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Ocean circulation estimations using GOCE gravity field models M.H. Rio 1, S. Mulet 1, P. Knudsen 2, O.B. Andersen 2, S.L. Bruinsma 3, J.C. Marty 3, Ch. Förste 4, O. Abrikosov 4 1 CLS, Ramonville Saint-Agne, France, 2 DTU Space, Copenhagen, Denmark, 3 CNES/GRGS, Toulouse, France, 4 GFZ Potsdam, Potsdam, Germany Abstract: The European GOCE Gravity consortium (EGGc), under ESA contract, computes gravity field models that only use GOCE and GRACE plus GOCE satellite data, respectively. Gravity field models that are constructed using both satellite and surface (gravimetry and mean sea surface) data are called combined models. The different geoid models (GRACE, GOCE, GRACE+GOCE, and combined models) are used together with an altimetric mean sea surface to compute the ocean Mean Dynamic Topography (MDT) and the associated mean geostrophic currents. This is done for different spatial resolutions by applying a filter to the MDTs. The mean currents obtained with the different geoid models are compared to the ocean mean geostrophic currents measured by a dataset of SVP buoy velocities available from 1993 to 2010 from which the Ekman currents are removed as well as the temporal variability measured by altimetry. In the construction of a combined gravity field model, surface and satellite data are mixed at the normal equation level in which the satellite part exclusively provides the low to medium degree coefficients (i.e. spatial resolution) of the model, whereas the surface data contain the information for the high degree coefficients. The model coefficients are computed using both data types in a transition band, which is selected based on the accuracy as a function of spatial scale of the data types. However, the scale at which the data types are mixed has a large impact on the smoothness of the model over the ocean, and therefore on the MDT and the derived currents. The differences between the mean geostrophic currents derived from gravity field models and inferred from drifter data or the combined MDT models are analyzed as a function of resolution and location, and notably for all of the ocean’s major current systems. Such an analysis allows quantifying the gain in accuracy compellingly: 1) from GRACE to GOCE models, 2) due to assimilating more and more GOCE data, 3) and to the inclusion of surface data in the models. Contact Computation of the ocean Mean Dynamic Topography (MDT) 100 km (DO 200) 200 km (DO 100) 350 km (DO 60) 250 km (DO 80) MSS – EGM_DIR_R1 MDT (cm) MDT=Mean Sea Surface - Geoid height Geoid The following models have been tested Filtering of the MDT with a gaussian filter 125 km (DO 160) Computation of the geostrophic currents Computation of synthetic estimate of mean geostrophic velocities from in-situ oceanographic measurements and altimetry (u,v) (u’ a,v’ a ) 200 km 100 km Comparison with independent data over the global ocean o Surface current velocities measured by SVP type drifting buoys and distributed by AOML over the period. (u,v) = (u,v) – (u’ a,v’ a ) METHOD 150 km (DO 133) o Drifter velocities are processed to extract only the geostrophic component: Ekman currents are modeled (Rio et al, 2011) and subtracted A 3 days low pass filter is applied along the drifter trajectories o Drifter velocities are filtered with a gaussian filter onto a regular grid o Altimetric Sea Level Anomalies from Aviso Improvement of GOCE over GRACE EGMTIM_R1EGMSPW_R1 MDT with GRACE ITG-GRACE_2010s Scales < 200 km Standard deviation is much smaller with MDT computed with GOCE geoid model than with GRACE geoid model. 2 months of GOCE data improve a lot compared with 7 years of GRACE data Scales > 200 km GOCE and GRACE have similar performances for the computation of MDT. ITG-GRACE_2010s Intensity of the velocities in the Gulf Stream area km We compute standard deviation of the difference between synthetic mean geostrophic velocity estimate and geostrophic velocities estimated from geoid models. The statistics are made over the global ocean. U: zonal component (cm/s) Standard deviation of the difference (cm/s) MDT (MSS_CNES_CLS10-EGM_DIR) filtered at 100 km Intensity of the velocities in Kuroshio area – 100 km Impact of more GOCE data ― From Release 1 to Release 4 Standard deviation of the synthetic mean geostrophic velocity estimate V: meridional component (cm/s) U: zonal component (cm/s) Calculation of an ‘optimally’ filtered GOCE MDT Conclusions When isotropic Gaussian filters are used to compute the ocean MDT from a MSS and a geoid model, the issue is to separate different error contributions. By removing the strong unrealistic errors in subduction areas due to geoid omission errors, the risk is to oversmooth the strong oceanic realistic gradient, in western boundary currents for instance. Therefore we rather apply an optimal filter. This is done by considering the raw heights from Figure 1 as observations of the MDT, to which an error field is associated (Figure 2), and by mapping these observations using an objective analysis. Error on the observations are estimated by taking the variance in 1° boxes of the difference between the observations and the GLORYS1V1 MDT. A first guess is used for the inversion, which is the large scale MDT obtained using a 200km resolution Gaussian filter (Figure 6) as well a the apriori knowledge of the MDT variance (Figure 3) and correlation scales –Figures 4 and 5). These are estimated from the GLORYS1V1 MDT. In order to highlight the superiority of the optimal filter compared to the classical gaussian filter, we show on the top right (resp. bottom