ESTIMATION OF A GLOBAL MEAN DYNAMIC TOPOGRAPHY COMBINING ALTIMETRY, IN SITU DATA AND A GEOID MODEL: IMPACT OF GRACE AND GOCE DATA

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1 ESTIMATION OF A GLOBAL MEAN DYNAMIC TOPOGRAPHY COMBINING ALTIMETRY, IN SITU DATA AND A GEOID MODEL: IMPACT OF GRACE AND GOCE DATA M.-H. Rio (1), F. Hernandez (2), J.-M. Lemoine (3) (1) Istituto di Scienze dell Atmosfera e del Clima, Via Fosso del Cavaliere, Roma, Italy (2) Collect Localisation Satellite, 8-10 rue Hermes, Parc Technologique du canal, Ramonville St Agne, France (3) LEGOS/GRGS, 18 avenue Edouard Belin, Toulouse Cedex4, France Abstract: The estimation of a precise and full scale Mean Dynamic Topography (MDT) is a crucial issue to compute absolute dynamic topography level from altimetric signal while so far only Sea Level Anomalies can be accurately deduced. The goal of this paper is to study the impact of recent Grace geoid model to estimate a long wavelength global MDT and understand how it can be combined to in situ and altimetric observations to obtain a full scale field. Also, the impact of future Goce data is assessed. The subtraction of a Grace geoid model to an altimetric Mean Sea Surface provides an improved estimate of the ocean MDT s spatial scales longer than 333 km in respect to the use of previous geoid models. Also, at high latitudes and in strong coastal currents, this information can be used to improve the Levitus climatology providing a first guess for the computation of a full resolution mean. Synthetic estimates of the full scale mean field are obtained subtracting synoptically the altimetric sea level anomaly to in-situ measurements of the full dynamical signal and are then used to improve the first guess using an inverse technique. In order to simulate the spatial resolution allowed by the use of future GOCE data, the obtained MDT is filtered from spatial scales shorter than 100 km and its efficiency to reference altimetric anomalies is investigated and compared to the full scale solution. A similar exercise is done in the Sicily channel area of the Mediterranean Sea. In this region, as in western boundary currents, rms differences to independent observations is reduced up to 15 % of the signal variance using the full scale field so that Goce data will still have to be combined to other high resolution MDT estimates to obtain a full scale solution appropriate to reference altimetric anomalies. 1 Introduction Data from GOCE (Gravity field and steady-state Ocean Circulation Explorer), whose launch is foreseen in 2006, should allow to estimate the Earth geoid with an unprecedented accuracy of around 1 cm at spatial scales down to 100 km. This will have a huge impact in geophysics [3]. In particular in oceanography, an accurate knowledge of the marine geoid will allow to compute absolute dynamic topography values from satellite altimetric measurements whereas so far only the variable part of the ocean dynamic topography (or Sea Level Anomalies SLA-) can be deduced from altimetric heights at an accuracy (2-3 cm) compatible with ocean circulation studies. The direct subtraction of a geoid model (i.e. the geoid height above a reference ellipsoid) from an altimetric Mean Sea Surface (MSS, i.e. the mean sea level over a given period above the same reference ellipsoid) results in an estimate of the ocean Mean Dynamic Topography (MDT) over the considered period. Obtained MDT can then be used to reference altimetric SLA, i.e. to compute -adding the MDT estimate to the SLA value- the ocean absolute dynamic topography. This is a crucial issue for the further understanding, modelling and forecasting of the ocean circulation from mesoscale to global scale. In particular, significant improvements should be obtained in transport estimation [4] as well as in data assimilating forecasting systems [6]. To compensate for the present lack of an accurate geoid at all scales, alternative solutions to estimate a MDT have been developed. They are based on climatological datasets [10], on General Circulation Models as OCCAM [1], on inverse modelling [5], on the combined use of altimetry and drifting buoy observations [11, 20]. Lately, a solution was obtained by [17] combining altimetry, a geoid model and in situ velocity and dynamic height measurements. Goal of this paper is to study the impact of the recently available Grace geoid models to estimate an accurate full scale MDT and to assess the impact of future GOCE data. In the first section, we characterize the efficiency of Grace-only MDT (i.e. issued from the direct combination of a GRACE geoid model and an altimetric MSS) to compute absolute altimetric signal. Results are used in section 2 to compute a full scale MDT combining altimetric, in situ and Grace data using a method by [17]. This solution is filtered in section 3 from spatial scales shorter than 100km in order to simulate future GOCE-only MDT and the efficiency of the filtered solution to reference altimetric anomalies in respect to the full scale solution is investigated. A similar exercise is also done in the Sicily channel area using a MDT calculated for the Mediterranean Sea by [16]. A summary of main results and conclusions are given in section 4. Proc. Second International GOCE User Workshop GOCE, The Geoid and Oceanography, ESA-ESRIN, Frascati, Italy, 8-10 March 2004 (ESA SP-569, June 2004)

