Seasonal sea level change from TOPEX/Poseidon observationand thermal contribution

J. L. Chen1,2, C. K. Shum3, C. R. Wilson2,4, D. P. Chambers1, B. D. Tapley1

1 Center for Space Research, University of Texas at Austin, 3925 W. Braker Lane, Suite 200, Austin, TX 78759-5321, USAe-mail: chen@csr.utexas.edu; Tel.: +1 512 471 5573; Fax: +1 512 471 35702Department of Geological Sciences, University of Texas at Austin, Austin, TX 78759, USA3Department of Civil and Environmental Engineering and Geodetic Science, Ohio State University, Columbus, OH, USA4NASA Headquarters, Washington, DC, USA

Received: 25 September 1998 /Accepted: 13 July 1999

Abstract. Seasonal steric sea-level change due to tem-perature variation in the mixing layer is assessed usingspace-measured sea-surface temperature data and his-torical in situ temperature measurements. The resultsare compared with TOPEX/Poseidon satellite altimetermeasurement at dierent large spatial scales. It isindicated that thermal eect accounts for much of theobserved seasonal variability, especially when averagingover zonal regions. Some regional seasonal patterns ofsea-level anomalies in the tropical oceans are wellrepresented by the thermal model prediction. Systematicdierences are shown between TOPEX/Poseidon obser-vation and thermal contribution at a 1±2 cm level. Thepotential causes for these dierences are discussed,including water mass exchanges among the atmosphere,land, and oceans, and error sources in the steric resultand geophysical corrections applied in TOPEX/Posei-don data.

Key words: TOPEX/Poseidon ± Sea-level change ±Thermal eect

1 Introduction

The TOPEX/Poseidon satellite altimeter has been mon-itoring global sea-surface height change every 10 daysfor over 6 years with an accuracy approaching 3±4 cmover a spatial scale of 20 km along the satellite groundtrack (Fu and Davidson 1995). The high spatialresolution and over 5 years' temporal coverage providea broad band of information about sea-level variationand geostrophic ocean circulation. Observed sea-surfaceheight is subject to change as a consequence of many

eects, including ocean tides and solid earth tides, thepole tides, atmospheric pressure loading, steric eectsintroduced by temperature and salinity variations withinthe oceans, and water mass redistribution associatedwith the global hydrologic and cryospheric cycles.

After all standard geophysical corrections are appliedto TOPEX/Poseidon data (Callahan 1993), there remainstrong seasonal sea-level variations at various spatialscales with a mean annual variability of 4±5 cm in thenorthern hemisphere and 2±3 cm in the southernhemisphere. The maximum and minimum sea-surfaceheights in the northern hemisphere are in September andMarch, respectively, and the phase is reversed in thesouthern hemisphere (see Fig. 1). It is generally believedthat these seasonal signals re¯ect the seasonal ¯uctua-tions of temperature over the oceans. Many investiga-tions (Repert et al. 1985; White and Tai 1995; Chamberset al. 1997) show that sea-level variations are highlycorrelated with heat storage change. The inferred heatstorage change using TOPEX/Poseidon-determined sea-level variations is in very good agreement with the heatstorage change calculated from temperature pro®les incertain basins (White and Tai 1995; Chambers et al.1997). However, in terms of geodynamic applicationsof satellite altimeter data, people are more interested inlarge-scale steric and non-steric sea-level change on aglobal basis.

