OSOcean ScienceOSOcean Sci.1812-0792Copernicus GmbHGöttingen, Germany10.5194/os-11-789-2015Sea level budget over 2005–2013: missing contributions and data errorsDiengH. B.CazenaveA.anny.cazenave@legos.obs-mip.frvon SchuckmannK.AblainM.MeyssignacB.https://orcid.org/0000-0001-6325-9843Laboratoire d'Etudes en Géophysique et Océanographie Spatiales – Centre National d'Etudes Spatiales (LEGOS-CNES), Toulouse, FranceInternational Space Science Institute (ISSI), Bern, SwitzerlandMediterranean Institute of Oceanography (MIO), Université de Toulon, Toulon, FranceCollecte Localisation Satellites (CLS), Ramonville, FranceA. Cazenave (anny.cazenave@legos.obs-mip.fr)6October20151157898027April201513May201527July201530July2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://os.copernicus.org/articles/11/789/2015/os-11-789-2015.htmlThe full text article is available as a PDF file from https://os.copernicus.org/articles/11/789/2015/os-11-789-2015.pdf
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 ∼ 0.55 mm yr-1 (i.e.,
∼ 17 % of the observed GMSL rate of rise). These trend differences
essentially result from differences in trends of the GMSL time series. Using
the ORAS4 reanalysis (providing complete geographical coverage of the steric
sea level component), we also show that lack of Argo data in the Indonesian
region leads to an overestimate of the absolute value of the residual trend
by about 0.25 mm yr-1. Accounting for this regional contribution leads
to closure of the sea level budget, at least for some GMSL products. At short
timescales (from sub-seasonal to interannual), residual anomalies are
significantly correlated with ocean mass and steric sea level anomalies
(depending on the time span), suggesting that the residual anomalies are
related to errors in both GRACE-based ocean mass and Argo-based steric data.
Efforts are needed to reduce these various sources of errors before using the
sea level budget approach to estimate missing contributions such as the deep
ocean heat content.
Introduction
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 ± 0.4 mm yr-1, a value only
slightly higher than the sum of the contributions (amounting to
2.8 ± 0.5 mm yr-1). Although of the same order of magnitude as
associated uncertainties, the 0.4 mm yr-1 difference may also reflect
missing contributions, e.g., the deep ocean contribution below 700 m depth
where the coverage of ocean temperature data before the Argo era was poor.
Estimating the deep ocean warming is an important issue in the context of the
current hiatus reported since the early 2000s in global mean air and sea
surface temperature evolution (e.g., Held, 2013; Trenberth and Fasullo, 2013;
Smith, 2013). Different explanations have been proposed to explain the
hiatus, ranging from reduced radiative forcing due to prolonged solar
minimum, increased aerosol emissions and small numerous volcanic eruptions,
changes in stratospheric water vapor, enhanced heat uptake by the deep ocean,
either in the Pacific or Atlantic regions (e.g., Trenberth and Fasullo, 2010,
2013; Hansen et al., 2011; Solomon et al., 2010; Guemas et al., 2013; Kosaka
and Xie, 2013; Balmaseda et al., 2013a; Watanabe et al., 2013; England et
al., 2014; Chen and Tung, 2014), to redistribution of heat in the
Indo-Pacific region (Nieves et al., 2015). The deep ocean heat uptake has so
far been the favored explanation of the hiatus considering that greenhouse
gases continue to accumulate in the atmosphere at an increasing rate (Peters
et al., 2012) and the Earth's energy imbalance at the top of the atmosphere
is still in the range 0.5–1 Wm-2 (e.g., Hansen et al., 2011; Loeb et
al., 2012; Trenberth et al., 2014). A recent study by Karl et al. (2015)
based on reprocessing of ocean and land surface temperature data claims that
there is no evidence of a hiatus during the last decade. While the hiatus is
still a matter of debate, attempts to estimate whether and how much the deep
ocean is warming remains an important issue. Accurate observations of sea
level rise and its components (ocean thermal expansion and ocean mass change)
can, in principle, help in constraining the deep ocean contribution, hence
its amount of warming (e.g., von Schuckmann et al., 2014). In particular,
satellite altimetry-based GMSL rise corrected for ocean mass change (for
example, using GRACE space gravimetry data over the oceans) provides an
estimate of the total (full depth-integrated) ocean thermal expansion (or
equivalently ocean heat content). Since the year 2005, comparison with
observed Argo-based ocean thermal expansion (down to ∼ 2000 m depth)
may help to quantify any deep ocean contribution (below 2000 m). In effect,
the sea level budget equation is described as follows:
GMSL = Ocean Mass + Steric sea level (0–2000 m)+ Steric sea level (>2000m)+ data errors.
