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Glacial-interglacial mean sea level pressure change due to sea level, ice sheet and atmospheric mass changes
Palaeogeography, Palaeoclimatology, Palaeoecology (Global and Planetary Change Section), 89 (1991) 333-340
333
Elsevier Science Publishers BN., Amsterdam
Glacial-interglacial mean sea level pressure change due to sea level, ice sheet and atmospheric mass changes. M a r i e - A n t o i n e t t e Mdli6res a, P a t r i c i a M a r t i n e r i e b, D o m i n i q u e R a y n a u d b a n d Louis L l i b o u t r y u a Laboratoire de Spectrom~trie Physique, associg NRS, Universit~ Joseph Fourier de Grenoble, B.P.87, 38402 St Martin d'Hbres Cedex, France b Laboratoire de Glaciologie et G$ophysique de l'Environnement, CNRS B.P.96, 38402 St Martin d'Hbres Cedex, France (Received September 18, 1989; revised and accepted April 17, 1990)
ABSTRACT
Mdli~res, M.-A., Martinerie, P., Raynaud, D. and Lliboutry, L., 1991. Glacial-interglacial mean sea level pressure change due to sea level, ice sheet and atmospheric mass changes. Palaeogeegr., Palaeoclimatol., Palaeoecol., (Global Planet. Change Sect.), 89: 333-340. The change in the global mean atmospheric pressure between glacial and interglacial periods is evaluated at sea level. This change originates in a modification of topography and in a possible variation in the atmospheric mass. In this calculation the atmosphere is at hydrostatic equilibrium, and the parameters describing the glacial period are varied in a plausible range. The result, with constant atmospheric mass, is a mean sea level pressure decrease of 9-15 hPa linked with the degiaciation. The corresponding pressure change at the reference level corresponding to the present day sea level does not exceed one hPa. When considering only the chonge in the atmospheric mass, an increase which does not exceed 2 hPa is found, linked with the deglaciation.
Introduction
The Earth's climate has been oscillating between glacial and interglacial conditions during the late Pleistocene. Such changes correspond to global and large modifications in the physical and chemical conditions at the earth's surface. The best documented period on this respect is the last deglaciation which occurred between the Last Glacial Maximum (LGM) 18 kyr ago and the Holocene, when the mean surface temperature increased by some 4 - 5 ° K , the atmospheric composition experienced significant changes, (increase in radiatively active gases, like CO 2 and CH4, decrease in dust content,...) and the large ice sheets of the Northern Hemisphere disappeared (except for Greenland) resulting in a mean sea level increase of the order of 100 m. We focus here on the change in the 0921-8181/91/$03.50
global mean sea level pressure resulting from a change in surface topography (through sea level and ice sheet changes) and atmospheric mass linked with glacial-interglacial changes. Climatic conditions at glacial maxima have been simulated by General Circulation Models (GCM) during the recent past (see for example Gates, 1976; Manabe and Hahn, 1977; Manabe and Broccoli, 1985; Kutzbach and Guetter, 1986; Rind, 1987; Joussaume, 1989). Only a few published GCM's results give explicitely the difference between glacial and interglacial mean sea level pressures (for example Gates, 1976; Rind, 1987; Joussaume, 1989). The corresponding change is of the order of 10 hPa (i.e. about 1% of the atmospheric pressure) and depends of the prescribed sea level change. These models usually include the change of topography without considerig isostatic readjustment and
© 1991 - Elsevier Science Publishers B.V.
334
work at constant atmospheric mass. Following a simplified a p p r o a c h (by considering the a t m o sphere at h y d r o s t a t i c equilibrium) we estimate, here, this m e a n glacial-interglacial pressure change at climatic equilibrium, taking into account post-glacial isostatic rebound and possible changes in atmospheric mass. F u r t h e r m o r e , this simple calculation allows us to indicate how sensitive is the result to the different p a r a m e t e r s involved. I t is also interesting to note t h a t polar ice cores contain an information on the paleo surface elevations of the ice sheet when measuring the a m o u n t of air t r a p p e d in the tiny air bubbles found in the ice cores. This is because the air is t r a p p e d in the bubbles near the surface at the atmospheric pressure. T h e interpretation of air content in ice, in t e r m s of past elevations of the ice formation site, requires in fact a knowledge of the air pressure at sea level and the air pressure elevation gradient during the past ( R a y n a u d , 1983). T h e conclusions of the present work will, thus, help us when interpreting the results of the air content measured along the deep ice cores. We will first discuss the effect of a change in t o p o g r a p h y and then the effect of a possible change of the atmospheric mass on the mean global pressure. Some aspects of this subject h a v e been discussed by Loewe {1973).
Change in earth topography In the present p a p e r we consider the atmosphere to be in h y d r o s t a t i c equilibrium. This crude evaluation has the a d v a n t a g e of clearly showing the i m p a c t of the different p a r a m e t e r s and setting limits to this pressure change. For sake of clarity we point out t h a t within the h y d r o s t a t i c hypothesis the surface ocean pressure P o e , is equivalent to the global m e a n annual sea level pressure, PSLP, used in G C M ' s (which includes the fictitious air assigned to the volume of land surface above sea level); we therefore will refer mainly to this last notation. In a first time we estimate the glacial interglacial change of the h y d r o s t a t i c pressure at the respective sea levels. In a second time, we esti-
M.A. MELIEREs ET AL.
m a t e the change of this pressure at the well defined altitude of the present sea level. T h i s q u a n t i t y is a priori d e p e n d a n t of the e a r t h t o p o g r a p h y due to the fact t h a t the a t m o s p h e r e is a compressible fluid: the L G M ice sheet,s are situated at different altitudes from the corresponding oceanic melted w a t e r and therefore occupy an equivalent a t m o s p h e r i c volume of different density. T h e consequences of the ice sheet melting on e a r t h t o p o g r a p h y are changes in: --the height of p a r t of the continental surface through the change in ice sheets (with consequent isostatic adjustment}, - - the sea level through the i n p u t of melted waters (and consequent isostatic adjustment}, and change in gravitational field.
