3.1 Temperature/salinity products
Argo floats record T/S at a relatively fine vertical resolution (typically 1-5 dbar in the upper oceanand coarser resolution at depth), from 2000 dbar to the sea surface. These measurements of T and S
are then stored in a file for that particular float at that particular location and time. Thus, it is notstraightforward to obtain, for example, T and S in a specific region (covered by several floats) or at
a location over a specific time range. This project will help users by creating binned T/S data that isfurther interpolated onto a vertical and horizontal grid. Since some users prefer to do their own
interpolation, we propose two different products: one gridded vertically at standard depths and theother gridded horizontally. In each case the data set will be in NetCDF format and will include,
besides the data, latitude, longitude, time, depth of measurement, and a flag indicating the region(e.g., marginal seas and subbasins will have a different ID). The dataset will be constructed so that
future data can be concatenated onto the end (rather than users having to replace the entire fileduring every update).
Argo-derived in situ temperature will be used along with salinity to compute potential temperatureand potential density. T/S/ρ will then be interpolated to standard depth levels (Levitus, 1982) for
the first data product. This product is designed for modelers, who typically want a verticallygridded product to validate their model or use for assimilation. The second product will include aninterpolation to a horizontal grid, nominally on a 1x1 degree grid. These products will be based on
10-day downloads of the profile and trajectory files from the US GDAC.
Additionally, derived quantities of mixed layer depth (MLD), based on a temperature criterion(Kara et al., 2000a) and barrier layer thickness (BLT) based on a density criterion (Kara et al.
2000b) will be produced from the above T/S/ρ data.

3.2 Absolute dynamic height and absolute geostrophic velocities
Dynamic height (DH) or geopotential height is defined as DH =p2∫ δ (T , S , p) ⋅ dp , wherep1

δ(T, S, p) = α (T,S,p) - α (00C, 35psu, p) is an anomaly of specific volume α. DH can be used as astreamfunction to determine the geostrophic velocity shear ∆V at level p1 relative to p2 :f x ∆V = - g∇(DH), where f is an upward looking inertial frequency vector and g is the acceleration
due to gravity. Traditionally, to obtain the estimate of absolute geostrophic velocity one uses theso-called dynamical method assuming a no-motion at the reference level p2. Although the intensityof currents usually does decay with depth, the “no-motion level” does not exist in reality.
Fortunately, an alternative approach is possible. DH can be interpreted as a quantity proportional tothe pressure associated with the geostrophic current, and the absolute dynamic height (ADH) atplevel p can be defined as ADH = SSH -∫ δ (T , S , p) ⋅ dp
0, where SSH is the sea surface height (akadynamic ocean topography at the sea surface). At the sea surface ADH is equal to SSH. The latteris the deviation of the shape of the ocean surface from the Earth’s geoid due to the ocean dynamics,and it was poorly known until recently. Maximenko and Niiler (2005) (see also, Niiler et al., 2003;
Maximenko and Niiler, 2006) combined the data of Lagrangian near-surface drifters, satellite
altimetry and wind to downscale the improved mean dynamic ocean topography (MDOT)

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computed by V. Zlotnicky (NASA/JPL) based on the GRACE (Gravity Recovery And Climate
Experiment mission) gravity model. Map of this MDOT is shown in Fig.3 and data can be obtained
at http://apdrc.soest.hawaii.edu/projects/DOT/ . Instantaneous SSH will be calculated by
combining the MDOT with the sea level anomaly (SLA) data gridded and distributed in nearrealtime and delay (improved) modes by the Aviso (CLS, France; Aviso, 1996). The SLA is on the1/3-degree Mercator grid, and maps are computed weekly with the optimal interpolation techniquedescribed by Ducet et al. (2000). A simple procedure will be applied to convert the Aviso SLA into
anomalies relative to 1992-2002, the period, for which MDOT of Maximenko and Niiler (2005) isdefined. We will not use the absolute sea level distributed by Aviso along with anomalies, as it isbased on Rio and Hernandez (2004) MDOT. The latter has been computed with statistical methods
as a synthesis of different kinds of data, one of which was dynamic height from CTD profiles
relative to 1000m. Therefore, Rio and Hernandez MDOT is based on an implicit assumption of“no-motion level” and is not appropriate for our study of the ocean structure at intermediate depths.

Figure 3. 1992-2002 mean dynamic ocean topography of Maximenko and Niiler (2005) available
at http://apdrc.soest.hawaii.edu/projects/DOT/ . Also included in the National Geographic
Atlas of the World, 8th Ed.

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Figure 4. Absolute mean dynamic height at 1000m calculated from the MDOT in Fig. 3 and World
Ocean Atlas 2001. Units are dyn.cm.

