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OCR for page 50
C~D IN
ALAR Saw
H. A. CHARMER
A. a. C~6 ~d Oogio~c Spread
Wean se~-level ~> be Deanna from two different points of YiOW; Both
act landing to solvent ji~ercDt results. With We
openly correct a_ _~_=
geodcsist we may define it as the e~ipotenti~1 surface which the oceans
would assume if unJistnrted By the rise ~] Ian of the Age and t, the
eFects of ~in] and bender. Starting with beam se~-level at any given
initial point the geoJesist Cal Jetormine, Dy precise spirit levelings such
FIG eqUipotc~ti~l surface. geodetically, ~! within the limits of iDStIU-
~ent~1 error, ~11 points on this so~f~ce would he at mean se~-leYel. Egg
sc~-level so defined Any tbercCore he c~llc] geodetic ma sc~-l~vel.
Gut along the sbolcs w~shc] by the sea me may also JeOne Scan se~Jevel
at any point as the ~ct~1 level of the sea at that point Jete~iDe] ty
verging the costly cb~ngiDg level at the point over ~ consiJer~ble
period of time. Wean sc~-level so determine] may be iistinguishc] Iron
geodetic se~-lc~cl by c~lL~g it local or glitch, geographic mean sc~]c~ct
#] it is to he notch, Ant st~rti~ from We same it point; geodetic
and gcogr~phlc mean se~-le~els Max or may not coincide at other points.
For in averaging the varying height of the sea the resultant or act elicits
of cb~nging metcorologic~1 conJihons Max Be Ji~ereDt at different places.
Thus ~ predominant Ding from ~ given direction gig make se~-level OD
the shore from ~bicb it blows lower ~D] OD the other shore bigger.
Tn sc~1 use as ~ J~tD~ plane Ion elevations in geopb~sic~1 investTg~-
tions, it if g~pb!y mean sc~-l3vcl that is employed. [or geo~phir
SPED level lies at lne nose of geodetic mean se~-lc~cl, since the initi~1
se~-level in geodetic leveling must he determine] hy averaging the height
of the sea at that initi~I point. Furtbermore, geodetic leveling of clan
the biggest precision is subject to instru~e~t~1 errors labia; ~ltbougb
very small for moic~te iist~Dces; Mao Become relatively large in leveling
. . .
bet~ecn widely sep~T~te] points. It is ~erefoTe customary to tape the
se~-level determine] t~ averaging the Beirut of the sea at Ji~erent points
along the coast as Beaning the mean se~level surI~ce.
Tbo level of the sea is at ~11 times disturbed b~ yin] ala tide. Over
how long ~ polio] gnat the height oT the sea De ~ver~gc] iU order to give
As mean level at that point ~ To answer this question it is obvious that
we must first investigate the variations to icy se~-level is subject.
so
OCR for page 51
AlEAN SEA-LEVEL
VARIATIONS IN SEA-LEVEL
The most obvious variation in the level of the sea at any place is that
clue to the tide. Twice daily, in rhythmic fashion, the sea rises and falls
in response to the mighty pulse of the tide-produci:ag forces. These forces,
as has been developed in a preceding chapter, may be grouped into three
classes; namely, semidaily, daily and long-period forces. The semidaily
forces are the principal tide-producin`~ forces, the daily forces are next
in importance; and the long-period forces are of such small magnitude
as to be of relatively minor importance.
The average length of the tidal day is 2a hours and 50.4 minutes.
Hence, if at frequent regular intervals during such a period the height
of the tide is measured and these heights averaged, the effects of the tide,
in so far as the semidaily and daily components are concerned, will be
eliminated, and a value of sea-level freed from the disturbing effects of
the tide will be obtained. The effects of the long-period tidal forces, as
explained above, are so small that for the present they may be disregardecl.
In tidal work it is customary to tabulate the height of the tide at the
beginning of each hour. Since the length of the tidal day is very nearly
So hours, it is obviously more convenient to derive daily sea-level from the
hourly heights of the tide as tabulated than from aliquot parts of the
tidal day of 2a hours and 30 minutes. Strictly, the first and last hourly
heights of the 25-hour period should each be given half weight in deriving
daily sea-level; but since daily sea-level is subject to disturbing effects
of far greater magnitude, no useful purpose is served by such. refinement.
As a matter of' fact it is sufficient to derive daily sea-level as the average
of the 24- hourly heights of the tide of the civil day, since this is most
convenient.
In this connection careful distinction must be made between mean sea-
level and half'-tide level. Mean sea-level at any point is defined as the
average level of the sea at that point and is determined b.y averaging the
height of the sea as measured at frequent intervals, generally every hour.
