Based on the sea level budget closure approach, this study investigates the
residuals between observed global mean sea level (GMSL) and the sum of
components (steric sea level and ocean mass) for the period January 2005 to
December 2013. The objective is to identify the impact of errors in one or
several components of the sea level budget on the residual time series. This
is a key issue if we want to constrain missing contributions such as the
contribution to sea level rise from the deep ocean (depths not covered by
observations). For that purpose, we use several data sets as processed by
different groups: six altimetry products for the GMSL, four Argo products
plus the ORAS4 ocean reanalysis for the steric sea level and three
GRACE-based ocean mass products. We find that over the study time span, the
observed differences in trend of the residuals of the sea level budget
equation can be as large as

For the 1993–2010 time span of the high-precision satellite altimetry era,
the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate
Change (IPCC) reported that the rate of global mean sea level (GMSL) rise
could be explained by the combined effects of land ice melt (42 %), ocean
thermal expansion (34 %) and anthropogenic land water storage decrease
(12 %) (Church et al., 2013). Over this period, GMSL rise observed by
altimeter satellites amounted to 3.2

We used six different products from six processing groups for the
altimetry-based sea level data:

Validation and Interpretation of Satellite Oceanographic (AVISO;

University of Colorado (CU Release 5;

National Oceanographic and Atmospheric Administration (NOAA;

Goddard Space Flight Center (GSFC version 2;

Commonwealth Scientific and Industrial Research Organization (CSIRO;

the CCI sea level data (

Trends estimated over January 2005–December 2013 for the GMSL, global ocean mass, Argo-based steric sea level, and residuals. Errors associated with “mean global ocean mass” and “mean Argo-based steric sea level” are estimated from the dispersion around the mean.

In the context of the ESA CCI Sea Level project, a new, improved product has been computed. It combines data from Topex/Poseidon, Jason-1 and Jason-2 with the ERS-1 and ERS-2 and Envisat missions, and is based on a new processing system with dedicated algorithms and adapted data processing strategies (Ablain et al., 2015). The main improvements include reduction of errors in the orbit solutions and wet/dry atmospheric corrections, reduction of instrumental drifts and biases, improved inter-calibration between satellite altimetry missions and optimized combination of the different sea level data sets. The CCI sea level products have been validated using different approaches, including a comparison with tide gauge records as well as with ocean re-analysis and climate model outputs (see Ablain et al., 2015, for more details). The CCI sea level data set is freely available over January 1993–December 2013.

Figure 1a shows the GMSL time series from January 2005 to December 2013 for
the six products presented above. Trend values estimated over this time span
are given in Table 1. We first note important trend differences between all
GMSL time series, up to 0.55 mm yr

We use three different data sets for estimating the ocean mass component: the
GRACE Release 05 products from the Center for Space Research of the
University of Texas (CSR RL05), the Deutsches GeoForschungsZentrum (GFZ RL05)
and the Jet Propulsion Laboratory (JPL RL05). The GRACE Release 05 ocean mass
data have been specifically processed by D. Chambers to study the ocean mass
temporal evolution (data available at

We used four Argo temperature and salinity data sets.

Three gridded data sets are provided by the following groups:

the International Pacific Research Center (IPRC;

the Japan Agency for Marine-Earth Science and Technology (JAMSTEC;

the SCRIPPS Institution of Oceanography (SCRIPPS;

Argo data sets do not cover the whole ocean before 2005 (von Schuckmann et
al., 2014; Roemmich et al., 2015). The study by Chen and Tung (2014) provides
a depth coverage map of in situ temperature and salinity measurements, and we
note that as of 2005, there are data up to at least 1500 m (e.g., almost
full coverage down to 1200 m and 50 % coverage between 1200 and
1500 m). Thus we computed the steric sea level time series (and associated
uncertainty; but note that only JAMSTEC provides errors), over January
2005–December 2013, integrating the data over the 0–2000 m depth range.
The global mean steric sea level time series from IPRC, JAMSTEC and SCRIPPS
are estimated over the 62.5