2 2 IMPACT OF GRACE DATA ON ESTIMATING THE OCEAN MDT 2.1 Estimation of grace-only MDT Two geoid models computed from GRACE data are currently available for testing. The first one, EIGEN- GRACE01S [12] was estimated at GFZ (GeoForschungsZentrum, Potsdam) from 39 days of Grace data while the second one, model GGM01 [18] was estimated at CSR (Centre for Space Research, University of Texas) with 111 days of Grace data. Reference [19] show the strong improvements in term of geostrophic currents evaluation permitted by the combined use of GGM01 model and an altimetric Mean Sea Surface (MSS) at scales longer than 500 km in respect to the previous geoid model EGM96 ([9]). In this study, we developed the EIGEN-GRACE01S geoid model at degree/order 48 (corresponding to a 416 km spatial resolution, for which the theoretical cumulated error level is optimal and equal to 7 mm) and subtracted it to MSS CLS01 ([2]) determined from 7 years of altimetric data (TOPEX and ERS1,2) and developed at the same degree/order to obtain a first Grace-only MDT (hereafter GR48 MDT). In order to assess the quality of Grace shortest scales, a similar solution (hereafter GR60 MDT) is computed at degree and order 60 (333 km spatial resolution). It exhibits a noisier signal at low and mid latitudes but gradients associated to the main currents are enhanced. 2.2 Efficiency of Grace-only MDT to reference altimetric anomalies We investigate the efficiency of the Grace-only MDT solutions to reference altimetric SLA. For that purpose, all drifting buoys deployed in the framework of WOCE and TOGA international programs from 1993 to 2000 are considered providing a significant dataset of more than velocities with a satisfying spatial coverage (although not homogeneous: highest densities are obtained in the North Atlantic ocean and the Eastern Pacific while few data are available south of 60 S). Velocities are processed in two steps in order to extract their only geostrophic component. First the Ekman current is estimated using a method by [15] and subtracted to the total current velocity. Then a 3 day low pass filtering is applied to get rid of tidal currents, inertial oscillations and other high frequency ageostrophic phenomena (Stoke s drift, internal waves ). Altimetric SLA are interpolated in term of velocity anomalies at the buoys days and positions using a multivariate objective analysis ([8]) and absolute altimetric velocities are obtained adding the mean geostrophic circulation associated to the various MDT solutions (mean geostrophic velocities are obtained through a simple differenciation between adjacent grid points). Root Mean Square (RMS) difference and vectorial correlation coefficient are then computed between the altimetric absolute velocities and the in-situ geostrophic velocities. cm/s Fig.1: RMS differences (left for the zonal component, right for the merid ian component) between in situ geostrophic velocities and absolute altimetric velocities computed using GR60 MDT. Black dots are superimposed on boxes where the use of Lev1500 MDT reduces the rms difference to observations. In Fig.1, zonal and meridian rms differences obtained using GR60 MDT are displayed into 20 by 20 boxes. For both velocity components, strongest differences (up to 25 cm/s) are obtained in the equatorial and tropical bands as well as in Western Boundary Currents (WBC). Elsewhere, differences are less than 15 cm/s. These values account for errors on Grace geoid model but also for errors on in situ geostrophic velocities (measurement and processing errors) and errors on interpolated altimetric velocity anomalies. At mid and low latitudes, away from western boundary currents, better results are obtained using GR48 MDT (not shown). In these areas, spatial scales smaller than 416 km as resolved by Grace data introduce noise in the MDT computation meaning that Grace data are not accurate enough at that resolution to correctly constrain the mean circulation field. Inversely, at high latitudes and in western boundary currents, the shortest scales present in GR60 MDT result in stronger and more realistic gradients.

