GOCE DATA PRODUCT VERIFICATION IN THE MEDITERRANEAN SEA

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1 GOCE DATA PRODUCT VERIFICATION IN THE MEDITERRANEAN SEA Juan Jose Martinez Benjamin 1, Yuchan Yi 2, Chungyen Kuo 2, Alexander Braun 3, 2, Yiqun Chen 2, Shin-Chan Han 2, C.K. Shum 2, 3 1 Universitat Politecnica de Catalunya, Gran Capitan s/n, Barcelona, Spain, , benjamin@fa.upc.es 2 Laboratory for Space Geodesy and Remote Sensing, Ohio State University, 2070 Neil Ave., Columbus, Ohio 43210, USA, Tel: , yi.3@osu.edu, kuo.70@osu.edu, chen.862@osu.edu, han.104@osu.edu, ckshum@osu.edu 3 Byrd Polar Research Center, Ohio State University, 10 Carmack Rd, Scott Hall, Columbus, Ohio , USA, Tel: , braun.118@osu.edu Abstract ESA's General Ocean Circulation Experiment (GOCE) mission is anticipated to generate Level 2 data products such as global geopotential model with geoid undulation accuracy of 1 cm RMS with a spatial resolution of 130 km or longer. We propose a calibration and validation effort to verify GOCE measurements and data products including the Level 2 geopotential model in the Mediterranean Sea, a water body of 4000 km by 1000 km area. This study used the POCM_4B ocean dynamic topography and the dynamic topography computed using XBT data from NOAA/NODC WOA 2001 data to aid the evaluations of recent geoid models from CHAMP and GRACE. Altimetric mean sea surfaces (ERS-2 and TOPEX) are also used globally and regionally (in the Mediterranean Sea) to assess accuracy of current geoid models. Preliminary monthly comparisons of the GRACE geoid for 7 months using the WOA01 data show good agreement globally and reasonable agreement in the Mediterranean Sea. To validate the GOCE gravity tensor data, accurate knowledge of geoid undulation over Mediterranean Sea, is needed via an appropriate upward continuation to the GOCE altitude. The inaccurate in situ regional geoid could present a problem for calibration and validation of gravity mapping sensors such as GOCE. 1. Validation Of s Using Altimeter Data Over ocean surfaces, geopotential models can be validated by evaluating their geoid undulatuons using a mean sea surface (MSS) model that is derived from satellite altimeter data and corrected for the ocean dynamic topography (ODT) signal, for example from global generation circulation models [1]. Current and future geopotential models based on data products of CHAMP, GRACE, and GOCE missions have increasing improved accuracy at long and medium wavelength harmonics. This means that the ODT correction data used for validation of these geopotential models should retain the short wavelength information that is present in original models like the POCM_4B ODT [2]. Thus, unlike in [1], where the low pass filtering was needed to the ODT data to filter out ocean current signals of short wavelengths, for which geoid models like are not accurate enough, the spherical harmonic approximation of the POCM_4B ODT model up to degree 360 [3] is used in this study. Four contemporary gravity models ( and based on the GRACE and other data; and included also the CHAMP data) are evaluated along with the model as the benchmark. To retain short wavelength information as much as possible, the spherical harmonic coefficients of the model were augmented to four models for harmonic degrees higher than the cut-off maximum degrees that are listed in Tables 1 3. The cut-off maximum degree for each gravity model is determined primarily based on the error degree variance compared with the signal power spectrum. Two separate mean sea surface models along the ground tracks of ERS-2 and TOPEX/POSEIDON (T/P) are used as the reference data of evaluation. Two models of along-track MSS were computed using the stacked ERS-2 altimeter data during and the TOPEX altimeter data for excluding the POSEIDON data. We edited data with RMS mesoscale ocean variability >15 cm. The POCM_4B model of ODT on a 0.4 Mercator grid has data gaps in the Mediterranean Sea, Black Sea, Red Sea, Caspian Sea, Hudson Bay, etc., and is available from S to N ocean-wide. An alternative dynamic height (DHT) model on a 1 grid is used also in study, which is based on the World Ocean Atlas 2001 (WOA01) database courtesy of NOAA/NODC. All layers down to 1000 m available in WOA01 are used for this DHT model. Table 1 summarizes ocean-wide geoid evaluation results for the 5 gravity models using the POCM_4B data as the ODT correction. Along the ground tracks of ERS-2, about 1.26 million data points are included in the statistics of all the 5 gravity models excluding edited data points that fall outside the difference range of -20 to 130 cm. For the TOPEX altimeter, statistics are based on about 0.44 million data points that fall within the same difference range. The augmented models and based on the GRACE data perform better than the Earth gravity 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 models of the CHAMP data in terms of standard deviation values. The benchmark model gives the best comparison in Table 1 and that could be explained by the inclusion of ERS-1 and T/P altimeter data in the model solution. Another reason might be the augmentation of high degree harmonic coefficients of the to all evaualted gravity models. Both MSS models show consistent comparison results. Table 1. Global Statistics of Difference MSS POCM_4B ODT Model Geoid Undulation Cut-off Max. Harmonic Degree of Model Table 2 summarizes the evaluation results for the case of using the alternative WOA01 dynamic height correction shows the same performance pattern of gravity models over oceans based on standard deviation values as in Table 1. Along the ground tracks of ERS-2, about 1.1 million data points were included in the statistics of all the 5 gravity models excluding wild data points that fall outside the difference range of -150 to 0 cm. For the TOPEX altimeter, statistics are based on about 0.35 million data points that fall within the same difference range. Table 2. Global Statistics of Difference MSS DHT Model Geoid Undulation Cut-off Max. Harmonic Degree of Model The same width of 150 cm difference ranges is used to compute statistics of Table 1 and Table 2 although mean differences of two cases of ODT/DHT are about 130 cm apart from each other. There are fewer data points in these 150 cm difference intervals when the WOA01 DHT is used than for the case of the POCM_4B ODT. Fig. 1 is an oceanwide plot of the ERS-2 MSS POCM_4B ODT geoid undulation difference data used for the evaluation result listed in Table 1 and Fig. 2 is the corresponding plot of Table 2 with the WOA01 DHT replacing for the POCM_4B ODT. Fig. 2 shows the DHT computed using WOA01 data (0 3000m and m). The abundance of small difference values in the Southern Ocean in Fig.3 may explain the fewer difference data samples of the WOA01 DHT case as well as larger standard deviations than those for the POCM_4B case. The small difference values in the Southern Ocean of Fig. 3 are primarily due to poor availability of ship XBT data used for the WOA01 DHT model. Fig. 1. Difference ERS-2 MSS POCM_4B Geoid Undulation