left) plot of Figure 6 the speed of the mean currents obtained using a 200km (resp. 100km) resolution Gaussian filter. Using the 100km resolution filter, the western boundary currents are nicely resolved but we obtain strong noise in the equatorial band. Using the 200km resolution Gaussian filter, the noise in the equatorial band is reduced, but the western boundary currents get much weaker (Figure 7). The optimal filtering manages to preserve the sharp gradients in the strong currents while smoothing the short scale noise of the equatorial band. ModelDataSH TG-GRACE2010s7 years of GRACE data180 EGM-TIM-R12 months GOCE data224 EGM-DIR-R12 months GOCE data240 EGM-SPW-R12 months GOCE data210 EGM-TIM-R26 months GOCE data250 EGM-DIR-R26 months GOCE data240 EGM-TIM-R31 year GOCE data250 EGM-DIR-R37 years of GRACE data and 1 year of GOCE data240 GOCO03S7 years of GRACE data and 18 months of GOCE data250 EGM-TIM-R42 years of reprocessed GOCE data250 EGM-DIR-R47 years of GRACE data and 2 years of reprocessed GOCE data260 EIGEN6C 7 years of GRACE data, 6 months of GOCE data+ altimeter data+ terrestrial gravity data 1420 EGM years of GRACE data+altimeter data+terrestrial gravity data2190 MSS = MSS CNES-CLS11 Standard deviation of the differences as a function of filtering scale for ITG-GRACE (pink), DIR-R2 (blue), DIR-R3 (green) and DIR-R4 (red) Using more GOCE data much improves the comparison to independent observations at scales shorter than 125 km. At 100 km, compared with EGM_DIR_R2, the gain of the zonal (resp. meridional) velocity is 26 % (resp. 13 %) with EGM_DIR_R3 and 49 % (resp. 55 %) with EGM-DIR-R4. The standard deviation values obtained with EGM-DIR-R2 and EGM-DIR- R3 for the meridional component of the velocity (zonal gradients of the geoid) were greater than the standard deviation of the observations at 100 km resolution. With the fourth release of the EGM-DIR geoid model, the standard deviation of the differences becomes lower than the standard deviation of the synthetic mean meridional velocities. For DIR-R4 and TIM-R4, the RMS difference to independent ocean velocity observations at the target resolution of GOCE of 100 km is 5 cm/s, which is a significant improvement compared to earlier GOCE solutions. RMS differences at 100 km resolution for ITG-Grace2010s are 17 and 18 cm/s for u and v, respectively. This highlights the huge step achieved at 100 km resolution in the computation of the ocean circulation thanks to GOCE. Taking into account the error in the in situ velocities of 3 cm/s [Hansen and Poulain, 1996; Poulain et al., 2012], GOCE data now allow for a description of the ocean circulation at 100 km with accuracy of ≈ 4cm/s (the corresponding MDT being consequently known at accuracy better than ≈ 3cm). This value is consistent with the expected 1–2 cm error level for the GOCE geoid at 100 km resolution coupled with a centimeter error level of the altimeter mean sea surface [Schaeffer et al., 2012]. Very similar results are obtained for EGM-TIM-R4 and EGM-DIR-R4 models, both for the zonal and meridional components of the velocity. At 75 km resolution the comparison to zonal velocities is slightly better with EGM-DIR-R4. At 75 km resolution, the differences to the meridional velocity observations get higher than the observation variance Both models behave better than GOCO03S (which is based on 18 months of GOCE data instead of 2 years for the 4th ESA release). The results are much degradated at all scales with EGM2008, which is at the moment, the combined geoid model available at the highest order/degree SH expension Similar improvement is obtained using the Time-Wise geoid models as illustrated in the Kuroshio area in terms of mean speed: the noise around the Izu-Bonin trench is significantly reduced. This improvement results from the decrease of both the omission (The first release was developed to a lower degree and order: DO 224 compared with DO 250) and commission geoid errors (the use of more GOCE data improves the accuracy of the geoid model at scales already resolved by the first release). Standard deviation of the differences at 100km resolution for the zonal (left column) and meridional (right column) velocities for EGM-TIM-R3, EGM-TIM-R4, EGM-DIR-R4 and EIGEN6C Column on the right gives the standard deviation of the zonal (top) and meridional (bottom) velocities at 100km resolution In many places, the standard deviation of the differences is reduced using the combined EIGEN6C model. However, lesser agreement for both velocity components is found with EIGEN 6C compared to the satellite-only solutions in the Arctic Ocean, the NA subpolar gyre, the Aghulas current, the Gulf Stream. In addition, for the meridional component, lesser agreement is also found in the Southern Atlantic Ocean, in the Gulf of Mexico, in the tropical East Pacific Ocean EGM_TIM_R1 EGM_SPW_R1 EGM_DIR_R1 MDTs with GOCE R1 Regional comparison at 100km shows the following results: EGM-DIR-R4 and EGM-TIM-R4 show very similar results everywhere, and a clear improvement compared to EGM-DIR-R3 Impact of the different approaches (DIR, TIM) Figure 1Figure 2 Figure 3Figure 4Figure 5 Figure 6 Optimally filtered GOCE MDT Figure 7 200km Gaussian filter Geostrophic velocity speed from the 200km Gaussian filtered MDT Geostrophic velocity speed from the Optimally filtered MDT Geostrophic velocity speed from the 100km Gaussian filtered MDT Geostrophic velocity speed from the Optimally filtered MDT Geostrophic velocity speed from the 200km Gaussian filtered MDT 100km filtered MDT EGMDIR_R2 EGM-DIR-R3 EGM-DIR_R4

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