3 These results represent a strong improvement in the mean ocean circulation description in respect to the use of previous geoid models. For comparison, same validation exercise was done using a MDT (hereafter EIG60 MDT) obtained combining the EIGEN2 geoid model (which was computed at GFZ integrating 6 months of CHAMP data [13]) and MSS CLS01 both developed at degree/order 60. RMS differences are enhanced by 10% in most boxes for both velocity components and between 20 and 50% at low latitudes for the zonal component. Global vectorial correlation is reduced to 0.61 (in respect to 0.65 with GR60 MDT). In order to further assess the efficiency of Grace only MDT to reference altimetric anomalies, we compare the previous rms differences to the corresponding values obtained using a climatology relative to 1500m derived from Levitus [10] hydrological dataset (hereafter Lev1500 MDT). Black points on Fig.1 correspond to 20 by 20 boxes where rms differences are reduced using Lev1500 in respect to both Grace-only MDT. Except for the East Pacific equatorial band they correspond mainly to the low and mid latitudes. In these regions, the smoother Lev1500 field is more efficient to reference altimetric SLA. Inversely, at high latitudes and in western boundary currents best results are obtained using the Grace-only MDT. 2.3 Use of Grace data to estimate a full scale MDT The previous section highlighted the significant information on MDT wavelengths larger than 333 km contained in Grace-only MDT at high latitudes and in strong currents. In a study by [17] a global and full scale Combined MDT (CMDT RIO03) was obtained using the following two steps method: First, a MDT was computed subtracting the geoid model EIGEN-2 to the MSS CLS01 at spherical harmonics degree 30. To provide the scales shorter than 660 km, the Lev1500 climatology was merged with the resulting MDT, both weighted by their respective errors. This solution provided a first guess for the computation of a global and full scale MDT. Then, a synthetic technique was used to combine in situ measurements and altimetric data: TOPEX and ERS1,2 altimetric anomalies were subtracted to in-situ measurements of the full dynamical signal (buoy s velocities from the WOCE-TOGA program from 1993 to 1999 and XBT, CTD casts from 1993 to 2001). The resulting values provided local estimates of the mean field - in term of currents or dynamic topography which were used to improve the first guess using an inverse technique. In a similar approach, we use the results obtained in section 2.1 to compute an improved MDT first guess and, integrating the synthetic estimates as in [17], an updated CMDT. In order to obtain a new first guess based on Grace data, we use the geostrophic velocities corresponding either to GR48 or GR60 MDT to correct the Lev1500 climatology gradients. Rms residuals computed in section 2.1 for the Lev1500 GR48 and GR60 MDT are used as weights for merging the different geostrophic velocity values (Rms differences are the root squared sum of measurement and processing errors of the buoy velocity and altimetric anomaly, which are the same in all three cases, plus the error on the considered MDT). The obtained first guess is displayed Fig. 2. It roughly corresponds to Lev1500 climatology at latitudes ranging between 40 S and 40 N and to Grace only MDT poleward of +/-40. The strong gradients present in the Grace-only MDT in the Kuroshio, the Gulfstream, the Aghulas current, the Falkland current and the Antarctic Circumpolar Current (ACC) have been conserved while unrealistic scales present in these solutions at low and mid latitudes have been smoothed. For the global ocean, rms differences to in situ velocities are reduced to 13.3 cm/s for the zonal component (resp cm/s for the meridian component) when using the new first guess to compute absolute altimetric velocities (to be compared to 14 cm/s and 14.1 cm/s with GR60 MDT, 13.9 cm/s and 13.9 cm/s with GR48 MDT, 13.5 cm/s and 13.2 cm/s with Levitus climatology). cm Fig.2: MDT first guess obtained merging Lev1500 climatology and Grace-only MDT.