Fig. 4 shows the mean absolute dynamic height at 1000m depth calculated from the World Ocean
Atlas 2001 (WOA) by referencing it to MDOT of Maximenko and Niiler (2005). It can be viewed
as a streamfunction of geostrophic circulation at this depth, whose map reveals a system of
relatively large-scale mid-latitude gyres and deep-penetrating jets, such as the Gulf Stream,
Kuroshio, and Antarctic Circumpolar Current with the associated signal of many tens of dynamiccentimeters. This map contains large uncertainties on the large scale due to the vague definition of
the “mean” in WOA and on the mesoscale due to the poor spatial resolution of WOA. Bothuncertainties will be significantly reduced in the proposed project.
While vertical excursions of Argo floats are preprogrammed, their horizontal displacements arecompletely due to ocean currents. The latter are known to be remarkably geostrophic away fromlateral, bottom and surface boundaries. This allows us to convert the deep (parking level) velocities
estimated with the technique described by Yoshinari et al. (2006) into estimates of horizontal
gradient vector of ADH and to use them as extra observations. In fact, addition of these twocomponents at every cycle of the float virtually triples the amount of effective observations of theADH at the parking depth, and will allow us to increase special resolution from 2-3 to 1-1½
degrees. To extrapolate values of ∇(ADH) vertically we will use a simple model of verticalstructure.
Yu et al. (2006) showed that much of vertical structure of low-frequency variability in an advanced
OGCM is successfully described by the local first baroclinic mode. Chen et al. (2007) showedusing Argo profiles and trajectories in the Kuroshio Extension that as much as “86% of the total
variance resides in the first baroclinic mode and 6% in the second baroclinic mode”. Many studies
combining altimetry with profiles (e.g., Roemmich and Gilson, 2001; Willis et al., 2003; Willis,2004) have also found that the two datasets greatly compliment each other and reveal deep signal
remarkably coherent with its expression at the surface. As deep Argo velocities are measured not atthe locations of profiles but between them, to assess the structure of vertically coherent modes in3the vicinity of every grid point we will select a cluster of the nearest profiles. The differences
between the profiles (at least three profiles are needed) will then be used to calculate the verticalstructure of the two-dimensional vector of ∇(ADH). Thus defined, ∇(ADH) corresponds torelatively large horizontal scale, while values of ∇(ADH) derived from the Argo velocities at theparking level correspond to smaller scale. We will assume that vertical structure is universal
throughout both scales and will do a vertical expansion of ∇(ADH) “observed” at the parking depthby adjusting (rotating and scaling) the vertical profile obtained on the previous step. Misfit between
thus-deduced ∇(ADH) at the sea surface and ∇(SSH) will be used to estimate maximum error.
For every 10-day period the ADH will be interpolated three-dimentionally with the variational
method described in one the following sections. Gridded ADH will then be used to calculate
absolute geostrophic velocities at latitudes higher than 30.

3.3 Other products
In addition to the gridded and vertically interpolated products described in the previous sections wewill release- in situ velocity data at the sea surface and at the parking depth calculated from the float
trajectories on every cycle;- profiles used for vertical extrapolation of ∇(ADH).
The full set of the products will be sufficient for the advanced user to be able to reproduce ourresults or to help develop alternative techniques of data analysis and gridding.
Also, we will calculate and publish new gridded climatological datasets and assessments of theseasonal cycle and interannual changes based of the short period of the Argo observations. These
climatologies will be compared with the results of other scientists, e.g., Willis (2006).

3.4 Near-realtime data updates and distribution
As a result of this project a (quasi-)automated system will be developed at the APDRC/IPRC thatwill allow 10-daily, near-realtime updates of all products at minimal cost to institutional funds. All
the products will be freely available on the APDRC servers. Bugs in the original data, detectedduring this project and/or reported by the users of our products, will be documented and forwarded
to the specific DACs hosting the problematic data. Climatologies and past data will be recomputed
when/if the original data are significantly improved by DACs. Periodic updates will also be done as
the “delayed” Argo (i.e., more thoroughly quality-controlled) data become available.

4. Mapping technique
A variational analysis technique will be used to interpolate temperature, salinity and absolutedynamic topography onto a three-dimensional spatial grid. The cost function
J = W1∙J1 + W2∙J2 + W3∙J3 + W4∙J44