Residual curves (January 2005–December 2013) computed for each of
the six GMSL products (AVISO, CU, NOAA, GSFC, CSIRO and CCI). Mean global
ocean mass (GOM) and mean Argo-based steric sea level are used. (For example:
“Residual AVISO”

We also used an updated version of the steric data set processed by von
Schuckmann and Le Traon (2011). This data set provides steric sea level and
associated uncertainty based on quality-controlled Argo-based temperature
and salinity data from IFREMER (

Figure 1c presents the four steric sea level time series and associated
uncertainties (except for IPRC and SCRIPPS, for which errors are not
provided) over 2005–2013. Trend values over the study time span can be found
in Table 1. Figure 1c shows significant discrepancies of several mm from one
time series to another at sub-seasonal to interannual timescales, in
particular in the early part of the record (e.g., in 2005) and late 2007 to
early 2008. Between 2005 and early 2008, the KVS time series is rather flat,
unlike the other steric time series. In terms of trends, we note differences
of up to 0.2 mm yr

Finally, we include the ORAS4 reanalysis from Balmaseda et al. (2013b)
(

Steric sea level trends and associated uncertainties are gathered in Table 1.

In the following, we present the residual time series (Eq. 2, called “residuals” hereinafter) over January 2005–December 2013. The main objective is to check whether the residual anomalies are correlated – or not – with one or several components of the sea level budget (GMSL, ocean mass, steric sea level; see Eq. 1). In a first step (Sect. 4), we look at residual trends, focusing on the trend differences between the residual time series obtained with different components (and different products for each component). These differences only inform on the residual trend obtained from a given combination of products, relative to other residual trends. They say nothing about the absolute residual trend values. In Sect. 8, we also estimate uncertainty of the absolute trend of the residuals.

In a second step (Sect. 5), we try to explain the short-term (from sub-seasonal to interannual) anomalies in the detrended residual time series and investigate whether these are real signals or errors in one or several components of the sea level budget equation. For that purpose, we correlate the detrended residual with each detrended component, successively. A significant correlation of the residuals with one component of the budget equation (GMSL, ocean mass, steric sea level) may indicate that this particular component is in error. In effect, if one (or more than one) component is error free, one may expect no correlation between the short-term anomalies of the residual time series and that particular component, since in that case this component should be compensated for by the sum of the other two components of the budget equation (Eq. 1).

Time series of GMSL differences with respect to the CCI GMSL (January 2005–December 2013).

Figure 2 shows residual time series computed for each GMSL estimate (i.e.,
AVISO, CU, NOAA, GSFC, CSIRO and CCI), using mean values of the three GOM and
four Argo-based steric sea level products. For the comparison, all curves
start at the same (arbitrary) value in January 2005. Table 1 gathers the
trend values over January 2005–December 2013 of the residual time series for
the different data combinations. Figure 2 indicates that over the January
2005–February 2007 time span, the residuals are in fairly good agreement. In
late 2007 (a period coinciding with the 2007–2008 La Niña), all
residuals are strongly negative. By mid-2008, we observe a step-like increase
in the residuals associated with some GMSL time series (AVISO, NOAA, CSIRO
and CCI), while a decrease is noticed for the CU and GSFC residuals until
mid-to-late 2011. The residual trends seem to fall into two groups (see
Table 1): (1) AVISO, NOAA, CSIRO and CCI, and (2) CU and GSFC, with large
trend differences, > 0.5 mm yr

Because the same “mean” ocean mass and “mean” steric sea level data are used when computing the residuals shown in Fig. 2, differences in residual trends necessarily result from trend differences in the GMSL time series. To investigate this further, we show in Fig. 3 difference time series between GMSL products, using the CCI GMSL as a reference.