Steric sea-surface height stands for the portion of sea-level change due to density variation, which is intro-duced by temperature and salinity variation and isdominated by thermal eect. We neglect salinity eectsin our steric estimation because of two considerations:the lack of reliable salinity data on worldwide oceanscales and the diculties in separating the salinity vari-ations due to ocean currents and salt convection fromthe salinity variations in the top of the mixing layer dueto fresh water in-¯ux and out-¯ux associated with pre-cipitation, evaporation and river discharge (in speci®cregions). The latter is caused by oceanic mass variation,which is actually part of the non-steric, or mass-relatedinformation. Steric sea-level change is a non-linear in-Correspondence: J. L. Chen

Journal of Geodesy (2000) 73: 638±647

tegral of temperature variation, because thermalexpansion coecients depend on temperature andpressure, especially temperature (see Fig. 2). A betterunderstanding of steric sea-level change leads to thepotentials in separating mass variation within the oceanfrom observed sea-level anomalies, which is of greatinterest to many studies, including water mass transportwithin the global hydrological cycle, oceanic impact onthe Earth rotational and gravitational change, and thevalidation of geophysical model performance in alti-meter data calibration.

The major diculty is the lack of observational dataover the entire depth of oceans. Satellite radiometershave been monitoring global sea surface temperature(SST) for over 15 years, but the steric sea-level changedepends on the temperature variations in the oceans atall depths (mainly in the mixing layer), which are onlyavailable from in situ observations, such as XBT andMBT. Due to the inadequate spatial and temporalcoverage of historical in situ measurements, a globalreal-time three-dimensional (3-D) temperature ®eld ofthe oceans is not available. However, if we focus onlarge-scale seasonal variations, the climatological tem-perature ®elds based on historical in situ measurement

will be valuable. The satellite SST data provide a meansto improve the accuracy for the surface layer(s), espe-cially in the southern oceans.

The steric contribution to global mean sea-level(MSL) change has been recently studied by Chen et al.(1998a) and Minster et al. (1999) using the climatologi-cal ocean temperature data in the NOAA World OceanAtlas 1994 (WOA94) (Levitus and Boyer 1994). Thesetwo studies only discuss the global mean steric eect.In this study, we estimate steric sea-level change usingboth climatological data and satellite SST measurementsat dierent large spatial scales, including basin, zonal,and global scales. The results are compared withcorresponding sea-level changes from TOPEX/Poseidonsatellite radar altimeter measurements. A 1° ´ 1° (lati-tude ´ longitude) monthly steric sea-level change dataset, covering the same period as the TOPEX/Poseidonmission, is derived in this study. At the end, we discusssome error sources that may aect this computation.

2 Data and models

2.1 TOPEX/Poseidon observations

We use the TOPEX/Poseidon sea-level measurements of10-day cycles 2 to 183 for the time period from October1992 to July 1997. The media, instrument, and geo-physical corrections applied include ionosphere delay,wet and dry troposphere delay, electromagnetic bias,tides, and the inverted barometer response. The TOPEXGeophysical Data Records (GDRs) orbits have beenreplaced with the new orbits computed with the JGM-3gravity ®eld model (Tapley et al. 1996), and the oceantide model has been replaced with the UT/CSR 3.0model (Eanes and Bettadapur 1995). The pole tide hasbeen corrected. Sea-level anomalies relative to a meansea-surface over 4 years are computed by interpolatingthe data to a ®xed grid and then removing the mean sea-surface height (Chambers et al. 1997). The sea-surfaceanomalies are then averaged into a uniform 1° ´ 1° gridfor each repeat cycle.

2.2 WOA94 climatology

The WOA94 objectively analyzed 1° ´ 1° monthly meantemperature ®elds represent 3-D seasonal ocean tem-perature variations (Levitus and Boyer 1994). Thesemean ®elds include 19 layers extending from the surfaceto 1000 m depth, and are derived from over 4.4 millionhistorical in situ temperature pro®les collected fromvarious instrument groups, including XBT, MBT, CDT,and traditional bottle measurements. About 0.5 millionare in the southern hemisphere and 0.1 million south of40° latitude in the southern hemisphere. The WOA94mean temperature ®elds are thought to representseasonal variations in the northern hemisphere andtropical regions fairly well (Levitus and Boyer 1994;Chambers et al. 1997). The relatively sparse measure-ments in the southern hemisphere, especially south of

1993 1993.5 1994 1994.5 1995 1995.5 1996 1996.5 1997 1997.5

–8

–6

–4

–2

0

2

4

6

8

Mea

n S

ea L

evel

(m

m)

Fig. 1. The mean sea-surface anomalies in regions between 20 and 50degrees in the northern (thick curve) and southern (thin curve)hemispheres, measured by TOPEX/Poseidon altimetry (cycles 2±183)

010

2030

24

68

1012

140

1

2

3

4

x 10–4

Temperature (˚C)Layers 1 – 14

The

rmal

Exp

ansi

on

Fig. 2. The interpolated thermal expansion coecients as a functionof temperature ()5 to 35 °C ) and the mean pressure of the top 14layers of WOA94

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40°, implies that the actual spatial resolution is muchworse than 1° ´ 1° in the southern hemisphere. Inaddition to the monthly mean temperature ®elds, anobjectively analyzed annual mean temperature ®eld isalso produced from all temperature pro®les regardless ofseason or year.

2.3 Optimum interpolation SST data

The Optimum Interpolation SST (OISST) data areproduced by combining satellite radiometer measure-ment, in situ observation, and the sea-ice model at theNational Center for Environmental Prediction (NCEP)(Reynolds and Smith 1994). The monthly OISST ®eldsare derived by a linear interpolation of the weeklyoptimum interpolation ®elds to daily ®elds, then thedaily values are averaged over a month. The analysisuses in situ observation, satellite radiometer SSTmeasurement, and the SST simulated by sea-ice cover.The in situ data are obtained from radio messagescarried on the Global Telecommunication System, and

the satellite measurements are from the operational dataproduced by the National Environmental Satellite, Dataand Information Service (NESDIS). The spatial resolu-tion of OISST ®elds is 1° ´ 1°. The OISST data weapplied span the period from October 1992 to July 1997,the same period as that of the TOPEX/Poseidon dataused here.

2.4 Improved 3-D ocean temperature ®eld

Figure 3 shows comparisons of global mean SSTdeviations from annual mean ®eld between the NCEPOISST data and the WOA94 climatological ®elds inMarch and September, respectively. In order to mini-mize the in¯uence of interannual variations, the OISSTmean ®elds are computed from all data in March orSeptember. The SST dierences between the OISST andWOA94 data in the two months are shown in the twobottom panels (e, f) of Fig. 3. In the tropical regions andsubtropical regions in the northern hemisphere, WOA94climatological data are in good agreement with the

(a) SST Anomaly in March (WOA94)

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(b) SST Anomaly in September (WOA94)

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(c) SST Anomaly in March (OISST)

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(d) SST Anomaly in September (OISST)

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(e) OISST – WOA94 in March

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(f) OISST – WOA94 in September

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50

Degree (oC)

–6 –4 –2 0 2 4 6

Fig. 3. a, b Climatological SST anomalies ®eld in March andSeptember with respect to the annual mean from the WOA94objectively analyzed temperature; c, d the mean OISST anomalies in

March and September, calculated using 4 years' OISST data (March1993±February 1997); e, f SST dierences between OISST andWOA94 SST (OISST±WOA94) in the two months

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NCEP OISST data, while in the southern hemisphereand high-latitude regions in the northern hemisphere,discrepancies are obvious. The SST dierences are lessthan 1 °C in most regions (Fig. 3e, f) and could be aslarge as 2±4 °C in the circum-Antarctic and high-latitude (northern hemisphere) regions.

The large discrepancies in the southern hemisphereand high-latitude regions are mainly due to the sparsehistorical in situ data samples in those regions and thedierent time spans used in computing the seasonalaverage. The WOA94 climatology is estimated from allavailable historical in situ temperature observationscollected over a long period (over a century), while theOISST seasonal average is computed from only 6 years'measurements. The strong interannual and decadal SSTvariations will be a major error source to these dis-crepancies. The long-term SST change due to globalwarming will also contribute signi®cantly to the dier-ences. Part of the large positive discrepancies (OISST ±WOA94) in high-latitude regions in the Paci®c and At-lantic (see Fig. 3e, f) is probably due to long-term SSTincrease associated with global warming eects.

