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Anstract: Global Sea Level Analysis Based on ERS-1 Altimeter Data (M. Anzenhofer, Th. Gruber, Ch. Reigber and M. Rentsch)
Anstract: Global Sea Level Analysis Based on ERS-1 Altimeter Data
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Global Sea Level Analysis Based on ERS-1 Altimeter Data

M. Anzenhofer, Th. Gruber, Ch. Reigber and M. Rentsch GeoForschungsZentrum Potsdam, Dept. 1, D-PAF, D-82230 Oberpfaffenhofen


Global sea level observations are necessary to answer the urgent questions about climate changes and their impact on the socio-economy. At GFZ/D-PAF, reprocessed ERS-1 altimeter OPR02 is used to generate a time series of monthly sea surface height models from April 1992 to March 1995. The reprocessing consists of D-PAF's improved satellite ephemerides, the inclusion of Grenoble tidal model, the removal of a time bias and application of different range corrections. The three year time series was taken to estimate the rate of change of global mean sea level. A +2 mm sea level rise per year was estimated, which is far below the assumed 30 to 50 cm in the next century. Regional trends, however, show extreme differences in the sea level variations: A sea level rise in the tropics and the Indian ocean (locally up to 10 cm/year), but a sea level fall in the eastern Pacific and higher latitudes. For the quality assessment, comparisons to tide gauge measurements were performed, indicating a high coherence to the ERS-1 result. The relation of sea level variations and climate change was examined in the global system ocean-atmosphere, which was represented by sea surface temperatures, wind speeds and wave heights. It was demonstrated that the sea level change can be attributed to interannual variability and El Niño.

Keywords: Sea Level, Altimetry, ERS-1, Ocean-Atmosphere, D-PAF


Urgent questions about possible climate changes may be answered by means of secular rates of change of the sea level. Trends in the sea level are considered as indicators of a global temperature rise caused by the increase of greenhouse gases. Between 1o and 4o Celsius can be expected for the next century. If this happens, then the sea level will rise 30 to 50 cm (Church et al.,1991; Houghton and Woodwell, 1989), caused by the melting of glaciers, polar ice caps and thermal expansion of the oceans (Church et al., 1991; Meier, 1984). Such a scenario would lead to socio-economic consequences that cannot be predicted (Broecker,1996). The presented results (see also: Anzenhofer and Gruber, 1996; Nerem,1995), however, show, that the sea level rise has regional characteristics, i.e. there are areas, which are much more affected than others.
Before the advent of satellite altimetry the sea level could only be observed through tide gauges. This data, however, has major disadvantages:

  • The global distribution is uneven due to their location on the shores of continents, and islands exclusively. Thus a global trend estimation of the sea level is impossible.
  • Tide gauge measurements may systematically be shifted due to post-glacial rebound or tectonic uplift towards other stations.

The advantage of altimetry is that the sea surface can be monitored in a continuous and repeated manner in a common reference datum. The required accuracy for studying the sea level, however, only fulfills data of the European satellites ERS-1 and ERS-2 and the US/French satellite TOPEX/POSEIDON. Due to the insufficient knowledge of altimeter drifts, other systematics and missing overlaps, measurements of SEASAT, GEOS-3 and GEOSAT (Allan, 1983; Bonavito et al., 1975; Cheney et al., 1991; Horai, 1982) cannot be used for a sea level study.
The paper at hand will show, that the secular changes of the sea surface are in the millimeter range, which is far below the accuracy of satellite orbits, altimeter range and altimeter corrections. Thus, a very careful data preparation and calibration is needed.
If the assumption of a sea level rise caused by global warming is true, then other parameters of the global system ocean-atmosphere must also exhibit changes in their temporal behaviour. For this purpose, sea surface temperatures, wind speeds and wave heights were analyzed in the same manner as sea surface heights. The changes obtained, then were correlated and interpreted within the framework of the ocean-atmosphere system.


The following chapter describes the different data used for the sea level study. The altimeter measurements is the base of the sea level study. Thus the data and its upgrade is described in detail.

Sea Surface Heights from ERS-1 Altimeter

Precise altimeter products (OPR) from the European Space Agency's ERS-1 mission (CERSAT, 1995) are used in this study as a baseline. For the sea level study consistently processed ERS-1 data for the period between launch and August 1995 were available. Due to the limited spatial resolution of the 3 day repeat cycle periods, however, only data from April 15, 1992 until March 20, 1995 was used. During the sea level study the other available data of the second multidisciplinary phase were not used, because they didn't cover a complete year. The annual cycle causes periodic sea surface changes whose power is much higher than that of possible secular sea level change. Thus, incomplete years of altimeter data cause systematic artifacts in the analysis result. Furthermore, OPR data starting with the second multidisciplinary phase have been processed with a new software version. A mixing of these versions could cause systematics in the range measurement and in other parameters, such as the microwave radiometer measurements.
Earlier investigations and the ERS cross calibration (Anzenhofer et al., 1996; Benveniste, 1996a, 1996b) have shown that the original OPR cannot be used for a sea level study. Additional corrections, the exchange of up-to-date geophysical corrections and the merging of consistent orbit ephemerides were necessary. They are listed in the following paragraphs.

