The Earth energy imbalance (EEI) at the top of the
atmosphere is responsible for the accumulation of heat in the climate
system. Monitoring the EEI is therefore necessary to better understand the
Earth's warming climate. Measuring the EEI is challenging as it is a
globally integrated variable whose variations are small (0.5–1 Wm-2)
compared to the amount of energy entering and leaving the climate system
(∼340Wm-2). Since the ocean absorbs more than 90 %
of the excess energy stored by the Earth system, estimating the ocean heat
content (OHC) change provides an accurate proxy of the EEI. This study
provides a space geodetic estimation of the OHC changes at global and
regional scales based on the combination of space altimetry and space
gravimetry measurements. From this estimate, the global variations in the
EEI are derived with realistic estimates of its uncertainty. The mean EEI
value is estimated at +0.74±0.22Wm-2 (90 % confidence
level) between August 2002 and August 2016. Comparisons against estimates
based on Argo data and on CERES measurements show good agreement within the
error bars of the global mean and the time variations in EEI. Further
improvements are needed to reduce uncertainties and to improve the time
series, especially at interannual timescales. The space geodetic OHC-EEI
product (version 2.1) is freely available at
10.24400/527896/a01-2020.003 (Magellium/LEGOS, 2020).
Introduction
Over the last decades, greenhouse gases and aerosol concentrations have
been increasing in the atmosphere, disrupting the balance in the Earth
system between incoming and outgoing radiation fluxes. Part of the outgoing
longwave radiation being blocked, the system has reemitted less energy
towards space than it has received from the Sun (Hansen et al., 2011;
Trenberth et al., 2014). This imbalance at the top of the atmosphere, known
as the Earth energy imbalance (EEI), is about 0.5–1 Wm-2 (von
Schuckmann et al., 2016). It is challenging to estimate the EEI from
top-of-atmosphere radiation fluxes since it is 2 orders of magnitude
smaller than the mean incoming solar radiation (340 Wm-2) (L'Ecuyer et
al., 2015).
Positive values of the EEI indicate that an excess of energy is stored in
the climate system. With its high thermal inertia and its large volume, the
ocean acts as a buffer, accumulating most of the excess of energy (more than
90 %; e.g. von Schuckmann et al., 2020b) in the form of heat. The other
climate reservoirs, the atmosphere, land, and cryosphere, play a minor role
in the energy storage at seasonal and longer timescales (von Schuckmann et
al., 2020b). As a result, the ocean heat uptake (OHU) prevails in the global
energy budget on timescales longer than several months. The global OHU
(GOHU) is therefore a good proxy of the EEI variations.
The OHU is positive when heat enters the ocean and negative when heat leaves
the ocean. It is the time derivative of the ocean heat content (OHC). OHC
change time series may be inferred by different approaches: (1) direct
measurement of temperature–salinity profiles mainly derived from the Argo
float network (von Schuckmann et al., 2020b), (2) re-analysis which
combines in situ measurements of temperature–salinity and space measurements
of sea level with ocean modelling (Stammer et al., 2016), (3) the
ocean surface net flux from satellite observations (Kato et al., 2018;
L'Ecuyer et al., 2015), and (4) the space geodetic approach (introduced in
Meyssignac et al., 2019, and this study; see also Hakuba et al., 2021). These
methods are complementary, with their own advantages and limitations
(Meyssignac et al., 2019). The direct measurement approach relies on in situ
measurements which are unevenly spatially distributed with poor sampling of
the deep ocean (below 2000 m depth), marginal seas, and below seasonal
sea ice. Re-analyses provide a more complete description of the ocean's
state that is consistent with the dynamics of the ocean but is subject to
large biases in the polar oceans, spurious drifts in the deep ocean, and
inaccurate initial conditions that may obfuscate a significant part of the
OHC signal related to EEI (Palmer et al., 2017). The ocean net flux approach
assesses the radiative and turbulent fluxes from satellite observations to
provide the spatial distribution of net heat fluxes at the ocean surface,
but it is tainted with large residuals and uncertainties (Kato et al., 2018;
L'Ecuyer et al., 2015). The space geodetic approach aims at measuring the
sea level changes due to the thermal expansion and saline contraction of the
ocean (also called steric sea level changes) based on differences between
the total sea level changes derived from satellite altimetry measurements
and the barystatic sea level changes from satellite gravity measurements.
This approach offers consistent spatial and temporal sampling of the ocean,
with a nearly global coverage of the oceans, except for the polar regions
(above 82∘). It also provides OHC change estimates over the
entire ocean water column.
The EEI shows time variations in response to anthropogenic emissions and
natural variability like ocean–atmosphere interactions or volcanic
eruptions. The coupled natural variability of the ocean and of the
atmosphere leads to monthly to interannual variations of the order of a few
Wm-2 (e.g. Loeb et al., 2018a). Decadal and longer-term variations of
the order of a few tenths of Wm-2 are associated with the anthropogenic
and the natural forcing of the climate system (e.g. von Schuckmann et al.,
2016). To evaluate these variations and particularly the small decadal and
longer-term response of EEI to anthropogenic or natural forcing, EEI should
be estimated with an accuracy better than 0.1 Wm-2. This is
particularly challenging, and it requires a fine characterisation of the
errors associated with the EEI estimates.
The originality of this study is to provide the OHC change and EEI from
space altimetry and space gravimetry with a comprehensive description of the
uncertainty. This space geodetic approach has three major advantages: it
covers the ocean down to the bottom, the spatial coverage is nearly global
(until 82∘ poleward), and it is based on a few instruments, which
enables an exhaustive description of error sources and a robust propagation
of errors from the measurements to the global OHC (GOHC) change estimate. A
preliminary estimate of the GOHC 10-year-trend uncertainty of ±0.32Wm-2 (90 % confidence level, CL) has been published with this
approach (Meyssignac et al., 2019). A central objective of this study is to
revisit this uncertainty estimate with a realistic and robust uncertainty
propagation scheme to enable its computation over any time span and help
reduce uncertainty. First, we provide regional and global estimates of OHC
change over the period from 2002 to 2016. Second, we rigorously and accurately
assess the uncertainty in GOHC change and EEI, propagating the errors from
the sea level and ocean mass change estimates and taking into account the
time correlations in errors. To reach these objectives, innovative
algorithms have been developed. We present them in this paper.
