1. Uncertainties of MDT and geostrophic currents estimated from GOCE and satellite altimetry: A case study in China's Marginal Seas Shuanggen Jin 1,2, Guiping Feng 1, Ole Andersen 3 1 Shanghai Astronomical Observatory, Chinese Academy of Sciences, China 2 Department of Geomatics Engineering, Bulent Ecevit University, Turkey 3 DTU Space, Technical University of Denmark, Kgs. 2800, Lyngby, Denmark Email: sgjin@shao.ac.cn; oa@space.dtu.dk

2. MDT and Antarctic Circumpolar Current www.themegallery.com Logo ACC from ITG_Grace2010(a) ， GOCE-TIM4(b) ， CNES-CLS09 MDT(c) ， and Drifter (d) EG M08 GRAC E GOC E CNES- CLS09 DTU1 0 MN0 5 SO SE 03.363.024.136.356.018.64EGM08 02.294.987.155.439.33GRACE 04.176.426.399.38GOCE 03.926.777.36 CNES- CLS09 07.948.01DTU10 09.60MN05 RMS of different MDTs around Antarctic ocean (Feng and Jin, J. Geodynamics, 2013)

3. Introduction Outline 1 Observation data and Methods 2 Results and Discussions 3 Conclusion 4

4. Geostrophic currents :  China’s marginal seas includes the South China Sea, East China Sea, Bohai Sea and Yellow Sea, which connects the Pacific Ocean, Indian Ocean through Taiwan, Luzon and Malacca Straits, and Sea of Japan through the Korea Strait.  The ocean circulation of the China’s marginal seas is very complex, which is influenced by monsoon over the sea, coastal rivers into the sea, the Kuroshio, nonlinear effects of tide and topography.  Satellite Gravimetry and Altimetry can monitor geostrophic currents, but errors and uncertainties in geostrophic velocity calculations may affect the interpretation of the ocean circulation patterns. 1. Introduction - Background

5. 1. Introduction –Traditional ways In situ observations of the ocean’ s temperature and salinity fields, Disadvantage: with sparse observations, especially in the Southern Ocean, suggesting nonzero bottom velocities MDT = Mean dynamic topography ( ~ ±2 m) MSS = Mean sea surface height (from altimetric measurements) N = Geoid height (from geoid models) Through geostrophy, the ocean’s geostrophic currents are closely related to the ocean’s mean dynamic topography (MDT)

6. GOCE (2009) (Gravity field and steady-state Ocean Circulation Explorer) GRACE (2002) (Gravity Recovery and Climate Experiment) GRACE measures the long wavelength structure of gravity and geoid with extremely high precision and can detect temporal changes in the earth system due to mass redistribution (ice, sea level, continental hydrology) GOCE gives much higher spatial resolution and allows to use the geoid as reference level surface for studies of ocean circulation or for geodynamics 1. Introduction –Satellite Gravimetry

7.  Satellite gravimetry provides a new opportunity to determine with high- precision the Earth’s gravitational field up to wavelengths of ~100-120 km, particularly GOCE with determining the 1~2 cm geoid at a spatial resolution lower than 100 km (Drinkwater et al., 2007).  There are two limitations to a detailed ocean circulation determination in China’s marginal seas from satellite. Firstly, the errors in the MDT may be larger near the coast than in the deep ocean regions. Secondly, besides the Kuroshio, Multiscale eddies play an important role in ocean circulation variability in China's Marginal Seas as seen from both satellite-derived geostrophic currents and in situ observations  In this paper, the errors and uncertainties of MDT and geostrophic velocities are investigated and analyzed in China’s marginal seas based on the newest satellite gravity field models and mean sea surface model. 1. Introduction - Motivations

8. 2. Observation data and Methods 2.1 Observation data Mean Sea Surface MSS_CNES_CLS_11 product recovering a 15-year period (1993-2009), based on 10 years of Topex/Poseidon data (first orbit), 3 years of Topex/Poseidon tandem, 8 years of ERS-2 data, ERS-1 geodesic data (2 phases at 168-days), 7 years of GFO, 7 years of Envisat and 7 years of Jason-1. computation on the nodes of a regular 1/30°×1/30° geographical grid CNES-CLS09 MDT model Oceanographic model, available over the world’s oceans, 0.25º grid ~ d/o 720 combined solution, based on 4.5 years of GRACE data, and 15 years of altimetry and in-situ data (hydrologic and drifters data).

9.  GOCE-TIM4 model  a GOCE-only solution based on measurements from November 2009 to June 2012 of GOCE orbits and gravity gradients.  Available up to degree/order 250  Using the timewise approach [Pail et al., 2011]  ITG-Grace2010s model  uncontrained static field from 2002-08 to 2009-08 of GRACE data only  Available up to degree/order 180 2.1 Observation data Gravity models [Mayer-Gürr et al., 2010]

10. 2.2 Methods --- Mean dynamic topography (MDT) N sh N gd SSH gd [N gd | SSH gd ] sh2gridgrid2sh N sh [N | SSH] sh MDT sh MDT g d LandOcean sh2grid --- Remove the continental leakage

11. Errors in MDT  The MDT can be represented as series of spherical harmonic functions  The error variance–covariance matrix of MDT from above equation is expressed as where is the variance–covariance matrix of the MSS (h), is the variance–covariance matrix of the geoid (N) and is the covariance matrix between h and N. www.themegallery.com Logo

12. 2.2 Methods ---From MDT to geostrophic velocities establishes the relationship between sea surface slope {∂H/∂ ϑ, ∂H/∂λ} and surface ocean circulation (velocity) the motion is parallel to the contour lines of MDT the slope is proportional to the velocity east direction component north direction component The direction of the resulting surface current Vectors is Their length is

13. Errors in geostrophic velocities  The accuracy of the surface geostrophic velocity fields depends on the accuracy of the spherical coefficients of the geodetic MDTs as well as omission errors for the higher order spherical harmonic constituents omitted in the geodetic MDT. The errors of geostorphic velocities can be described as: www.themegallery.com Logo

14. 3. Results and Discussions 3.1 MSS errors and Geoid errors The top is the errors of the CLS11 MSS in the China’s Marginal Seas. The bottom is the errors of the geoid from different gravity models in the China’s Marginal Seas, (a) ITG- Grace2010 and (b) GOCE-TIM4

15. 3.2 MDT errors The propagated errors from the harmonic coefficients to the MDT in China’s Marginal Seas based on ITG-Grace2010 gravity model (a) and GOCE-TIM4 gravity model (b).

16. RMS probability density distribution based on (a) ITG-Grace2010 MDT and (b) GOCE-TIM4 MDT

17. 3.4 Cumulative error in MDTs The cumulative error in geodetic MDTs based on ITG-Grace2010 and GOCE-TIM4 in China’s Marginal Seas for truncation degree up to L=90, 120, 150 and 180, respectively.

18. 3.3 Geostrophic currents Mean geostrophic velocities in China’s Marginal Seas from GRACE geoid (ITG-Grace2010) (a), GOCE geoid (GOCE-TIM4) (b), drifters’ measurements (c) and (d) CNES-CLS09 MDT

19. 3.3 Errors in Geostrophic Currents www.themegallery.com Logo Cumulative errors in total velocity (a) east direction velocity (b) and north direction velocity (c) in China’s Marginal Seas with degrees of up to L=90, 120, 150 and 180, respectively.

20. Comparison with drifters  Table. Comparison of geostrophic current velocities from GRACE and GOCE with the drifters’ results in China’s Marginal Seas. www.themegallery.com Logo RMScorrelationRMScorrelationRMScorrelation GRACE18.20.4015.30.6016.00.21 GOCE16.10.4314.00.6515.20.26 CNES-CLS0917.40.4214.90.5916.00.25

21. 4. Conclusions  For the MDT, the total mean RMS of ITG-Grace2010 MDT is around 22.75 cm, while the RMS of the GOCE-TIM4 MDT is about 9.89 cm. The RMS of the GOCE-TIM4 MDT is significantly smaller than the ITG-Grace2010 results in each grid point in China’s Marginal Seas, especially near and along the coastlines and near the islands.  The GRACE geoid error accounts for 85.35% of the ITG-Grace2010 MDT errors, while the GOCE geoid error accounts for 67.71% in the GOCE-TIM4 MDT errors.  The errors of geostrophic currents from GRACE are smaller than the GOCE results for truncation degrees 90 and 120. However, when the truncation degree is higher than 150, the GRACE mean errors increase rapidly and becomes larger than the GOCE results.  The total mean error from ITG-Grace2010 model is around 40.1 cm/s, while the mean error of the geostrophic surface velocities based on GOCE-TIM4 is about 12.6 cm/s. The GOCE results are also much closer in agreement with drifters’ results than the GRACE in China’s Marginal Seas.

22. Thanks for your attention! Prof. Dr. Shuanggen Jin Email: sgjin@shao.ac.cn; sgjin@beun.edu.tr Website: http://www.shao.ac.cn/geodesy Jin, S.G., G.P. Feng, and O. Anderson (2014), Errors of mean dynamic topography and geostrophic currents estimates in China's Marginal Sea from GOCE and satellite altimetry, J. Atmos. Ocean. Tech., 31(11), 2544-2555, doi: 10.1175/JTECH-D-13-00243.1.