4 After integration of synthetic estimates as in [17], a new full scale CMDT is obtained (hereafter CMDT-Grace) and displayed in Fig.3. This new version differs from the previous one only in areas where no synthetic estimates were available, i.e. mainly at high latitudes (the Antarctic Circumpolar Current and the North Atlantic subpolar gyre). In these regions, the MDT obtained is now based on the use of Grace geoid model instead of previous EIGEN2 model. To quantify globally the impact of using synthetic estimates to resolve the shortest scales of the MDT, we once again compared the absolute altimetric velocities obtained using the CMDT-Grace to the in situ geostrophic velocities. As the drifting buoy velocities for the period have been used in the CMDT computation (to derive synthetic velocities), we use for the comparison all velocities available for the only year A 13.2 cm/s rms difference is obtained for both velocity components as well as a 0.71 correlation coefficient. This represents a significant improvement in respect to values obtained using the MDT first guess (values equal respectively to 13.8 cm/s, 13.8 cm/s and 0.67). 3 IMPACT OF FUTURE GOCE DATA 3.1 Global ocean Fig.3: CMDT-Grace (cm) In spite of the strong improvements allowed by the recent Grace geoid models in term of large scale ocean circulation, shortest scales of the Mean Dynamic Topography are not resolved yet with enough accuracy to correctly reference altimetric anomalies for oceanographic studies. Future GOCE data should allow to compute a MDT at a 100 km resolution with a 1 cm accuracy. In a study by [7] the spatial scales associated with the major North Atlantic currents have been quantified analysing the MDT issued from various high resolution General Circulation Models. According to this study, most oceanic signal of the MDT will be correctly resolved by the direct combination of satellite altimetry and GOCE geoid models. Only a few centimetre amplitude signal located in the strong coastal currents should remain unresolved. In this section, we investigate the efficiency of future GOCE derived MDT to compute absolute altimetric signal in order to understand if/where the direct combination of a GOCE geoid model and an altimetric MSS will be sufficient to correctly reference altimetric anomalies and to identify the areas where highest resolution MDT will be needed. To simulate a future Goce-only MDT, we filtered from CMDT-Grace estimated in section 2.2 all spatial scales shorter than 100 km. Absolute altimetric velocities were then computed using either the full scale or the filtered solution and rms differences with in -situ geostrophic velocities were calculated in 20 by 20 boxes like in previous section. Fig.4 features in percent of variance the rms difference reduction obtained using the full scale solution instead of the filtered one for the zonal and meridian components of the velocities. Black boxes correspond to areas where the rms difference is reduced (by maximum 2%) when using the filtered solution. In these regions, the scales shorter than 100 km contained in the CMDT are not realistic and should be smoothed. They mainly correspond to low ocean variability areas and are more numerous for the meridian component than for the zonal component. At low and mid latitudes, away from western boundary currents, reduction is less than 5%. For both components of the velocity, most significant reductions are obtained in western boundary currents as the Gulfstream (up to 12% (resp. 9%) reduction for the zonal (resp. meridian) component), the Kuroshio (more than 15% (resp. 10%) reduction for the zonal (resp. meridian) component), the Aghulas current (8% reduction for both components) and at high latitudes. In these strong currents areas, the MDT contains spatial scales shorter than 100km that should be resolved in order to correctly reference altimetric anomalies. Consequently, in these areas, a best MDT estimate will be obtain combining future Goce-only MDT to independent higher resolution MDT estimates.