The physical assumptions underlying the estimation of the EEI from space
geodetic measurements are introduced in Sect. 2. Section 3 describes the
sea level and ocean mass variations and thermal expansion data used as
input for the computation of OHC changes and the EEI over the 15-year period
from August 2002 to August 2016 (Sect. 4.1). Error propagation and
uncertainty calculations are performed independently (Sect. 4.2). Results are
gathered in Sects. 5 and 6 for the OHC change and the EEI respectively,
including comparisons with estimates mainly based on the in situ Argo
network. Conclusions and perspectives for improvement of the EEI record are
given in Sect. 7.
In this article, all uncertainties are reported with a 5 %–95 %
confidence level interval (also noted 90 % CL).
Physical principle
In the space geodetic approach, OHC changes are estimated from steric sea
level changes, which are due to the thermal expansion and the haline
contraction of the ocean column of water. Steric sea level changes are
calculated as the difference between total sea level changes and ocean mass
changes (e.g. Forget and Ponte, 2015; Meyssignac et al., 2017, and references
therein). It is expressed by the sea level budget equation where the total
sea level change (ΔSLtotal) is the sum of the ocean mass change
(ΔSLmass) and the ocean steric sea level change. The latter is
composed of two terms, the ocean thermal expansion change (ΔSLthermosteric) and the ocean halosteric change (ΔSLhalosteric) following Eq. (1):
ΔSLtotal=ΔSLmass+ΔSLthermosteric+ΔSLhalosteric.
At the global scale, the ocean salinity change is negligible (Gregory and Lowe,
2000; Llovel et al., 2019; Gregory et al., 2019), as it only contributes to
about 1 % of the global mean sea level change (Gregory and Lowe, 2000).
Therefore Eq. (1) can be simplified, and the global mean thermosteric sea
level change (ΔGMTSL) is obtained from the difference between the
global mean sea level change (ΔGMSL) and the global mean ocean mass
change (ΔGMOM):
ΔGMTSL=ΔGMSL-ΔGMOM.
Then, the GOHC change (ΔGOHC) is derived by dividing the thermal
expansion change by the expansion efficiency of heat (EEH), denoted
ε at a global scale as in Eq. (3) (see Melet and Meyssignac, 2015,
for more details):
ΔGOHC=ΔGMTSLε.
(Note that, at a global scale, on multiannual timescales, because the current
rate of ocean warming is greater than the interannual variability in GOHC –
see Cheng et al., 2021 – ΔGOHC is always positive, and the
EEH is always defined and calculable as ε=ΔGMTSL/ΔGOHC.)
At a global scale, on annual and longer timescales, the heat stored by the
Earth in response to the EEI is essentially stored in the ocean because the
heat capacity of the ocean is much larger than the heat capacity of the rest
of the climate system (Palmer and McNeall, 2014; Melet and Meyssignac,
2015). The fraction of energy entering the ocean α is around 0.9.
The EEI can now be retrieved from the GOHU, the temporal derivative of GOHC,
by dividing it by α the fraction of energy entering the ocean
(Eq. 4). α is set to 0.9, the recent estimate from von Schuckmann
et al. (2020b). Beforehand, GOHC change is filtered out to remove the signals
related to the intrinsic ocean variability, mostly happening in the mixed
layer above the pycnocline. For short timescales (<2–3 years),
this signal does not correspond to any response to global warming (Palmer
and McNeall, 2014) and therefore must be removed to infer variations in the
EEI:
EEI=GOHUα=1αdGOHCdt.
At a regional scale the physical principles are identical to those for the global
scale except for two differences. First, the regional sea level changes
(ΔSL) depend on the salinity changes, and thus to derive the regional
thermosteric sea level changes (ΔTSL), we need to correct for the
regional halosteric sea level change (ΔHSL) effect following the
equation
ΔTSL=ΔSL-ΔOM-ΔHSL.
Second, at a regional scale, it occurs for a water column that the OHC
change over the entire column is null while the thermosteric sea level
change is not. A typical example is when the heat uptake of a water column
above the thermocline is compensated for by an equivalent heat loss below the
thermocline. In such a case the total heat uptake of the entire water column
is by definition zero but the thermosteric sea level change is strictly
positive. This is because the expansion of the sea water above the
thermocline (which occurs in warmer water) exceeds the contraction below the
thermocline (which occurs in colder water). In such a situation the
expansion efficiency of heat is not defined and cannot be calculated. A way
around this issue is to consider ocean heat content (OHC) (rather than ocean
content changes, ΔOHC) and thermosteric sea level (TSL) (rather than
thermosteric sea level changes, ΔTSL) and to define an integrated
expansion efficiency of heat (IEEH) E as follows:
E=TSLOHC.
The IEEH is in mJ-1 like the EEH. At regional scale, the IEEH is always
calculable because the ocean heat content is never null. Thus, the IEEH
allows us to derive estimates of regional OHU from estimates of the regional
thermosteric sea level (TSL) with the following equation:
OHU=dOHCdt=d(TSL/E)dt.
In this work we use Eqs. (3) and (4) to derive estimates of the GOHU and
the EEI. We use Eqs. (6) and (7) to derive estimates of the regional OHU.
We verify the consistency of the global and regional estimates of the ocean
heat uptake by comparing the global sum of OHU with GOHU (see Sect. 4).