The residual term defined as the difference between observed GMSL and
observed estimates of ocean mass and steric sea level down to 2000 m depth
(see Eq. 2 below) includes the deep ocean contribution (called “Steric sea
level > 2000 m”) and data errors:
Residual=GMSL-Ocean mass-Steric sea level (0–2000 m)=Steric sea level (>2000m)+ data
errors.
Attempts to estimate the deep ocean contribution from the sea level budget
approach were performed in two recent studies (Llovel et al., 2014; Dieng et
al., 2015). Dieng et al. (2015) considered two periods (2005–2012 and
2003–2012) that correspond to the availability of new observing systems for
estimating thermal expansion and ocean mass (nearly full ocean temperature
and salinity coverage down to 2000 m from Argo floats and direct ocean mass
measurements from GRACE space gravimetry, respectively). In Dieng et
al. (2015), time series of satellite altimetry-based sea level (five
different data sets), thermal expansion (eight different products;
integration down to 1500 m) and ocean mass (three products) components were
analyzed in order to estimate the residual term of Eq. (2). Llovel et
al. (2014) performed a similar study over the 2005–2013 time span but with
fewer data sets. Another attempt concerning this issue is by von Schuckmann
et al. (2014). These studies came to the same conclusion; i.e., the residual
term in Eq. (2) is contaminated by overly large data errors to provide any
robust deep ocean contribution estimate. Here we build upon these previous
studies, in particular that from Dieng et al. (2015). We focus on the
2005–2013 time span corresponding to maximized Argo coverage and compute the
steric sea level component integrating the data down to 2000 m. We also
include in our analysis the new sea level product from the European Space
Agency (ESA) Climate Change Initiative (CCI) project
(www.esa-sealevel-cci.org), available up to December 2013. The main
objective of the present study is to investigate whether the residual time
series of the sea level budget (Eq. 2) may be attributed to errors associated
with the components (GMSL, ocean mass, steric sea level) or not. This is an
important issue to be addressed before trying to estimate any missing
contribution.
Data and methodSea level data
We used six different products from six processing groups for the
altimetry-based sea level data:
Validation and Interpretation of Satellite Oceanographic (AVISO; http://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/actualitesindicateurs-des-oceansniveau-moyen-des-mersindexhtml.html);
University of Colorado (CU Release 5;
http://sealevel.colorado.edu/);
National Oceanographic and Atmospheric Administration (NOAA;
http://www.star.nesdis.noaa.gov/sod/lsa/SeaLevelRise/LSA_SLR_timeseries_global.php);
Goddard Space Flight Center (GSFC version 2;
http://podaac-ftp.jpl.nasa.gov/dataset/MERGED_TP_J1_OSTM_OST_GMSL_ASCII_V2);
Commonwealth Scientific and Industrial Research Organization (CSIRO;
www.cmar.csiro.au/sealevel/sl_data_cmar.html); and
the CCI sea level data (http://www.esa-sealevel-cci.org/products).
The first five sea level data sets are based on Topex/Poseidon, Jason-1 and
Jason-2 data averaged over the 66∘ S–66∘ N domain, except
for the CSIRO data averaged over 65∘ S to 65∘ N. For each
product, a set of instrumental and geophysical corrections is applied
(details are given on the websites of each data set). In addition, the effect
of glacial isostatic adjustment (GIA, i.e., a small correction of
-0.3 mm yr-1; Peltier, 2004) is accounted for in each sea level time
series except for the NOAA data set. Thus we corrected the latter for the GIA
effect, using the -0.3 mm yr-1 value (i.e., resulting in an addition
of 0.3 mm yr-1 to the GMSL time series). The sea level time series
used in this study cover the period January 1993–December 2013. The five sea
level time series (AVISO, CU, GSFC, NOAA and CSIRO) are obtained either by
directly averaging the along-track sea surface height data (e.g., CU) or by
firstly gridding the unevenly distributed along-track data and then
performing grid averaging (e.g., AVISO and NOAA). In all cases, an area
weighting is applied. In addition to the geographical averaging method, other
differences exist between the GMSL data sets because of the applied
geophysical and instrumental corrections and the number of satellites
considered (discussion on these differences can be found in Masters et al.,
2012, and Henry et al., 2014).
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.
Global meanGMSL trends (mmyr-1)Residual trends (mmyr-1)sea level(residual computed with mean(GMSL)global ocean mass and meanproductArgo-based steric sea level)AVISO3.170.3CU2.83-0.03NOAA3.260.42GSFC2.80-0.07CSIRO3.350.49CCI3.110.26Global oceanGlobal ocean mass trendsCCI residual trendsmass(mmyr-1)(mmyr-1)CSR2.010.28GFZ2.110.18JPL2.000.29Mean2.04±0.08Argo-based stericArgo-based steric seaCCI residual trendssea levellevel trends (mmyr-1)(mmyr-1)KVS0.74±0.130.33IPRC0.760.31JAMSTEC0.94±0.160.14SCRIPPS0.830.24Mean0.82±0.08ORAS4 (0–5350 m)1.14-0.06
(a) Global mean sea level (GMSL) time series (January
2005–December 2013) from the five satellite altimetry processing groups
(AVISO, CU, NOAA, GSFC and CSIRO) and CCI. (b) Global ocean mass
(GOM) time series and associated uncertainty (shaded area) (January
2005–December 2013) from GRACE, based on the data from CSR (black curve),
GFZ (green curve) and JPL (red curve). (c) Argo-based monthly global
mean steric sea level time series (January 2005–December 2013) (integration
down to 2000 m) from four processing groups (KVS, IPRC, JAMSTEC and
SCRIPPS). Shaded areas represent uncertainties of the JAMSTEC and KVS steric
sea level data.
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-1 between GFSC and CSIRO data. The
lowest trends (around 2.8 mm yr-1) are obtained for the CU and GSFC
data sets. Higher trends (from 3.11 to 3.35 mm yr-1) are obtained for
CCI, AVISO, NOAA and CSIRO GMSL time series. At shorter timescales (from
sub-seasonal to multi-annual), significant discrepancies of several mm are
observed between the different GMSLs, especially between 2005 and 2008, and
between mid-2010 and mid-2011. The latter period coincides with a strong La
Niña event.
Ocean mass data
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 http://grace.jpl.nasa.gov). In
effect, gridded Release 05 data cannot be used to compute ocean mass changes
because the area-weighted global mean is set to zero (as warned on the
http://grace.jpl.nasa.gov/data/get-data/monthly-mass-grids-ocean
website). The Chambers RL05 GRACE ocean data are publicly available from
https://dl.dropboxusercontent.com/u/31563267/ocean_mass_orig.txt. They
are provided as global mean (averaged over the 90∘ S–90∘ N
domain) time series with associated uncertainties. The data processing is
described in Johnson and Chambers (2013) (see also Chambers and Schroeter,
2011, and Chambers and Bonin, 2012). The GIA component has been subtracted
from each GRACE ocean mass time series using the GIA correction computed as
described in Chambers et al. (2010). Figure 1b shows the global ocean mass
(called GOM hereafter) time series and associated uncertainties over
2005–2013 for the CSR, GFZ and JPL products (see also Table 1 for trend
values and associated uncertainties; note that mean value uncertainties
quoted in Table 1 are estimated from the dispersion between available
products. These represent lower bounds of errors). All three GOM products are
quite close to each other, in terms of both trend and short-term
fluctuations.
Steric data
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;
http://apdrc.soest.hawaii.edu/projects/Argo/data/gridded/On_standard_levels/index-1.html);
the Japan Agency for Marine-Earth Science and Technology (JAMSTEC;
ftp://ftp2.jamstec.go.jp/pub/argo/MOAA_GPV/Glb_PRS/OI/); and
the SCRIPPS Institution of Oceanography (SCRIPPS;
http://sio-argo.ucsd.edu/RG_Climatology.html).
These data sets are available at monthly intervals on a global
1∘× 1∘ grid down to 2000 m, over the period
January 2005 to December 2013, January 2001 to August 2014, and January 2004
to December 2013, respectively.
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∘ S–64.5∘ N,
60.5∘ S–66∘ N and 61.5∘ S–64.5∘ N
domains, respectively.
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” = “GMSL from AVISO minus Mean GOM minus Mean
Argo”.)
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 (http://wwz.ifremer.fr/lpo_eng/content/view/full/83074), with integration down to 2000 m depth and
averaged on a 5∘× 10∘ grid. The method to derive the
gridded products is described in detail in von Schuckmann and Le Traon (2011).
In the following, we call this data set “KVS”. The KVS data set
covers the 60∘ S–60∘ N domain. Area weighting is applied
to all data sets when averaging.
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-1, the KVS data giving a lower steric trend than
the other three (this is actually due to the rather flat start of the KVS
curve in 2005).
Finally, we include the ORAS4 reanalysis from Balmaseda et al. (2013b)
(https://icdc.zmaw.de/easy_init_ocean.html?&L=1#c2231). This
reanalysis is based on the Nucleus for European Modelling of the Ocean (NEMO)
circulation model (version 3.0) with data assimilation. Assimilated data
include temperature and salinity profiles over 1958–2009 from the v2a
version of the EN3 database constructed by the Met Office Hadley Centre (Good
et al., 2013), along-track altimetry-based sea level anomalies and global sea
level trend from AVISO, sea surface temperature and sea ice from the ERA-40
archive (prior to November 1981), from NCEP (National Centers for
Environmental Prediction) OI version 2 (1981 until December 2009) and from
OSTIA (Operational Sea Surface Temperature and Sea Ice Analysis; January 2010
onwards). The ORAS4 temperature and salinity data are available at monthly
intervals over 42 depth levels ranging from the ocean surface down to 5350 m
depth, on a global 1∘× 1∘ grid from January 1958 to
December 2014 (see Balmaseda, 2013b, for more details). To estimate the ORAS4
global mean steric sea level, the data are averaged over the
66∘ S–66∘ N domain.
Steric sea level trends and associated uncertainties are gathered in Table 1.
Residual time series (GMSL minus ocean mass minus steric sea level)
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).
Residuals with trends
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-1, between them. The
positive residual trends in Table 1 correspond to group 1, whereas residual
trends of group 2 are negative.
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 -0.67 and -0.91 mm yr-1, respectively), while for
all other GMSL time series the residual trends are in the range -0.05 to
0.08 mm yr-1. Other differences noticed in Fig. 3 beyond 2010 are less
clear but may be related to the averaging method with a stronger impact
during the 2011 La Niña. More investigation and collaborative work
between the different processing groups are needed to fully understand and
reduce the reported differences in the GMSL time series.
Residual sea level time series (January 2005–December 2013)
computed with the CCI GMSL. (a) Mean of the four Argo products and
each GOM product; (b) mean of the three global ocean mass (GOM) data
sets and each Argo product.
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 ∼ 0.1 mm yr-1 trend differences are noted; see Fig. 4a). For the Argo products,
their effect on the trend differences is < 0.2 mm yr-1 (see Fig. 4b).
We do not show similar figures for other GMSL products because the
differences in the residual trends computed between all Argo products (and
all ocean mass products as well) are similar to those computed with the CCI
GMSL.
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.
Detrended residuals
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.
Global meanThe rms of the residual computedCorrelationsea levelwith mean global ocean mass(detrended GMSL(GMSL)and mean Argo-based stericand associatedproductsea level (mm)detrended residual)CCI1.380.02AVISO1.320.26CU1.360.55GRACE-basedThe rms of the CCI residualCorrelationglobal oceancomputed with mean(detrended global oceanmass productArgo-based steric seamass and associatedlevel (mm)detrended residual)CSR1.370.46GFZ1.460.55JPL1.560.57Argo-basedThe rms of the CCI residualCorrelationsteric seacomputed with mean(detrended steric sealevelglobal ocean masslevel and associated(0–2000 m)(mm)detrended residual)KVS1.590.53IPRC1.560.51JAMSTEC1.560.51SCRIPPS1.450.50
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 (a), AVISO (b), and
CU (c). The detrended GMSL from CCI, AVISO and CU are superimposed
on each residual, respectively.
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. (a) CSR; (b) GFZ; (c) JPL.
Residual time series (January 2005–December 2013) computed for each
of the three GMSL: CCI (a), AVISO (b), and CU (c).
Mean global ocean mass (GOM) and each of the four steric sea level products
(IPRC, JAMSTEC, SCRIPPS and KVS) are used for computing the residuals.
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 (a), JAMSTEC (b),
IPRC (c), and KVS (d); superimposed, the corresponding
detrended steric sea level time series.
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.
GMSL short-term (from sub-seasonal to interannual)
errors
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.
Short-term (from sub-seasonal to interannual) errors in
the global ocean mass
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.
Short-term (from sub-seasonal to interannual) Argo-based
steric sea level errors
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.
