Argo observations from 2005 to 2013 are used to characterize spatial scales
of temperature and salinity variations from the surface down to 1300 m.
Simulations are first performed to analyze the sensitivity of results to
Argo sampling; they show that several years of Argo observations are
required to estimate spatial scales of ocean variability over
20

Thanks to outstanding international cooperation, Argo – the global array of profiling floats (Roemmich et al., 2009) – reached its initial target of 3000 floats in operation in 2007. Argo floats measure every 10 days temperature and salinity from the surface down to 2000 m and deliver their data both in real time for operational users and after scientific quality control for climate change research and monitoring. Argo has revolutionized oceanography by providing for the first time a near-real-time global description of the ocean state that is fully complementary to satellite observations. An overview of Argo achievements is given in Freeland et al. (2010). Argo data have been used to better understand global and regional sea level rise and ocean heat content variations (e.g., von Schuckmann and Le Traon, 2011), to analyze large-scale ocean circulation and mesoscale variations (e.g., Roemmich et al; 2007; Dong et al., 2014) and large-scale salinity variations related to the global hydrological cycle (Durack and Wijffels, 2010). Argo has strong complementarities with satellite altimetry, and Argo data are now systematically used together with altimeter data for ocean analysis and forecasting (e.g., Guinehut et al., 2012; Le Traon, 2013; Oke et al., 2015).

The availability of global temperature and salinity data sets over several
years is a unique opportunity to better characterize the statistics of ocean
mesoscale variability at global scale. Although Argo does not resolve
mesoscale variability due to its 3

The paper is organized as follows. Data and methods are presented in Sect. 2. The capability of Argo sampling to estimate spatial correlation scales is analyzed with simulated data in Sect. 3. Section 4 provides a global calculation of spatial scales and discusses the main results. Conclusions and perspectives are given in Sect. 5.

We used Argo observations from 2005 to 2013 as obtained from the Coriolis data center. Data from 2005 to 2012 are delayed-mode quality-controlled data from the CORA database (Cabanes et al., 2013). Data from 2013 are near-real-time data from the Coriolis Argo Global Data Assembly Center (one of the two Argo GDACs). An additional quality control with regional climatology checks was applied to these near-real-time data sets.

After several tests (see discussion in Sect. 3), correlation scales were
calculated over several large-scale areas to provide a sufficient number of pairs of
observations at different zonal and meridional distances. Correlations were
computed both for temperature and salinity and for the surface down to 1300 m. The following steps are used for the calculation:

The Levitus 2009 seasonal climatology is removed from Argo profile observations.

All temperature and salinity Argo data (from 2005 to 2013) within a given
box (e.g., 20

The covariance for a given zonal (d

Covariances are then normalized by the variance to get correlation values:

The formal error variance on the correlation, noted

An analytical correlation model is then fitted to the discrete correlation
estimations through a non-linear weighted least-square curve fitting method
based on the Levenberg–Marquardt algorithm. Formal errors (see point 5
above) are taken into account in the adjustment (weights). The correlation
model follows the covariance model proposed by Arhan and Colin de
Verdière (1985).

To analyze the sensitivity of results to Argo sampling, a simulation study
was performed. The main objective is to test the impact of realistic Argo
sampling by using actual Argo float positions in 2005 and 2013 in the North
Pacific. Over a 20

Large-scale areas where temperature and salinity spatial correlations were calculated.

2-D covariance calculated in a 20

2-D covariance calculated in a 20

2-D covariance calculated in a 100

Simulation of the impact of Argo sampling on the estimation of correlation functions.

We generated 52 weekly (i.e., 1 year) simulated temperature 2-D fields on a
20

Results show that the estimations of correlation functions are highly
sensitive to the Argo sampling. The typical error for a covariance or
correlation value is about 0.25–0.4 for the 2005 sampling and 0.15–0.25 for
the 2013 sampling over a 1-year time period. Correlation scales (assuming
an a priori knowledge of the covariance function shape) can be determined
with an accuracy of about 20 to 30 km for 2005 and 10 to 20 km for 2013.
These results are obviously dependent on the number of observation pairs
available for a given spatial d

These results show that 1 year of Argo observations over a 20

Variations of zonal and meridional spatial scales for temperature (left) and salinity (right) according to depth for box 18 (high-latitude Southern Hemisphere). Dotted lines represent standard fitting errors.

Variations of zonal and meridional spatial scales for temperature (left) and salinity (right) according to depth for box 9 (equatorial Indian and Pacific). Dotted lines represent standard fitting errors.

A preliminary calculation of spatial scales (

Variations of zonal and meridional spatial scales for temperature (left) and salinity (right) according to depth for box 2 (midlatitude North Atlantic). Dotted lines represent standard fitting errors.

Results for one box (box 3) in the North Pacific are
shown in Figs. 4 and 5 for temperature at two different depths (200 and
1000 m). In that box, correlations are well estimated with a typical error
below 0.1 due a large number of observation pairs

Zonal and meridional spatial scales vary as expected with latitudes. Compared to midlatitude regions, scales are much larger in the tropical and equatorial regions. Figure 6 shows, for example, the correlation function for temperature at 200 m in the whole equatorial Pacific. Zonal and meridional scales are estimated to about 900 and 350 km. The zonal scales are smaller than those derived from TAO observations and larger than those derived from altimeter data (e.g., Kessler et al., 1996; Jacobs et al., 2001). This may be due to both the techniques used to compute scales (e.g., removing of large-scale signals before computing altimeter spatial scales) and the sparse spatial sampling of TAO observations. As expected and well observed from altimetry and in situ observations, there is a strong anisotropy with zonal scales 2–3 times larger than meridional scales. It is interesting to note that, compared to the Pacific Ocean, smaller zonal scales are observed in the Indian (box 9 – zonal scale of 780 km at 200 m for temperature) and Atlantic (box 8 – zonal scale of 360 km at 200 m for temperature) tropical–equatorial oceans.

They are also interesting variations of scales according to depth. Figures 7, 8 and 9 show the vertical distribution of scales both for temperature and salinity for several areas (boxes 2, 9 and 18). At the surface or in the mixed layer, scales are much larger because they reflect large-scale atmospheric forcing (heat flux, evaporation and precipitation). Note, however, that a mean seasonal cycle is removed prior to the calculation. Below the mixed layer, scales are more representative of mesoscale dynamics and are consistent with scales derived from satellite altimetry. There is a general tendency (not systematic though) for an increase of temperature scales at depths larger than 800–1000 m although the correlation functions are noisier there because of lower signals. This may reflect a smaller influence of mesoscale variability at deeper depths, but this should be investigated further.

There are significant differences between salinity and temperature scales
(see Figs. 7, 8 and 9). At the surface and in the mixed layer where we
observe large spatial scales, differences may reflect differences in scales
between

A similar calculation was done by Resnyanskii et al. (2010) but with a more limited Argo data set (2005–2007). Our results are in a qualitative agreement with theirs although they found larger scales. This may be due to the differences in data sets but also to differences in the way spatial scales were computed. They did not remove, in particular, biases in the Levitus climatology.

This study was a first attempt to estimate spatial scales of temperature and
salinity at different depths from the Argo global ocean observing system. A
careful error analysis was carried out, and it shows that several years of
Argo observations are required for a precise enough (error on correlation
below 0.1 to 0.2) estimation of correlation functions over 20

These data were collected and made freely available by the International
Argo Program and the national programs that contribute to it
(