A natural approach to increasing the accuracy of theWOA94 climatology is to use the NCEP OISST data toimprove the WOA94 mean temperature ®elds at thesurface. Vertical temperature pro®les will play a key rolein determining how to eectively combine these twodata sets. We chose several regions to study the meanvertical temperature pro®le using both the WOA94 cli-

Fig. 4. The geographic distribution of the eight selected regions (A±H, corresponding to the temperature pro®les shown in Fig. 5)

A

BC

D

EF

GH

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20

40

60

Fig. 5. Eight climatological predictions of vertical temperaturepro®les (A±H) in the northern and southern Indian, Paci®c, andAtlantic Oceans. Each region is a 20° ´ 20° (latitude by longitude)box

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matological temperature ®eld and historical in situtemperature pro®les. Figure 4 shows the geographicaldistribution of eight selected regions in the northern andsouthern Indian, Paci®c, and Atlantic oceans. Theseeight regions are nearly randomly selected and the onlyconsideration is to have an even coverage of the oceans.The temperature pro®les of these eight regions areshown in Fig. 5A±H. In most regions, the mean tem-peratures of the top three layers (the top 0±25 m of the

mixing layer), are very close to the surface temperature®eld. Based on this ®nding, and the study of other areas,we use the NCEP OISST data to replace the top threelayers of our proxy 3-D ocean temperature ®eld, andretain layers 4±14 (25±500 m depth) from the WOA94climatology. The choice of a 25-m (i.e., the thickness ofthe top three layers of WOA94) replacement is conser-vative. We need to balance two kinds of error sources:one is from WOA94 due to poor sampling (especiallyin the southern hemisphere and high-latitude regions)and long-period average eects, and the other is fromOISST due to vertical temperature variations. If wechoose a deeper layer (e.g. 50 or 100 m), we will signif-icantly increase errors in steric estimates by neglectingthe temperature decrease in deeper layers.

3 Thermal expansion model

As we discussed above, in this study we focus on stericsea-level change due to thermal expansion. The thermalexpansion coecient C is de®ned as (Knauss 1979)

C ÿ 1q

oqoT

1

in which T is temperature; q is density of seawater; C is afunction of temperature (T), pressure (P), and salinity

Table 1. The standard depth de®nitions and the mean thickness ofthe top 14 layers of the WOA94 seasonal mean temperature ®elds

Layer Depth (m) Thickness (m)

1 0 52 10 103 20 104 30 155 50 22.56 75 257 100 258 125 259 150 37.510 200 5011 250 5012 300 7513 400 10014 500 100

93 93.5 94 94.5 95 95.5 96 96.5 97 97.50

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(deg

) &

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cm)

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Fig. 6. The global zonal MSL variations in each 10° latitude band ina the northern hemisphere and b southern hemisphere. The thin solidlines represent the TOPEX/Poseidon observation, and the thick solid

lines are the steric model prediction. The time series are verticallyoset to corresponding latitude zone by adding the mean latitudein degree

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(S). Compared to temperature and pressure, the salinityeect on C is very small, and the salinity of the top fewhundred meters of seawater is close to a constant (35&).The experimental values of C as a function of T, P, andS given by Knauss (1979) are adopted in this model. Wehave interpolated the original C table into 1° intervalsfrom )5 to 35 °C and to the mean pressure of each ofthe 14 layers of the proxy ocean temperature ®elddescribed in Sect. 2.4. Figure 2 shows the interpolatedthermal expansion coecient matrix.