In this study, total sea level change is observed from space with radar
altimetry missions (see Sect. 3.1), ocean mass change is observed from
space with the gravimetry missions (see Sect. 3.2), and the global EEH and
regional IEEH are estimated from in situ observations of ocean temperature
and salinity (see Sect. 3.3). Although EEH and IEEH are derived from in
situ data, this approach is called “space geodetic approach” because all
dynamic variables are retrieved from satellite remote sensing.
DataSea level
In this study we used a sea level daily gridded dataset for the global ocean
(Taburet et al., 2019; Legeais et al., 2021) that is distributed by the
Copernicus Climate Service (C3S) and contains the sea level anomalies around
a mean sea surface above the reference mean sea surface computed over
1993–2012, also referred to as the total sea level change. Data are available
over the entire altimetry area from January 1993 onward. They are provided
on a daily basis at a spatial resolution of 0.25∘×0.25∘. Thanks to rigorous processing of altimetry measurements
based on a two-satellite altimetry constellation, homogeneous altimetry
standards applied over time (e.g. geophysical corrections, orbit solutions) and solid validation activities carried out upstream, C3S sea level
products are dedicated to the monitoring of the long-term sea level
variations. As C3S sea level grids are not corrected for the global
isostatic adjustment (GIA), a correction is applied a posteriori. It is
derived from an ensemble mean of regional GIA corrections computed with the
ICE-5G model and with various viscosity profiles (27 profiles) used in
Prandi et al. (2021) (Spada and Melini, 2019). The average GIA value over
oceans is -0.28mmyr-1, close to the generally accepted value of -0.3mmyr-1 (e.g. WCRP Global Sea Level Budget Group, 2018). An additional
correction of -0.1mmyr-1 (GRD) is considered for the deformations of
the ocean bottom in response to modern melt of land ice (Frederikse et al.,
2017).
The description of the errors and the uncertainties on the long-term
stability of the sea level estimate in these products were provided by
Ablain et al. (2019) and Prandi et al. (2021) for the global and regional
scales respectively. Over the whole altimetry period (January 1993–December
2020), the GMSL shows a significant rise of +3.52±0.35mmyr-1. Focusing on the period of interest in this study (August
2002–August 2016), the GMSL increase is +3.57±0.40mmyr-1
(AVISO GMSL indicator). At the regional scale, the sea level rise
distribution ranges between 0 and 6 mmyr-1, with uncertainties ranging
from ±0.8 to ±1.2mmyr-1, pointing out that the sea
level is rising everywhere over the globe. Recent studies also showed that
sea level is accelerating at 0.12±0.07mmyr-2 at the global
scale (Ablain et al., 2019) and ranges between -1 and +1mmyr-2 at the regional scale (Prandi et al., 2021).
Ocean mass
The Gravity Recovery and Climate Experiment (GRACE) mission, launched in
2002, allowed continuous monitoring of ocean mass change over the study
period (Tapley et al., 2004). GRACE was decommissioned in 2017, and its
successor GRACE Follow-On (GRACE-FO) was launched in May 2018. This study
stands as a proof of concept, demonstrating the capability to deliver space
geodetic estimates of the OHC change and EEI and their associated
uncertainties. The study period is therefore limited to April 2002–August
2016 when the GRACE data show the best quality. This restricted period
enables us to avoid (i) instrumental issues deprecating the quality of the GRACE
data at the end of the mission (e.g. Wouters et al., 2014), (ii) the
11-month data gap between GRACE and GRACE-FO, (iii) instrumental issues
during the GRACE-FO mission on the accelerometers, and (iv) eventual biases
between the GRACE and GRACE-FO missions (e.g. Chen et al., 2020; Landerer et
al., 2020). Ocean mass variations observed by GRACE are mainly due to
freshwater exchanges with the continents (including ice melting and water
cycle) at the global scale, and also to the ocean circulation at the regional
scale. However, estimating the rates of global and regional ocean mass
change with GRACE data remains a challenging task due to numerous processing
choices that can strongly affect the results and lead to a large variety of
solutions with significant uncertainty (Uebbing et al., 2019). In this
study, we considered the GRACE LEGOS ensemble V1.4
(http://ftp.legos.obs-mip.fr/pub/soa/gravimetrie/grace_legos/V1.4,
last access: 19 January 2022)
updated from Blazquez et al. (2018). This ensemble version includes 216
solutions, based on fully normalised spherical harmonic solutions from six
different centres and a large variety of choices for post-processing
corrections including the corrections of the geocentre motion, the
oblateness of the Earth, the atmosphere ocean dealiasing, the filtering of
the noise responsible for the characteristic stripes of GRACE gravity data,
the leakage correction, and the GIA. More details of this update and the
appropriate references can be found in Appendix A. This ensemble
approach allows a robust estimation of the uncertainties associated with
state-of-the-art ocean mass change estimates based on GRACE measurements
(see Blazquez et al., 2018, for more details). In addition to spherical
harmonics, the ocean mass change can also be estimated from mascon solutions
provided by the Jet Propulsion Laboratory (JPL RL06), the Center for Space
Research (CSR RL06), and the Goddard Space Flight Center (GSFC RL06). These
three mascon solutions use the same post-processing corrections for the
geocentre motion (Sun et al., 2016), for the oblateness of the Earth (C20)
and the low harmonic degrees (C30) of the gravity field (Loomis et al.,
2019), for the dealiasing of the atmosphere and ocean signals (AOB1B RL06
from Dobslaw et al., 2017), and for GIA (ICE6G-D from Peltier et al., 2018).
Comparing these three mascons with the subset of the LEGOS ensemble that uses
the same post-processing corrections leads to similar ocean mass change
estimates (see Fig. A1 in Appendix A), which confirms the consistency of the
mascon solutions with the spherical harmonics solutions and gives confidence
in their representation of mass transport. Within the LEGOS ensemble, the
subset which uses the mascon post-processing choices shows ocean mass
changes in the upper range of the ensemble estimates. This corroborates the
major role of post-processing choices on the estimation of global ocean mass
change estimates and stresses the need to quantify the associated
uncertainty.
