Flechtner F.M., Gruber Th., G?ntner A., Mandea M., Rothacher M., Sch?ne T., Wickert J. (Eds.) System Earth via Geodetic-Geophysical Space Techniques

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Radar Altimetry Derived Sea Level Anomalies 323

for ERS-1 and ERS-2, by NASA/CNES for TOPEX/Poseidon and JASON-1, and by NOAA for

GEOSAT. This i s publication no. GEOTECH-1252 of the GEOTECHNOLOGIEN programme of

BMBF, grant 03F0434A. Altimetry and orbit data is available through the ADS system at GFZ

http://adsc.gfz-potsdam.de/ads.

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Combining GEOSAT and TOPEX/Poseidon

Data by Means of Data Assimilation

Manfred Wenzel and Jens Schröter

1 Introduction

The global sea level is exceedingly reacting on variations of the climate. A warming

of the world ocean or the melting of large continental ice sheets for example would

lead to a sea level rise that would affect directly a large part of mankind. These

effects are reasonable well studied on the global scale but they are still uncertain on

regional or even local scale. For the period of the TOPEX/Poseidon altimetric mea-

surements Wenzel and Schröter (2006, 2007) showed that the sea level trends vary

substantially in space and time and that they are closely associated with heat and

salt anomalies in the ocean. By assimilating the TOPEX/Poseidon measurements

into a global ocean circulation model they were able to separate the individual parts

contributing to the sea level change (steric effects, oceanic fresh water budget). But

longer time-series of the global distribution of sea level variability are needed to con-

ﬁrm these results because the climate-induced decadal and secular sea level changes

may be concealed by seasonal, annual and interannual variations, which may act as

noise masking long-term trends. One step in this direction is to utilize sea surface

height (SSH) data from the GEOSAT altimetric mission (1987–1989) in combina-

tion with the TOPEX/Poseidon data (1993–2000). Both datasets will be assimilated

into a global ocean circulation model. By doing this the data gap between GEOSAT

and TOPEX/Poseidon can be ﬁlled in a dynamically consistent manner. We will then

be in a position to separate sea level rise due to inﬂow of continental waters from

warming of the ocean for a much longer time period and reduce estimation error.

2 Model and Data

For our purpose we use the Hamburg Large Scale Geostrophic model (LSG, Maier-

Reimer and Mikolajewicz, 1991; Maier-Reimer et al., 1993). In conjunction with its

adjoint this model has been used successfully for ocean state estimation (e.g. Wenzel

M. Wenzel (B)

Alfred Wegener Institute for Polar and Marine Research, 27570 Bremerhaven, Germany

e-mail: manfred.wenzel@awi.de

325

F. Flechtner et al. (eds.), System Earth via Geodetic-Geophysical Space Techniques,

Advanced Technologies in Earth Sciences, DOI 10.1007/978-3-642-10228-8_26,



Springer-Verlag Berlin Heidelberg 2010

326 M. Wenzel and J. Schröter

and Schröter, 2006, 2007). It has 2 × 2 degree horizontal resolution, 23 vertical

layers (varying from 20 m thickness for the top layer to 750 m for the deepest ones)

and the implicit formulation in time allows for a time step of 10 days. The uti-

lized global OGCM has a free surface. Mass conservation is achieved by taking into

account the volume and mass of the surface freshwater ﬂux as well as by includ-

ing the steric effects of thermal expansion and haline contraction. This offers the

possibility to combine altimetric measurements with hydrographic data in a dynam-

ically consistent manner. Details about the assimilation procedure can be found e.g.

in Hellmer et al. (2005).

Here we perform two assimilation experiments. First we make use of all available

data from altimetry of both satellite missions called GEOSAT-TOPEX/Poseidon

(GETO). It is mostly a substantial extension of the previous work reported in

Hellmer et al. (2005) and Wenzel and Schröter (2007). The relative reference

between the satellite altimeters is uncertain, as there was no period of overlap.

We accept this fact by referencing GEOSAT to its own temporal mean. The gap

to TOPEX/Poseidon is ﬁlled by the ocean model. As it turned out the results for this

gap were not satisfactorily and a second assimilation experiment was performed

using additional data.

