The Data Unification and Altimeter Combination System (DUACS) produces sea level global and regional
maps that serve oceanographic applications, climate forecasting centers,
and geophysics and biology communities. These maps are generated using an
optimal interpolation method applied to altimeter observations. They are
provided on a global
The Data Unification and Altimeter Combination System (DUACS) generates, as part of the CNES/SALP project and the Copernicus Marine Environment and Monitoring Service (CMEMS), delayed-time (DT) multi-mission altimeter sea level anomaly (SLA) level 3 (along-track cross-calibrated) and level 4 (multiple sensors merged as maps or time series) products. A full reprocessing of these products is carried out approximately every 3 years and covers the period 1993–now. The reprocessing benefits from improvements associated with optimized mapping parameters and new altimeter corrections which are based on standards recommended for altimeter products by the different agencies and expert groups (Ocean Surface Topography Science Team – OSTST, the ESA Quality Working Group and the ESA Sea Level Climate Change Initiative project members). The previous reprocessing was released in 2014 (DUACS-DT2014; see Pujol et al., 2016) and the new release, namely DUACS-DT2018, is available since April 2018 (Taburet et al., 2019).
The level 4 DUACS-DT global maps are constructed from optimal interpolation
(Bretherton et al., 1976; Le Traon et al., 1998; Ducet et al., 2000) of level 3 altimeter observations and are provided on a regular
The effective resolution corresponds to the spatiotemporal scales of
the features that can be properly resolved in the maps. The spatiotemporal
resolution of the previous level 4 global SLA products was estimated by
Chelton et al. (2011, 2014) and Chelton and Schlax (2003) based on estimates of the mapping errors in sea surface height (SSH) fields constructed from altimeter data or spectral ratio analysis between maps and along-track altimeter data. Their analysis suggested a midlatitude spatial resolution capability of the observations ranging from
In the present study, we further investigate the effective resolution of the DUACS-DT gridded products using a spectral approach. The objective of the paper is threefold: (1) to deliver the spatial distribution of the effective resolutions as key information to the users about the quality and the limitations (in term of resolution) of the newly produced DUACS-DT2018 gridded products, (2) to access and compare the spatial and temporal resolution capabilities of the DUACS-DT2018, DUACS-DT2014 and DUACS-DT2010 maps (i.e., to identify the impact of system upgrades), and (3) to verify the impact of the varying satellite constellation on the effective resolutions of the maps. The paper is organized as follows. The data and method are introduced in Sect. 2. In Sect. 3, we present our results. Finally, a discussion and a conclusion are provided in Sect. 4. A sensitivity study on the choice of spectral criterion to estimate the resolution and a comparison of various approaches to estimate the resolution is given in the appendices.
In the present study, we consider two kinds of data.
The maps of SLA are constructed using optimal interpolation, based on the a priori statistical knowledge of the field (e.g., variance, correlation scales, noise). The mapping procedure is based on merging of calibrated multi-satellite altimeter (level 3) data and follows the same protocol as described by Pujol et al. (2016) for the DUACS-DT2014. Taburet et al. (2019) give the full description and validation of the DUACS-DT2018 global and regional products. The main differences between the DUACS-DT2014 and the DUACS-DT2018 processing consist of an improved along-track processing (e.g., improved orbit correction, wet troposphere correction, ocean tide correction and a new mean sea surface) and updated a priori knowledge of the SLA variance and optimized selection of the data in the optimal interpolation. The maps tested here are computed specifically for this study in several constellation scenarios, keeping at least one mission out to allow an independent assessment of the resolution. The DUACS-DT products, formerly known as AVISO products, are referenced in the CMEMS catalogue as “OCEAN GRIDDED L3/4 SEA SURFACE HEIGHTS AND DERIVED VARIABLES REPROCESSED” products.
Our method to estimate the effective spatial resolution is based on the
ratio between the spectral content of the mapping error and the spectral
content of independent signals (along-track observations previously
mentioned).