When considering the same mask as the altimetry product, the GMOM trend in
the LEGOS ensemble reaches 1.83±0.21mmyr-1 for the period
from August 2002 to August 2016, in agreement with the state-of-the-art
estimates. Regional variations in ocean mass trends are fairly small (up to
3.66 mmyr-1) when considering the ensemble mean. Except at high
latitudes and for shallow seas, variations in the ocean bottom pressure due
to the ocean circulation or changes in the geoid are relatively small
compared to the global ocean mass increase (Piecuch and Ponte, 2011; Piecuch
et al., 2013).
Expansion efficiency of heat (EEH) and integrated expansion efficiency of heat (IEEH)
The EEH expresses the change in ocean density due to heat uptake. It
represents the ratio of the thermosteric sea level change over the heat
content change under a given heat uptake. As such it allows estimation of
changes in OHC from changes in thermosteric sea level (following Eq. 3).
The EEH can be calculated from known ocean variables (IOC et al., 2010) as
the derivative of specific volume with respect to temperature
(m3kg-1∘C-1) divided by specific heat capacity
(Jkg-1∘C-1). The EEH is dependent on temperature,
salinity, and pressure; it increases with temperature, salinity, and pressure
(Russell et al., 2000). Thus, integrated over the entire water column the
EEH is expected to mainly vary with latitude, together with vertically
integrated salt content and temperature. In time, the change in EEH is
expected to be negligible over the study period, because the warming pattern
is unlikely to change much at decadal timescales (Russell et al., 2000;
Kuhlbrodt and Gregory, 2012).
The IEEH is different from the EEH. The IEEH expresses the ratio of the
thermosteric sea level over the heat content. As such it allows estimation of
OHC from thermosteric sea level (following Eq. 6). The IEEH can be
calculated from known ocean variables (IOC et al., 2010) as the specific
volume (m3kg-1) divided by the specific enthalpy (Jkg-1).
The IEEH is dependent on temperature, salinity, and pressure; it increases
with temperature and pressure and decreases with salinity (see Fig. B1 in
Appendix B). Note that, because IEEH decreases with salinity while EEH
increases with salinity, when integrated over the entire water column, the
spatial variations in the IEEH are expected to be different from the spatial
variations in EEH.
For the calculation of EEH at the global scale, monthly gridded temperature and
salinity fields from 11 Argo solutions were used to compute the ratio
between GMTSL change and GOHC change. These monthly ratios are averaged over
time and then averaged together to provide a global EEH estimate of 0.145±0.001mYJ-1 representative of the 0–2000 m ocean
column for the period 2005–2015, excluding marginal seas and areas located
above 66∘ N and 66∘ S. This regional extent corresponds
to the spatial extent that is regularly sampled by the in situ Argo network.
The global EEH estimated here is in good agreement with previous estimates
of 0.12±0.01mYJ-1 (equivalent to
0.52 Wm-2/mmyr-1) representative of the 0–2000 m ocean column over 1955–2010 from
in situ observations (Levitus et al., 2012) and 0.15±0.03mYJ-1 for the full ocean depth over 1972–2008 (Church et al., 2011). Its
uncertainty is however much smaller because the EEH computation is based on
the Argo network that has a precise estimate of ocean temperature and
salinity down to 2000 m depth and relies only on effective measurements that
were processed homogeneously (e.g. interpolated data are excluded, and the same
horizontal and vertical mask is used). Previous studies from Levitus et al. (2012) and Church et al. (2011) used an ensemble of temperature and
salinity products that covered the whole ocean over the past decades with
in-filled data where measurements are lacking. The differences in the
in-filled data explain the large uncertainty Levitus et al. (2012) and
Church et al. (2011) found in the estimate of the EEH. Here we restricted
the study to the region and the time span covered by Argo. Our approach
based on recent data products that sample the global ocean provides a more
accurate estimate of the EEH, which enables us to significantly reduce the
uncertainties of the GOHC change estimate (see Sect. 4.2 on the error
propagation and uncertainty calculation). However, as the sampling of Argo
is not fully global (measurements are sparser above 66∘ latitude
and below 2000 m depth) our estimate of the global EEH is likely biased by a
few percent. It is likely biased high because the bottom layer, below 2000 m
depth, is less salty than upper layers, which would result in a slightly
lower global EEH estimate if it was accounted for in the computation.
For the calculation of the IEEH at a regional scale, monthly gridded
temperature and salinity fields from 11 Argo solutions were also used to
compute the ratio between local TSL and local OHC. Figure 1 shows the
associated spatial grid (3∘×3∘) of the IEEH estimate (allowing us to visualise its spatial availability at the same
time). The value of the IEEH for each
cell is the temporal mean of the ratio between the local TSL and the local
OHC over the period 2005–2015. The IEEH grid is applied in this study to
calculate OHC at regional scales (see Sect. 4.1. OHC change and EEI
calculation) and further derive the regional OHU.
Integrated expansion efficiency of heat (IEEH) coefficients (mJ-1) at the regional scale (3∘×3∘). See text.
Ancillary data
For comparison purposes, OHC change and EEI are also estimated from in situ
ocean temperature and salinity from Argo datasets covering the first 2000 m
depth range. We considered the IAP, IFREMER, IPRC, ISHII, EN4, JAMSTEC,
NOAA, and SIO datasets. Differences in ocean temperature among these
products are due to the different strategies in data editing, temporal and
spatial data gap filling, and instrument bias corrections (see Boyer
et al., 2016). All Argo products are post-processed homogeneously in the
framework of this study for integration of temperature and salinity to
derive the ocean heat content (e.g. one single integration scheme,
climatology computed over the same period 2005–2015). Regional OHC change is
retrieved relying on the thermodynamic equation of seawater (McDougall and
Barker, 2011). Although IAP, IFREMER, ISHII, EN4, and NOAA products
extrapolate the temperature and salinity profiles over the whole ocean, the
ensemble of Argo-based GOHC change is calculated here after applying the
most restrictive Argo geographical mask among Argo products (it corresponds
to the Argo mask of the SIO product; see Fig. 1 for the spatial extent of
the mask). This approach enables us to get consistent and comparable GOHC
change from the different Argo products. A deep ocean contribution of heat
storage of +0.07±0.06Wm-2 is added for the layers below
2000 m (following Purkey and Johnson, 2010; Desbruyères et al., 2016).