Half-tide level is the plane that lies exactly midway between high water
and low water. If the curve representing the rise and fall of the tide
were that of a simple sine curve, the planes of mean sea-level and of
hall-tide level would coincide. But the tide curve is not a simple sine
curve; it is compounded of a number of simple sine curves, some of' which
have fixed phase relations with respect to each other. The average rise
of high water above mean seat-level is therefore, generally, not exactly the
same as the average fall of low water below mean sea-level; and hence
mean sea-level and half-tide level generally differ.
As determined from day to day the relation of half-tide level to sea-
level at any point may differ because of differences in meteorological
OCR for page 52
~2
FIGURE OF THE EAR TH
conditions. But when averaged over periods of a year or more the relation
between the two is very nearly constant. From observations it is found
that at certain places half-tide level lies above mean sea-level, while at
other places it is below mean sea-level. Thus, as a rule, on the Atlantic
coast of the United States half-tide level lies below mean sea-level by
about one-tenth of a foot while on the Pacific coast it is above mean sea
level by about half that amount.
The relation between half-tide level and mean sea-level at any point
depends upon the amplitude and phase relations between the various
constituents of the tide at that point. A formula expressing this relation
quantitatively in the harmonic notation has been given by Harris.t From
the formula connecting the two it becomes clear that half-tide level is
subject to a variation depenct~ng on the longitude of the moon's node,
with a period of 18.6 years. It is obvious, therefore, that although mean
sea-level and half-tide level at any point generally do not differ much,
the two terms cannot be used as synonymous.
If sea-level freed from the tide, as explained above, is derived for a
number of days it is found to vary from day to day. In New Yorl:
Harbor, for example, during, the winter, sea-level from one day to the
next may vary by more than a foot; and within any one month sea-level
for two different days may differ by more than two feet. Such changes
obviously are to be ascribed to variations in wind and weather, for it is
a well-known fact that a wind blowing towards the shore tends to raise
sea-level along the shore while a wind blowing from the shore tends to
lower it.
But not in winter only does sea-level vary from day to day. In summer,
too, it varies, though obviously not as much as in winter. During the
summer, sea-level in New York Harbor may differ from one day to the
next by as much as half a foot; and within one month sea-level for two
cliff'erent days may differ by a foot or more. This arises from the fact
that both wind and also variations in barometric pressure bring about
fluctuations in sea-level. Any arm of the sea may be regarded as a hu~,e
inverted water barometer: when the atmospheric pressure over this
arm of the sea rises) the level of the water will be depressed, and when
the pressure falls, the level of the water will be raised.
Owing to effects of wind and weather, sea-level exhibits considerable
'' This variation becomes
especially marked in regions subject to storms of great intensity, par-
ticularly those fronting shallow bodies of water. Thus during the year
1915 a severe storm raised the level of the sea at Galveston, Texas, about
10 feet above its normal level so that during that year the difference
between the highest and lowest daily sea-level was more than 11 feet.
differences as between one day and another.
OCR for page 53
CLEAN SEA-LEVEL
,53
In tidal risers in which there is considerable variation of' -l'resh-water
discharge, daily sea-level exhibits greater variation than along an open
coast, this variation being especially marked in the upper reaches of the
rivers. The Hudson River furnishes an example. From flee open sea-
coast to the head of tidewater on the Hudson is a distance of' about 1~0
nautical refiles. In the year 19a the difference between the highest awl
lowest values of daily sea-level at the places mentioned below were as
I'ollows: open coast near the entrance to New Yorl; Harbor, o.4 feet;
Fort Hamilton, within the entrance to New York Harbor, 6.0 feet.;
Albany, near the head of tidewater, 15.2 feet.
It is obvious that changes in sea-level from day to day must, in general,
be much the same at points which are near each other, and subject to
similar meteorological conditions. As will be seen later, advantage is
taken of this fact in determining the plane of mean sea-level from short
series of observations by correcting the sea-level derived from these obser-
vations to a mean value. Exactly how far two points may be separated
and still exhibit similar sea-level changes depends upon a number o:t'
factors. Within a long tidal river subject to considerable variation in
fresh-water run-off', the changes in daily river level may be quite different
:I'or points relatively near each other. But on the open coast and in tidal
waters not sub ject to large variations in fresh-water discharge, the changes
in daily sea-level resemble each other closely over areas of' considerable
extent.
Figure ~ gives, diagrammatically, the daily heights of sea-level for
the month of April, 1923, at five stations on the Atlantic coast from
Portland, NIaine, to I'ernandina, Florida. A glance shows that at Port-
land and Boston the sea-level changes resemble each other closely. At
Atlantic City these changes are decidedly different from those of Portland
and Boston, and, although the curves for Charleston and Fernandina
resemble each other, they differ from the preceding curves.