The two groups of GMSL products mentioned above appear much more clearly in
Fig. 3. We note that the AVISO, NOAA and CSIRO curves (corresponding to group
1) follow a different trajectory compared to the CU and GSFC curves (group
2), except during 2008–2010. This is particularly clear during 2005–2008
and to a lesser extent beyond 2010. The sources of these differences have
been investigated in two recent papers by Masters et al. (2012) and Henry et al. (2014).
These studies showed that the choice of the geophysical corrections applied
to the data and the averaging method to calculate the GMSL from along-track
data are the two main causes of differences between the GMSL time series. For
example, AVISO and CU apply different averaging methods that significantly
impact the GMSL products (Henry et al., 2014). Moreover, from 2005 to
mid-2008, a time span corresponding to the use of Jason-1 satellite data,
these groups use different orbit solutions and different corrections for
ocean tides and sea surface bias, while beyond mid-2008, they use exactly the
same orbit solution and same sea surface bias correction (see the respective
websites for more details). Thus, differences between AVISO and CU GMSL time
series are to be expected over 2005 to mid-2008. This is indeed what Fig. 3
shows over this time span. To check the CU and GSFC residual drop somewhat
further, we computed the residuals trends between January 2005 and June 2008
for all GMSL time series. We find highly negative related residual trends for
CU and GFSC (of

Residual sea level time series (January 2005–December 2013)
computed with the CCI GMSL. (

In a next step, we examine the contribution of the ocean mass and steric
components to the residual trend for each GMSL product. Figure 4a and b shows
residual curves for the CCI GMSL computed with each ocean product and each
steric sea level product. Results show that the different ocean mass
products show almost similar residual trends (up to

From this section, we conclude that trend differences observed in the residual time series (Fig. 2) are dominated by differences in the altimetry-based GMSL products.

Figure 2 shows that the residual time series also display important high-frequency (sub-seasonal to interannual) anomalies of up to 4 mm amplitude. These anomalies are highly correlated for all GMSL products, in particular for AVISO, NOAA, CSIRO and CCI data sets. In the following, we analyze the detrended residual time series. Only three GMSL data sets are considered: the AVISO, CU and CCI GMSL data (AVISO and CU being representative of group 1 and group 2, respectively). In order to understand whether a given variable (GMSL, ocean mass or steric sea level) is responsible for all – or part – of the observed short-term (from sub-seasonal to interannual) residuals, we correlate this variable (trend removed) with its associated (detrended) residual. What we would expect, if all data sets were error free, is to see no correlation between the detrended variable and its associated (detrended) residual. Therefore, a low correlation may be interpreted as a “good result”, i.e., little contamination by errors of the associated variable. Such an interpretation may not be unique however. Limitations of this approach are discussed in Sect. 6.

Correlations estimated between detrended residual time series and the associated detrended component. Estimated rms of the corresponding detrended residual time series.

Detrended residual time series (January 2005–December 2013) (mean
global ocean mass (GOM) and mean Argo-based steric sea level are used to
compute the residual) for CCI (

Detrended residual time series (January 2005–December 2013)
computed with the CCI GMSL, mean Argo-based steric sea level and different
ocean mass products. Associated detrended global ocean mass (GOM) time
series superimposed. (

Residual time series (January 2005–December 2013) computed for each
of the three GMSL: CCI (

Detrended residual time series of CCI GMSL (January 2005–December
2013) computed with the mean global ocean mass (GOM) and each of the four
steric sea level products: SCRIPPS (

Residual time series (January 2005–December 2013) computed with the CCI GMSL, and the mean of the four Argo products (black curve) and ORAS4 data (dotted curve). The detrended CCI GMSL is superimposed (dashed curve).

Correlation coefficient between residuals computed from noisy GMSL, noisy steric sea level and perfect ocean mass for 100 drawings of lots. Blue and red points correspond to cases 1 and 2, respectively (see text). The horizontal black line is the correlation of the nominal case (as described in Sect. 5.2).

Steric sea level difference ORAS4 minus mean Argo time series (trend not removed) (black curve) (January 2005–December 2013) up to 2000 m depth. The dashed curve is the Indonesian steric sea level time series estimated from ORAS4 up to 2000 m depth. The starry curve is the steric sea level time series from ORAS4 below 2000 m depth.