From the de®nition of thermal expansion coecientC [Eq. (1)], it is quite easy to derive the sea-surfaceheight change (DH) due to temperature variations (DT)under the assumption that there is no horizontal ex-pansion. This assumption is accurate as long as therelative changes of ocean area with respect to the totalocean area due to sea-level variations are negligible. Thisis apparently the case in reality (even for enclosed andsemi-enclosed seas). However, it will be questionable incoast regions. If the thickness of the seawater layer is H,mean temperature is T, and mean pressure is P, thesteric sea-level change (DH) is

DH CT ; P � DT � H 2

In order to derive the total steric sea-level change at agiven grid point (latitude a, longitude k) from the proxyreal-time ocean temperature ®eld, we simply perform theintegration over the 14 layers. The temperature devia-tion DT(a, k, i, t) is calculated from the temperaturevariation relative to the annual mean (the 4-year meanfor OISST and the climatological annual mean forWOA94) at each given point (a, k), in each layer (i), at agiven time (t).

DHa; k; t X14i1

CTi; Pi � DT a; k; i; t � Hi 3

Table 1 lists the thickness (Hi) of each of the 14 layers.One should be aware that if we neglect the salinity eecton steric sea-level change, this algorithm to computesteric sea-level change via thermal expansion coecientis identical to the approach using density variation asapplied in Minster et al. (1999).

4 Results and comparisons

4.1 TOPEX/Poseidon sea-level variation

Using the sea-level anomaly grids determined fromTOPEX/Poseidon, we calculate the mean sea-levelvariations at dierent spatial scales. Figure 6 shows thezonal mean sea-level variations in each 10° latitude band

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80

Hei

ght (

cm)

Basin Average

North Pacific

South Pacific

North Atlantic

South Atlantic

North Indian

South Indian

Fig. 7. The basin averages of MSL height in the northern andsouthern Paci®c, Atlantic, and Indian Oceans. The thin solid linesrepresent the TOPEX/Poseidon observation, and the thick solid linesare the steric model predictions. The time series are oset vertically fora concise display

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0

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2

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5

Hei

ght(

cm)

Global and Hemispheric Mean Sea Level

Northern Hemisphere

Southern Hemisphere

Global Mean Sea Level

Fig. 8. The global and hemispheric MSL variations from TOPEX/Poseidon measurement and steric model estimation. The thin solidlines represent the TOPEX/Poseidon observation, and the thick solidlines are the steric model predictions

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from 60°S to 60°N (i.e., 60°S±50°S, 50°S±40°S, . . . ,40°N±50°N, 50°N±60°N). An area weighting function(i.e., each grid point is weighted by cosine of the latitudeof the grid) has been applied in calculating the mean sea-level change. Strong seasonal variations exist in mostlatitude regions, especially in the northern hemisphere.The dominant seasonal variation is found at the mid-latitudes near 30°N±50°N in the northern hemispherewith a mean seasonal variability of about 5±6 cm. Theseasonal signal in the southern hemisphere is mostnotable at mid±high-latitude regions (20°S±50°S) with amean annual amplitude near 2±3 cm. The maximum andminimum sea-surface heights in the northern hemisphereare in late summer/early fall (September) and late winter/early spring (March), respectively, and the phase isreversed in the southern hemisphere, with a maximum inMarch and a minimum in September. The seasonalvariation almost disappears in circum-Antarctic andsouthern tropical regions.

Figure 7 shows the MSL variations for northern andsouthern Paci®c, Indian, and Atlantic Oceans, and

Fig. 8 shows the global MSL variation and the MSLvariations in the northern and southern hemispheres.The seasonal variation is evident in dierent basins,especially the strong seasonal signals in the northernPaci®c and Atlantic with a mean annual variabilityaround 4±5 cm. The global MSL variation also shows aclear seasonal signal of nearly 1 cm amplitude, and hasthe same phase as the northern hemisphere (maximumin September and minimum in March).

