## 1. Introduction

[2] The Gravity Field and Steady-State Ocean Circulation (GOCE) satellite was successfully launched in March 2009. As the first Earth Explorer core mission from the ESA Living Planet program, it will provide by the end of its 20 months lifetime an estimate of the geoid's scales down to 100 km with centimetric accuracy [*European Space Agency*, 1999]. After the huge success of the Gravity Recovery and Climate Experiment (GRACE) mission [*Tapley et al.*, 2003], this represents another important milestone for the measurement of the Earth's gravity field. Among the main beneficiaries of these successive improvements is the oceanographic community working with altimetric data. The geoid height N is indeed the missing quantity needed to compute (equation (1)) the ocean absolute dynamic topography (the sea level h above the geoid) from the altimetric measurement (the sea level *η* above a reference ellipsoid). Under the geostrophic assumption, ocean surface currents can then be derived from the absolute dynamic topography values

[3] In practice, the absolute dynamic topography cannot be computed as the simple difference between the altimetric measurement and the geoid height, as this would require the knowledge of the geoid with centimetric accuracy at scales down to a few hundred meters. An altimeter provides one sea level height measurement roughly every 350 m along track, which are commonly averaged in order to reduce noise (standard along-track AVISO products for instance contains one measurement every 7 km). Alternatively, Sea Level Anomalies h′_{p} = *η*′_{p} relative to a given time period P are computed using the repeat-track method [*Cheney et al.*, 1983], in which along-track mean altimetric profiles 〈*η*〉_{P} are subtracted from the instantaneous altimetric heights *η*. To reconstruct the full dynamical signal h from the altimetric anomaly h′_{p}, an accurate estimate of the ocean mean dynamic topography (MDT) for the time period P is needed. The most straightforward approach (hereinafter called the “direct method”) is to subtract a geoid model from an altimetric Mean Sea Surface (MSS) defined as the gridded mean profiles 〈*η*〉_{P}, after making sure that both surfaces are consistent, and notably that they are expressed relative to the same ellipsoid and tide system (all details are given by *Hughes and Bingham* [2008]). However, an altimetric MSS resolves much shorter spatial scales (down to 10–20 km) than recent satellite-only (i.e., computed from space gravity data only) geoid models and, in order to match the spectral content of both surfaces, some form of filtering is needed. This can be done using simple filters such as Gaussian or Hamming [*Tapley et al.*, 2003; *Jayne*, 2006; *Bingham et al.*, 2008]. In order to remove as much noise as possible while minimizing signal attenuation, more complex filters may be used. For example, *Vianna et al.* [2007] and *Vianna and Menezes* [2010] developed an adaptive filter, based on principal components analysis techniques, while *Bingham* [2010] applied a nonlinear anisotropic diffusive filtering method. Whatever the filter used, the spectral content of the latest satellite-only geoid models based on GRACE data still limits the spatial resolution of the MDT computed through the direct method to scales larger than 200–300 km [*Rio*, 2010]. In order to estimate the MDT scales shorter than 200–300 km, different methods have been developed in the past few years.

[4] A first way to proceed is to improve the geoid resolution. This can be done using in situ gravimetric data [*Hunegnaw et al.*, 2009; *Thompson et al.*, 2009]. As in situ gravimetric data are limited in spatial extension, only regional improvements of the geoid are obtained. Global improvement can be achieved though using the shortest scales information of the altimetric MSS (the smallest spatial scales of the MDT being larger than those of the MSS, the smallest spatial scales of the altimetric MSS are only due to the smallest spatial scales of the geoid and can therefore be used to enhance the geoid). This method is commonly used to enhance the resolution of the satellite-only geoid models, resulting in the so-called “combined” geoid models which are developed to a higher degree and order than their satellite-only counterpart. In the case of the recent EGM08 earth gravity model [*Pavlis et al.*, 2008], both in situ gravimetric data and altimetry-derived gravity anomalies have been used to compute the spherical harmonic coefficients of the gravity field up to degree and order 2400 (∼8 km resolution). *Andersen and Knudsen* [2009] used this geoid model, together with the DNSC08 altimetric MSS to compute spatial scales of the MDT greater than 75 km. The EGM08 model was also used recently by *Vianna and Menezes* [2010] for MDT computation on a 0.1° resolution grid.

[5] A second approach developed to compute high-resolution MDT is to first compute a large-scale MDT using the direct method and further improve it by using external oceanographic data to resolve the shortest scales. This method was applied by *Maximenko and Niiler* [2005] and *Maximenko et al.* [2009] using drifting buoy velocities, as well as by *Rio and Hernandez* [2004] and *Rio et al.* [2005, 2007] using both hydrological profiles and drifter velocities.