will include members penalizing in the three-dimensional space domain the following deviations:
J1: Deviation of the gridded T/S/ADH from the corresponding collocated profile data.
J2: Deviation of gradient of the gridded ADH from the gradient value assessed from collocated data.
The latter values at the parking level will be deduced from the float velocities throughgeostrophic equations and extrapolated in vertical as described in Section 3.2.
J3: Deviation of tilts of the isotherm and isohaline from the tilt of the isopycnal (i.e., variations ofwater properties on the isopycnal will be discouraged). Compressibility of the sea water will betaken into account.
J4: Non-smoothness as characterized by the harmonic or biharmonic operator.
The solution minimizing the costfunction J is controlled by relative values of the weights Wi , notby the weights themselves. It can be shown that J1 is more significant at large scale and J2 is moresignificant at small scale. The ratio W1/W2 sets the threshold scale, on which both terms are equallysignificant. The threshold will be set equal to 2-3 degrees latitude/longitude. W3 will be large for Tand S and equal to zero for ADH. W4 will be set small enough to only suppress the noise on thegrid scale.
The calculations will start with the analysis of the local vertical structure of ∇(ADH) and errors ofthe simple vertical model. The model will be used to extrapolate the gradient of ADH vertically,
and the errors will be accounted while defining the weights W2.
Next, gridded ADH will be computed by minimizing the costfunction J. Temperature and salinity
will be interpolated using the dynamical information of the shape of isopycnals assessed from thegridded ADH and locally linearized equation of state of seawater. Absolute geostrophic velocities
will be derived from ADH by differentiating in the horizontal direction.
As a separate task, MLD and BLT will be interpolated horizontally with the cost function
consisting only of terms J1 and J4.

9. References
Archiving, Validation, and Interpretation of Satellite Oceanographic Data (AVISO), in Aviso
Handbook for Merged TOPEX/Poseidon products, 3rd ed., Toulouse, France, 1996.
Chen, S., B. Qiu, and P. Hacker, 2007: Profiling float measurements of the recirculation gyre southof the Kuroshio Extension in May-November 2004, J. Geophys. Res., 112, C05023,
doi:10.1029/2006JC004005.
Ducet, N., P. Y. Le Traon, and G. Reverdin, 2000: Global high-resolution mapping of ocean
circulation from TOPEX/Poseodon and ERS-1 and -2, J. Geophys. Res., 105(C8), 19,47719,488.
Kara, A. B., P. A Rochford, and H. E. Hurlburt, 2000a: An optimal definition for ocean mixedlayer depth. J. Geophys. Res., 105, 16,803-16,821.

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Kara, A. B., P. A. Rochford, and H. E. Hurlburt, 2000b: Mixed layer depth variability and barrierlayer formation over the North Pacific Ocean. J. Geophys. Res., 105, 16,783-16,801.
Levitus, S., 1982: Climatological Atlas of the World Ocean, NOAA Professional Paper 13, 173pp.
Lyman J. M., J. K. Willis, G. C. Johnson (2006), Recent cooling of the upper ocean, Geophys. Res.
Lett., 33, L18604, doi:10.1029/2006GL027033.
Maximenko, N.A., and P.P. Niiler, 2005: Hybrid decade-mean global sea level with mesoscale
resolution. In N. Saxena (Ed.) Recent Advances in Marine Science and Technology, 2004, pp.
55-59. Honolulu: PACON International
Maximenko, N.A., and P.P. Niiler, 2006: Mean surface circulation of the global ocean inferredfrom satellite altimeter and drifter data. In 15 years of Progress in Radar Altimetry, ESA
Publication SP-614, July 2006.
Niiler, P.P., N.A. Maximenko, and J.C. McWilliams, 2003: Dynamically balanced absolute sea
level of the global ocean derived from near-surface velocity observations. Geophys. Res. Lett.,
30 (22), 2164, doi:10.1029/2003GL018628, 2003.
Rio, M.-H., F. Hernandez, 2004: A mean dynamic topography computed over the world ocean fromaltimetry, in situ measurements, and a geoid model, J. Geophys. Res., 109, C12032.
Roemmich, D., and J. Gilson, 2001: Eddy Transport of Heat and Thermocline Waters in the North
Pacific: A Key to Interannual/Decadal Climate Variability?, J. Phys. Oceanogr., 31(3), 675687.
Schiermeier, Q., 2007: Artefacts in ocean data hides rising temperatures, Nature, 447, 8-9.
Willis, J.K., Roemmich, D., Cornuelle, B., 2003: Combining altimetric height with broadscaleprofile data to estimate steric height, heat storage, subsurface temperature, and sea-surface
temperature variability, J. Geophys. Res., 108(C9), 3292, doi:10.1029/2002JC001755.
Willis, J., 2004: Combining Satellite and In Situ data to Make Improved Estimates of Upper-Ocean
Thermal Variability on Eddy to Global Scales. PhD thesis, University of California San Diego.
Willis, J. K., L.-L. Fu, 2006: Mid-depth circulation of the World Ocean: a first look at the Argoarray, In 15 years of Progress in Radar Altimetry, ESA Publication SP-614, July 2006.
Yu, P., S. L. Morey, and J. J. O’Brien, 2006: Development of New Techniques for Assimilating

Satellite Altimetry Data into Ocean Models
http://www.coaps.fsu.edu/~morey/GoM/08_Yu_Peng_WGNE_2006.pdf
Yoshinari, H., N. A. Maximenko, and P. W. Hacker, 2006: YoMaHa'05: Velocity data assessedfrom trajectories of Argo floats at parking level and at the sea surface, IPRC Tech. Note No. 4,20p.
( http://apdrc.soest.hawaii.edu/projects/yomaha05/data/YoMaHa05_060227.pdf )6