  • Time Tagging: It was found by different groups (Anzenhofer et al., 1996a; Benveniste, 1996a, 1996b) that the OPR data contains a time tagging error. For its estimation the method described by Marsh and Williamson (1982) was used, which relates the crossover differences and the range derivative differences between ascending and descending arcs with the time bias. The processing of 3 years of ERS-1 data indicated a time bias of +1.5 msec. The time bias was considered by adding it to the measurement times and by remerging of the satellite ephemerides.
  • Satellite Ephemerides: The original OPR data set is based on D-PAF orbits revision 1, which are computed from a former gravity field model PGM035 (Schwintzer et al., 1993). Orbit ephemerides based on this gravity model have a radial accuracy of 15 cm. This is not accurate enough for a sea level study. Therefore, a reprocessing of all orbits was initiated with the up-to-date gravity model PGM055, which is an upgraded GRIM4-S4 gravity field (Schwintzer et al., 1996). The radial error of these orbits was reduced to 8 cm.
  • Altimeter Range: During the cross-calibration of the ERS- 2 altimeter against the ERS-1 altimeter it was apparent, that two additional corrections have to be applied to the altimeter ranges (Benveniste, 1996a, 1996b). These corrections are necessary to compensate for two effects: Firstly, the drift of the on-board ultra-stable oscillator (USO drift), which causes an increasing range error. Secondly, range jumps are produced by changes in the clock asymmetry caused by low temperatures during switch-off of the instrument after instrument anomalies. The effect of both corrections are shown in figure 1.

  • Figure 1: ERS-1 Range Corrections

    The corrections are provided as time-sorted tables by ESRIN.

  • Ionosphere: The ERS-1 altimeter is a single-frequency instrument. This is the major disadvantage towards TOPEX/POSEIDON, where the ionospheric correction can be derived from the dual-frequencies. Therefore, ionospheric models must be introduced to ERS-1 altimeter data. Besides the Bent model (Bent et al., 1975; Llewellyn and Bent, 1973), IRI95 (Bilitza, 1996) was merged to the data in order to intercompare two different ionospheric models.
  • Ocean Tide and Loading: For elastic ocean tides and loading effects the recent FES95.1 model (LeProvost et al., 1996) was additionally included to the standard data sets.

Wave Heights from ERS-1 Altimeter

The slope of the altimeter return signal is highly correlated with the ocean wave heights. If the altimeter pulse is reflected by a calm sea surface then the backscattered energy curve plotted versus the elapsed time is steep. A turbulent sea surface with high waves results in multiple reflections of the altimeter pulse and thus a flat backscattered energy curve. The coherence in turn is used to refer the wave heights to the steepness of the backscattered altimeter signal (Hancock et al., 1980).

Wind Speed from ERS-1 Altimeter

Just as the wave heights, the wind speed has an influence on the altimeter return signal. The radar backscatter returned to the satellite is modified by wind-driven ripples on the sea surface and, since the energy of these ripples increases with wind velocity, backscatter increases with wind velocity.

Sea Surface Temperatures from NMC

The sea surface temperatures used for the study were not taken from ERS-1's ATSR. Instead the global sea surface temperature grids from the U.S. National Meteorological Center (NMC), Washington were retrieved (Reynolds, 1987; Reynolds and Smith,1993). NMC mixes in-situ measurements (ships and buoys) and AVHRR data of the NOAA satellites. The base of the mixed models are in-situ data. The satellite measurements then are used to complement areas with sparse data distribution. By means of a regression analysis, a transformation of the satellite's skin to bulk temperatures is performed. By an optimum interpolation technique, weekly sea surface temperature grids are interpolated. The spatial resolution of the global grids is 1ox1o degree (Reynolds and Smith, 1993). Monthly grid models are also available.

Tide Gauges

The tide gauges used for the sea level study are obtained from the PSMSL Public Access Directory, where the files of the permanent service for mean sea level are stored. The PSMSL data set comprises monthly and annual means of sea level (Pugh, 1987; Woodworth, 1996) measured at tide gauge stations.