1. Calculation
T h e relation between the surface pressure at a given location, P~, and the a t m o s p h e r i c mass, m, is complicated and includes the ellipsoidal shape of the earth as well as the variation of g (the acceleration due to gravity) with altitude and latitude. This point has been investigated by Trenberth{1981). Nevertheless, in the present case where we are concerned only with the pressure difference between glacial and interglacial periods, we shall consider the e a r t h ms spherical and take g to be constant. We t h e n have:
mR =
Jearth surfaceP~ d S
(1)
W e evaluate this relation for glacial and interglacial conditions. A s s u m i n g t h a t the atmosphere is a t h y d r o s t a t i c equilibrium, the relation between pressure and altitude is dP
P
M~,g
-
R~
dz
(2)
M~ being the molar weight of air and R the gas constant. In the troposphere, the linear dependence of t e m p e r a t u r e with "altitude T( z I = T( z o ) - b( z
z o)
335
GLACIAL-INTERGLACIAL MEAN SEA LEVEL PRESSURE CHANGE
implies t h a t the variation of pressure with alt i t u d e is given by:
(Fig. 1), this relation can be expressed using Eq. 3 as a function of PSLP
,.,, , [ T ( z ) I ~ P( z ) = rl'z°J~ T----(~o) ,
mg = PSLP So¢ + 1 -
(31
To~
Scont
where:
gM~ s = bR
+ 1
(4)
W h e n considering the simplified t o p o g r a p h y
_ _rzi='
Sice
(5)
This last relation enables us to calculate PSLP2 a t the glacial epoch (index 2) as a function of PSLP1, the one at interglacial epoch (index 1), if the respective elevations, areas, temperatures, lapse rates and atmospheric masses are known. This calculation is performed for the following numerical values and hypotheses: T h e atmospheric mass is t a k e n as constant. A possible change of this m a ~ is discussed in the next paragraph. We consider a global warming of 5 K (estim a t e d from Rind and Peteet, 1985) between the glacial and interglacial period. T h e sensitivity of the pressure variation to the t e m p e r a t u r e is estimated b y considering different cases of warming (between 10 o and 0 ° C). - - T h e present day mean air t e m p e r a t u r e at sea level is 290 K (Oort, 1983). --We also consider d i f f e r e n t lapse r a t e scenarios: b I = b e = 6.5 K kin-1 and b 1 = 6.5 K k m -1, b2 = 7.5 K krn -1. This last case corresponds to a drier glacial atmosphere. -T h e sea surface is t a k e n as constant and equal to the present d a y value: 361 × 106 k m 2. I t means t h a t we neglect the decrease (of the order of a few percent) in t h e sea surface due to
T h e difference in cryosphere between the two epochs is characterized here b y the existence at the glacial period of a single fictitious ice sheet which has since melted. This fictitious ice sheet is assumed to have uniform thickness, hice, and to occupy a surface area Si~~. We divide the surface of the e a r t h into three parts: one relative to the oceans, one to the continents (excluding the area where the L G M ice sheet extends, b u t including the present ice sheets); and one to the L G M ice sheet. Each p a r t is characterized b y its surface area (So¢, Scont , S i c e ) , its mean elevation (_Zoo, Zcont, Zice) and its mean surface pressure (POP, PcP, PIP)- This last q u a n t i t y depends on the surface distribution with altitude. Nevertheless it can be shown t h a t t h e y can be closely approximated b y the pressure at the m e a n altitude. Moreover, this approximation is particularly justified in the present case of pressure change between two epochs where S¢o~t has the same surface distribution with altitude. For each epoch, the atmospheric mass is related to surface pressure by (1). We have m g = P o p S o c -{- P c p S c o n t -F P i p S i c e
To¢
l
,z.
hice 1":,':,':,~'~,':,':,"[~
L Zcont1
,-,-'-,'-:-,'-:-X-:,,',,',~, oc
i:!:!:!:!:i:!:{!:?:i:!:i:i ,:,~,:,:,~,:,:~,:,~,:,:,:,
",'"'"','':'C';':':':':
~ Zz0c2 1~
,
Sot2
,
,
,
,
,
Scont2
,
,
,
,
,
,
:::::::::::::::::::::::::::
.
Sice2
Socl
ii?i?i?i?iiiii iiiiiiiiiii_ . _I_ Scont1
Sice1
Glacial Interglacial Fig. 1. Notations used for the simplified topography of the Earth at interglacial (subscript 1) and at the glacial period (subscript 2).
336 the emergence of the continental margins: as the altitude of this emerged land is only a few tens of meters, the surface of this land will be treated ms p a r t of the ocean. - - T h e equivalent oceanic melt water thickness, h, (originating from the melting of the glacial ice sheet) is t a k e n to be the m e a n value given in C L I M A P (1981), i.e. 130 m. We also consider the cases of 100 m and 160 m. - - T h e glacial ice sheets which melted during the deglaciation are simulated, as mentioned previously, by a single fictitious ice sheet with a simplified shape, occupying the surface area (Sic e) with a c o n s t a n t thickness. T h e ice volume is deduced from the melt w a t e r volume, assuming an ice density of Pice = 0.92. Deduced from this ice volume the surface area is 18 × 106 k m 2 implying a m e a n ice thickness of 2834 m and a value of 133 × 106 k m 2 for Scont. We let this surface area v a r y from 20 × 106 to 16 × 106 k m ~ in order to cover the plausible range of m e a n ice cap elevation. -T h e present m e a n elevation of the continent is estimated to be 811 m (deduced from Trenberth, 1981). --Accurate estimates of the elevation differences (sea level, continent, ice sheet) require a knowledge of the a d j u s t m e n t of the earth's crust to t h e redistribution of ice and w a t e r surface loads. Such an investigation implies complex calculations requiring hypotheses a b o u t the internal structure of the earth. A t t e m p t s have been m a d e to constrain b o t h the ice load and the E a r t h ' s response from the observed sea levels (sea for example Peltier and Andrews, 1976; Farrel and Clark, 1976; Peltier, 1988; Officer et al., 1988; N a k a d a and Lambeck, 1988). In the present calculation we evaluate the differences in elevation in the f r a m e w o r k of simplified hypotheses and show t h a t the final result is not sensitive to these hypotheses. We consider two extreme scenarios: (1) At the glacial period, continents and oceans were in isostatic equilibrium. Hence the m e a n elevation of the glacial ice sheet relative to the continent, (zie~2- Zoo,t2), is given by ( 1 p i c J r ) h i ~ , r being the a s t h e n o s p h e r e / w a t e r density ratio due to the bed-rock depression of
M.A. M E L I E R E S E T AI.
the ice load. Calculations are performed for r equal to 3.6 and 3. After melting, isostatic readj u s t m e n t of deglaciated surfaces and waterloaded oceans occurred and is complete at the interglacial period. Hence the m e a n elevation of the deglaciated area is the s a m e as the m e a n continental elevation. T h e oceanic crust being at isostatic equilibrium, the difference in sea level, (z(~l -5,~2), is equal to (1 .... l f l r ) h (the oceanic melt w a t e r thickness). (2) We also consider the extreme scenario of zero isostatic a d j u s t m e n t , either at t h e glacial or interglacial period. Consequently the sea level change, (5(~ 1 -Zo¢2), is equal to the equivalent oceanic m e l t w a t e r thickness and the quantity, (Site2- 5co, t2) ) is equal to hi(.~, the thickness of the fictitious ice sheet. -We do not consider the change in sea level due to the t h e r m a l expansion of the oceanic water, which can be roughly e s t i m a t e d to be of a few meters. We have tested t h a t including such a change does not alter the final conclusion. -As we are concerned only by the m e a n sea level we do not include the effect of a change in the gravitational field originating in the change in the mass distribution: this will affect the sea levels surrounding the continents where glacial ice sheet will melt b u t will not change the m e a n sea level. 2.
Results
We first use the Eq. 5 in order to esimate the present global m e a n sea level pressure PSLP1,and compare it with the measured one. We use this calculation as a simple test of our set of p a r a m e ters. We obtain a value of 1011.5 h P a using an a t m o s p h e r i c mass of 5.136× 1011 kg as estim a t e d by T r e n b e r t h et al. (1987), t o g e t h e r with a g value of 9.81 m s- 2. T h i s estimation coincides very closely with the 1011 h P a of Trenb e r t h et al. (1981). T h e change in sea level pressure (PsL[~2PSLm), corresponding to the different cases mentioned above (and listed in the caption of T a b l e 1) is obtained from eq. 5. Results are given in T a b l e 1. If we t a k e the first scenario (results given in the first line of T a b l e 1), the pressure
GLACIAL-INTERGLACIALMEANSEA LEVELPRESSURECHANGE
337
TABLE 1 Mean pressure change between the interglacial (subscript 1) and glacial (subscript 2) period T2
h
Azo¢
Azi~
AP,~
AP2
AP(z = 0
(K)
(m)
(m)
(m)
(hPa)
(hPa)
(hPa)
285 285 285 290 280 285 285 285 285 285
130 100 160 130 130 130 130 130 130 130
94 72 116 94 94 87 94 94 130 94
2110 1623 2597 2110 2110 1965 1899 2373 2834 2110
11.4 9.0 13.8 10.8 12.1 10.7 11.5 11.3 15.0 11.5
11.5 8.8 14.2 11.3 11.7 10.6 11.5 11.5 15.9 11.5
-0.1 (1) + 0.2 (1) -0.4 (1) - 0.5 (1) 0.4 (1) 0.1 (2) 0.0 (3) - 0.2 (3) - 0.9 (4) 0.0 (5)
Notations: h: equivalent oceanic melt water thickness; Azoc = zo¢1- zo¢2: difference in sea level; Azice= Zice2 -- Zcont2: c h a n g e in the elevation of glacial ice sheet above continent: A P e , = PSLP2- P S L P I : pressure difference at sea level between the glacial and the interglacial period; AP2 = PSLP2- P ( z ~ 0)2: pressure difference occurring at the glacial period between the two altitudes corresponding to the glacial sea level and the interglacial sea level, (see t e x t ) . A P ( z = 0 ) = P ( z = 0 ) 2 - PSLPI: -pressure difference between glacial and interglacial period and present at the present sea level. The mean pressure changes are calculated with the following conditions: ( 1 ) : isostatsy holds with r = 3.6 (see text), deglaciated surface are of 18 x 106 km2, lapse rates of 6.5 K kin- 1, TI = 290 K; (2): as in (1) but r = 3; (3): as in (1) but Sic~ = 20 and 16 x 106 kin2; (4): as in (1) but no isostnsy adjustment; (5): as in (1) but b2 = 7.5 K krn -1.
d e c r e a s e a t sea level f r o m glacial to i n t e r g l a c i a l c o n d i t i o n s is 11.4 h P a . T h e s e n s i t i v i t y of t h i s r e s u l t to t h e d i f f e r e n t p a r a m e t e r s i n v o l v e d i n t h i s c a l c u l a t i o n is s m a l l : Changing the equivalent melt water t h i c k n e s s of + 30 m (i.e. t h e ice v o l u m e of + 23%) m o d i f i e s t h i s p r e s s u r e c h a n g e of + 1.2 h P a , Changing the other parameters in a plausible r a n g e ( t e m p e r a t u r e c h a n g e f r o m 0 t o 10 K , a s t h e n o s p h e r e / w a t e r d e n s i t y f r o m 3.6 t o 3, ice s h e e t s u r f a c e f r o m 20 t o 16 x l 0 s k m 2, i s o s t a s y or n o t , l a p s e r a t e f r o m 6.5 t o 7.5 K k m - 1 ) let t h i s c h a n g e v a r y b e t w e e n 10.8 a n d 15.0 h P a , -G l o b a l l y t h e r e s u l t s show t h a t d e p e n d i n g o n t h e v a r i o u s a s s u m p t i o n s , t h e difference i n sea level p r e s s u r e v a r i e s i n t h e r a n g e of 9 - 1 5 h P a w h e n l o w e r i n g t h e sea level b e t w e e n 72 a n d 130 m, a l o w e r i n g w h i c h c o r r e s p o n d s t o a m e a n t h i c k n e s s of t h e m e l t w a t e r l a y e r c o v e r i n g t h e r a n g e of 1 0 0 - 1 6 0 m. T h e s e r e s u l t s a r e of t h e s a m e o r d e r as t h e o n e s o b t a i n e d using the GCM's. For example, Gates
(1976) f o u n d a 12.7 h P a c h a n g e i n PSLP for a 85 m sea level lowering, R i n d (1987) a 11.5 h P a c h a n g e for 120 m, a n d J o u s s a u m e a 14.2 h P a c h a n g e for 150 m. T h e c o r r e s p o n d i n g e s t i m a t i o n w i t h i n t h e h y d r o s t a t i c e q u i l i b r i u m gives respect i v e sea level p r e s s u r e s c h a n g e of 10.1 ± 1 h P a , 13.7 ± 1 h P a a n d 15.7 ± 1 h P a . T h e u n c e r t a i n t y o r i g i n a t e s i n t h e p l a u s i b l e r a n g e of p a r a m e t e r s (T, b, S i ~ ) g i v e n i n T a b l e 1. T h e c h a n g e s calculated by the GCM's include both change in topography and in atmospheric circulation. Thus t h e difference b e t w e e n t h e i r r e s u l t s a n d o u r ' s comes f r o m t h e d i f f e r e n c e i n t h e w a y t h e topogr a p h y is r e p r e s e n t e d a n d f r o m t h e i n f l u e n c e of t h e c h a n g e i n a t m o s p h e r i c c i r c u l a t i o n . T h e comp a r i s o n of t h e r e s u l t s s h o w s t h a t s u c h differences do n o t exceed a few h P a . We have estimated the change in the hydros t a t i c p r e s s u r e a t t h e r e s p e c t i v e sea levels. I t is sometimes more relevant to estimate the change i n t h e h y d r o s t a t i c p r e s s u r e a t t h e a l t i t u d e of t h e p r e s e n t sea level ( t h a t we will n o t e z = 0); we
338
call it z~P( z = 0). T h e mean pressure P ( z = 0 ) 2 , at LGM, at altitude z = 0 is given by Eq. 2, as a function of PSLP2" T h e q u a n t i t y P ( z = 0)1, corresponding to the interglacial period, is equivalent to PSLP1- T h e change A p ( z = 0), given in T a b l e 1, is very small (between 0 and 1 hPa), w h a t e v e r different hypotheses are adopted (isostasy or not, different melt ice volume, different ice sheet surface, different t e m p e r a t u r e lapse rate, different temperature). T h i s can be interpreted in the following manner. T h e ice sheet relative to the glacial period will occupy an equivalent air volume V with a density p fixed by the t e m p e r a ture and the pressure at the elevation range of the ice sheet. At the same time, ocean evaporation liberates a volume V ' which is filled with air having a density p' fixed by the sea level t e m p e r a t u r e and pressure. T h e altitude of the ice sheet formation is such t h a t the air mass displaced by the growth of the ice sheet (pV) closely compensates the air mass occupying the sea level free volume (p'V'). In other words, the change of volume due to the w a t e r density difference ( V ' = 0.9V) is closely compensated by the air density difference between the m e a n ice sheet altitude and the sea level (p' > p). We now e s t i m a t e the order of m a g n i t u d e of pressure change related to a change in the a t m o s p h e r i c mass.
Change in atmospheric mass A change Am in the atmospheric mass will induce a change in the m e a n sea level pressure, which can be obtained from Eq. 5: A m / m = A PsLP/PsL P. This change is estimated here assuming a present atmospheric mass of 5 x 10 is kg ( T r e n b e r t h et al., 1987). T h e main causes for a change in a t m o s p h e r i c mass between glacial and interglacial period a p p e a r to be degassing of the ocean due to warming, changes in a t m o spheric gaseous constituents (H20, 02, CO 2. . . . ) and liberation of t r a p p e d air by ice melting. We assume no change in outgassing from volcanoes.
M.A. M E L I E R E S E T AL
gible. We first consider a global w a r m i n g of 5 K in the 200 m oceanic mixing layer (285 K to 290 K). T h e change in solubility of N 2 and O~ implies a degassing of 8 x 101:* kg using the solubility coefficients for sea w a t e r given by Weiss (1970) and corresponds to an increase in the m e a n preasure of 0,016 hPa. If we consider the extension of this new surface equilibrium to the bulk of the ocean (neglecting the existence of an internal sink or source for N~ and 02) i.e. taking into account a time long enough c o m p a r e d to the t u r n o v e r time of oceanic waters, then the increase of 5 K would imply a degassing of 0.3 hPa. These quantities are likely to be an overe s t i m a t e because the associated changes in the mean oceanic t e m p e r a t u r e are unlikely to be so large.
Change in gaseous constituen£~ Modifications in the oceanic and biosphere reservoirs on the t i m e ~ a l e of glacial-interglacial changes m a y act as sources and sink for various constituent.s of the a t m o s p h e r e (CO2, CH4, Ou . . . . ). Indeed, analyses of the air enclosed in ice cores indicate concentration changes of a b o u t 80 p p m v for CO 2 (see for instance Barnola et al., 1987) and of a b o u t 0.3 p p m v for C H 4 ( R a y n a u d et al., 1988; Stauffer et al., 1988). T h e implication of these changes in these m i n o r a t m o s p h e r i c constituents on the a t m o s p h e r i c pressure is small and account respectively for pressure increase of 8 10 2 and 3 10 4 h P a between t h e glacial and interglacial time. Also models which describe changes in carbon cycling over glacial-interglacial changes predict a modification in the oxygen (a m a j o r a t m o s p h e r i c constituent) concentration: the glacial 02 concentrations could h a v e been higher by up to a factor 1.006 t h a n the interglacial 02 level (Sowers et al., 1989). T h i s would lead to a m a x i m u m decrease of 1.2 h P a of the mean pressure between glacial and interglacial periodes.
Air liberated [rom ice melting Oceanic degassing We consider an u p p e r limit of this effect and show t h a t the induced pressure change is negli-
T h e volume (STP) of air t r a p p e d in polar ice is a b o u t 10% of the ice volume ( R a y n a u d and Lebel, 1979). T h e volume of m e l t ice is e s t i m a t e d
339
G L A C I A L - I N T E R G L A C I A L M E A N SEA L E V E L P R E S S U R E C H A N G E
(see above) to be 51.2 × 106 km 3. Taking into account the altitude and temperature at which the air bubbles were formed, this corresponds approximately to an additional 4.4 × 10~ kg of air in the atmosphere and causes an increase of 0.9 hPa on going from glacial to interglacial conditions.
Cha~ge in water vapor The atmospheric water vapor content, e(w), is strongly dependent on the surface temperature of the Earth, T~. The calculation of e(w) is not straightforward, but the correlation between e(w) and T~ can be estimated for the present l an d - water distribution at the surface of the E a r t h by using the results of two large scale observations on the present state of the Earth, each concerning one hemisphere. T hey are related to the monthly average of e(w) and T~ for each hemisphere separately and therefore include the extreme climatic conditions of winter and summer. As the hemispheres are weakly coupled with a coupling time scale of about a month, we can treat these results are being independent. We will first consider the estimation of the monthly surface temperature (land and ocean), for each hemisphere made by Oort (1983). The monthly atmospheric water vapor content is given by Trenberth et al. (1987). Both e(w) and T~ present extrema at the same time (around February and August) and have parallel yearly variations. Correlation existing between e(w) and T~ is used to estimate the relation A e / A T for each hemisphere within the small range of temperature variation involved here. The difference between the monthly temperature extrema is 13.5 K for N.H. and 6.1 K for the S.H. Th e amplitude of the variation of the monthly atmospheric water vapor content is 1.45 hPa for the N.H. and 0.85 hPa for the S.H. These values lead to a variation of 0.11 hPa K -1 for the N.H. and 0.14 hPa K-1 for the S.H. The difference between the two hemispheric gradients reflects mainly the difference in the l andocean distribution (the larger free water surface of the S.H. leading to a slightly stronger gradients). A mean gradient of 0.12 hPa K -~ repre-
sents the global E a r t h condition, in the range of the temperature variations considered here. These results can be extended to estimate the change in the atmospheric water vapor content between the interglacial (mean T~: 17°C) and glacial conditions (mean T~: 12°C). T he consequence is t hat a warming of 5 K implies an increase of 0.6 hPa. Another estimation can be obtained from the lower troposheric temperature, on which the integrated vapor pressure seems to depend more than surface temperature. These higher level temperatures show ranges of 8 K for the N.H. and 5 K for the S.H. In t h a t sense h 5 K warming implies a 8-9 mm increase in precipitable water, leading to an increase of 0.8-0.9 hPa. Note t hat in these calculation we have assimilated the glacial conditions to the present winter conditions: we have taken into account only the dominant temperature effect and neglected the land-ocean change, which has a smaller effect. These variations, when considered all together tend to increase the atmospheric mass between the glacial and interglacial period, and correspond to an increase in the mean sea level pressure of the order of 2 hPa when the possible change in 02 content is not included or 0.7 hPa in the opposite case. Conclusion We have estimated the changes in the global mean sea level pressure and in the global mean pressure at the altitude of the present sea level between the glacial and the interglacial periods, by considering the atmosphere at hydrostatic equilibrium, the E art h being described with a very simplified topography. We have considered separately the effects of a change in topography and of a change in atmospheric mass. The change in topography originates from the changes in the ice sheets and in the related sea level variation. Depending on the various hypotheses, the difference in sea level pressure varies in the range of 9-15 hPa for a rising in sea level covering the range of 72-130 m. Comparison with GCM results show t h a t this change might only be weakly affected by atmospheric
340
circulation (a few h P a or less). T h e m e a n pressure change a t the present sea level altitude is shown to be less t h a n 1 hPa. This result is shown to be practically independent of the various hypotheses adopted: isostatic r e a d j u s t m e n t or not, different ice melting volumes, different ice sheet elevations and areas, different temp e r a t u r e lapse rates, different t e m p e r a t u r e changes... T h e change in atmospheric mass, when considering the various possibilities, lead to a sea level pressure increase from the glacial to t h e interglacial period of less t h a n 2 hPa. T h e interest of the present calculation is to evaluate and set limits on the i m p a c t of the different h y p o t h e s e s on the m e a n pressure change between glacial and interglacial periods.
Acknowledgements I t is a pleasure to t h a n k Michel Vallon and E r i k Geissler for their valuable c o m m e n t s and we are very greatful to S. J o u s s a u m e for helpfull discussions.
References Barnola, J.M., Raynaud, D., Korotkevich, Y.S. and Lorius, C. 1987. Vostok ice core: a 160.000-year record of atmospheric CO2. Nature, 329: 408-414. CLIMAP. Projects Members, 1981. Seasonal Reconstruction of the Earth's Surface at the last Glacial Maximum. Geol. Soc. Am. Map Chart Ser., MC-36. Farrel, W.E. and Clark, J.A., 1976. On post-glacial sea level. Geophys. J. R. Astron. Soc., 46: 647-667. Gates, W.L., 1976. The numerical simulation of ice-age climate with a global general circulation model. J. Atmos. Sci., 33: 1844-1873. Joussaume, S., 1989. Simulations du clirnat au dernier maximum glaciaire h l'aide d'un moddle de circulation atmospherique incluant une modelisation du cycle des isotopes de l'eau et des poussi~es d'origine ddsortique. Thesis. Univ. Paris 6, 507 pp. Kutzbach, J.E. and Guetter, P.J., 1986. The influence of changing orbital parameters and surface boundary conditions on climate simulations for the past 18,000 years. J. Atmos. Sci., 43: 1726-1759. Loewe, F., 1973. f~ber ~mderungen des Luftdrucks w~hrend der Eiszeit. Z. Gletscherkd. Glazialgeol. 9: 229-230.