3 Fig. 2. Dynamic height topography (DHT) computed using WOA2001: m (top), m (bottom) Fig. 3. Difference ERS-2 MSS WOA01 Geoid Undulation

4 Table 3. Difference MSS WOA01 DHT Model Geoid Undulation in the Mediterranean Sea Cut-off Max. Harmonic Degree of Model At 2833 points along the ERS-2 tracks and at 6 points along the T/P tracks, the alternative DHT data are available in the Mediterranean Sea, where none of the POCM_4B ODT data are available. Table 3 shows the evaluation results of the 5 earth gravity models using all available difference data points without editing out any wild data along altimeter ground tracks. In this regional case, both models based on the GRACE data as well as the model of CHAMP data out-perform the model, again, based on standard deviation values. Table 4. Difference MSS POCM_4B ODT Model Geoid Undulation in the North Atlantic Another region in the North Atlantic bounded by 40 W/10 E and 50 N/65 N is selected as a test area. Table 4 summarizes the evaluation results of this region using the POCM_4B data as the ODT correction. Along the ERS-2 tracks, data points are included in statistics of each gravity model excluding edited data points that fall outside the difference range of -20 to 130 cm. The TOPEX statistics for each gravity model are based on data points that fall within the same difference range. Table 4 shows that new models based on the GRACE or CHAMP data have smaller standard deviation values than the model. Fig. 4 shows the difference data along ERS-2 tracks that are used to get the statistics of model in Table 4. Fig. 4. Difference ERS-2 MSS POCM_4B Geoid Undulation in the North Atlantic