Examining the locations of these stations it is found that, though
Boston lies about 100 miles south of Portland, both harbors lie open to
the same arm of the sea known as the Gulf of Maine. Atlantic City is
about 250 miles south of Boston but lies in a different embayment of'
the coast; this fact, together with diff':erences in meteorological conditions,
makes the daily sea-level changes at the two places show but little
similarity. Charleston and Fernandina are almost exactly the same clis-
tance from each other as Atlantic City and Boston, but, lying in the same
embayment of' the coast, they exhibit similar chancres in. daily sea-level.
From day to day wind and weather may vary widely and thus give
rise to relatively wide variations in daily sea-level. But within a Onto
such variations obviously tend to balance out. Clearly, if we average the
OCR for page 54
a4
FIGURE OF THE EARTH
hourly heights of the sea over a period of a month, the level derived will
be a much closer approximation to mean sea-level than was daily sea-level.
Furthermore, such monthly heights of sea-level should show considerably
less variation than daily sea-level.
o
is lo /5 20 25 30
1 1 1 1 1 1 1 1 1 1 1 1 1
, ~ ~
1 is, ~ ~;\
~5
~? po _ ~
- ~ h~r/es 'cat
Fernand/na
~ A I/f~nt/f: ~/-tL
\~
FIG. 1. Daily sea-level, Atlantic coast stations, April 1923.
An example o:t' the variations to which monthly sea-level is subject
is shown in Fissure ~ for the same stations, for which Figure 1 illustrates
the variations of daily sea-level. The diagrams give the monthly hei,~,hts
of sea-level for each of the months of the years 1"2:3 anl 192-~. For
Fernand;~-~a the plotting, stops at the end of J~une 1924, the station
OCR for page 55
IDEA SEA-LEVEL
having been discontinued at that time. It is seen at once that although
the monthly sea-level does not vary as much as daily sea-level, neverthe-
less it shows a relatively wide variation. From month to month seat-level
varies several tenths of a foot and within a year the monthly height of
sea-level may rotary by as much as a foot.
/923
Jan ~ Or Ju/u
~ 1 1 1 ~1 i 1 ~ ~ 1 ~ ~ 1 1 ~ 1 1 1 1 ~ 1
MA ~
A, Porf/~nd
Feet
I
/92~
Oct Tom A,c r ua/y Oct Dec
Boston A
~ i
At/~n tic cite ~
~-q
:\Vl~
/ Q \ o
1
~/~ j >; ~C~ --ton
cowl
1~
Fern c~ndin~
FIG. 2.-Monthly sea-level, Atlantic coast stations, 1923-1924.
For daily sea-level Figure 1 shows that the variations at Atlantic City
are different from those at Boston and Portland. But for monthly sea-
level the curves of :Figure 2 show similar cl~arlą,es at the three stations
with regard to the larger variations. Indeed, with respect to these larger
variations there is considerable resemblance in all five of the curves of
the figure. In other words, the variations of sea-level from month to
month appear much the same over large areas.
At first glance the heights of monthly sea-level at any one station shown
in :Figure 2 appear to vary in haphazard fashion. A closer examination,
OCR for page 56
OCR for page 57
MEAN SEA-LEVEL
Whatever the causes responsible for bringing, about the annual variation
in sea-level it is reasonable to suppose that the features exhibited at any
place are representative for a considerable area in its vicinity. Observa-
tions bear this supposition out. Thus the annual variation of' sea-level at
Boston resembles closely that at Portland. Similarly, the annual variation
at Atlantic City, New Jersey, and at Baltimore, Maryland, resembles that
at New York, while that at Charleston, South Carolina, resembles clearly
that at Fernandina.
Within tidal rivers subject to wide variations in amount of run-off,
especially in the upper reaches, the annual variation may diiT'er consider-
ably from that at a near-by point along the open coast. This is due to
the fact that in the restricted channel of the river the variation in run-off
is the principal factor in the variation of level. Thus, while in New Yorl:
TIarbor at the mouth of the Hudson the annual variation in sea-level is
. .
as shown by the second curve of Figure 3, the high monthly stage coming
in the summer and fall, at Albany, near the head of' tide-water, the high
stage comes in April, coinciding with freshet conditions in the river.