M.A. MELIERES ET AI,. Manabe, S. and Broccoli, A.J., 1985. The influence of continental ice sheets on the climate of an ice age. J. Geophys. Res., 90: 2167-2190. Manabe, S. and Hahn, D.J., 1977. Simulation of the tropical climate of an ice age: J. Geophys. Res., 82: 3889-3911. Nakada, M. and Lambeck, K., 1988. The melting history of the late pleistocene Antarctic ice sheet. Nature, 333: 36-40. Oort, A.H., 1983. Global atmospheric circulation statistics, 1958-1973, Geophys. Fluid Dyn. Lab., Princeton, N.J. NOAA Prof. Pap., 14. Officer, C.B., Newman, W.S., Sullivan, J.M. and Lynch, D.R., 1988. Glacial isostatic adjustment and mantle viscosity. J. Geophys. Res., 93: 6397-6409. Peltier, W.R., 1988. Lithospheric thickness, Antarctic deglaciation history and ocean basin discretization effects in a global mode of postglacial sea level change: a summary of some sources of nonuniqueness. Quat. Res., 29: 93-112. Peltier, W.R. and Andrews, J.T., 1976. Glacial isostatic adjustment; I. The forward problem. Geophys. J. R. Astron. Soc., 46: 605-646. Raynaud, D., 1983. Total gas content. In: G. de Q. Robin (Editor), The Climatic Record in Polar Ice Sheets. Cambridge Univ. Press, pp. 79-82. Raynaud, D. and Lebel, B., 1979. Total gas content and surface elevation of polar ice sheets: new evidence. Nature, 281: 289-291. Raynaud, D., Chappellaz, J., Bamola, J.M., Koroykevich, Y.S. and Lorius, C.,1988. Climatic and CH 4 cycle implications of glacial-interglacial CH 4 change in the Vostok ice core. Nature, 333: 655-657. Rind, D., 1987. Components of the ice age circulation. J. Geophys. Res., 92: 4241-4281. Rind, D. and Peteet, D., 1985. Terrestrial conditions at the Last Glacial Maximum and CLIMAP sea-surface temperature estimates: are they consistent? Quat. Res., 24: 1-22. Sowers, T., Bender, M. and Raynaud, D., 1989. Elemental and isotopic composition of occluded 02 and N 2 in polar ice. J. Geophys. Res., 94 (D4): 5137-5150. Stauffer, B., Loehbrormer, E., Oeschger, H. and Schwander, J., 1988. Methan concentration in the glacial atmosphere was only half that of the preindustrial Holocene. Nature, 332: 812-814. Trenberth, K.E., 1981. Seasonal variations in global sea level pressure and the total mass of the atmosphere. J. Geophys. Res., 86: 5238-5246. Trenberth, K.E., Christy, J.R. and Olson, J.G., 1987. Global atmospheric mass, surface pressure and water vapor variations. J. Geophys. Res., 92: 14,815-14,826. Weiss, R.F., 1970. The solubility of nitrogen, oxygen and argon in water and seawater. Deep-Sea Res., 17: 721-735.
333
Elsevier Science Publishers BN., Amsterdam
Glacial-interglacial mean sea level pressure change due to sea level, ice sheet and atmospheric mass changes. M a r i e - A n t o i n e t t e Mdli6res a, P a t r i c i a M a r t i n e r i e b, D o m i n i q u e R a y n a u d b a n d Louis L l i b o u t r y u a Laboratoire de Spectrom~trie Physique, associg NRS, Universit~ Joseph Fourier de Grenoble, B.P.87, 38402 St Martin d'Hbres Cedex, France b Laboratoire de Glaciologie et G$ophysique de l'Environnement, CNRS B.P.96, 38402 St Martin d'Hbres Cedex, France (Received September 18, 1989; revised and accepted April 17, 1990)
ABSTRACT
Mdli~res, M.-A., Martinerie, P., Raynaud, D. and Lliboutry, L., 1991. Glacial-interglacial mean sea level pressure change due to sea level, ice sheet and atmospheric mass changes. Palaeogeegr., Palaeoclimatol., Palaeoecol., (Global Planet. Change Sect.), 89: 333-340. The change in the global mean atmospheric pressure between glacial and interglacial periods is evaluated at sea level. This change originates in a modification of topography and in a possible variation in the atmospheric mass. In this calculation the atmosphere is at hydrostatic equilibrium, and the parameters describing the glacial period are varied in a plausible range. The result, with constant atmospheric mass, is a mean sea level pressure decrease of 9-15 hPa linked with the degiaciation. The corresponding pressure change at the reference level corresponding to the present day sea level does not exceed one hPa. When considering only the chonge in the atmospheric mass, an increase which does not exceed 2 hPa is found, linked with the deglaciation.
Introduction
The Earth's climate has been oscillating between glacial and interglacial conditions during the late Pleistocene. Such changes correspond to global and large modifications in the physical and chemical conditions at the earth's surface. The best documented period on this respect is the last deglaciation which occurred between the Last Glacial Maximum (LGM) 18 kyr ago and the Holocene, when the mean surface temperature increased by some 4 - 5 ° K , the atmospheric composition experienced significant changes, (increase in radiatively active gases, like CO 2 and CH4, decrease in dust content,...) and the large ice sheets of the Northern Hemisphere disappeared (except for Greenland) resulting in a mean sea level increase of the order of 100 m. We focus here on the change in the 0921-8181/91/$03.50
global mean sea level pressure resulting from a change in surface topography (through sea level and ice sheet changes) and atmospheric mass linked with glacial-interglacial changes. Climatic conditions at glacial maxima have been simulated by General Circulation Models (GCM) during the recent past (see for example Gates, 1976; Manabe and Hahn, 1977; Manabe and Broccoli, 1985; Kutzbach and Guetter, 1986; Rind, 1987; Joussaume, 1989). Only a few published GCM's results give explicitely the difference between glacial and interglacial mean sea level pressures (for example Gates, 1976; Rind, 1987; Joussaume, 1989). The corresponding change is of the order of 10 hPa (i.e. about 1% of the atmospheric pressure) and depends of the prescribed sea level change. These models usually include the change of topography without considerig isostatic readjustment and
© 1991 - Elsevier Science Publishers B.V.
334
work at constant atmospheric mass. Following a simplified a p p r o a c h (by considering the a t m o sphere at h y d r o s t a t i c equilibrium) we estimate, here, this m e a n glacial-interglacial pressure change at climatic equilibrium, taking into account post-glacial isostatic rebound and possible changes in atmospheric mass. F u r t h e r m o r e , this simple calculation allows us to indicate how sensitive is the result to the different p a r a m e t e r s involved. I t is also interesting to note t h a t polar ice cores contain an information on the paleo surface elevations of the ice sheet when measuring the a m o u n t of air t r a p p e d in the tiny air bubbles found in the ice cores. This is because the air is t r a p p e d in the bubbles near the surface at the atmospheric pressure. T h e interpretation of air content in ice, in t e r m s of past elevations of the ice formation site, requires in fact a knowledge of the air pressure at sea level and the air pressure elevation gradient during the past ( R a y n a u d , 1983). T h e conclusions of the present work will, thus, help us when interpreting the results of the air content measured along the deep ice cores. We will first discuss the effect of a change in t o p o g r a p h y and then the effect of a possible change of the atmospheric mass on the mean global pressure. Some aspects of this subject h a v e been discussed by Loewe {1973).
Change in earth topography In the present p a p e r we consider the atmosphere to be in h y d r o s t a t i c equilibrium. This crude evaluation has the a d v a n t a g e of clearly showing the i m p a c t of the different p a r a m e t e r s and setting limits to this pressure change. For sake of clarity we point out t h a t within the h y d r o s t a t i c hypothesis the surface ocean pressure P o e , is equivalent to the global m e a n annual sea level pressure, PSLP, used in G C M ' s (which includes the fictitious air assigned to the volume of land surface above sea level); we therefore will refer mainly to this last notation. In a first time we estimate the glacial interglacial change of the h y d r o s t a t i c pressure at the respective sea levels. In a second time, we esti-
M.A. MELIEREs ET AL.
m a t e the change of this pressure at the well defined altitude of the present sea level. T h i s q u a n t i t y is a priori d e p e n d a n t of the e a r t h t o p o g r a p h y due to the fact t h a t the a t m o s p h e r e is a compressible fluid: the L G M ice sheet,s are situated at different altitudes from the corresponding oceanic melted w a t e r and therefore occupy an equivalent a t m o s p h e r i c volume of different density. T h e consequences of the ice sheet melting on e a r t h t o p o g r a p h y are changes in: --the height of p a r t of the continental surface through the change in ice sheets (with consequent isostatic adjustment}, - - the sea level through the i n p u t of melted waters (and consequent isostatic adjustment}, and change in gravitational field.