The algorithm to compute the spatial effective resolution follows four main
steps:
A coastal editing is applied in a 100 km coastal band (only for the global products) to remove the increased errors in the coastal area. Gridded data are interpolated to the locations of the independent along-track data. Along-track and interpolated data are divided into overlapping 1500 km long segments every 300 km for the global products (500 km long segments for the Mediterranean Sea products and 300 km long segments for the Black sea products). Each segment is saved in a database and referenced by its median (longitude, latitude) coordinates. Finally, between latitudes 90–90
The method (applied to the altimetry product) is illustrated in Fig. 1
with the data selection and interpolation step for the spectral analysis. The
total number of averaged segments in each 1
Schematic illustration of the methodology:
A comparison of SLA maps with an independent tide gauge dataset is carried out
to estimate the effective temporal resolution. The approach is like the
estimate of the effective spatial resolution and based on the computation of
the ratio between the spectral content of the mapping error and the spectral
content of the true tide gauge signal (Eq. 2):
We computed the effective temporal resolution from each tide gauge time
series of the GLOSS-CLIVAR network. The temporal domain covers the period
1 January 1993–31 December 2015. The computation for each time series follows three main steps:
At each tide gauge location, we extract the gridded SLA time series that is most highly correlated with tide gauge time series (note that the maximum distance separation of the grid point that is most highly correlated with each tide gauge is 100 km on average and can be as large as 300 km) Each highly correlated time series (based on correlation criterion The effective temporal resolution at each tide gauge location is given by the period
Note that this estimation of the temporal resolution is subject to an
important caveat: the estimation is based mainly on coastal locations which
may be contaminated by altimetry errors. Additionally, it may not be
fully representative of the temporal resolution of the DUACS maps which
combine various oceanic regimes (e.g., coastal, offshore high variability,
offshore low variability regimes). Our results may therefore be crude but
useful estimates of the temporal resolution.
We somewhat subjectively define the effective resolution to be the
wavelength above which the NSR exceeds 0.5. In other words, it corresponds
to the threshold where the mapping error variance is 2 times smaller than
the observed true signal variance. The methodology used here is similar to
that by Chelton et al. (2019), except that Chelton et al. (2019) consider the
NSR in the spatial domain, whereas we here consider the NSR in the
wavenumber domain. To illustrate and discuss the impact of the choice of the
NSR criterion on the resolution, a sensitivity study is provided in
Appendix B. We demonstrate that the resolution can be
Effective spatial resolution, in kilometers, of the DUACS-DT2018 maps for
The effective spatial resolution of the DUACS-DT2018 global maps is shown in
Fig. 2a. Resolution was computed for maps constructed with three
altimeters (CryoSat-2, HY-2, Jason-2) over the period 12 April 2014–31 December 2015 and Saral/AltiKa data were used as an independent dataset. We believe that this
assessment of the spatial resolution based on maps constructed with three
altimeter missions may be considered a reasonable averaged estimate since
about three altimeter missions are used in the merging for the CMEMS
products 70 % of the time over the period 1 January 1993–15 May 2017. The resolution ranges from
The effective temporal resolution of the DUACS-DT2018 maps ranges from 2 to
140 d (Fig. 3). The temporal resolution is heterogeneously
distributed over the global ocean, particularly in the intertropical band
where a wide range of scales is found, linked to the mixture of continental
tide gauges and island tide gauges, with the latter being more
representative of open-ocean conditions. At mid-to-high latitudes the
zonally averaged temporal scales are between 14 and 45 d,
coherent with the temporal correlation scales applied in the mapping
process. The globally averaged effective temporal resolution is estimated to be
Effective temporal resolution in days of the DUACS-DT2018 maps. Unit in days.
The globally averaged resolutions of about 200 km by 34 d are consistent with the resolutions reported by Chelton et al. (2011, 2014) and Pujol et al. (2016). Using the spectral ratio method (see Appendix B), they found spatial resolution slightly better than 200 km at midlatitude in the Pacific Ocean.
We here investigate the impact of the DUACS upgrade from 2010 to 2018
to highlight the progress of the DUACS processing. Resolutions were computed
for maps constructed with two altimeters (TOPEX/Poseidon and Jason-1) over
the period 1 January 2003–31 December 2004 and Geosat Follow-On data were used as an independent dataset. To identify the impact of the DUACS upgrade, we computed the relative improvement or deterioration of the effective resolutions (expressed in percentage) for the upgrade DT2010 to DT2014, and DT2014 to DT2018 (Fig. 4). A negative (positive) value means finer (coarser) resolution with the upgrade. The comparison of the DT2010 and DT2014 processing shows finer resolution (improvement
Gain/loss of effective spatial resolution for
Similar comparison is performed for the Mediterranean and Black Sea regional
products focusing on the upgrade DT2014 to DT2018. Resolutions were computed
for regional DUACS maps constructed with three altimeters (Jason-2,
CryoSat-2, HY-2) over the period 12 April 2014–31 December 2015 and Saral/AltiKa was used as an independent dataset. The resolution capability of the Mediterranean Sea maps is slightly finer (
The DUACS-DT2018 and the DUACS-DT2014 maps have mean effective temporal
resolutions of
Gain/loss of effective temporal resolution between DT2018 and DT2014. Negative values mean that the resolution capability is better in DT2018 than DT2014.
