b) momentum transfer between atmospressure differencc between 80" S and 80" N could phere and earth. W e have utilized the former
be balanced by a reasonable positive differencc in method, and arrived at results consistent with
the two small polar .caps of 10' of latitude.
astronomic observations; as described in the abovc
4. In their above quoted paper W. H. MUNKand note, V A N DEN DUNCEN
et al. (1950)I utilized the
R. L. MILLER
(1950) report about our paper (VAN DEN
latter method, with similar results.
DUNGEN
et al. 1949) in terms such that it could bc
It is true that for our method it would have been
understood that we were not aware of the importance highly desirable to have had available additional
for the problem stated of the correction from sea mcridional sections in the Southern Hemisphere,
level pressure to local pressure.
and wc havc said so in our article. In van den Dungen's method, the pressure effect due to mounW e believe that every reader who will havc read
through our paper wiII be aware that this was not
tains and a choice for the frictional coefficient bethe case. Our scheme was fully developed by one tween air and land, and air and water, is also not
without uncertainties. Since the transfer of angular
of our students, Miss M. LAURENT(1949. 1950).
momentum over six months from the westerlies or
the easterlics to the earth is large compared to the
I< E F E K E N C E S
nngdar momentum of thc atmosphere at any instant,
PI
LAUREN:,M., 1949: Sur les fluctuations dc piriodc
annuelle de la rotation de la Terrc. Acnd r . dc
Belgiqrie, 81111.Cl. dcs Sc., sc Sbr., 35. 1 2 ,
pp. 1125-1140.
Sur Ics fluctuations de pPriodc annuelle de la rotation de la Tcrre. Acnd. r. de Belgiqrw, Biill. Cl
des S r . , .cc Sir., 36, 2 , pp. 138-147.
~
I This papcr was apparently published at about thc
ratne timc as our paper, but n o copy has as yet been
available to us. In our article we refer to van den
Dungen's carlier paper in which the variations in the
earth's rotation arc ascribed to latitudinal changes of
air tnassc\.