For comparisons with the seasonal variation of' sea-level along the
Atlantic coast of' the United States illustrated in lTigure 3, there are
shown in Figure 4 the curves of annual variation at several stations on
the Gulf and Pacific coasts. Key West, Florida, Pensacola, Florida, and
Galveston, Texas, constitute the Gulf coast stations and San Diego,
California, San Francisco, California., and Seattle, Washington, the
Pacific coast stations. The curves for the three Gulf stations, though
they exhibit distinctive individual features, nevertheless resemble each
other in many respects. There is also considerable resemblance between
them and the curve for Fernandina. The curves for the Pacific coast
stations differ markedly from those for the Atlantic and Gulf stations;
and it is to be observed, too, that they differ considerably from each other.
Without pursuing this phase of:' the subject further it is clear that in
the variation of sea-level from month to month there is a large element
of' periodicity, and that this periodic annual variation at any place is
marked by distinctive local characteristics. Furthermore, at places near
each other, or more precisely at places within a given region subject to
similar climatic and meteorologic conditions, the annual variation is
much the same.
If' the height of' sea-level at any place is averaged over a year it is
obvious that the periodic annual variation is eliminated. Within a year,
too, the effects of varying meteorological conditions, which find reflection
in the changes of sea-level from day to day and from month to month,
will tend to balance out. Sea-level averaged over a year may therefore be
expected to give a much closer approximation to mean sea-level than
OCR for page 58
FIGURE OF THE EARTH
sea-level derived from a month of observations.
tions continued over a number of years bear this out, as may be seen from
an inspection of Inure 5 in which the yearly heights of sea-level at
The results of observa
Feef
2
Jan Fed tour Apr that June Join Auk Sent act //ov Dec
. 1 ~ 1 1 1- 1 1- 1 ~1 ,
hey wes7" >f \
Dolor b
of
_ _ P~7s~co/ct
~ - 'I
:<,,,,~/ Go//vesfon
oL ~
own Sun ~r~ncisco ~ my, O
\~
~in/ ~0
~ So/n D/eJo
FIG. 4. Annual variation in sea-le`-el' Gulf and Pacific stations.
New YOr~7 Galveston and Ball Francisco for a number of years are shown
in di.a~,rammatic form.
For New World and San Francisco :Figure ~ gives the heights of sea-
level for the 28 successive years from 1899 to 1926. For Galveston the
observations begin in 1.904, so that the :-early sea-level heights in the
-~,,u~e fun for the 23 year period from 1904 to 1926. For each dia~,ram
OCR for page 59
MEAN SEA-LEVEL
~9
the horizontal line represents mean sea-level at that place derived by
averaging the height of sea-level over the period of observations shown. As
a rule, it is seen that from one year to the next sea-level varies by about
~ tenth of a foot. At times, however, this variation may be as much as
a quarter of a foot or even more, as exemplified at each station shown in
Figure b.
Feet
0.5
0.0
1900 /905 /9/0 /9/5 1920 /925
I T T I T I I
/vevl/
it,
.
L
York
AFT
fit
y ~
l I I I T
~4
1 1 1 1 1 1
I
G>/~
_ yes ton
Get
~ L' l\
\~)1 San Fit
~ \
T ~
1
'
o/ncisco
FIG. 5.-Yearly sea-level. New Yolk, Galveston and San Francisco.
A comparison of the diagrams of Figure ~ brings to light the fact that
the variations in yearly sea-level at the three places bear no apparent
relation to each other. But if we compare New York with other stations
on the Atlantic coast of the United States, Galveston with stations off
the Gulf coast, and San lTrancisco with stations on the Pacific coast, we
find, as a rule, considerable resemblance in the variations of sea-level
from year to year. In other words, along ally extended coast line the
OCR for page 60
60
FI GURE OF THE EAR TH
variation in yearly sea-level is much the same over a wide area. :For the
Pacific coast this is illustrated in Figure 6 by the curves of variation
of yearly sea-level for San Francisco and Seattle.
A glance at Figure 6 shows that notwithstanding the fact that Seattle
.~ Alp ~ro~r~icr>~ ore Mars tenon r;r)~) miles snort the variations in sea
CUll~L Call ~1 ~11~1~ ~ ~ ~ ^~^ ~^
~ W 1 ~ ~
level from year to year are In large measure similar. Not that. these
changes are exactly the same; but when sea-level during any one year its
at a high level phase at Seattle it is, as a rule, also at a high level phase
at San Francisco; and similarly with a low level stage.
Is the variation in seat-level from year to year accidental, or is it
subject to more or less periodicity? Glancing, at Figures ~ and 6 there
1 1 1
Feet
0.5 _
0.0 -~
/900 /905 /9/0 /9/5 /920 /925
1 1 1 1 1 1
Seo/t
+/e
l
/
t
I I I I I I I I I M1 1 I- T
'\1 \~
\ All/ ~
A ! ~ ~
' Sari ~,~
FIG. 6. Yearly sea-level, Seattle and ,S;~n Francisco.
appear to be evidences of cycles with periods of something like Tour years
and nine years respectively. Unfortunately, however, there is not a
sufficient body of data from which to draw definite conclusions in the
matter.