1. Calculation
T h e relation between the surface pressure at a given location, P~, and the a t m o s p h e r i c mass, m, is complicated and includes the ellipsoidal shape of the earth as well as the variation of g (the acceleration due to gravity) with altitude and latitude. This point has been investigated by Trenberth{1981). Nevertheless, in the present case where we are concerned only with the pressure difference between glacial and interglacial periods, we shall consider the e a r t h ms spherical and take g to be constant. We t h e n have:
mR =
Jearth surfaceP~ d S
(1)
W e evaluate this relation for glacial and interglacial conditions. A s s u m i n g t h a t the atmosphere is a t h y d r o s t a t i c equilibrium, the relation between pressure and altitude is dP
P
M~,g
-
R~
dz
(2)
M~ being the molar weight of air and R the gas constant. In the troposphere, the linear dependence of t e m p e r a t u r e with "altitude T( z I = T( z o ) - b( z
z o)
335
GLACIAL-INTERGLACIAL MEAN SEA LEVEL PRESSURE CHANGE
implies t h a t the variation of pressure with alt i t u d e is given by:
(Fig. 1), this relation can be expressed using Eq. 3 as a function of PSLP
,.,, , [ T ( z ) I ~ P( z ) = rl'z°J~ T----(~o) ,
mg = PSLP So¢ + 1 -
(31
To~
Scont
where:
gM~ s = bR
+ 1
(4)
W h e n considering the simplified t o p o g r a p h y
_ _rzi='
Sice
(5)
This last relation enables us to calculate PSLP2 a t the glacial epoch (index 2) as a function of PSLP1, the one at interglacial epoch (index 1), if the respective elevations, areas, temperatures, lapse rates and atmospheric masses are known. This calculation is performed for the following numerical values and hypotheses: T h e atmospheric mass is t a k e n as constant. A possible change of this m a ~ is discussed in the next paragraph. We consider a global warming of 5 K (estim a t e d from Rind and Peteet, 1985) between the glacial and interglacial period. T h e sensitivity of the pressure variation to the t e m p e r a t u r e is estimated b y considering different cases of warming (between 10 o and 0 ° C). - - T h e present day mean air t e m p e r a t u r e at sea level is 290 K (Oort, 1983). --We also consider d i f f e r e n t lapse r a t e scenarios: b I = b e = 6.5 K kin-1 and b 1 = 6.5 K k m -1, b2 = 7.5 K krn -1. This last case corresponds to a drier glacial atmosphere. -T h e sea surface is t a k e n as constant and equal to the present d a y value: 361 × 106 k m 2. I t means t h a t we neglect the decrease (of the order of a few percent) in t h e sea surface due to
T h e difference in cryosphere between the two epochs is characterized here b y the existence at the glacial period of a single fictitious ice sheet which has since melted. This fictitious ice sheet is assumed to have uniform thickness, hice, and to occupy a surface area Si~~. We divide the surface of the e a r t h into three parts: one relative to the oceans, one to the continents (excluding the area where the L G M ice sheet extends, b u t including the present ice sheets); and one to the L G M ice sheet. Each p a r t is characterized b y its surface area (So¢, Scont , S i c e ) , its mean elevation (_Zoo, Zcont, Zice) and its mean surface pressure (POP, PcP, PIP)- This last q u a n t i t y depends on the surface distribution with altitude. Nevertheless it can be shown t h a t t h e y can be closely approximated b y the pressure at the m e a n altitude. Moreover, this approximation is particularly justified in the present case of pressure change between two epochs where S¢o~t has the same surface distribution with altitude. For each epoch, the atmospheric mass is related to surface pressure by (1). We have m g = P o p S o c -{- P c p S c o n t -F P i p S i c e
To¢
l
,z.
hice 1":,':,':,~'~,':,':,"[~
L Zcont1
,-,-'-,'-:-,'-:-X-:,,',,',~, oc
i:!:!:!:!:i:!:{!:?:i:!:i:i ,:,~,:,:,~,:,:~,:,~,:,:,:,
",'"'"','':'C';':':':':
~ Zz0c2 1~
,
Sot2
,
,
,
,
,
Scont2
,
,
,
,
,
,
:::::::::::::::::::::::::::
.
Sice2
Socl
ii?i?i?i?iiiii iiiiiiiiiii_ . _I_ Scont1
Sice1
Glacial Interglacial Fig. 1. Notations used for the simplified topography of the Earth at interglacial (subscript 1) and at the glacial period (subscript 2).
336 the emergence of the continental margins: as the altitude of this emerged land is only a few tens of meters, the surface of this land will be treated ms p a r t of the ocean. - - T h e equivalent oceanic melt water thickness, h, (originating from the melting of the glacial ice sheet) is t a k e n to be the m e a n value given in C L I M A P (1981), i.e. 130 m. We also consider the cases of 100 m and 160 m. - - T h e glacial ice sheets which melted during the deglaciation are simulated, as mentioned previously, by a single fictitious ice sheet with a simplified shape, occupying the surface area (Sic e) with a c o n s t a n t thickness. T h e ice volume is deduced from the melt w a t e r volume, assuming an ice density of Pice = 0.92. Deduced from this ice volume the surface area is 18 × 106 k m 2 implying a m e a n ice thickness of 2834 m and a value of 133 × 106 k m 2 for Scont. We let this surface area v a r y from 20 × 106 to 16 × 106 k m ~ in order to cover the plausible range of m e a n ice cap elevation. -T h e present m e a n elevation of the continent is estimated to be 811 m (deduced from Trenberth, 1981). --Accurate estimates of the elevation differences (sea level, continent, ice sheet) require a knowledge of the a d j u s t m e n t of the earth's crust to t h e redistribution of ice and w a t e r surface loads. Such an investigation implies complex calculations requiring hypotheses a b o u t the internal structure of the earth. A t t e m p t s have been m a d e to constrain b o t h the ice load and the E a r t h ' s response from the observed sea levels (sea for example Peltier and Andrews, 1976; Farrel and Clark, 1976; Peltier, 1988; Officer et al., 1988; N a k a d a and Lambeck, 1988). In the present calculation we evaluate the differences in elevation in the f r a m e w o r k of simplified hypotheses and show t h a t the final result is not sensitive to these hypotheses. We consider two extreme scenarios: (1) At the glacial period, continents and oceans were in isostatic equilibrium. Hence the m e a n elevation of the glacial ice sheet relative to the continent, (zie~2- Zoo,t2), is given by ( 1 p i c J r ) h i ~ , r being the a s t h e n o s p h e r e / w a t e r density ratio due to the bed-rock depression of
M.A. M E L I E R E S E T AI.
the ice load. Calculations are performed for r equal to 3.6 and 3. After melting, isostatic readj u s t m e n t of deglaciated surfaces and waterloaded oceans occurred and is complete at the interglacial period. Hence the m e a n elevation of the deglaciated area is the s a m e as the m e a n continental elevation. T h e oceanic crust being at isostatic equilibrium, the difference in sea level, (z(~l -5,~2), is equal to (1 .... l f l r ) h (the oceanic melt w a t e r thickness). (2) We also consider the extreme scenario of zero isostatic a d j u s t m e n t , either at t h e glacial or interglacial period. Consequently the sea level change, (5(~ 1 -Zo¢2), is equal to the equivalent oceanic m e l t w a t e r thickness and the quantity, (Site2- 5co, t2) ) is equal to hi(.~, the thickness of the fictitious ice sheet. -We do not consider the change in sea level due to the t h e r m a l expansion of the oceanic water, which can be roughly e s t i m a t e d to be of a few meters. We have tested t h a t including such a change does not alter the final conclusion. -As we are concerned only by the m e a n sea level we do not include the effect of a change in the gravitational field originating in the change in the mass distribution: this will affect the sea levels surrounding the continents where glacial ice sheet will melt b u t will not change the m e a n sea level. 2.