In addition to the MSL time series, sea-level variationcan be directly described by 2-D sea-level anomalies,especially for some regional seasonal patterns with smallspatial scales. In order to minimize the interannualvariability and high-frequency signals, we have calcu-lated the monthly MSL anomaly ®eld using all TOPEX/Poseidon cycles in a given month regardless of years.For example, the mean sea-level anomaly ®eld in Marchis calculated by averaging a total of 15 cycles (18, 19, 20,54, . . . ,) in March during the nearly ®ve years fromOctober 1992 to July 1997. The MSL anomalies inMarch and September are shown in Fig. 9a, b. The

(a) Sea Level Anomaly in March (T/P 93 – 97)

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(b) Sea Level Anomaly in September (T/P 93 – 97)

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(c) Steric Height in March (WOA94+OISST)

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(d) Steric Height in September (WOA94+OISST)

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(e) TOPEX/Poseidon – Steric in March

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(f) TOPEX/Poseidon – Steric in September

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cm–15 –10 –5 0 5 10 15

Fig. 9. a, b MSL anomalies determined by TOPEX/Poseidon inMarch and September; c, dmean steric sea-level variations determinedby WOA94 and OISST data during the same time. The average iscalculated using all observations in March regardless of years in both

TOPEX/Poseidon data and the steric model grids; e, f sea-surfaceheight dierences between TOPEX/Poseidon observation and stericestimate in March and September, respectively

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seasonal sea-level changes in the northern and southernhemispheres and the ¯ipped phases are well representedin these two plots. Although in the MSL time series (seeFig. 6) seasonal signal in the tropical regions is not ob-vious, there are clearly some strong seasonal changes inthese regions, especially the narrow zonal banded pat-terns in the tropical Paci®c and Atlantic, and the lessregular regional patterns in the Indian Ocean.

4.2 Steric sea-level change and comparisons

Monthly steric sea-surface height grids (1° ´ 1°) arederived using the proxy real-time 3-D global tempera-ture ®eld and the thermal expansion model discussedabove. We calculated the mean steric sea-surface heightsfor the same 10° latitude zonal regions as used in theTOPEX/Poseidon data, and plotted them together withthe TOPEX/Poseidon observations in Fig. 6. The zonalmean steric sea-surface height variations show strongand dominant seasonal signals in both the northern andsouthern hemispheres, with a larger seasonal variabilityin the northern hemisphere (4±5 cm) than in thesouthern hemisphere (2±4 cm). The model-derived zonalmean steric sea-level variations are in very goodagreement with the TOPEX/Poseidon observations,especially in the northern hemisphere, e.g., in the30°N±40°N band, both TOPEX/Poseidon observationand steric estimate indicate a strong seasonal variability

of 5±6 cm with the same phase (maximum heightsin about September). Some larger discrepancies occurin the tropical and the high-latitude regions, i.e., thecircum-Antarctic regions. The dierences betweenTOPEX/Poseidon measurement and steric estimate areshown in Fig. 10.

The mean steric sea-level variations in the northernand southern Paci®c, Atlantic, and Indian oceans arealso calculated and compared with the TOPEX/Poseidonresults in Fig. 7. Accordingly, the model-derived globalsteric sea-level variation is shown in Fig. 8, together withthe estimates in the northern and southern hemispheres.Our model-derived steric sea-level variations also pro-vide very good agreements with the TOPEX/Poseidonmeasurements at basin scales, especially in the northernPaci®c, Atlantic, and Indian Oceans. However, in thesouthern hemisphere, the estimated steric heights aregenerally larger than the TOPEX/Poseidon observations,and the TOPEX/Poseidon observed global mean sea-level variation is out of phase with our steric modelprediction (see Fig. 8). In the next section, we will discusssome possible causes for these discrepancies.