[6] Finally, the computation of high-resolution MDTs can be achieved by synthesizing all oceanographic information available (in situ and space measurements of the ocean state) in a dynamically consistent way through inverse modeling [*LeGrand et al.*, 2003], or through data assimilation into ocean general circulation models [*Ferry et al.*, 2010]. In that case, model outputs are averaged to obtain an estimate of the MDT over the required period.

[7] These continuous improvements achieved in recent years for estimating the MDT have led to a growing number of scientific studies using absolute altimetric heights [e.g., *Fu*, 2006; *Qiu and Chen*, 2010; *Saraceno et al.*, 2009]. Also, a number of ocean current products have been produced [*Bonjean and Lagerloef*, 2002; *Larnicol et al.*, 2006; *Sudre and Morrow*, 2008] that are obtained as the sum of the geostrophic component from absolute altimetry and an estimate of the Ekman component. These surface currents can be used for a number of applications such as ocean model validation, support to offshore activities, search and rescue, and oil spill monitoring. Operational ocean forecasting systems have also greatly benefited from higher-resolution MDTs. In the framework of the Geoid and Ocean Circulation in the North Atlantic (GOCINA) project, the use of an improved MDT in three different European operational forecasting systems led to changes in transport across key sections between Scotland and Greenland of up to 10–20% for mass transport and of about 30% for heat transport, resulting in an increased agreement with in situ observations [*Knudsen et al.*, 2006].

[8] Despite the indisputable progress that has been made in recent years toward estimating the ocean's mean circulation, further improvements are still needed, both in term of resolution and accuracy, to fully exploit the altimetric data in oceanographic applications.

[9] In this paper, we describe the calculation of a new global 1/4° resolution MDT, the CNES-CLS09 MDT, and the associated mean geostrophic currents for the time period P = 1993–1999. The approach is based on the three steps methodology used by *Rio and Hernandez* [2004] and *Rio et al.* [2005]. Compared to the MDT computed by *Rio et al.* [2005], hereinafter called the RIO05 MDT, a number of improvements have been made with the aim of providing, in preparation for the exploitation of GOCE data, a combined MDT based on updated data sets (as described in section 2) and methodology.

[10] The first step of the method is to compute a large-scale estimate of the MDT (the so-called first guess) by filtering the difference between an altimetric MSS and a geoid model. A filtering technique based on optimal interpolation has been developed (section 3), which is much more efficient compared to the classical Gaussian spatial filtering applied by *Rio and Hernandez* [2004] and *Rio et al.* [2005]. Next, synthetic estimates of the MDT 〈h〉 and the associated mean geostrophic currents (〈u_{g}〉, 〈v_{g}〉) are calculated. These are simply obtained, for a given time t and geographical position, by subtracting from the instantaneous in situ measurements of the ocean dynamic topography h(t) or the ocean geostrophic surface current u_{g}(t),v_{g}(t), the time variable (h′_{a}(t), u′_{a}(t), v′_{a}(t)) component as measured by altimetry:

[11] Two different types of oceanographic in situ measurements are used in this study, surface velocities measured by drifting buoys and dynamic heights computed from in situ hydrological profiles. To ensure consistency with the physical content of the altimetric height and velocity anomalies, the implementation of the synthetic method requires the preliminary processing of the in situ data as follows:

[12] 1. The proper modeling and removal from the raw drifting buoy velocities of the Ekman currents due to the ageostrophic response of the ocean to wind stress forcing is required. The Ekman model used for processing the drifting buoy velocities in the RIO05 MDT computation had been derived by *Rio and Hernandez* [2003]. A new model, fully described in section 4, has been developed for the present study.

[13] 2. The correction of the dynamic heights computed relative to a given reference depth (the depth of the T/S profile used) for the missing barotropic component and the deep baroclinic component (from the profile's depth to the bottom) is also required. For the RIO05 MDT computation, a single reference level of 1500 m was chosen for all hydrological profiles, limiting the number of data to areas with bathymetric depths greater than 1500 m. In this study, a methodology has been implemented to take into account the information from hydrological profiles whatever their reference depth (section 5). This allows us to include profiles taken in shallow waters and data from deeper profiles in our calculation.

[14] Finally, the synthetic estimates are used to improve the large-scale solution (both for mean heights and mean geostrophic velocities) from the direct method through a multivariate objective analysis (section 5.3). The final 1/4° global CNES-CLS09 MDT is validated against independent observations and other existing MDTs in section 6. Conclusions and perspectives are given in section 7.