Results
We first use the Eq. 5 in order to esimate the present global m e a n sea level pressure PSLP1,and compare it with the measured one. We use this calculation as a simple test of our set of p a r a m e ters. We obtain a value of 1011.5 h P a using an a t m o s p h e r i c mass of 5.136× 1011 kg as estim a t e d by T r e n b e r t h et al. (1987), t o g e t h e r with a g value of 9.81 m s- 2. T h i s estimation coincides very closely with the 1011 h P a of Trenb e r t h et al. (1981). T h e change in sea level pressure (PsL[~2PSLm), corresponding to the different cases mentioned above (and listed in the caption of T a b l e 1) is obtained from eq. 5. Results are given in T a b l e 1. If we t a k e the first scenario (results given in the first line of T a b l e 1), the pressure
GLACIAL-INTERGLACIALMEANSEA LEVELPRESSURECHANGE
337
TABLE 1 Mean pressure change between the interglacial (subscript 1) and glacial (subscript 2) period T2
h
Azo¢
Azi~
AP,~
AP2
AP(z = 0
(K)
(m)
(m)
(m)
(hPa)
(hPa)
(hPa)
285 285 285 290 280 285 285 285 285 285
130 100 160 130 130 130 130 130 130 130
94 72 116 94 94 87 94 94 130 94
2110 1623 2597 2110 2110 1965 1899 2373 2834 2110
11.4 9.0 13.8 10.8 12.1 10.7 11.5 11.3 15.0 11.5
11.5 8.8 14.2 11.3 11.7 10.6 11.5 11.5 15.9 11.5
-0.1 (1) + 0.2 (1) -0.4 (1) - 0.5 (1) 0.4 (1) 0.1 (2) 0.0 (3) - 0.2 (3) - 0.9 (4) 0.0 (5)
Notations: h: equivalent oceanic melt water thickness; Azoc = zo¢1- zo¢2: difference in sea level; Azice= Zice2 -- Zcont2: c h a n g e in the elevation of glacial ice sheet above continent: A P e , = PSLP2- P S L P I : pressure difference at sea level between the glacial and the interglacial period; AP2 = PSLP2- P ( z ~ 0)2: pressure difference occurring at the glacial period between the two altitudes corresponding to the glacial sea level and the interglacial sea level, (see t e x t ) . A P ( z = 0 ) = P ( z = 0 ) 2 - PSLPI: -pressure difference between glacial and interglacial period and present at the present sea level. The mean pressure changes are calculated with the following conditions: ( 1 ) : isostatsy holds with r = 3.6 (see text), deglaciated surface are of 18 x 106 km2, lapse rates of 6.5 K kin- 1, TI = 290 K; (2): as in (1) but r = 3; (3): as in (1) but Sic~ = 20 and 16 x 106 kin2; (4): as in (1) but no isostnsy adjustment; (5): as in (1) but b2 = 7.5 K krn -1.
d e c r e a s e a t sea level f r o m glacial to i n t e r g l a c i a l c o n d i t i o n s is 11.4 h P a . T h e s e n s i t i v i t y of t h i s r e s u l t to t h e d i f f e r e n t p a r a m e t e r s i n v o l v e d i n t h i s c a l c u l a t i o n is s m a l l : Changing the equivalent melt water t h i c k n e s s of + 30 m (i.e. t h e ice v o l u m e of + 23%) m o d i f i e s t h i s p r e s s u r e c h a n g e of + 1.2 h P a , Changing the other parameters in a plausible r a n g e ( t e m p e r a t u r e c h a n g e f r o m 0 t o 10 K , a s t h e n o s p h e r e / w a t e r d e n s i t y f r o m 3.6 t o 3, ice s h e e t s u r f a c e f r o m 20 t o 16 x l 0 s k m 2, i s o s t a s y or n o t , l a p s e r a t e f r o m 6.5 t o 7.5 K k m - 1 ) let t h i s c h a n g e v a r y b e t w e e n 10.8 a n d 15.0 h P a , -G l o b a l l y t h e r e s u l t s show t h a t d e p e n d i n g o n t h e v a r i o u s a s s u m p t i o n s , t h e difference i n sea level p r e s s u r e v a r i e s i n t h e r a n g e of 9 - 1 5 h P a w h e n l o w e r i n g t h e sea level b e t w e e n 72 a n d 130 m, a l o w e r i n g w h i c h c o r r e s p o n d s t o a m e a n t h i c k n e s s of t h e m e l t w a t e r l a y e r c o v e r i n g t h e r a n g e of 1 0 0 - 1 6 0 m. T h e s e r e s u l t s a r e of t h e s a m e o r d e r as t h e o n e s o b t a i n e d using the GCM's. For example, Gates
(1976) f o u n d a 12.7 h P a c h a n g e i n PSLP for a 85 m sea level lowering, R i n d (1987) a 11.5 h P a c h a n g e for 120 m, a n d J o u s s a u m e a 14.2 h P a c h a n g e for 150 m. T h e c o r r e s p o n d i n g e s t i m a t i o n w i t h i n t h e h y d r o s t a t i c e q u i l i b r i u m gives respect i v e sea level p r e s s u r e s c h a n g e of 10.1 ± 1 h P a , 13.7 ± 1 h P a a n d 15.7 ± 1 h P a . T h e u n c e r t a i n t y o r i g i n a t e s i n t h e p l a u s i b l e r a n g e of p a r a m e t e r s (T, b, S i ~ ) g i v e n i n T a b l e 1. T h e c h a n g e s calculated by the GCM's include both change in topography and in atmospheric circulation. Thus t h e difference b e t w e e n t h e i r r e s u l t s a n d o u r ' s comes f r o m t h e d i f f e r e n c e i n t h e w a y t h e topogr a p h y is r e p r e s e n t e d a n d f r o m t h e i n f l u e n c e of t h e c h a n g e i n a t m o s p h e r i c c i r c u l a t i o n . T h e comp a r i s o n of t h e r e s u l t s s h o w s t h a t s u c h differences do n o t exceed a few h P a . We have estimated the change in the hydros t a t i c p r e s s u r e a t t h e r e s p e c t i v e sea levels. I t is sometimes more relevant to estimate the change i n t h e h y d r o s t a t i c p r e s s u r e a t t h e a l t i t u d e of t h e p r e s e n t sea level ( t h a t we will n o t e z = 0); we
338
call it z~P( z = 0). T h e mean pressure P ( z = 0 ) 2 , at LGM, at altitude z = 0 is given by Eq. 2, as a function of PSLP2" T h e q u a n t i t y P ( z = 0)1, corresponding to the interglacial period, is equivalent to PSLP1- T h e change A p ( z = 0), given in T a b l e 1, is very small (between 0 and 1 hPa), w h a t e v e r different hypotheses are adopted (isostasy or not, different melt ice volume, different ice sheet surface, different t e m p e r a t u r e lapse rate, different temperature). T h i s can be interpreted in the following manner. T h e ice sheet relative to the glacial period will occupy an equivalent air volume V with a density p fixed by the t e m p e r a ture and the pressure at the elevation range of the ice sheet. At the same time, ocean evaporation liberates a volume V ' which is filled with air having a density p' fixed by the sea level t e m p e r a t u r e and pressure. T h e altitude of the ice sheet formation is such t h a t the air mass displaced by the growth of the ice sheet (pV) closely compensates the air mass occupying the sea level free volume (p'V'). In other words, the change of volume due to the w a t e r density difference ( V ' = 0.9V) is closely compensated by the air density difference between the m e a n ice sheet altitude and the sea level (p' > p). We now e s t i m a t e the order of m a g n i t u d e of pressure change related to a change in the a t m o s p h e r i c mass.