CAUSES OF VARIATION
The larger variations in sea-level, whether from day to day, montn
to month or year to year, are undoubtedly to be ascribed to changes in
meteorological conditions, such as barometric pressure, wind, and rain-
fall. bVit.h regard to barometric pressure, a first approximation to the
resultant changes in sea-level may be easily derived from general con-
siclerat.ions, as follows. Mercury is 13.2 times as heavy as sea water; hence
.
.,
OCR for page 61
lIEAN SEA-LEVEL
61
a change in local barometric pressure of one inch should be reflected by
an inverse change of 13.2 inches in the local level of the sea. In round
numbers, therefore, the chance in sea-level in feet should be inversely
as the change in barometric pressure in inches.
The relation of the change in sea-level to change in pressure has been
investigated at a number of places. Nearly a century ago the French
hydrographer :T)aussy tabulated the sea-level at Brest for different local
barometric pressures and found the value 14.? as the ratio of change
of sea-level to change of barometer. A few years later Sir John Lubbock
obtained a value for this ratio of 11.1 for Liverpool and 7.0 for London.
From observations made on his Arctic expedition at Port Leopold in the
Arctic Archipelago in 1848, Sir James Foss found the ratio to vary from
11.6 to 13.~. From six years of observations at Boston, Massachusetts,
NYm. :Ferrel in 1873 found the ratio to be 7.3.
~ review of these earlier investigations and of the subsequent work
to the year 1018 is given by Sir Charles Closed Here it will be sufficient
to mention only those of more recent date. In 1924 Alfred Wegener
discussed observations made by him during, the winter of 1907 on the
northeast coast of Greenland, from which he found the ratio of change
in sea-level to cha.n>,e in barometric pressure to be from i! to 12. In the
same year, from a comprehensive study of observations at seven stations
in the British Isles, A. T. Doodson found this ratio to vary from 6 to 13,
and Ogura, from observations at a number of small islands in the western
part of the North Pacific, found it to vary from 12 to more than 30. In
1925 Hessen discussed the observations made at the winter station of the
German South Polar Expedition in the Gauss in 1902 and found the
ratio to be 12.
Absolute agreement between the observed value for the above ratio and
its theoretical value cannot, obviously, be expected. In the first place,
other factors enter which must be evaluated, such as wind and river
discharge. And in the second place, the change in level must correspond,
not to the local changes in pressure, but rather to the difference between
local pressure and the pressure out in the open sea. In other worcls,
changes in sea-level are to be correlated with pressure gradients. This
procedure was introduced by Witting in 1918, and when this method
is employed the observed ratio tends to approximate the theoreti cat
static ratio of 13.2. In effect, too, the use of pressure gradients intro-
duces correction factors for the wind.
The effect of wind on seat-level has been investigated at a number of
places. By correlating the observed wind and tide on the coast of Holland
F. L. Ort.t 4 in IS07 arrived at a formula for the eject of the wind in
terms of velocity and direction. More recently Harold Jefireys,5 by treat
OCR for page 62
~2
FIGURE OF THE EARTII
in', mathematically the question of the effect of:' a st-eacly wind on that
sea-level near a straight shore, arrived at general formula -l'o~: this
special case.
An interesting phase of the effects of wind and pressure on sea-level
leas to do with the time element. Ferrel had noted that at Boston changes
in sea-level anticipated changes in barometric Pressure. In lairs paper on
. . . . ~ , . . .
the meteorological pertur~a.~ons of sea-level and tides, Doodson 6 dis
cusses this question briefly and suggests that such anticipations of'
vie
changes In atmospheric pressure are probably due to the different rates
with which disturbances travel through air and through water.
:From the preceding discussion it is clear that. in so far as the variat.;on`,
in daily seat-level are concerned, the effective causes are to be found
primarily in the variations of wind and of barometric pressure. lit
places within the influence of rivers carrying, the drainage waters :t'ron:~
large areas, the variation in river discharge is also a -factor of importance.
For the change in sea-level from month to month it appears reasonable
to fool; to the same causes that were -~:'oun.d responsible for tile ch.a~.~oe
in level from day to day. But the variation of' level frown month to month
exhibits a large element of periodicity. Can we :6nd a like periocl.;c
variation in atmospheric pressure or in wind to account for the annual
variation in sea-level?