Since the number of altimeter data processed by DUACS varies with
time (according to the availability of satellites and the data quality), we
investigated the impact of the constellation on the effective spatial
resolution. Figure 6 illustrates the impact of the number of altimeters (two or three missions) used in the mapping on the effective spatial resolution. We
verify, with our diagnostic, modest increases of resolving capabilities in
the DUACS maps with increasing number of altimeters and found a globally
averaged gain of resolution of
Impact of the satellite constellation on the effective resolution – ratio of effective resolution of
Regional gains of resolution can be larger than 10 %. Additionally, it is possible to identify the improved resolving capability when a new mission is introduced into DUACS: for example, Fig. 6a illustrates the improved resolving capability when mission HY-2 is introduced into the mapping, Fig. 6b illustrates the improved resolving capability when mission CryoSat-2 is introduced in the mapping. It is shown that the major contribution of the HY-2 mission in the mapping is in the high variability regions (Gulf Stream, Kuroshio, Agulhas systems) while CryoSat-2 contributes in the mid-to-high-latitude regions. On the global scale, the distribution of the effective spatial resolution is shifted toward shorter scales when the number of missions used in the merging increases (Fig. 7) or when recent altimeters are used in the interpolation (e.g., compare the resolution maps from DT2018 constructed with historical Jason-1/Envisat vs. the maps from DT2018 constructed with currently operational missions Jason2/HY-2 or Jason-2/CryoSat2).
Distribution of the effective spatial resolution for various altimeter merging configuration.
The present study investigates the resolving capability of the DUACS
delayed-time gridded products (Global, Mediterranean Sea and Black Sea)
delivered through the CMEMS catalogue. The key results are summarized in
Table 1. Our method is based on the noise-to-signal spectral ratio to
estimate the resolution. While along-track altimeter data resolve wavelength
scales on the order of a few tens of kilometers (Dussurget et al., 2011; Dufau
et al., 2016), we found that the merging of these along-track data into
continuous maps in time and space leads to properly resolved structures with
a wavelength scale of 100 km (a feature radius scale of
Summary of the DUACS products spatial and temporal resolutions. (1) Not estimated due to the limited amount of tide gauges in the Mediterranean Sea and Black Sea.
These results are consistent with previous investigations. Based on a
spectral ratio approach (cf. Appendix B), Chelton et al. (2011) estimated a
wavelength resolution of
Zonally averaged eddy scale (as in Chelton et al., 2011; and computed from the DUACS-DT2018 two satellites maps) and feature radius resolution of the mesoscale structures that can be properly mapped in DUACS (i.e., derived as 0.25
The comparison of the DUACS-DT2018 reprocessing with former DUACS
reprocessing (DT2010 and DT2014) reveals that finer structures are mapped in
the global and regional Mediterranean Sea DT2018 products. For the Black Sea
product, the interpretation is more complex due to the small dimension of
the basin and the limited amount of spectral computation. Globally, we found
that the largest improvements reach 20 % and are mainly in high
variability regions, associated with the new mapping standard (e.g.,
optimized selection of the along-track data, new a priori knowledge of the
signal variance based on 25 years of altimetry data, updated correlation
scales for the regional Mediterranean Sea product) and new altimeter
standards (e.g., instrumental and atmospheric corrections, tide corrections,
intercalibration method). The improvement patterns between DT2014 and
DT2010 global maps are similar to those found by Pujol et al. (2016) using statistical comparison between maps and independent along-track, and drifter, datasets. The improvement patterns between DT2018 and DT2014 global maps coincide with those found by Taburet el al. (2019) for the validation of the DT2018 products. Using statistical comparison between maps and independent along-track altimeter data, Taburet et al. (2019) also found improvement (
Several studies showed that at least two altimeters are required to
accurately map the SSH mesoscale structures (Le Traon and Dibarboure, 1999;
Ducet et al., 2000; Pujol and Larnicol, 2005; Dibarboure et al., 2011; Chelton et al., 2007, 2011) and up to four altimeters are required for near-real-time products (Pascual et al., 2006) because only past observations are available for the mapping. This reduced number of observations has an impact on the estimation of the sea surface height. The present study reinforces these findings, showing that the resolution capability increased
It is worth noting that we probably underestimate the resolution capability
of the maps since we are estimating the spatial effective resolution of
degraded maps to keep an independent dataset aside. The resolution might
hence be somewhat finer in the distributed CMEMS products. Although the
satellite constellation ranges from 1 to 5 altimeter(s) between 1 January 1993 and 15 May 2017, we believe that our estimation of the spatial resolution based on maps constructed with three altimeter missions may be considered a reasonable averaged estimate since about three altimeter missions are used in the merging for the CMEMS products 70 % of the time over the period 1 January 1993–15 May 2017. We can expect
To conclude, the number and the quality of altimeters simultaneously operational, the along-track configuration and sampling pattern, the weight given to the altimeter data in the mapping procedure, and the choice of threshold SNR are key factors controlling the resolution capability of the DUACS gridded products. One may expect that in permitting to observe finer mesoscale or sub-mesoscale structures (Dufau et al., 2016; Pujol et al., 2012), future instrumental systems based on large-swath altimeters (such as Surface Ocean and Water Topography – SWOT) combined with new mapping techniques based on dynamic interpolation (Ubelmann et al., 2016) will push the resolution of maps toward new limits.