In order to look at some regional seasonal patternswe have seen in the TOPEX/Poseidon data, such as thezonal banded structures in the tropical Paci®c and At-lantic Oceans, and the less regular seasonal patterns inthe tropical Indian Ocean, we calculate the mean stericsea-surface heights in March and September (using thesame average scheme applied in the TOPEX/Poseidon

93 93.5 94 94.5 95 95.5 96 96.5 97 97.50

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(deg

) &

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93 93.5 94 94.5 95 95.5 96 96.5 97 97.5

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Fig. 10. MSL residuals in each 10° latitude zone (60°S±60°N) of the northern and southern hemisphere after steric eects are removed fromTOPEX/Poseidon measurement

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data), and show them in Fig. 9c, d. These regional sea-sonal patterns are well predicted by our steric model,especially the banded structure in the tropical Atlanticand the irregular seasonal patterns in the tropical IndianOcean. The double-banded pattern in the tropical Paci®cis also seen in the model estimate, but not as clearly asthat in the TOPEX/Poseidon observations.

5 Discussion

This study con®rms that thermal expansion is respon-sible for much of the large-scale seasonal variationsobserved by TOPEX/Poseidon altimeter, especiallywhen averaging over zonal regions and basin scales(80±90% of the seasonal variability in the northernhemisphere; see Fig. 6). Some regional seasonal patternsin the tropical regions are also well predicted by thissteric model. The results from this study indicate thathistorical in situ observational data and satellite SSTdata are valuable in determining seasonal steric sea-levelheight. If one could remove mass signals via indepen-dent techniques, e.g. using the future Gravity Recoveryand Climate Experiment (GRACE) mission's observa-tions, satellite altimeter measurements would lead to abetter understanding of the steric sea-level and heat-storage change within the oceans. The latter bears asigni®cant role in understanding global climate change.

The large discrepancies, especially those in thesouthern hemisphere, are mainly due to the sparsetemperature measurements (Fig. 9e, f). Another majorfactor is that the TOPEX/Poseidon results are averagedover a 5-year period (with frequent El NinÄ o events), andthe steric estimates are primarily based on climatologicaldata averaged over a much longer time period. The sea-level height changes from TOPEX/Poseidon measure-ment and steric estimate both indicate a considerablystronger seasonal signal in the northern hemisphere thanthose in the southern hemisphere. The relative weakerseasonal variability could be another reason for thepoorer agreement in the southern hemisphere.

The phase dierence in global MSL variations be-tween TOPEX/Poseidon observation and steric modelprediction (Fig. 8) implies a systematic dierence be-tween the two determinations. In addition to the errorsources mentioned above, this may come from a varietyof other sources. The water mass redistribution betweenthe oceans, atmosphere, and continental water cycle(including snow/ice sheets) may have signi®cant eectson TOPEX/Poseidon observed global MSL change,which are not part of and not included in the stericestimate. Recent studies (Chen et al. 1998a; Minsteret al. 1999) have indicated that the seasonal variationsof continental water storage change and atmosphericwater vapor ¯uctuation together may introduce about1 cm of changes in global MSL. Their estimated globalMSL change based on hydrological models agrees verywell (within a couple of mm in amplitude) with TOPEX/Poseidon observation if the steric eects are removed.

The systematic dierence (shown in Figs. 8 and 10)with a mean seasonal variability at a 1±2 cm level could

also be from the geophysical corrections applied in theTOPEX/Poseidon data, especially the IB correction andwet tropospheric delay correction. It is generally be-lieved that the standard IB correction (i.e., using aconstant reference pressure; Callahan 1993) applied inTOPEX/Poseidon data will introduce an incorrect sea-sonal signal (about 5 mm in amplitude) in global MSLdetermination (Rao® 1998). If we do not apply any IBcorrection (Chen et al. 1998a) or apply a modi®ed IBmodel, e.g., using a non-constant reference pressure(Minster et al. 1999), the magnitude of seasonal globalMSL change will be signi®cantly reduced to several mm.