Argo-based EEI estimates are then derived from Argo-based GOHC change with
the same method as for the space geodetic approach described in Sect. 4.1.
The different Argo products provide heterogeneous uncertainty estimates.
Different products consider different sources of uncertainty, and none of the
products provide a comprehensive estimate of the uncertainties (see Table 1
in Meyssignac et al., 2019). The absence of a common reference estimate of
the uncertainty in Argo gridded temperature products is an issue that has
been identified in the climate community. There is currently a community
effort that is undertaken in the World Climate Research Programme (the GEWEX
EEI assessment, see http://gewex-eei.org/, last access: 19 January 2022) to tackle this
problem. This effort should take a few years, and the results are not
available yet. For the time being uncertainties on the Argo-based GOHC
change and EEI are derived from the ensemble dispersion. This type of
uncertainty mainly describes the discrepancy between the various centre
products involved in the ensemble. It represents the uncertainty associated
with different approaches to develop the data quality control and the data
processing. It does not comprise any errors related to time and space
correlation in temperature measurements or potential systematic temperature
and salinity measurement biases among products and potential systematic
sampling biases among products. So these uncertainty estimates are likely
underestimated.
OHC change estimate is also provided by the Ocean Monitoring Indicator (OMI)
from the Copernicus Marine Service (CMEMS) (von Schuckmann et al., 2020a).
The yearly indicator is the ensemble mean of five GOHC change solutions from
reanalyses and optimal interpolations of altimetry data and in situ
measurements (including Argo data). The OMI indicator is based on integrated
temperature differences along a vertical profile in the ocean, down to 700 m
depth, and averaged between 60∘ S and 60∘ N. Note that
uncertainties on the CMEMS GOHC change are also derived from the ensemble
dispersion.
EEI variations are also observed from space by the Clouds and the Earth's
Radiant Energy System (CERES) instruments. They enable monitoring of the
incoming and outgoing radiative fluxes at the top of the atmosphere. CERES
instruments allow retrieval of EEI variations (EBAF TOA fluxes, 2019) from
weekly to decadal timescales with an uncertainty of ±0.1Wm-2, but the time-mean EEI is measured with an
accuracy of ±3.0Wm-2 due to calibration issues (Loeb et al., 2018b).
Our estimates of OHC change and EEI are compared with OHC change and EEI
estimates from Argo, reanalyses, and CERES in Sects. 5 and 6.
Data processingOHC change and EEI calculation
A dedicated data processing chain was specifically developed in order to
calculate the OHC change and the EEI from space geodetic measurements,
following the physical principle described in Sect. 2. Changes in OHC at
global and regional scales and the EEI are provided in a dedicated product
referred to as “MOHeaCAN v2.1” (see Sect. 7).
The first step consists in preprocessing the time series of total sea level
and ocean mass change over the specific period. Total sea level and ocean
mass change grids are downsampled to a 3∘×3∘ spatial resolution
(∼300 km) and averaged on a monthly basis to match the
effective spatial and temporal resolutions of GRACE products.
The second step is dedicated to the calculation of the global time series of
OHC change and the EEI. GMSL and GMOM time series are calculated at each
time step (monthly) using a weighted average taking into account the sea
surface in each cell. The GOHC change is then obtained by taking the
difference between the GMSL and GMOM time series (Eq. 2) and dividing by
the global value of EEH coefficient (Eq. 3). GOHC change is expressed per
unit of area (Jm-2), when divided by the surface of the Earth at the
top of the atmosphere (5.13×1014m2), for a reference
height of the top of the atmosphere at 20 km altitude (the same as EBAF;
Loeb et al., 2018b). The EEI estimate is then derived from the temporal
variations in the GOHC, by calculating the derivative, i.e. the GOHU, using
numerical forward differences and adjusting it to account for energy
contributions from other climate reservoirs (Eq. 4). Beforehand, GOHC
change time series is filtered out by applying a low-pass filter (Lanczos)
with a cut-off period of 3 years in order to remove high-frequency content
related to the intrinsic ocean variability (Palmer and McNeall, 2014) and
the mesoscale activity that is visible in altimetry but not in gravimetry
(described in Sect. 2).
The last step aims at calculating changes in OHC at regional scales. Monthly
steric sea level grids are directly deduced at 3∘×3∘ spatial resolution
from the difference between the collocated sea level and ocean mass grids.
Contrary to the global scale, the ocean salinity change cannot be neglected
at regional scales (see Eq. 1), and halosteric contribution to sea level
expansion should be removed to retrieve the regional thermal expansion
variations in the ocean. Nevertheless, at this stage of the study, the
regional OHC change grids are obtained from the steric sea level grids
divided by the grid of IEEH coefficients without accounting for ocean
salinity change and therefore should be interpreted carefully. This has no
impact on the estimate of the OHC trend over the full period 2005–2015
because the IEEH has been calculated over this period, and the salinity
effect is thus implicitly counted in the local IEEH coefficients. However,
over other periods or smaller periods included within 2005–2015, the local
IEEH is expected to be slightly different as the local salinity changes with
time, and this calculation of the OHC should be considered an
approximation. The approximation is accurate at the level of a few percent
because local changes in salinity are small compared to the total salt
content of the water column (according to the Argo record). In this study we
have chosen this conservative approach with a constant IEEH because the
salinity anomaly data shows important inconsistencies at annual and
inter-annual timescales among Argo products (e.g. Ponte et al., 2021).