If we examine the annual variation ill atmospheric pressure at ally
place along the coast it is found to have a somewhat similar character
to the variation In sea-ievet, In so far as phase is concerned; but this
~l~nil~l `~nrinti~n in nro~llrn ;q so small as to be suite inadequate to
~1114~' · ~ ~ V ~ ~ ~ ~ 1 ~
account for the annual variation in sea-level. For example, the atmos-
pheric pressure at New York is, as a rule, highest in the winter months
and lowest in the summer months. This, therefore, corresponds to low
sea-level in winter and high sea-level in summer. But the difference
in pressure as between winter and summer is only one-tenth of an inch,
which would account for an annual variation of but a little more than
an inch in sea-level, or less than 20 per cent of the observed periodic
variation. In this connection, however, it is of interest to note that
an harmonic analysis of the annual variations in sea-level and in atmos-
~heric pressure at New York gave evidence of the existence of like
components with periods of a year, a half a year, a quarter of a year, acid
a sixth of' a year.7
In attempting, to correlate the annual variation in sea-level with the
seasonal variation in direction and force of the wind, the problem becomes
complicated when the attempt is made to relate them quantitatively. In
certain places, as for example in monsoon regions, the wind must be an
important factor in bringing about the annual variation in sea-level.
OCR for page 63
~\ =~-~[
~ a
on
Ibus, P. 8. Omit Onus ~ very close correlation Between the nub vari-
ations in se~-level ~] in the elective velocity and direction of the ~in]
in the B~ of ~eng~1~0 also in the Arabian Seam Bowever, ~ is only
necessary to refer hack to Figure 3 ~] Dote Ant ~11 along the Atlantic
coast of the Pnited States ~ very roIlsiJer~hle cage in se~-level takes
place Between the months of October and December, notwithstanding the
fact that at grab of the stations the Gino during these months is Irons
, . . . .
the same phenol 1ng ulTectlon.
On investigating the erects of the various causes that m~> he elective
in Bringing about the Inn variation of se~-level on the coast of Japan,
\o~itsU and Ok~moto concluded Ant the primary I~ctor is the se~son~1
variation in the demise of sea mater Brought about by cb~nges in temper~-
ture an] s~linit>.° Next in importance was the Satiation of barometric
pressure. Together these two ejects were fonn] to Coconut for very nearly
all of the actually otae~ve] ~DnU~1 variations in se~-level at the sin Stations
OD the coast of Japan investigate].
It is to be note] further abut in regions of strong nontiJ~1 currents
the e~rth~s rotation brings about ~ force Enrich is eJective in distn~ting
ae~-le~cl. Ibis Iorce, tag so-c~llc] deRecting force of the ebbs rotations
tends to msLe the Cater on the right-b~nd bank of ~ stream (looking
in the direchon of motion) biter in the northern bem~pbere and lover
in the southern bemis~bere. Thence, Where seRsoD~l VRTi~tioDs in the
velocity or direction of nontid~1 currents occUr, se~-level cages will take
place ~ccordin~y.
In regal] to the variations in se~-level Irom bear to dear, it m~ be
said abut these UDdoubtedly reRect cages in the yearly values of such
factors as barometric pressures wiris, nontiJ~1 currents, and temperature
and density of sea mater. Go quantitative studies of this pose of the
quest appear to bane been makes tat the causes abut bring about the
gaily and annul variations in se~-levet whim mere considered abodes
may reasonably Be invoked to account for the variations from gear to gear.
As Ads noted TO connection limb the discussion of this variation it is
region~1 and not ~ loam pbenomenon, exhibiting similar cb~cteriatirs
over large areas. All along the Atlantic coast of the Plaited State the
variation in se~-level Irom gear to gear is mUcb the same, sn] ~ simian
statement holds with respect to the P~ciCc coast. D,Arcy W. Ibompson
found tat this variation lass mUcb the same on the coast of great Britain
as on the germ ~nisb ~d Svedisb co~sts>°
In ascribing tag variations in se~-level at gay point to variations in
meteorologir~1 coIIditions and in the pb~sic~1 conditions of the sea mater,
it is tacitly assumed that the mean level of the sea as ~ Bole ~em~Tns
constant. BUt Any not this mean level of the sea itself Be subject to
5
OCR for page 64
~4
FIGURE OF THE EARTH
variations ? In answer to this question it may be observed that a change
in the mean level of the sea may arise either from a change in the volume
of the ocean basins or from a change in the volume of the ocean waters.
Earth movements may be cited as a cause adequate to change the volume
of the ocean basins. Ancl as causes that may bring about changes in
the volume of the water the following may be mentioned: increase of
water through volcanic action or through decreased glaciation; decrease
of water consequent on chemical binding during the alteration of rocks
or on increased glaciation.