The seasonal steric sea-level change associated withtemperature variation over the oceans is vital informa-tion required to separate mass variation from observedsea-level anomalies. The 1±2 cm residual signals (aver-aged over large spatial scales) are signi®cant enough tobe the vital driving forces for many geodynamical vari-ations, e.g., the Earth rotation and gravitational ®eldvariation (Wilson 1995; Chen et al. 1998b) and geocen-ter motion (Chen et al. 1999), and provide observationalconstraints on the global water mass budget for thecontinental water cycle and atmospheric water vapor(Chen et al. 1998a; Minster et al. 1999). This research isan attempt to investigate this challenging problem usingsatellite SST measurement and historical in situ obser-vation. The derived monthly 1° ´ 1° grids of steric sea-level change will provide a chance to study the massvariation within the oceans using TOPEX/Poseidon(including its extended mission Jason-1) measurements,which play key roles in studying oceanic impacts ongeodetic observations.

We have combined the NMC Optimum InterpolationSST data with the WOA94 objectively analyzed tem-perature ®elds to produce a proxy 3-D global oceantemperature model. This approach is based on the factthat seasonal signals are dominant in the top few hun-dred meters, and the mean temperature in the ®rst fewlayers are quite close to the sea-surface temperature forthe areas we examined (see Fig. 5). This combination isapplied to improve the accuracy of WOA94 mean tem-perature ®elds, especially in the southern hemisphere.Because the physical process of downward heat ¯uxtransfer from the surface is complicated, one cannotsimply infer the vertical temperature pro®le from surfacetemperature data without completely understanding theprocess, even if we know the mixing layer depth. On theother hand, the deep layers (4±14 in this model) providesigni®cant contributions to the total steric sea-surfaceheight due to the comparable variability of seasonaltemperature variation (see Fig. 5), so historical in situtemperature data play an important and unique role instudying steric sea-level change.

Quantitative assessment of the improvement by usingOISST data is dicult to estimate at the moment.A better agreement with TOPEX/Poseidon measure-ment is not an essential indicator of the improvement.This is mainly because non-steric sea-level variations (ormass-change-associated sea-level variations) obviouslyexist within the oceans, and are clearly demonstrated insome recent studies (Chen et al. 1998a, b, 1999; Minster

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et al. 1999). A reliable assessment of the improvementcan only be estimated if we are able to remove the non-steric signals via independent techniques, e.g., using thefuture GRACE observations. However, we are con®dentof the improvement because the OISST temperature®eld is widely considered a better description of thesurface temperature variation than the WOA94 clima-tology, especially in the southern hemisphere (Reynoldsand Smith 1994).

This approach has many limitations and is only usefulin the ®rst order of approximation. Because the temper-ature data of only the top 25 m are mainly from real-timeobservations (satellite SST), which is a small portion ofthe total mixing layer, this study is not able to providereliable estimates of the interannual steric sea-levelchange. However, we do see some interannual steric sea-level change signals in speci®c regions, e.g. the easternand western tropical Paci®c, which are correlated withTOPEX/Poseidon measurements, although the ampli-tudes are much smaller (10±20% of what we get fromTOPEX/Poseidon determination in the eastern Paci®c,for example). In some speci®c regions (e.g., region D inFigs. 4, 5), the temperature dierences between the sur-face and the 25-m depth are as large as 1 °C. So, thisdirect combination will overestimate the steric eects,in some senses. The selection of dierent temporal ref-erences (4-year mean or long-term mean) and referencedepths will also aect the steric estimates. As more in situobservational data (like XBT, MBT) and satellite SSTdata become available, we can expect a more reliable 3-Docean temperature ®eld, which will lead to a further un-derstanding of steric sea-level change at various temporaland spatial scales over the oceans. A challenging task ishow to dynamically integrate historical in situ measure-ments, remote sensing data, and recent XBT observa-tions into a physically coherent 3-D ocean temperaturemodel via objective analysis or data assimilation.

Acknowledgments. The authors would like to thank the editor,Francois Barlier and three anonymous reviewers for their con-structive comments and suggestions. They, also thank AnnyCazenave for helpful discussions. This research was supported bythe National Aeronautics and Space Administration under grantsNAGW-2615 and NAG5-3129.

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