The DUACS source code is not publicly available. The code for the spectral analysis is released under GNU General Public License v3.0 and is available at
Chelton et al. (2011, 2014) estimated the resolution of the DUACS-DT2014
maps based on the calculation of the spectral magnitude ratio between the
reference Stammer (1997) along-track spectrum and gridded SSH spectra.
Similarly, we here estimate the resolution based on the spectral ratio
between independent along-track and gridded SSH signals (Eq. A1). It is
defined as follows:
Chelton et al. (2011, 2014) estimated the resolution of the DUACS-DT2010 and
DUACS-DT2014 as the wavenumber at which the power is a factor of 2 smaller
than the Stammer (1997) spectrum. From their analysis, they estimated
a spatial resolution of
The resolution estimated with the SR method is shown in Fig. A2a and the difference between the effective and useful resolutions is shown in Fig. A2b. The useful resolution of the DUACS-DT2018 maps ranges from 100 km at high latitude to 500 km near the Equator. The ratio of effective to useful resolution suggests somewhat finer resolution in the intertropical band using the SR approach and somewhat finer resolution at high latitude with the NSR approach. In other words, the amplitude of the mapped SSH spectral content is better in the intertropical band than the phase, whereas it is the opposite at high latitude. This feature highlights the difficulty to properly map propagating equatorial waves in DUACS. The two methods are equivalent at midlatitudes.
The transfer function (
The resolution estimated with the transfer function method is shown in Fig. A3a and the difference between the effective resolution and the transfer function resolution is shown in Fig. A3b. The transfer function resolution of the DUACS-DT2018 maps ranges from 100 km at high latitude to 400 km near the Equator. The difference between effective resolution vs. transfer function resolution suggests somewhat finer resolution using the transfer function. This is directly linked to the fact that the along-track data are here nonindependent. The assessment is undertaken below the track that is used in the filtering system. This diagnostic gives the filtering property of the system but suffers from nonindependency of the along-track dataset. The resolution may be different off-track.
These methods share the same number of spectrum calculation and number of
segments used in the calculation (see Fig. A1) and each method has
advantages and drawbacks. The spectral magnitude ratio compares the
amplitude of the signals and the transfer function estimates the filtering
properties from assimilated along-track data. The functions NSR(
Number of segments used in the spectral computation for
Illustration of the various spectral functions used to estimate the resolution at 45
We here investigate and discuss the impact of the NSR criterion on the
estimation of the effective resolution. NSR criterion is used to define the
resolution limit of the map. In the present study, we choose the NSR criterion of NSR criterion of NSR criterion of NSR
Figure B1a represents the effective resolution using NSR
Despite the areas of missing values in Fig. B1b and c, we quantify the difference in effective resolution between criterion NSR
In conclusion, we here demonstrate that the choice of the NSR criterion has
an impact on the estimation of the resolution. Setting a more conservative
criterion of NSR
Effective resolution computed for three different SNR criteria:
Ratio of NSR at longitude 346
Ratio of effective resolution computed with
CU initiated the study. MB and CU designed the study and implemented the Scuba tools. GT, MIP, FF, JFL, YF, AD, DC, GD and NP helped in the design and discussion of the results. MB wrote the paper with contributions from all coauthors.
The authors declare that they have no conflict of interest.
This article is part of the special issue “The Copernicus Marine Environment Monitoring Service (CMEMS): scientific advances”. It is not associated with a conference.
This work is a contribution to the CMEMS R & D activities, the CNES-SALP project and the BOOST-SWOT project. We would like to thank Lee Lueng Fu for his suggestions on the paper, Tom Farrar for his detailed and inspiring review, and one anonymous referee. All their comments significantly added value to this paper.
This paper was edited by Emil Stanev and reviewed by Tom Farrar, Fu Lee Lueng, and one anonymous referee.
This research has been supported by the ANR (grant number ANR-17-CE01-0009-01).