There can be no question but that during geologic time such changes
in the mean level of the sea have taken place consequent on the operation
of the causes enumerated. Daly ii has directed attention to the probability
of a general lowering of the mean level of the sea, during the humar~
period, of about 20 feet. However, in view of the enormous volume of
the ocean waters, changes in the mean level of the sea must be extremely
small even over periods measured in scores of years. And in the problem
of the determination of mean sea-level as a datum plane, the variations
in the mean level of the sea need be considered only in connection with
periods measured in centuries.
THE DETF,RMI~- XTION OF MEAN SEA-LEVEL
In view of the variations to which sea-level is subject, the determinations
of mean sea-level involves two different problems. The first is, how lone,
a series of observations is required to give an accurate determination of
mean sea-level at any point aloe, the coast? The second problem is,
how can the sea-level from a short series of observations be corrected to
a mean value ?
It is clear that, as a general rule, the longer the period of observations
the closer will the value obtained for sea-level approximate mean sea-
level. In connection with tidal work a period of 19 years is considered
as constituting a full tidal cycle, for during this period of time the more
important of tidal variations will have gone through complete cycles.
It is therefore customary to regard results derived from 19 Rears of tide
observations as constituting mean values. Hence sea-level derived from
~ 9 years of observations has frequently been taken as constituting a
primary determination of mean sea-level and as giving, accurately the
datum of mean sea-level.
:For the practical purposes of datum plane determination, 19 years
is a considerable period of time. Cannot the period necessary for securing,
an accurate determination of mean sea-level be shortened? It will be
recalled that in our consideration of the variation in sea-level front
year to year, which is illustrated graphically by Figures ~ and 6, there
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MEAN SEA-LEVEL
65
appeared evidences of a cycle with a period of something like nine years.
This means that a close approximation to mean sea-level may be derived
directly from observations covering a period of nine years. Determina-
tions of sea-level front observations covering periods of nine years or
more may be denominated primary determinations; those based on less
than nine years may be called secondary determinations.
Very satisfactory secondary determinations of mean sea-level may be
derived from observations coverings, periods of from one to three years,
by taking advantage of the fact that the variation in sea-level from year
to year is much the same over considerable areas. By comparing with
simultaneous observations at a station at which a long series of observa-
tions is at hand, corrections may be derived for reducing the secondary
determination of sea-level to a mean value. An example will make this
clear.
Suppose that at the beginning of 1917 it had been desired to secure
as accurate a determination of mean sea-level at San Diego, California,
as possible from one year of observations. A tide gauge would have been
put in operation and the hourly heights of the tide averaged throughout
the year, and sea-level that year would have been derived as reading 6.44
feet on the fixed tide staff used in connection with the tide observations.
:For that same year sea-level at San lTrancisco read 8.48 feet on the tide
staff used at that place. But from 19 years of observations covering the
period from 1899 to the end of 1917, mean sea-level on that same staff
read 8.~5 feet. Hence seat-level for 1917 was 0.07 foot below the mean
value for the 19-year period. And though San Diego its about. 600 miles
distant from San Francisco the variations in seat-level from year to tear
must be much the same at the two places. Therefore, to correct the 191rY
value of sea-level at San Diego to a mean value, a. correction of - 0.07
foot is indicated, which gives the determination of mean seat-level at
San Diego as 6.51 feet.
Had the observations at San Diego been made the following year, the
height of sea-level on the same staff would have read O.69 feet or 0.26
foot higher than the year before. At San lTrancisco, seat-level in 19:18
read 8.70 feet. Comparing this latter height with the height of meaner
sea-level of 8.~5 feet, a correction of -0.15 foot is indicated. Applyin,
this correction to the 1918 sea-level value of 6.69 feet at San Diego, the
value determined for mean sea-level is 6.~4 feet.
At San Gino there are continuous observations covering, the 19-year
period from 1906 to 192.~. The clirect primary clet.ermination of mean
sea-level from this 19-~rear series gives it as 6.~4 feet on the staff. Sea-
level for 1917 therefore differed by +0.10 foot from the mean sea-level,
and that for 1918 by -0.10 foot. By comparison with simultaneous
OCR for page 66
Representative terms from entire chapter:
barometric pressure
66
FIGURE OF THE EARTH
observations at San Francisco, mean sea-level valises. are derived drool
each of these years of observations which in the one case agree exactly
with the direct determination of mean sea-level and in the other case
differ by but three-hundredths of a foot.