Change in atmospheric mass A change Am in the atmospheric mass will induce a change in the m e a n sea level pressure, which can be obtained from Eq. 5: A m / m = A PsLP/PsL P. This change is estimated here assuming a present atmospheric mass of 5 x 10 is kg ( T r e n b e r t h et al., 1987). T h e main causes for a change in a t m o s p h e r i c mass between glacial and interglacial period a p p e a r to be degassing of the ocean due to warming, changes in a t m o spheric gaseous constituents (H20, 02, CO 2. . . . ) and liberation of t r a p p e d air by ice melting. We assume no change in outgassing from volcanoes.
M.A. M E L I E R E S E T AL
gible. We first consider a global w a r m i n g of 5 K in the 200 m oceanic mixing layer (285 K to 290 K). T h e change in solubility of N 2 and O~ implies a degassing of 8 x 101:* kg using the solubility coefficients for sea w a t e r given by Weiss (1970) and corresponds to an increase in the m e a n preasure of 0,016 hPa. If we consider the extension of this new surface equilibrium to the bulk of the ocean (neglecting the existence of an internal sink or source for N~ and 02) i.e. taking into account a time long enough c o m p a r e d to the t u r n o v e r time of oceanic waters, then the increase of 5 K would imply a degassing of 0.3 hPa. These quantities are likely to be an overe s t i m a t e because the associated changes in the mean oceanic t e m p e r a t u r e are unlikely to be so large.
Change in gaseous constituen£~ Modifications in the oceanic and biosphere reservoirs on the t i m e ~ a l e of glacial-interglacial changes m a y act as sources and sink for various constituent.s of the a t m o s p h e r e (CO2, CH4, Ou . . . . ). Indeed, analyses of the air enclosed in ice cores indicate concentration changes of a b o u t 80 p p m v for CO 2 (see for instance Barnola et al., 1987) and of a b o u t 0.3 p p m v for C H 4 ( R a y n a u d et al., 1988; Stauffer et al., 1988). T h e implication of these changes in these m i n o r a t m o s p h e r i c constituents on the a t m o s p h e r i c pressure is small and account respectively for pressure increase of 8 10 2 and 3 10 4 h P a between t h e glacial and interglacial time. Also models which describe changes in carbon cycling over glacial-interglacial changes predict a modification in the oxygen (a m a j o r a t m o s p h e r i c constituent) concentration: the glacial 02 concentrations could h a v e been higher by up to a factor 1.006 t h a n the interglacial 02 level (Sowers et al., 1989). T h i s would lead to a m a x i m u m decrease of 1.2 h P a of the mean pressure between glacial and interglacial periodes.
Air liberated [rom ice melting Oceanic degassing We consider an u p p e r limit of this effect and show t h a t the induced pressure change is negli-
T h e volume (STP) of air t r a p p e d in polar ice is a b o u t 10% of the ice volume ( R a y n a u d and Lebel, 1979). T h e volume of m e l t ice is e s t i m a t e d
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G L A C I A L - I N T E R G L A C I A L M E A N SEA L E V E L P R E S S U R E C H A N G E
(see above) to be 51.2 × 106 km 3. Taking into account the altitude and temperature at which the air bubbles were formed, this corresponds approximately to an additional 4.4 × 10~ kg of air in the atmosphere and causes an increase of 0.9 hPa on going from glacial to interglacial conditions.
Cha~ge in water vapor The atmospheric water vapor content, e(w), is strongly dependent on the surface temperature of the Earth, T~. The calculation of e(w) is not straightforward, but the correlation between e(w) and T~ can be estimated for the present l an d - water distribution at the surface of the E a r t h by using the results of two large scale observations on the present state of the Earth, each concerning one hemisphere. T hey are related to the monthly average of e(w) and T~ for each hemisphere separately and therefore include the extreme climatic conditions of winter and summer. As the hemispheres are weakly coupled with a coupling time scale of about a month, we can treat these results are being independent. We will first consider the estimation of the monthly surface temperature (land and ocean), for each hemisphere made by Oort (1983). The monthly atmospheric water vapor content is given by Trenberth et al. (1987). Both e(w) and T~ present extrema at the same time (around February and August) and have parallel yearly variations. Correlation existing between e(w) and T~ is used to estimate the relation A e / A T for each hemisphere within the small range of temperature variation involved here. The difference between the monthly temperature extrema is 13.5 K for N.H. and 6.1 K for the S.H. Th e amplitude of the variation of the monthly atmospheric water vapor content is 1.45 hPa for the N.H. and 0.85 hPa for the S.H. These values lead to a variation of 0.11 hPa K -1 for the N.H. and 0.14 hPa K-1 for the S.H. The difference between the two hemispheric gradients reflects mainly the difference in the l andocean distribution (the larger free water surface of the S.H. leading to a slightly stronger gradients). A mean gradient of 0.12 hPa K -~ repre-
sents the global E a r t h condition, in the range of the temperature variations considered here. These results can be extended to estimate the change in the atmospheric water vapor content between the interglacial (mean T~: 17°C) and glacial conditions (mean T~: 12°C). T he consequence is t hat a warming of 5 K implies an increase of 0.6 hPa. Another estimation can be obtained from the lower troposheric temperature, on which the integrated vapor pressure seems to depend more than surface temperature. These higher level temperatures show ranges of 8 K for the N.H. and 5 K for the S.H. In t h a t sense h 5 K warming implies a 8-9 mm increase in precipitable water, leading to an increase of 0.8-0.9 hPa. Note t hat in these calculation we have assimilated the glacial conditions to the present winter conditions: we have taken into account only the dominant temperature effect and neglected the land-ocean change, which has a smaller effect. These variations, when considered all together tend to increase the atmospheric mass between the glacial and interglacial period, and correspond to an increase in the mean sea level pressure of the order of 2 hPa when the possible change in 02 content is not included or 0.7 hPa in the opposite case. Conclusion We have estimated the changes in the global mean sea level pressure and in the global mean pressure at the altitude of the present sea level between the glacial and the interglacial periods, by considering the atmosphere at hydrostatic equilibrium, the E art h being described with a very simplified topography. We have considered separately the effects of a change in topography and of a change in atmospheric mass. The change in topography originates from the changes in the ice sheets and in the related sea level variation. Depending on the various hypotheses, the difference in sea level pressure varies in the range of 9-15 hPa for a rising in sea level covering the range of 72-130 m. Comparison with GCM results show t h a t this change might only be weakly affected by atmospheric
340
circulation (a few h P a or less). T h e m e a n pressure change a t the present sea level altitude is shown to be less t h a n 1 hPa. This result is shown to be practically independent of the various hypotheses adopted: isostatic r e a d j u s t m e n t or not, different ice melting volumes, different ice sheet elevations and areas, different temp e r a t u r e lapse rates, different t e m p e r a t u r e changes... T h e change in atmospheric mass, when considering the various possibilities, lead to a sea level pressure increase from the glacial to t h e interglacial period of less t h a n 2 hPa. T h e interest of the present calculation is to evaluate and set limits on the i m p a c t of the different h y p o t h e s e s on the m e a n pressure change between glacial and interglacial periods.
Acknowledgements I t is a pleasure to t h a n k Michel Vallon and E r i k Geissler for their valuable c o m m e n t s and we are very greatful to S. J o u s s a u m e for helpfull discussions.
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