Instead of using low-confidence salinity anomaly data, at
this stage we prefer to assume a constant IEEH estimated from salinity climatologies that are
more reliable. This approach leads to an estimate of regional OHC with a
lower uncertainty, but the downside is that the level of confidence in
regional OHC is lower. Note that the GOHC change can also be deduced from
the regional OHC grids by computing regional OHC anomalies and summing all
cells weighted by their area. We checked this approach and found that it
leads to similar estimates of GOHC change and GOHU to those of the global
approach described before in Eq. (3).
Error propagation and uncertainty calculation at global scale
One of our main objectives is to provide the uncertainty associated with the
OHC change and EEI estimates. In this study the error propagation is
performed only at the global scale. It is much more complex to propagate the
uncertainty at regional scales because it requires the description of the spatial
correlation of the errors in satellite altimetry and space gravimetry data,
which is not a simple task. At this time estimates of these errors are not
available in the literature, but this work is currently ongoing and should be
the subject of further publications in the coming years. Meanwhile we focus
on the uncertainty at a global scale. A rigorous approach is proposed here,
providing the variance–covariance matrix (Σ) of the errors for the
GOHC change and EEI time series at a global scale. To obtain the Σ
matrices of the GOHC change and EEI time series, errors must be propagated
from the GMSL and GMOM monthly time series as represented in Fig. 2. The
first step consists of estimating the variance–covariance matrices for the
sea level (ΣGMSL) and the ocean mass (ΣGMOM) time
series.
Propagation of errors from the global mean sea level (GMSL) change
and global mean ocean mass (GMOM) change time series until the global ocean
heat content (GOHC) change and Earth energy imbalance (EEI) time series.
ΣGMSL is inferred from the GMSL error budget of Ablain et al.
(2019) over the period 2002–2016. In short, the elementary
variance–covariance matrices (Σerrori) corresponding to each
error described in the GMSL error budget (Ablain et al., 2019) are first
calculated independently of each other. Each matrix is calculated from a
large number of random draws (>1000) of simulated error signals
whose correlation is modelled. Their shape depends on the type of errors
prescribed, which can be of several kinds: jumps, time-correlated errors, or
long-term drifts. Assuming errors are independent, ΣGMSL is given
by the sum of all Σerrori (see Ablain et al., 2019, for the
details of the calculation).
For the calculation of ΣGMOM, we use an ensemble approach where
the ensemble of GMOM time series (Xi) is directly used to calculate the
covariance between each time series:
ΣGMOM(i,j)=cov(Xi,Xj)8=E[(Xi-E[Xi])(Xj-E[Xj])],
where E is the mean operator. This approach is reliable when GMOM ensembles
are large enough, so that the dispersion between the members of the ensemble
adequately represents the GMOM uncertainties. We use this approach with the
LEGOS ensemble of 216 ocean mass solutions, but we can not apply it with the
ensemble of mascon solutions which has only three distinct members. For the
mascon ensemble, the uncertainty is simply computed as the standard
deviation between the three solutions. The second step consists in
calculating the variance–covariance matrices for the GMTSL time series
(ΣGMTSL). The GMTSL is obtained by calculating the differences
between the GMSL and the GMOM. We consider the errors in GMSL independent
from the errors in GMOM and estimate ΣGMTSL as the sum of
ΣGMSL and ΣGMOM. Note that this assumption is not
verified in reality as some errors are correlated between GMSL and GMOM like
the errors related to the GIA correction and the error associated with the
positioning of the reference system (in particular to the geocentre
position). But the amplitude of these errors is very different in altimetry
and space gravimetry. While the errors in GIA correction and in the geocentre
position are important in space gravimetry (see Uebbing et al.,
2019; Blazquez et al., 2018), their effect on satellite altimetry is small
(see Ablain et al., 2019, and reference therein). Thus,
overall, the correlation in satellite altimetry and space gravimetry of the
GIA and the geocentre correction errors is expected to be low, and we neglect
it here.
In the third step we propagate the errors in the calculation of the GOHC
change. As the GOHC change is derived from the GMTSL by dividing it by the
global coefficient of EEH ε, the uncertainty on ε
(eε) also has to be considered:
GOHC(t)=GMTSL(t)±eGMTSL(t)ε±eε.
The error propagation for the division of the two uncorrelated variables
GMTSL(t) and ε with a respective uncertainty eGMTSL(t) and
eϵ leads to the following form for the variance–covariance
matrix of GOHC change time series (ΣGOHC) (see Taylor, 1997,
Eq. 3.8):
ΣGOHC=1ε2ΣGMTSL+εeε2GOHC⋅GOHCt.
This equation shows that GOHC errors depend on the uncertainty eϵ but also on the value of ε.
The last step is the propagation of errors in the EEI, obtained after
filtering and deriving the GOHC with respect to time and adjusting it with
α the fraction of energy entering the ocean. These complex
operations do not allow us to express the errors of the EEI with a literal
expression as for the GOHC change (Eq. 10). An empirical approach is then
proposed to first derive the variance–covariance matrix of GOHU time series
(ΣGOHU). It firstly consists in generating a set of GOHC error
time series (ek) whose variance–covariance matrix is ΣGOHC.
They are obtained by the product of the Cholesky decomposition of ΣGOHC (ΣGOHC=AAt) and a random vector (Rk)
following a Gaussian vector of mean 0 and covariance matrix of the identity:
ek=ARkt.
Each ek is then filtered by a low-pass filter at 3 years to provide a
set of GOHU error time series from which the variance–covariance matrix
ΣGOHU is easily inferred (see Eq. 8). Finally, ΣEEI
is obtained simply from ΣGOHU taking into account the α
fraction of energy stored in the ocean but neglecting any of its errors:
ΣEEI=1α2ΣGOHU.
