1. Determination of the Mean Dynamic Topography at the Coast using the Geodetic and Ocean Approaches and Consequences for Worldwide Height System Unification Philip Woodworth and Chris Hughes Liverpool University and National Oceanography Centre GOCE User Workshop, Paris, 26 November 2014

2. Background to the Talk We use Mean Dynamic Topography (MDT) at the coast obtained from MSL measured at tide gauges with GPS, minus geoid from new models (Geodetic Approach). We also use MDT values from ocean models (Ocean Approach). Consistency between approaches provides confidence in the quality of the new geoid and ocean models. Confidence allows us to consider using ocean models everywhere along a long coastline allowing traditional datums to be related.

3. Sea Level Slope along the NE American Coast Sea level (MDT) is shown by modern ocean models to fall travelling north from Florida But some historic studies showed either a positive or negative slope The main problem in previous studies came from systematic errors in the datum (‘level surface’) provided by national levelling systems, with sea level measured with respect to those poorly-known datums

4. MSL above National Datums – N America Atlantic Red, Blue: MSL above datum (USA, Canada), Black: Ocean Model

5. MSL above National Datums – N America Atlantic Nova Scotia

7. Measure the Slope of Sea Level by MSL – Geoid (Geodetic Approach) Sea Level (or MDT) at tide gauges expressed as MSL (ellipsoidal heights using GPS) minus geoid The geoid model provides the ‘level’ surface, instead of the national levelling system Compared to ocean models (Ocean Approach) the use of the new geoid models shows that the historic debate on direction of slope along this coastline has been ‘won’ by the ocean modellers But some ocean models are better than others.

8. Geodetic Approach (using 6 recent geoid models) Ocean Approach Two ‘clusters’ of ocean models (11 total) Higginson et al. 2014

11. Geodetic Approach (using 6 recent geoid models) Ocean Approach Two ‘clusters’ of ocean models (11 total) Higginson et al. 2014

12. 11 Ocean Models ECCO2 Menemenlis et al. [2008] OCCAM Marsh et al. [2009] Liverpool Woodworth et al. [2012] NOC NEMO HYCOM Chassignet et al. [2009] (2 versions) Mercator www.myOcean.eu Glorys2v3 www.myOcean.eu UR025 www.myOcean.eu CGLORS www.myOcean.eu MJM105b www.myOcean.eu

13. Centre = Geodetic MDT (red) and Ocean MDT from first cluster of models(black) Right = Geodetic MDT (red) and Ocean MDT from second cluster of models (black)

14. Mercator Model Left = MDT Right = black (coast), magenta (200m), green (2000m)

15. Other Comparisons of Geodetic and Ocean Approaches to MDT along Various Coastlines Our work had until recently concentrated on the American and European coastlines of the North Atlantic and the American Pacific coast. Recently extended to a Mediterranean study. A similar study on sea level slopes along the Pacific coast of N America and Japan coast by Lin et al.

16. Rio et al. (2014) Ocean MDT

18. Black = European coast, Open = African coast, Blue = Islands (using DIR5 extended to 2190 using EGM08)

19. Tide gauges can judge between Mediterranean ocean models Dark blue: AVISO MDT, Black: Rio et al., Other colours = ocean models.

20. Relative Performance of the REL5 Models In a recent set of studies we have looked at MDT at tide gauges using the REL5 models and compared findings to previous ones. We used same sets of tides gauges in N America Atlantic, Pacific and Gulf, Europe and Mediterranean as in previous studies and for same epoch 1993-2002 Conclusions are that the new geoid models are as good as (or slightly better than) the previous ones. However, there are common errors in all the models we have used for comparison to tide gauges in that all use EGM08 extensions for higher degrees e.g. DIR5 to 220 with EGM08 extension to 2190.

21. Overall Comparison of Dynamic Topography at Tide Gauges with Ocean Models So far I have shown results from particular coastlines as case studies But we can also make an overall comparison of tide gauge MDT with ocean models (and AVISO 2014 mean dynamic topography) 113 tide gauge stations used All data discussed in this section are 5-year means (1996-2000)

22. Tide gauge data + GPS position + TUM2013x geoid (i.e. TUM 2013 extended beyond degree 720 using EGM08) Average of NemoQ, Nemo12, and Aviso 2014 MDTs

23. Root mean square error, as a function of geoid used and model/MDT product. All tide gauges included.

24. Root mean square error, as a function of geoid used and model/MDT product. “Worst” tide gauge missed out.

25. Root mean square error, as a function of geoid used and model/MDT product. “Worst” 3 tide gauges missed out.

26. Root mean square error, as a function of geoid used and model/MDT product. “Worst” 5 tide gauges missed out.

27. Root mean square error, as a function of geoid used and model/MDT product. “Worst” 10 tide gauges missed out.

28. Conclusions Progress has been made, thanks to the availability of new geoid models, in understanding the slopes of sea level along many coastlines. Overall agreement between the Geodetic and Ocean Approaches to coastal MDT are at approximately the 5 cm level. [If you think about it: several cm variability in a 5- or 10-year mean MSL; several cm uncertainty from the GPS measurement and levelling. So 5 cm is a reasonable number, even before considering the errors in ocean models.]

29. Conclusions The comparisons provide an interesting comparison of ocean models, and a validation of the accuracy of the new geoid models, admittedly in once special area (the coast). For worldwide HSU, 5 cm is the present level of accuracy with which ocean models can be used to simulate MDT changes between neighbouring coastlines which have so far used their traditional national datums.

30. Conclusions How to extend this sort of work worldwide? A difficulty is that, while there are many tide gauges around the world, not all have had campaign or continuous GPS receivers near them. Even when there is CGPS, many gauges and GPS have not been connected by the essential levelling ties. This represents a major organisational challenge for global sea level and geodetic programmes.