The sea level investigations are performed by comparing monthly grid models with a long-term mean. The transition to relative measures enables the usage of small values. For the long-term mean a simple averaging of the 36 monthly (3 years) grid models is performed. Monthly solved grid models of sea surface heights means, that the data of one month are equally weighted and interpolated to one grid model. The spatial resolution is always 1 degree. The monthly grids come from different instruments and sources. Further on, for the generation of grid models different editing and quality criteria are used. This implies grid models with undefined nodes that are not common to other grid models. Investigations in the global system ocean-atmosphere have demonstrated (Fu and Cheney, 1995), that there exist significant seasonal differences between northern and southern hemisphere. This means that if grid models with different numbers of defined and undefined grid nodes are intercompared, then systematic shifts may happen. In order to avoid this error source, a common masking for all grid models was performed.

For sea surface height, sea surface temperature, wind speed, wave height and altimeter corrections (for quality assessment) two analyses have been performed to extract variations within the investigation time period:

  1. Global Rate of Change. The first step of this method is to subtract the monthly grid models from the long-term mean (3-year model). Then the differences in the grid nodes are simply averaged to one mean. The obtained value now represents the mean deviation from a stationary state. The successive processing of all monthly grids leads to a time series which in turn is used to estimate the rate of change. This is done by a regression analysis. The regression coefficient (and its standard deviation) defines the global rate of change for the abovementioned parameters, like sea surface height, sea surface temperature, wind speed, wave height and altimeter corrections.
  2. Local Rates of Change. With the availability of the global rate of change value the question is raised, whether the trend is evenly distributed over the oceans or if there are regional characteristics. Therefore, a regression analysis was performed for each grid node of the monthly models. The estimated regression coefficients (and standard deviations) or local rates of change then were visualized by raster plots.

Result and Quality Assessment

Due to the large number of different investigations, table representations comprise the results.

Sea Level Trend

Figure 2: Sea Level Trend

Sea Level Trend: The global rate of change indicates a sea level rise of globally +2.0±1.9 mm/yr. Regional characteristics, however, are evident, a sea level rise in the tropics and around the western boundary currents and a sea level fall in the eastern Pacific and in higher latitudes. But,the global trend is far below the anticipated 30 to 50 cm for the next century. The value coincides with former tide gauge investigations (Fu and Cheney, 1995; Trupin and Wahr, 1990).

Figure 3: Sea Surface Temperature Trend

Sea Surface Temperature Trend: For the sea surface temperatures the global rate of change marks a slight global warming of +0.042±0.032 K/yr. A significant disproportion between northern and southern hemisphere trends is evident, a warming in the southern and a cooling in the northern hemisphere. A coherence between the sea level and the sea surface temperature trends, however, can be found around the western boundary currents and the tropics. It is physically impossible that the obtained disproportion has stationary character. Thus an interannual variability with periods greater than 3 years is more realistic, e.g. decadal period (Latif et al., 1995; Groetzner et al., 1996).

Figure 4: Wind Speed Trend

Wind Speed Trend: The global rate of change indicates also a positive trend of +64±29 mm/s/yr. The anticorrelation to the sea surface temperature is clearly visible. This fact excludes data and processing errors of the sea surface temperatures. The increase of wind speeds in the northern and decrease in the southern hemisphere confirms an interannual variability mentioned above.

Figure 5: Wave Height Trend

Wave Height Trend: The expected high coherence with wind speed trends, as shown above, is evident, a positive trend of the wind speed leads to an increase of corresponding wave heights and vice versa. The global trend is positive +11±12 mm/yr, too.

For the quality assessment of the sea level result, the altimeter corrections were examined in the same manner as sea surface temperatures or wind speeds: the corrections were gridded, filtered by the common mask and global/local rates of change were estimated.

Figure 6: Wet Tropospheric Trend

Figure 7: Dry Tropospheric Trend

On the sea surface the wet tropospheric correction has a global trend of +0.8±0.5 mm/yr. This value points to a markable influence on the sea level result. The coherence with the sea surface temperatures, as seen in figure 3, reflects an internal consistency and thus data quality. The correction derived from ERS-1 radiometer is believed to be accurate. With a global trend of -0.1±0.3 mm/yr the dry troposphere has almost no influence on the sea level result. Only small regional structures are visible. The correction is believed to be very accurate.

Figure 8: EM-Bias Trend

Figure 9: Inv. Barometer Eff. Trend

Similar to the dry tropospheric correction, the EM-bias has almost no influence on the sea level estimate. The global trend is only +0.1±0.2 mm/yr. Due to its dependence on wave heights, the regional structures of wave heights are visible. With a global trend of -0.4±1.3 mm/yr the inverse barometer effect influences the sea level estimate. The trends, however, have regional structures. These are concentrated around the main pressure cells of the atmosphere. The correction is critical, because pressure data are mainly derived from model runs and not from real measurements.