Once variance–covariance matrices are known, the statistical parameters
(e.g. trend, acceleration) can be fit at any time spans from a linear
regression model (y=Xβ+ϵ) applying an ordinary least square
(OLS) approach, where the estimator of β with the OLS, noted
β^, is
β^∼(XtX)-1Xty,
and where the distribution of the estimator β^ takes into
account Σ and follows a normal law:
β^=N(β,(XtX)-1(XtΣX)(XtX)-1).
This mathematical formalism was fully described in Ablain et al. (2019) to
estimate the uncertainties of the GMSL trend and acceleration. It is applied
in this study to derive the realistic uncertainties of GOHC and EEI trends.
The uncertainty envelope can also be derived from the square root of the
diagonal terms of Σ.
Ocean heat content change: results and comparisonGlobal and regional OHC change
The GOHC trend is +0.70±0.20Wm-2 for the period from August
2002 to August 2016 (Fig. 3a). It indicates the rate at which oceans
accumulate heat and gives an estimate of the average GOHU. This value is
significant when compared to its uncertainty of ±0.20Wm-2. In
this trend uncertainty, the contribution from satellite altimetry
uncertainty is higher than the contribution from space gravimetry
uncertainty (see Table C1 in Appendix C). The GMSL error budget provided by
Ablain et al. (2019) is by construction comprehensive and conservative (all
choices are conservative; in particular the representation of the error in
wet tropospheric correction and its time correlation are probably slightly
overestimated) and leads to GMSL errors that are likely slightly
overestimated. In addition, the total GMSL errors have been validated
against independent measurements from tide gauges (e.g. Watson et al., 2015),
so there is high confidence that the 90 % CL uncertainty in GMSL used
here is an upper bound of the real uncertainty in GMSL. GMOM errors are
deduced from an ensemble of GRACE solutions (update of Blazquez et al.,
2018) accounting for all known sources of errors including instrumental
errors (e.g. taking into account using solutions from different centres) and
post-processing choices (e.g. geocentre, oblateness, filter, GIA). Although
we are confident the various post-processings used in the
solution set, which are currently state of the art, provide a reliable coverage of the real associated
uncertainty, we can not rule out the possibility that the resulting GMOM
uncertainty is slightly underestimated because of some unknown small
undetected systematic bias among state-of-the-art post-processing. Another
issue is that there is no validation of GMOM against independent data
available yet. The global freshwater budget offers a potential approach to
validate the GMOM estimates against independent estimates derived from the
sea ice volume changes and the ocean global salinity estimates (e.g. Munk,
2003). But the first results show that estimates of the global ocean
salinity are not accurate enough to provide an efficient validation (Llovel
et al., 2019). For these reasons, we have a smaller confidence in the GMOM
uncertainty estimate than in the GMSL uncertainty estimate, leading to a
confidence in our GOHC change uncertainty estimate that is between medium
and high. Note that compared to previous estimates in Meyssignac et al.
(2019) the uncertainty in GOHC change is reduced here. This is essentially
due to the updated estimate of the global EEH coefficient with Argo data
that leads to a smaller uncertainty than the estimate of Levitus et al.
(2012) used in Meyssignac et al. (2019) (see Sect. 3.3).
Times series of (a) global ocean heat content (GOHC) change and
(b) Earth energy imbalance (EEI) from a space geodetic approach (MOHeaCAN
v2.1) over the August 2002–August 2016 period. Data spatial distribution
considered for the GOHC change computation is presented in Fig. 1. The
uncertainty envelopes are superimposed (at 1-sigma). Uncertainties on trends
and means are reported within a 90 % confidence level (1.65-sigma). The
GOHC change curve is shifted along the ordinate axis to start from the
origin in 2002. Grey areas correspond to data gaps in the gravimetry product
used for the space geodetic GOHC change.
Regional OHC trends for the period from August 2002 to August 2016 are
generally positive, ranging from -1 to +2×10-3Wm-2 (Fig. 4).
As the OHC is an integrative variable, it depends on the area considered in
the computation. In this case the difference between the surface considered
in the GOHC change and the surface considered in regional OHC change is of
the order of 2×10-4, explaining the difference of 3 orders of magnitude
between the typical GOHC and the typical regional OHC changes. The spatial
patterns depicted by the GOHC trends are highly correlated to climate mode
fingerprints retrieved for example in steric anomalies (e.g. Pfeffer et al.,
2018). These include for instance the Pacific Decadal Oscillation, dividing
the North Pacific along a typical northeast–southwest chevron pattern
(e.g. Mantua and Hare, 2002), and the El Niño–Southern Oscillation
(e.g. Enfield and Mayer, 1997), consisting of a typical west–east
oscillation of the temperature in the tropical and South Pacific. The
spatial patterns observed in the North Atlantic are likely related to the
warming of the Gulf Stream in the northeast Atlantic and to the cooling of
the Atlantic Meridional Overturning Circulation (AMOC), bringing warm waters
from the tropical Atlantic to the northwest Atlantic (e.g. Ruiz-Barradas et
al., 2018). The positive anomaly in the Indian Ocean is likely related to
the warm pool, recording higher temperature increase during the last decades
than the global ocean (e.g. Rao et al., 2012; Weller et al., 2016; Lee et
al., 2015).
Map of ocean heat content trends from the space geodetic approach
(MOHeaCAN v2.1) computed over the August 2002–August 2016 period,
3∘×3∘ resolution.