The only continuous dataset for sea level for the whole assimilation period is land

based and consists of tide gauge records. In a preliminary study it was found that

the direct use of sea level time series at tide gauge stations has only little inﬂuence

on the general model behaviour. There are simply too many reasonable dynamically

consistent solutions for a local sea level that are the effect of regional changes in

wind forcing or local density variations in the ocean which are inside the observed

variability We therefore produced a global dataset for sea surface height which is

reconstructed from tide gauges and observed variability patterns as measured by

TOPEX/Poseidon in analogy to the study by Church and White (2006). The second

experiment is then denoted GEOSAT-TOPEX/Poseidon-Reconstructed (GETORC).

Let us next describe the datasets used in the experiment GETO in detail:

• Monthly sea surface temperatures (SST) for the period 1987–2000 (Reynolds

et al., 2002).

• Gridded ﬁelds of 10 day averages of sea surface height anomalies (SSHA)

as measured by the TOPEX/Poseidon altimetric mission for the period

1993–2000, provided by GeoForschungsZentrum Potsdam (GFZ; S. Esselborn,

pers. communication). These anomalies are combined with the SHOM98.2

mean sea surface height (MSSH; available online at the time of writ-

ing at: http://www.cls.fr/html/oceano/projets/mss/cls_shom_en.html) referenced

to the EIGEN-GRACE01S geoid (available online at the time of writing

at: http://www.gfz-potsdam.de/grace/results/grav/g001_eigen-grace01s.html)to

give absolute dynamic height values.

• Preliminary re-processed gridded ﬁelds of 10 day averages of sea surface

height anomalies (SSHA) as measured by the GEOSAT altimetric mission for

the period 1987–1989, provided by GeoForschungsZentrum Potsdam (chapter

“Radar Altimetry Derived Sea Level Anomalies – The Beneﬁt of New Orbits

Combining GEOSAT and TOPEX/Poseidon Data by Means of Data Assimilation 327

and Harmonization” by Schöne et al., 2009, this issue). These anomalies are

referenced to their own temporal mean.

• Temporal mean transports of mass, freshwater and heat as obtained by differ-

ent authors and as they are summarized e.g. by Bryden and Imawaki (2001)

and by Wijffels (2001). Transport constraints are not applied for the Antarctic

Circumpolar Current (ACC).

• The climatological mean temperatures and salinities from the WOCE Global

Hydrographic Climatology (WGHC; Gouretski and Koltermann, 2004) in com-

bination with the mean annual cycle from the World Ocean Atlas (WOA01;

Conkright et al., 2002). These data are supplied to the assimilation procedure

with small weights thus serving only as background information.

• The mean annual cycle of temperatures, salinities and horizontal velocities on

two sections in the Weddell Sea area and on four sections in the Ross Sea.

These data are taken from high resolution model experiments of the Weddell

Sea (Schodlok et al., 2002) and the Ross Sea (Assmann and Timmermann, 2005)

whose water mass characteristics and circulation are in good agreement with local

observations.

In the second experiment GETORC, we additionally use SSHA ﬁelds that

are reconstructed from tide gauges and an EOF basis deduced from the

TOPEX/Poseidon data, in analogy to Church and White (2006). These data will

be applied for the whole period 1987–2000.

3 Results

The data assimilation produces minor changes in atmospheric forcing which is in

agreement with observed atmospheric variability. Further, the initial temperature

and salinity ﬁelds of the ocean can be adjusted. Both changes result in a tem-

poral evolution of the modelled ocean which is as close to the observations in

space and time as possible and follows the exact model equations. All ocean ﬁelds

are in dynamic equilibrium and data counterparts can be modelled in satisfactory

agreement with the observed values. It is found that the initial state has only little

inﬂuence on the evolution. The most important changes are in the wind and thermal

forcing. Freshwater ﬂuxes have small local effects, however their global integral

directly inﬂuences the global sea level variation.

Figure 1 shows the modelled global mean sea level anomaly (GMSLA) after

assimilation for the experiment GETO in comparison to the above mentioned

satellite measurements. While the model reproduces the GMSLA derived from

TOPEX/Poseidon quite well this is not the case for GEOSAT. Even the trend

during the period 1987–1989 is not reproduced. The model prefers a positive

trend while the data show a negative one. Anyhow, the modelled positive trend

seems to be more realistic to some extent as one can conclude from the GMSLA

reconstructed by Church and White (2006) from tide gauge records that shows a

positive trend throughout the period 1986–2000. Furthermore, Fig. 1 shows that

from hydrographical data alone the assimilation has no reason to produce a sea

328 M. Wenzel and J. Schröter

Fig. 1 Temporal evolution of the global mean of the sea level anomaly from assimilation exper-

iment GETO compared to the satellite data used. Because the GEOSAT data are anomalies only

with no own reference, they are adjusted to have the same temporal mean as the model solution.

For comparison the SSHA data reconstructed from tide gauges (blue curve) are included together

with the error bars (blue shading) taken from Church and White (2006)

level rise as strong as given by Church and White (2006), although its steric part

during this period appears to be reasonable. To demonstrate the latter Fig. 2 shows

the evolution of the oceans heat content from experiment GETO. Its trend ﬁts well

to the results of Levitus et al. (2005). Therefore, the missing part must contribute to

the oceanic fresh water budget (eustatic sea level change) that remains unrestricted

during most of the assimilation period as long as the models SSHA is constrained by

data only for disconnected sub-periods that do not have a common reference, i.e. as

for TOPEX/Poseidon an absolute reference is needed for the GEOSAT data before

reliable statements are possible for the past 20 years. Another possibility to improve

the situation would be to link the different SSHA datasets by additional information

about the evolution of the sea level during the whole assimilation period.

Consequently we produced the second experiment GETORC. The SSHA data

reconstructed from tide gauges are utilized as additional information during the

whole assimilation period. Also for GETORC the negative trend from the GEOSAT

data during 1987–1989 is not reproduced (Fig. 3). Nevertheless, now the tem-

poral evolution of the GMSLA ﬁts well to the one given by Church and White

(2006) for the whole period 1987–2000. Beside this, during the time with the

TOPEX/Poseidon SSHA employed (1993–2000) it is even further improved. This

improvement is not only conﬁned to the GMSLA. It also applies to the spatial

structure of the sea level. The root mean square (RMS) value for the difference

between the modelled SSH and the data is only slightly smaller for GETORC than

for GETO during the GEOSAT period (1987–1989), but it is signiﬁcantly reduced

Combining GEOSAT and TOPEX/Poseidon Data by Means of Data Assimilation 329

Fig. 2 Temporal evolution of the global oceans heat content anomaly for the depth ranges

[0–700 m], [700–2,750 m] and [2,750 m-bottom]. For the upper 700 m the corresponding annual

mean values derived from Levitus et al. (2005) are included

Fig. 3 Temporal evolution of the global mean of the sea level anomaly from assimilation exper-

iment GETORC compared to the satellite data used. Note that in this experiment the SSHA data

reconstructed from the tide gauges are assimilated!

for the TOPEX/Poseidon period (Fig. 4a, b). In general the RMS differences now

coincide approximately with the values that result from the differences between the

SSHA data derived from altimeter and the ones reconstructed from tide gauges.

Accordingly the spatial correlations between model and data have increased for

330 M. Wenzel and J. Schröter

Fig. 4 Upper row: temporal evolution of the spatial RSM of the difference between the model

SSHA and the data. Lower row: the corresponding correlations for the two experiments GETO

(left: a, c)andGETORC(right: b, d). For comparison the light grey shading gives the corre-

sponding values for the difference between the tide gauge reconstruction and the satellite data

both periods (Fig. 4c, d). Both facts strongly indicate that the model solution proﬁts

from assimilating this additional dataset that bridges the gap between GEOSAT and

TOPEX/Poseidon.

To analyse the regional distribution of the modelled sea level trend (Fig. 5) in

more detail it is dissected into the parts that stem from the eustatic contribution, i.e.

the ocean fresh water budget, and from the steric effects, i.e. thermal expansion and

haline contraction. On global average the eustatic part (Fig. 5b) contributes about

two thirds (1.98 mm/year) to the total sea level rise (2.95 mm/year, Fig. 5a) although

on regional to local scale it is less important than the thermosteric (Fig. 5c) and the

halosteric part (Fig. 5d). Both, the thermosteric and the halosteric changes, are of

the same order of magnitude locally and they nearly compensate in large parts of

the world ocean, as has been demonstrated already by Wenzel and Schröter (2006,

2007), whereas on global average the halosteric trend is negligible (0.05 mm/year)

compared to the thermosteric (0.92 mm/year).

A further inspection of the results on a global scale shows, that about half of

the thermosteric sea level rise stems from an upper ocean warming (0–700 m). The

development of the heat content of this layer (Fig. 6a) is mainly constrained via the

sea surface temperature and by the climatological hydrographic annual cycle and it

ﬁts well to the estimates of Levitus et al. (2005), even better than for experiment

GETO (Fig. 2). In the lower depth ranges (700–2,750 m and 2,750 m-bottom) we

ﬁnd ocean warming, an increasing heat content too. Both layers add about one quar-

ter to the total heat surplus each, i.e. together as much as the upper 700 m. Thus, the

Combining GEOSAT and TOPEX/Poseidon Data by Means of Data Assimilation 331

Fig. 5 (a) Local sea level trend dissected into its (b) eustatic, (c) thermosteric and (d)halosteric

contribution. Note the enlarged colour scale for the eustatic part!

Fig. 6 (a) Temporal evolution of the global oceans heat content anomaly for the experiment

GETORC as in Fig. 2, (b) the resulting global mean sea level anomaly dissected into its

thermosteric, halosteric and eustatic contribution

deep ocean adds an essential contribution to the total (thermo)steric sea level rise.

In any case, the global steric sea level variations give only about one third of the

total trend. The subordinate importance of the steric trend compared to the eustatic

during this period has already been stressed by Jevrejeva et al. (2008). Furthermore,

in comparison with the eustatic variations, the steric show a much weaker annual

cycle that is out of phase (Fig. 6b), a well known result from hydrology.

4 Summary and Conclusions

In order to assess the sea level rise for periods longer than the continuous observa-

tions by TOPEX/Poseidon we performed two assimilation experiments. Both use the

GEOSAT mission data additionally and bridge the gap between these observations

332 M. Wenzel and J. Schröter

in a dynamically consistent manner in accordance with standard ocean observations.

It is found that the global fresh water ﬂuxes of the ocean remain uncertain to such an

extent that the evolution of the sea level cannot be concluded from measurements

of ﬂuxes or estimates of land ice melting. Without continuous records of the sea

level no reliable estimates can be made, as has been demonstrated in the experiment

GETO.

We therefore used additional observations provided by time series of sea level at

tide gauges. From these data global maps of sea level anomalies were constructed

using the EOF technique applied in Church and White (2006). These maps are sub-

sequently assimilated in addition to the sea surface height anomalies from altimetry.

Experiment GETORC then provides the answer to the total sea level rise and to

its temporally and spatially varying contributions. Ocean warming accounts for

one third of global sea level rise by steric expansion. Half of it is conﬁned to the

upper 700 m of the ocean, in good agreements with the independent analysis of

Levitus et al. (2005). The other half of oceanic thermosteric expansion is found in

equal parts above and below the depth of 2,750 m. That is we diagnose very strong

warming of the deep ocean which cannot be deducted from the very sparse in situ

observations alone. In addition to warming of the ocean we ﬁnd an inﬂow of fresh

water with amplitude close to 2 mm/year. This value is also on the high side but it is

supported by the analysis of Jevrejeva et al. (2008). Wrapping up we can conclude

that a relative reference has been found between the satellite missions GEOSAT and

TOPEX/Poseidon which is physically reasonable and in accordance with oceanic

observations, in particular tide gauge records.

Acknowledgement This is publication no. GEOTECH-1253 of the GEOTECHNOLOGIEN pro-

gramme of BMBF, grant 03F0434B. We are grateful to the anonymous reviewer for helpful

comments and suggestions.

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