Figure 10: Ionospheric Trend

Figure 11: Tide Gauges Trend

The global trend of the ionospheric correction (Bent model) on the sea level is -8.6±1.7 mm/yr, which is four times the sea level trend estimate. The regional influence looks like a global systematic shift. The huge value itself demonstrates that the ionospheric correction is the most critical point of the sea level study. As described above, the tide gauges data are retrieved from the PSMSL archive. To show the excellent coherence between the sea level trend and tide gauges measurements, only tide gauges are investigated, which cover the time period between April, 1992 and March, 1995. Then a regression analysis of the tide gauge time series was performed. The trend values were gridded with a large influence circle to get a filled raster plot for intercomparison.

By overlaying the sea level trend image (figure 2) and the image above almost all positive and negative sea level trends are confirmed by tide gauge measurements.

The ERS-1 altimeter is a single-frequency instrument. This means that the ionospheric correction cannot be retrieved from path delays as it is done for TOPEX/POSEIDON dual-frequency measurements. Thus, the ERS-1 ionospheric correction must be computed from ionospheric models, like Bent, IRI90 or IRI95. These models strongly depend on solar activity. Anomalies like sun storms cannot be modeled. Thus, the ionospheric correction based on models can never be as accurate as dual-frequency derived corrections. In order to find the appropriate model for the sea level study, the Bent and IRI95 models are compared with TOPEX ionospheric corrections. Therefore, the differences of Bent and TOPEX corrections (IRI95 and TOPEX corrections as well) were computed and displayed as a time series. Then both time series passed through a regression analysis:

  • Trend of (Bent - TOPEX): -0.7 ± 0.9 mm/yr
  • Trend of (IRI95 - TOPEX): -2.8 ± 1.3 mm/yr

It seems that the Bent model matches the real ionosphere much better than IRI95. The estimated values demonstrate again that the ionospheric correction is the most critical point of the sea level study. A change to IRI95, for example, leads to a global sea level fall of -1 mm/yr.


The investigation of upgraded ERS-1 altimeter data yielded a global sea level rise of +2 mm/year within April 1992 and March 1995. For the same time period wind speeds, wave heights and sea surface temperatures were analyzed. Global positive trends were found as well. Besides global trends, local rates of change were estimated, too. A sea level rise was detected in the tropics and in the Indian ocean and a sea level fall in higher latitudes, respectively. The local rates of change of wind speeds, wave heights and sea surface temperatures exhibited a disproportion between variations on the northern and southern hemisphere. Correlation to the sea level change could be identified. A high coherence between parameters of the global system ocean-atmosphere was evident and could be demonstrated. Thus, it can be supposed that the variations can be attributed to periods larger than the investigated 3 years (Hastenrath, 1984; Houghton and Woodwell, 1991; Latif et al., 1995). The small amounts of global and local rates of change raise the question about their significance. Therefore, the altimeter corrections were individually processed and analyzed. It was found that deficiencies with respect to their quality and long-term behaviour exist. Especially the ERS-1 ionospheric correction, which is derived from a model, is very critical. Depending on the model adopted for the correction, either a sea level fall or a sea level rise can be produced. Investigations, however, have shown, that the Bent model matches much better the ionospheric correction derived from TOPEX dual-frequency measurements than the IRI95 model. Thus a sea level rise is more likely.

The question about the long-term behaviour of the sea level trend is attempted to be answered by a 14 years time series of sea surface temperatures.

Analysis oy 14 years of SST

Figure 12: Analysis of Sea Surface Temperatures and Amplitude Spectrum

The low-passed sea surface temperature time series shows that longer periods of global warming and cooling happened in the past. Volcanic eruptions, El Niño/ENSO and other phenomena (decadal period) can be attributed as reasons for the temperature changes (Keeling et al., 1989; Latif et al., 1995). Due to the relationship between the sea level and sea surface temperatures (Stammer and Wunsch, 1994), it can be concluded that longer periods of sea level rise and fall happened in the past, too. Thus, the analysis time period of 3 years is much too short for long-term predictions. During the sea level study it became clear that the altimeter corrections and their accuracy make a significant sea level estimate questionable. By embedding the sea level in the global system ocean-atmosphere, however, it is possible to answer open questions and to verify the results.

Two major requirements for future activities must be set up:

  1. Long-term observations of oceanic and atmospheric parameters are absolutely necessary for climate studies.
  2. Well calibrated and overlapping data of different sensors/missions is needed. Corrections to data must all have the same level of accuracy.


A number of data was provided by different institutes. We thank the F-PAF for the operational provision of ERS OPR2 altimeter data. The IRI95 model was kindly provided by D. Bilitza. A thank belongs to O.B. Andersen and R. Ray for the preparation of the FES95.1 tidal loading modules. The range correction tables for ERS-1 were obtained from ESRIN/ESA. A special thank belongs to Richard Reynolds from NMC, Washington, for the preparation of sea surface temperature models and his helpful comments.


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Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry