Inverted barometer effects and steric changes effects on hydrostatic response of ocea

Welch, G.

English

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HYDROSTATIC SEA LEVEL CHANGES 
Summary Report by G . W e l c h  
I t  has long been realized by oceanographers that, because the force of 
gravity dominates other forces in the oceans, the long-time response of the 
oceans m u s t  be a hydrostatic one. (Water seeks its own level.) It is an  
open question. how short a t i m e  the long-time response may be applied to. 
The hydrostatic response of the ocean may be conveniently divided into four 
physical effects: glacial melting and rainfall response, steric changes, the 
inverted barometer, and the equilibrium tide. The equilibrium tide is not in- 
cluded i n  this  paper because the diurnal, semi-diurnal, and lunar fortnightly 
terms probably do not have hydrostatic response, and the higher terms are un- 
important. Changes in the total m a s s  of the oceans, although the largest 
amplitude single variation in sea surface level, are too slow to be of interest 
for satellite observations. So I shall treat only the inverted barometer effect 
and the effect of steric changes. 
' 
Consider the Navier-Stokes equation: 
d,u 
dt -=- =.--!- vp - v$ + frictional terms and non-conservative forces 
On the Earth, @ gives the sum of gravitational and centrifugal potentials, 
and there are no major non-conservative body forces. Assume that vertical 
velocities, accelerations, and frictional forces are negligible, where the unit 
vector i n  the vertical direction is defined by 
Then the vertical equation becomes 
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is nearly 
d 6  
Now on the Earth along any plumb line,  the magnitude of 
constant throughout the depth of the ocean. Let  d a  --- % t d ) v )  Or g(eJ qJ 
on the Earth Then along a given plumb line 
-
dir d ‘ 2  
(0 .9  ~ ~ ~ ~ ~ f l ~ ~ r ) ,  we can write 
This is the hydrostatic equation, For our purposes it is more convenient to 
write it as 
Now, a t  a given point on the  surface of the ocean, we integrate this 
-h to the surface at + ’y) 
+ h) 
and get 
between p ( -h ) and 0 ,  introducing an  
absolute error of about 1 c m  in height and a relative error of about c m .  
o( , the specific volume of sea water, is a function of pressure, salin- 
ity, and temperature and may be expressed as the specific volume under standard 
conditions plus the effects of deviations due to deviations in the three vari- 
0 ables . The standard conditions are p = 0 T= 0 C, S = 35%0. So 
O I . = 4 ( C 3 5 % o , ~ O C , O o a C i a q ~ J ) ~  Jp tS; + &  *&r oJ,,p+d;,p*6;,Tp 
If you choose -h such that p ( -h) is a constant in t ime ,  then the integral of the 
first two terms gives a constant which may be used to determine a zero point 
The remainder of the terms are called d 
experimentally determined that &s,xp .- a -is:.negligible. So 
or the steric anomaly. It has  been 
I *. 
J. .62 4 Sr 4 Js,r +dS,p Q &p 
The terms 6; *& +dr,ri’As,r are frequently called the thermosteric anomaly. 
This  gives the formula for experimentally determining the sea level anomaly 
due to anomalies in the structure of specific volumk of the water column. 
The quantity 9 7 is often called the dynamic height anomaly of the sea 
surface. 7 can be determined a t  different t i m e s ,  and variations of steric 
level computed as a function of t i m e .  The data required are values of temper- 
ature and salinity vs pressure (depth) a t  a given deep water station. 
The inverted barometer effect is the hydrostatic (steady state) response 
to a change of atmospheric pressure. Consider a column of fluid of density P 
from the reference depth -h to the free surface at pressure pm,, , In this 
case, we make a very s m a l l  error by assuming p =constant. The hydrostatic 
equation now is $ = - P g  
or integrating I &* ~ p ( -h) p - pg (r 4) 
*P by & p  will change "7 by "7 such that p y  Z- 
G7H P9 
Changing 
To a very close approximation, the sea surface is depressed by 1 c m  for 
every 1 mb. increase in atmospheric pressure. 
complete in a few days. 
This adjustment is essentially 
The observations of sea level are taken at tide gauges. These are 
located a t  the shores of continents and islands. Those of atmospheric pressure 
are taken a t  meteorological stations, which are usually located near major 
cities and airports. The pressure a t  these stations is then adjusted to sea 
level. Both of these variables are monitored several t i m e s  each day at each 
station, so that  monthly averages are likely to be representative of monthly 
averages of the variables. The temperature profiles are by necessity done in 
the  deep ocean away from the coasts. These are likely to be done at certain 
stations once every several months with bathythermographs a Temperature and 
salinity data are taken more seldom with hydrographic casts, These data are 
sparse enough that monthly averages over many years are about the best  that 
can be done, So the data are scarce in time and unevenly distributed in  space, 
4 
following the geographical, distribution of islands and the comfort zones of 
oceanographers. The results obtained, no doubt, are biased by the  un- 
evenness of the grid. 
In order to evaluate the  pressure term, the annual mean pressure cycle 
over the ocean mus t  be subtracted from the data before the inverted barometer 
response is calculated. If the spectrum of pressure variations is calculated, 
it contains much more high frequency power than the analagous spectra for 
the other variables. In several cases, it resembles a white noise spectrum. 
Both seasonal studies and cross-correlation studies show that the pressure 
effect is m o s t  important both annually and non-anually at higher latitudes. 
Seasonal studies show that in  high latitudes, pressure effects are more pro- 
nounced in winter than in  summer. This reflects what we know about the 
distribut'ion of pressure variations both in space and in time. 
The steric anomalies due to temperature variations are found to be 
largest in mid-latitudes, They are lower both in the tropics and in the arctic 
regions. In the mid-latitudes and the tropics, the annual and non-annual 
variations s e e m  to be of about equal importance. The particularly low value 
in the arctic regions is somewhat puzzling, as it implies either non-hydro- 
static response or a predominately salinity caused variation of the steric 
anomaly. 
In most parts of the oceans, salinity variations have little or no effect 
on steric level variations. Where they are important, however, they can be 
surprisingly large. The largest value is in the Bay of Bengal, where there is 
an  annual term of 41 c m .  They are also significant (greater than 5 cm.)  at 
some southern hemisphere stations In all cases I the significant salinity 
variations are connected with unusually deep temperature variations a 
5 
The total hydrostatic response at the t i m e  periods under consideration 
appears to agree very well with recorded changes of sea level over almost all 
of the oceans. There is a significant difference associated with coastal 
effects near some coasts. For periods of less than a year, the variations are 
pressure dominated by latitudes greater than 40 ,. and temperature dominated 
at lower latitudes. Results are summarized in the following table, 
0 
? 
EFFECT . HIGHEST LOWEST AVERAGE 
SALINITY 
TEMPERATURE 
PRESSURE 
TOTAL STERIC 
BIBLIOGRAPHY 
LaFond, E.C., "Variations of Sea Level on the Pacific Coast of the United 
States", Journal of Marine Research,& 17-29 (1939) 
hFond,E.C., Processing Oceanographic Data, H 0 Pub NO 614, U.S. N a v y  
Hydrographic Office, Washington D.C. (1951) - This is the standard 
cook book for processing hydrographic and bathythermograph stations 
It  also contain8 tablee of d . 
Listigen, Eugenie, and Pattullo, June, "The PrincipalFactors Influencing the 
Seasonal Oscillation in Sea Level" , Journalxof Geophysical Research, 
66: 845-852 (1961) 
Montgomery, R. B. and Wooster, W. S .: I "Thermosteric Anomaly and the Analysis 
of Serial Oceanographic Data", Deep Sea Research, 2: 63-70 (1954) 
Pattullo, June; Munk , Walter; Revelli , Roger; and Strong, Elizabeth, The 
Seasonal Oscillation in Sea Level:, Journal of Marine Research, 2:88.1156 
(1955) - This is the best source for a comprehensive treatment of the 
annual steric term and the recorded sea level. 
Roden, Gunnar I. , "On the Non-Seasonal Variations in Sea Level along the 
West Coast of North America',' ,"Journal of Geophysical Research, 65: 2809- 
2826 (1960) - Mr. Roden specializes in the statistical approach and is a 
wealth of information concerning correlations and power spectra. 
. Roden, Gunnar I . ,  "On Sea Level, Temperature, and Salinity Variations in  the 
Central Tropical Pacific and on Pacific Ocean Island", Journal of Geo- 
physical Research, 68: 455-472 (1963) 
Rossiter, J.R. , "Long Term Variations in Sea Level, The Sea Vol  I ,  pp 590-608 
Saur, J.F. T., "Study of Sea Level at Six Stations in the Eastern North Pacific 
Ocean:' Journal of Geophysical Research, 67: 2781 ff 
Stommel , Henry, "Varities of Oceanographic Experience" Science , February 
15, 1963, ~ ~ 5 7 2 - 7 6  4 
I 
Sverdrup, Johnson, and Fleming, The Oceans, pp 403-409. This is the oceano- 
graphic bible before lj941 


Hydrostatic sea level changes

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