5 T 2. Comparison Of Month To Month Steric Sea Level Changes As seen in Fig. 3, the WOA01 ocean dynamic height data in the Southern Ocean region are not reliable primarily due to paucity of ship survey measurements. The variation of monthly average steric global sea level derived from altimetric sea surface height data along with the ocean mass variation signal in the GRACE data is compared with the WOA01 counterpart. The latter that serves as the ground truth data of steric sea level change is a time series of monthly average of the WOA01 ocean dynamic height data for each of 8 selected months from April 2002 to July The test data of steric sea level change are the TOPEX sea level anomalies, with respect to the OSU95 mean sea surface, compensated for the mass variation effect on the sea level change detected by GRACE. The GRACE data derived sea level changes due to mass variation were computed from the residual height of monthly GRACE geoid solutions relative to a reference GRACE geoid solution. The GRACE geoid solutions are based on low degree harmonics complete to degree 15. Fig. 5 shows good agreement of both sets of monthly average steric sea level change data of which blue curve represents T the WOA01 data. To illustrate the agreement of temporal variation whose T amplitude is smaller than 0.8 cm, mean of each curve is removed in Fig. 5. Fig. 5. Month to month global steric sea level changes Fig. 6 shows reasonable agreement of both sets of monthly average steric sea level change data for the case of the Mediterranean Sea. 3. GOCE Validation Fig. 7 shows the proposed GOCE calibration and validation scheme using the Mediterranean Sea. Assuming that the geoid (top left) from the Mediterranean Sea is known, for example, using ERS-2 data with steric measurements (see Section 1), the geoid is upward continued using the Abel-Poisson kernel (first- and second-derivatives) to the GOCE altitude of 262 km and computed as the diagonal tensor components, Txx (top right), Tyy (bottom left) and Tzz (bottom right). It is noted that if the in situ geoid accuracy is much worse than that of GOCE accuracy, there would be a problem with using this technique.

6 Fig. 6. Month to month steric sea level changes in the Mediterranean Sea Fig. 7. ERS-2 inferred geoid in the Mediterranean Sea (top left). Gravity tensor upward continued to the GOCE altitude in the XX- direction (top right), YY-direction (bottom left) and ZZ-direction (bottom right). 4. Conclusions

7 Ocean-wide evaluations of geoid models are limited by the quality of oceanographic data used. This is an issue in the calibration and validation practices of advanced gravity sensors and data products. The sea level change that is determined from the TOPEX altimeter data with a correction of the GRACE data implied mass variation demonstrates good agreement with oceanographic data of steric sea level change. To validate the GOCE gravity tensor data, accurate knowledge of geoid undulation over the calibration region, i.e., the Mediterranean Sea, is needed, which presents an issue for calibration and validation of gravity mapping sensors such as GOCE. Acknowledgement This research is partially supported by the Spanish National Science Foundation. The Ohio State University team is supported partially by grants from NASA s Interdisciplinary Science investigation and Solid Earth and Natural Hazards program. References 1. Lemoine F.G., et al. The development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA), NASA/TP , Goddard Space Flight Center, Stammer D., Tokmakian R., Semtner A., and Wunsch C., How well does a 1/4 global circulation model simulate large-scale oceanic observations? J. Geophys. Res., Vol 101, , Rapp R.H., The Development of a Degree 360 Expansion of the Dynamic Ocean Topography of the POCM_4B Global Circulation Model, NASA/CR , Goddard Space Flight Center, 1998.