To analyze the impact of the short-term GMSL errors on the residuals, we simply superimpose the detrended GMSL with its associated residual (also detrended). Figure 5a–c shows, for AVISO, CU and CCI data, the detrended residual curves and associated detrended GMSL. In Table 2 are given the correlation between the detrended residual curve and its associated detrended GMSL as well as the root-mean squares (rms) of the residual time series. On sub-seasonal to interannual timescales, most of the observed GMSL anomalies have been reduced after subtracting the ocean mass and steric sea level components from the GMSL data. Nevertheless, some anomalies still remain (see Fig. 5a–c). This is particularly striking for the 2007–2008.5 time span. This period corresponds to a La Niña event. While the 2011 La Niña is well explained by the mass plus steric components (see Boening et al., 2012, and Cazenave et al., 2014), it is surprising that the same data sets do not explain the negative GMSL anomaly related to the 2007–2008 La Niña. During the period February 2007 to June 2008, the correlation computed between the CCI, AVISO and CU residual curves and associated detrended GMSL amounts to 0.79, 0.89 and 0.92, respectively. This high correlation and amplitude comparison suggests that the residual anomaly during this particular time span at least partly comes from the GMSL data. We cannot rule out however that the steric or ocean mass components also contribute. We will indeed see below that the observed discrepancy at this particular date also partly arises from errors in the GRACE and Argo data.

Over the whole time span (2005–2013), the correlations are 0.02, 0.26 and 0.55 for the CCI, AVISO and CU GMSL, respectively (see Table 2). The lowest correlation is obtained for the CCI data, indicating that the CCI residuals contain fewer GMSL short-term errors than the other two data sets.

We perform a similar comparison with the GRACE-based ocean mass products. For that purpose we only consider a single GMSL data set (i.e., CCI) and superimpose the detrended CCI residual time series computed separately for each ocean mass product with the corresponding detrended GRACE data set. These are shown in Fig. 6a–c. In Table 2 are given the correlation between the detrended residual curve and its associated detrended ocean mass component. The rms of the residual time series are also given.

The correlation is relatively high in all three cases, 0.46, 0.55 and 0.57 for the CSR, GFZ and JPL data, respectively. The detrended global ocean mass and residual time series coincide almost perfectly between mid-2006 and mid-2007 and between mid-2009 and early 2012 (Fig. 6). This indicates that the short-term residual errors are largely affected by errors in GRACE-based ocean mass products. During the 2007–2008 La Niña, we also observe a significant correlation between the detrended ocean mass and associated residual of 0.57, 0.69 and 0.69, respectively, for the CSR, GFZ and JPL data.

The rms of the residual time series based on the IPRC, JAMSTEC, SCRIPPS and KVS Argo data (linear trend removed from each time series) are in the range 1.3–1.6 mm (see Fig. 7 and Table 2). The lowest rms are obtained with SCRIPPS data when using the CCI and CU GMSL. For AVISO, the lowest rms are obtained with the KVS steric sea level. Overall, no best Argo product emerges, rms differences being small.

As mentioned previously, in the early part of the time series (2005–2006), we note larger dispersion between all Argo products compared to the subsequent years. These differences can be explained by a still incomplete global coverage of Argo data during this period (Lyman and Johnson, 2014; Roemmich et al., 2015). We note that the negative anomaly coinciding with the 2007–2008 La Niña is still present in the residual curves, with almost the same amplitude as in the GMSL data, indicating that the GMSL, or the mass or the Argo-based steric components (or all of them), are in error at that particular date.

We next examine the correlation between the residual time series and the detrended steric sea level, considering each Argo product successively. Figure 8a–d shows the detrended residual time series computed with the CCI GMSL superimposed on the detrended steric sea level time series. Each of the four steric products (SCRIPPS, IPRC, JAMSTEC and KVS) is considered. In each case the mean global ocean mass is used for computing the residual.

Examination of Fig. 8 shows that lowest residual rms are obtained with the SCRIPPS time series, but the rms difference with other Argo products is small. We also note that the short-term residual fluctuations are significantly correlated with the associated (detrended) Argo-based steric sea level time series at some periods, for example between mid-2010 and mid-2013, and especially when using the IPRC data. This indicates that the short-term fluctuations of the residuals partly reflect Argo-based steric sea level errors during this period.

Errors in Argo-based steric sea level estimates arise from different sources
(gaps in some regions, data editing, mapping techniques, etc.; Abraham et
al., 2013; Lyman and Johnson, 2014; von Schuckmann et al., 2014). To
investigate further the effect of Argo sampling, as well as other Argo data
processing errors, on the residual time series, we recomputed the residuals
using steric data from the ORAS4 ocean reanalysis (Balmaseda et al.,
2013b). The integration is performed over the whole ocean depth range
(0–5350 m) and between 66

One important objection that can be made to our approach is the following:
suppose for example that only the GMSL and steric time series are in error
(e.g., affected by white noise) and that the ocean mass data are perfect.
Then, corresponding residuals and ocean mass time series would be correlated.
Following the logic of our approach, one may thus conclude that it is the
ocean mass that is in error. To investigate this potential drawback, we did
the following test.

We first computed a “perfect” ocean mass time series from the difference between (observed) mean GMSL and mean Argo-based steric sea level.

Next, we applied a random noise to the mean GMSL and mean steric time
series. Two cases have been considered: case 1 corresponds to a random error
between

Then, we computed the corresponding residual time series (i.e., noisy GMSL minus noisy steric sea level minus perfect ocean mass), and correlated these with the “perfect” ocean mass time series.

Figure 10 shows a plot of these new correlations for the two cases. We note that most correlations fall below those of the nominal case (as described in Sect. 5.2). For case 1, in 82 % of the simulations, the correlation worsens. For case 2, this number increases to 92 %. We conclude that if the ocean mass time series is perfect and the GMSL and steric sea level data are noisy, the residuals appear poorly correlated with the ocean mass time series. Thus, a high correlation very likely reflects errors in the mass component.

In Sect. 5 (detrended residuals), we investigated temporally correlated errors between the three data sets (GMSL, steric sea level, ocean mass). This was the motivation for applying a correlation approach. The test described above shows that the proposed method is meaningful and that the conclusions drawn in Sect. 5 are largely valid.

The ORAS4 minus mean Argo time series (integration down to 2000 m; trend not
removed) is shown in Fig. 11. It displays significant short-term
fluctuations, up to 4 mm, and a trend of 0.28 mm yr

In this study, we estimated the sea level budget over the 2005–2013 time
span using a large set of different observational products for the satellite
altimetry-based sea level (six products), GRACE-based ocean mass (three
products) and steric sea level (five data sets). We analyzed the residual
time series (i.e., observed GMSL minus the sum of mass plus steric
components) and attempted to attribute an error source to the residual trends
and short-term residual anomalies. We found that errors in the GMSL products
have a large impact on the residual trends. Trend differences of up to
0.55 mm yr

In terms of absolute residual trends, we identified the contribution of the
Indonesian region, not covered by Argo, as contributing about
0.25 mm yr

This suggests that the sea level budget can be closed when using the CCI,
AVISO and NOAA data. Hence, in these cases, the deep ocean (below 2000 m)
contribution appears negligible. It is worth mentioning that the residual
trend (with the CCI GMSL) amounts to about zero (exactly
0.00 mm yr

Another result from our study is the attribution of the short-term (from sub-seasonal to interannual) anomalies of the residual time series to errors in both Argo-based steric sea level and GRACE-based ocean mass. Short-term errors in these two components sometimes act in concert (thus amplifying the residual errors, e.g., during the 2007–2008 La Niña) or affect the residuals at different periods (e.g., over 2011–2014 for Argo, or in 2006 for GRACE).

To summarize the findings of this study, the main source of differences
reported in the residual trends appears to be related to altimetry-based sea
level data processing. In terms of absolute residual trends, missing Argo
data in the Indonesian region contribute as much as 0.25 mm yr

We thank M. Balmaseda for providing us with the ORAS4 reanalysis data set. We also thank J. François Legeais and L. Zawadski for helpful discussions about errors in altimetry data processing. H. B. Dieng is supported by a PhD grant from the European Space Agency in the context of the Climate Change Initiative Programme. Edited by: J. M. Huthnance