5 % altimetric signal variance Fig.4: Reduction (in percent of altimetric signal variance) in RMS difference between in situ and altimetric velocities obtained (left for the zonal component, right for the meridian component) using full scale CMDT-Grace in respect to a simulated Goce-only MDT to reference altimetric anomalies. 3.2 The Mediterranean Sea case The Mediterranean Sea is a basin particularly well suited to study the impact of future GOCE data as its mean circulation is largely unknown and features spatial scales shorter than 100 km. A MDT was computed for the global Mediterranean Sea on a 1/16 resolution grid by [16] using a method similar to [17]. The first guess used issued from 7 years ( ) of MFSTEP model outputs. Synthetic estimates were computed from drifting buoy velocity data over the same period and simultaneous interpolated altimetric velocity anomalies. The resulting synthetic mean dynamic topography (SMDT) is displayed for the Sicily channel on Fig.5. In this area, hydrographic measurements from the SYMPLEX experiment (April-May 1996) are available for validation. Dynamic heights relative to 400m were computed (profile locations are displayed as black dots in Fig.5) and compared to absolute altimetric heights obtained using the SMDT. A 0.96 regression slope and a 4.5 cm rms difference was found between the two datasets (black points and line in Fig.5). In order to simulate the MDT that would issue from the direct use of future Goce data, we averaged the 1/16 SMDT into 1 by 1 boxes (corresponding at that latitude to roughly 75 km by 100 km boxes). Using this 1 resolution SMDT to reference altimetric anomalies, the comparison to in-situ dynamic heights was deteriorated (blue points and line in Fig.5). The regression slope decreased to 0.88 and the rms difference increased to 4.7 cm, illustrating the importance in this area of MDT scales shorter than 100 km. In most areas of the Mediterranean Sea, future Goce derived MDT will still have to be combined to other MDT high resolution estimates in order to obtain a full scale MDT appropriate for referencing altimetric anomalies. However, this represents a huge improvement in respect to the present state: using the GR60 MDT (green points and line in Fig.5), we obtained a 0.61 regression slope and a 6.9 cm rms difference. cm Fig.5:Left: Synthetic Mean Dynamic Topography in the Sicily channel area. Locations of hydrologic profiles relative to 400m measured during the SYMPLEX experiment are superimposed as black dots. Right: Regression diagram between the SYMPLEX in situ dynamic heights relative to 400m (ordinate) and the absolute altimetric heights (abscissa) computed using the SMDT (black dots and line), a simulated GOCE MDT (blue dots and line) and present state Gr60 MDT (green dots and line).

6 4 CONCLUSION This paper investigated the efficiency of combining recent EIGEN-GRACE01S geoid model and an altimetric MSS to estimate a Mean Dynamic Topography designed for referencing altimetric anomalies. Efficiency was tested comparing in situ geostrophic velocities available for the global ocean from 1993 to 2000 to absolute altimetric velocities obtained adding the altimetric anomalies to the Grace derived mean circulation field. A global 14 cm/s rms difference was found for both velocity components, indicating a huge improvement at all latitudes in respect to the use of previous geoid models. The availability in a close future of improved model EIGEN-GRACE02S [14] whose cumulated error at all degree is reduced by a factor 2 in respect to present EIGEN-GRACE01S solution should lead to further significant improvements. At spatial scales longer than 333 km, the Grace derived MDT features in strong coastal currents and at high latitudes more realistic gradients than Levitus climatology relative to 1500m. Inversely, at low and mid latitudes, away from Western Boundary Currents, the Levitus climatology was found more efficient to reference altimetric anomalies. Consequently, a long wavelength MDT was obtained merging informations from both solutions weighted by their respective errors. This MDT was used as first guess to estimate a full scale MDT integrating synthetic estimates of the full resolution mean field. To simulate the impact of future GOCE data, the full resolution MDT was filtered fro m spatial scales shorter than 100 km. In western boundary currents, the use of the filtered solution to compute absolute atlimetric velocities led to an increase by 15% of the rms difference to the in-situ observations in respect to the use of the full scale solution. Similar results were found in the Sicily channel area of the Mediterranean Sea. These results highlight the presence in the ocean MDT of significant spatial scales shorter than 100km. In these areas, future Goce derived MDT will need to be combined to other high resolution MDT estimates to correctly reference altimetric anomalies. 5 REFERENCES [1] Fox, A.D, Haines,K., Interpretation of Water Mass Transformations Diagnosed from Data Assimilation. Journal of Physical Oceanography, 33 (3): [2] Hernandez, F. et al., Surface Moyenne Oceanique: Support Scientifique à la mission altimetrique Jason-1, et à une mission micro-satellite altimétrique. Contrat SSALTO Lot2 - A.1. Rapport final n CLS/DOS/NT/00.341, CLS, Ramonville St Agne. 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