It is to be observed that, in general, it may be tal~en that when corrected
by simultaneous observations at some suitable station not too -far away,
a year of observations will give a mean sea-level determination correct
to within 0.05 foot and -f:'our years will give it correct to within 0.02
foot. To derive a satisfactory value of mean sea-level from one month
of observation, care must be taken to choose a comparison station that
is subject to a like annual variation in seat-level. NVhen so compared, a
month of observations will give mean sea-level correct to within 0.1 foot.
And even one dater of observation, if corrected by comparison with a
suitable near-by station, can be depended upon to give mean sea-level
correct within a quarter of' a -foot.
THE MEAN SEA-LLY]3L SURFACE
In the introductory paragraphs to this paper attention was clirectecl
to the fact that, starting with mean sea-level at a given initial point,
~,eodetic and geographic mean sea-levels may or may not coincide. In
other words, the surface of mean sea-level as determined directly from
observations may not he an equipotential surface. Thus Jolly calls atten-
tion to the I'act that precise leveling in Great Britain shows that from
Newlyn on the English Channel to Dunbar on the North Sea-an air line
distance of about 400 nobles, but twice that distance along, the coa.st-
`~,eodetiG and '~eo',raphic Clean sea-level diverge 0.81 foot.1'' Avers in a
recent study gives the results of precise leveling in the United States
which show deviations between geodetic and geographic mean sea-level
of very nearly ~ -feet as between tl~e Atlantic and Pacific coasts.
~ r ~ ~ · ~ 1 · I 1_ _
The i'act that the mean sea-level surface cteterm~nect oy averaging ~e
varying height of tl~e sea and the sea-level determined by geoclet.ic levelings,
cl.o not coincide means that `~,eo~,raphic mean sea-lex-el does not define ~
strictly level surface. This is not surprising since this mean seat-level at
any point reflects the net or resultant effects of climatic and meteorologic
conditions, which clearly are different at different places.
The deviations of' the mean sea-level surface from a level surface are
small, but they introduce a complicating, factor in the ~,eoclesist's work
of spreaclin~ nets of precise level lines over large areas. Indeed, it is this
leveling, T.': the ~eo~lesist that brings out both the l'act of the deviation
~.~1 its n~,~itt-~
MEAT!; SEA-LEVEL
RBEERENCES
67
1. Harris, R. A. Manual~of tides, Part III. U. S. Coast and Geodetic Surv. Rept.
for 1894, p. 127-187 (1895~). Reference on p. 148.
2. Marmer, H. A. Tidal datum planes. U. S. Coast arid Geodetic Surv. Special
Publication No. 135: 1-142 (1927). Reference on p. 70~73.
3. Close, Sir Charles. The fluctuations of mean sea-level with special reference
to those caused by variations in barometric pressure. Geogr. J., 52: 51-58
(1918) .
4. Ortt, F. L. The effect of wind and atmospheric pressure on the tides. Nature,
5~;:80-84(1897).
5. Jeffreys, Harold. The effect of a steady wind on the sea-level near a straight
shore. Phil. Mag., 46: 114-125 (1923).
6. Doodson, A. T. Meteorological perturbations of sea level and tides. Monthly
Notices R. Astron. Soc., Geophysical Supplement, vol. 1, no. 4: 123-147
(1924).
7. Marmer, H. A. Tides and currents in New York Harbor. U. S. Coast and
Geod. Surv., Special Publication No. 111: 1-174. Reference on p. 47-48.
8. Galle, P. H. On the relation between wind on current and mean sea level in
the Indian and the Atlantic oceans and the adjacent seas. Proceedings of
the Koninklijl~e Al~ademie van ~ etenschappen te Amsterdam, vol. 28,
no. 10: 90~-918.
9. Nomitsu, Takaharu, and Okamoto, Motojiro. The causes of the annual varia-
tion of the mean sea level along the Japanese coast. Memoirs of the Col-
lege of Science Kyoto Imperial University, Ser. A, vol. X, no. 3: 12~161
(1927) .
10. Thompson, D'Arcy W. On mean sea level and its fluctuations. Fishery Board
for Scotland ScientificInvestigations 1914, No. 4: 1-45' (March 1915). Refer-
ence on p. 25~-31.
11. Daly, R. A. A general sinking of sea-level in recent time. Proc. Nat.
Acad. Sci., 6: 246-250 (1920).
12. Reference cited under No. 2, p. 63-64.
13. Close, Sir Charles. The second geodetic levelings, of England and TVales, 1912-
1921 (1922): 1-62. Reference on p. 34.
14. Avers, H. G. A study of the variation of mean sea-level from a level surface.
Bull. Nat. Research Council No. 61:56-58 (1927).