Sea level budget using the ORAS4 ocean reanalysis
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∘ S and 66∘ N. Figure 9 shows
the residual time series 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. Differences in residuals shown in Fig. 9 directly
result from differences in the steric time series (all other parameters being
the same). In terms of residual rms, we see little difference between the
considered steric sea level products, even if at some periods (e.g., between
mid-2010 and mid-2011) the steric curves do not agree very well with each
other. For most of the time span, there is good coherence between the mean of
the four Argo time series and ORAS4. However, the correlation between the
residuals and the detrended CCI GMSL is slightly lower when using the mean of
the four Argo products than when using the reanalysis.
Limitation of the approach presented in Sect. 5 (detrended analysis)
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 -2 and +2 mm; case 2 corresponds to a random error between -4
and +4 mm (corresponding to typical data uncertainties at interannual
timescales). One-hundred drawings of lots have been performed for each case.
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.
Contribution of the Indonesian region and other areas not covered
by Argo; uncertainty in the absolute residual trend
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-1 (the ORAS4
steric trend being larger than the mean Argo trend). The ORAS4 reanalysis
provides gridded steric data with no gaps, unlike the Argo products. In
effect, the coverage of Argo data is not fully global, some regions (e.g.,
the Indonesian region and the Gulf of Mexico) not being covered. In Fig. 11,
the ORAS4 contribution for the 2000–5350 m depth layer is also shown. It
only explains the 0.06 mm yr-1 sea level trend and (as expected) shows
no short-term anomalies, as seen in the residual curve when using Argo. It is
likely that both trend difference and short-term anomalies seen in ORAS4
minus Argo time series result from gaps in the Argo geographical coverage
(von Schuckmann et al., 2014). This is illustrated also in Fig. 11, which
shows the steric sea level contribution from the Indonesian region
(0–2000 m layer) computed with ORAS4. Part of the short-term anomalies of
the difference curve is due to the lack of Argo data in this region (e.g., in
2011, coinciding with the La Niña event). Moreover, in terms of trend,
the Indonesian region explains about the whole trend difference between
Argo-based and ORAS4-based steric sea level. This suggests that the steric
sea level trend estimated when using Argo is underestimated by
∼ 0.25 mm yr-1. Hence, the residual (GMSL minus steric sea level
minus ocean mass) trend may be in error (i.e., overestimated) by about this
amount. This has important implications for the missing contributions derived
from the sea level budget approach.
Conclusion
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-1 between the different GMSL time series are reported. Such
trend differences actually prevent one from accurately constraining missing
contributions. These trend differences largely arise from differences in
processing the Jason-1 satellite data (e.g., choice of the averaging method
and geophysical corrections), as previously discussed by Masters et
al. (2012) and Henry et al. (2014). While trying to identify the outliers and
select the best corrections to be used is beyond the scope of the present
study, we stress that this is definitely an important goal to pursue in the
future.
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-1 (the computed residual trends being overestimated by
about this amount). Contributions from other regional gaps in the Argo
coverage (e.g., the Gulf of Mexico) estimated using ORAS4 data are found to
be negligible as far as absolute residual trends are concerned. Thus, if we
account for the residual trend overestimate due to lack of Argo data in the
Indonesian region, the residuals computed with the CCI, AVISO and NOAA GMSL
data (using Argo) become close to zero (i.e., 0.00 mm yr-1,
0.04 mm yr-1 and 0.16 mm yr-1, respectively), while residual
trends computed with the CU and GSFC data become negative
(-0.29 mm yr-1 and -0.33 mm yr-1, respectively).
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-1) when using ORAS4 (0–2000 m; Indonesian region
accounted for), in agreement with the above statements. Moreover, as
mentioned above, the ORAS4 steric sea level trend for the 2000–5350 m depth
range amounts to 0.06 mm yr-1. However, further investigation is
needed on that issue before drawing any definitive conclusion.
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-1.
Accounting for this value leads to closure of the sea level budget, at least
with the CCI, AVISO and NOAA GMSLs. At sub-seasonal to interannual
timescales, the main source of uncertainty arises from short-term errors in
GRACE and Argo data. More work is required by the different communities
involved in either satellite altimetry or GRACE and Argo data processing, to
clearly identify the causes of these errors and reduce/eliminate them. This
is a challenge of primary importance if we want to precisely address a number
of key issues, like the deep ocean heat uptake and its role in the current
“hiatus”.
Acknowledgements
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
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