Comparison with estimates based on in situ temperature profiles
To evaluate our GOHC change estimate, we compare it with estimates over the
period 2005–2015. The processing of the Argo gridded ocean in situ
temperature products into GOHC change time series is described in Sect. 3.4. The comparison is restricted to the period January 2005–December 2015,
because the coverage of the Argo network becomes nearly global only after
2005 and because afterwards issues in the Argo salinity products lead to
artefacts in the salinity climatology and further in the GOHC change
products. Over 2005–2015, the space geodetic GOHC trend of +0.71±0.23Wm-2 is in agreement within the uncertainties with the Argo-based
GOHC trend of +0.59±0.13Wm-2 and also with the CMEMS GOHC
trend of +0.60±0.25Wm-2 (Table 1).
Global ocean heat content (GOHC) trend and associated uncertainties
as estimated from the various datasets depicted in this paper. Uncertainties
are given within a 90 % CL.
Data typeSource Spatial coverage (a)GOHC trend (Wm-2) Temporal sampling (b)Depth range (c)1/2005–12/20158/2002–8/2016Temperature andEnsemble of OHC change solutions (a) Argo mask (Fig. 1)+0.59±0.132Not availablesalinity profilesprovided by several international (b) Monthly samplingfrom Argogroups1(c) 0–2000 m and deep oceannetworkcontribution of +0.07 Wm-2Combination ofEnsemble of OHC change solutions (a) Global 60∘ S–60∘ N+0.60±0.253+0.60±0.253in situ datafrom CMEMS (Ocean Monitoring (b) Annual sampling(2003–2016)(Argo network)Indicator) (c) 0–700 mand reanalysesSpace geodetic dataSea levelEnsemble mean of 216(a) Argo mask (Fig. 1)+0.71±0.23+0.70±0.20grids fromsolutions based on(b) Monthly samplingC3Sspherical harmonic(c) 0–bottomapproach (detailed inthis paper)Ensemble mean of three+0.56±0.214+0.57±0.185solutions based onmascon approach(JPL, CSR, GSFC)
1 List of Argo international groups:
EN4 dataset from the Met Office Hadley Centre (Good et al., 2013),
including MBT and XBT data corrected by Gouretski and Reseghetti (2010) and
Levitus et al. (2012);
IAP (Institute of Atmospheric Physics of the Chinese Academy of Sciences),
including MBT and XBT data corrected by Gouretski and Reseghetti (2010) and
Levitus et al. (2012);
IPRC (combined to altimetry data);
IFREMER (Gaillard et al., 2016; Kolodziejczyk et al., 2017);
Ishii et al. (2017);
JAMSTEC (Japan Agency for Marine-Earth Science and Technology) MILA GPV
(Mixed Layer dataset of Argo, Grid Point Value) product dataset (Hosoda et
al., 2010);
NOAA (National Oceanic and Atmospheric Administration) data (Huang et al.,
2017); and
SIO (Scripps Institution of Oceanography) climatology monthly gridded
1∘×1∘ data (Roemmich and Gilson, 2009).
2 Uncertainty given by the dispersion of the ensemble and uncertainty
on deep ocean contribution.
3 Uncertainty given by the dispersion of the ensemble.
4 Uncertainty derived from the approach described in this study
(gravimetry data uncertainty is simply computed as the standard deviation
between the three mascon solutions). GOHC trends obtained with each mascon
dataset – JPL: 0.60 Wm-2, CSR: 0.55 Wm-2, GSFC: 0.54 Wm-2.
5 Uncertainty derived from the approach described in this study
(gravimetry data uncertainty is simply computed as the standard deviation
between the three mascon solutions). GOHC trends obtained with each mascon
dataset – JPL: 0.61 Wm-2, CSR: 0.56 Wm-2, GSFC: 0.54 Wm-2.
As an indication, the average GOHC trend deduced from another combination of
altimetry and gravity measurements has also been calculated using three
GRACE mascon solutions (see Table 1). A low value of 0.56 Wm-2 is
obtained for the 2005–2015 time period, but it is still consistent with the
MOHeaCAN product as it is in the uncertainty range of the GOHC trend
estimated from the MOHeaCAN product (+0.71±0.23Wm-2). To
more precisely check the consistency between the mascon-based estimate of
the GOHC trend and the MOHeaCAN estimate, we re-estimate the MOHeaCAN GOHC
trend over 2005–2015 using only the sub-ensemble of GRACE spherical harmonic
solutions that is based on the same post-processing choices as the mascon
solutions. In this case we find a result (+0.61±0.18Wm-2)
that is closer by less than 0.05 Wm-2 to the mascon-based estimate.
This precise consistency at the level of 0.05 Wm-2 gives confidence in
our estimate. The residual difference could be due to sources of errors that
were omitted in the calculation of the spherical harmonic ensemble, such as
incomplete leakage errors or differences in the regularisation process of
the mascon solutions and the spherical solutions.
The space geodetic GOHC interannual variations of 5×107Jm-2 are
presented in Fig. 5. We find the interannual variations in GOHC change to be in
agreement with Argo-based estimates for timescales greater than 3 years,
low during the period from 2006 to 2011, and high during the period from
2011 to 2015 (Fig. 5). At shorter timescales (lower than 3 years),
variations in GOHC change are poorly correlated. At these timescales, part
of the signal is due to the internal variability of climate (e.g. ENSO) that
may not be detected in the same way by both space geodetic and Argo-based
estimates because of their different time and space resolution. In addition,
GOHC variations depicted by all datasets suffer from a lack of accuracy at
these timescales to analyse any differences in a significant way (see the
large uncertainty envelope at sub-annual timescales shown in Fig. 5).
Interannual variations in global ocean heat content (GOHC) change.
A 13-month low-pass filter is applied after removing periodic signals
(annual and semi-annual) and trend. Red lines correspond to space geodetic
estimates where estimates based on mascon ocean mass are represented as dashed
lines and MOHeaCAN v2.1 is represented by the mean value (solid red) and the
uncertainty at 1-sigma (shaded areas). Blue lines correspond to the
Argo-based estimates from 2005. Grey areas correspond to the data gaps in
the gravimetry product used for the space geodetic GOHC change.
At the regional scale, over the period 2005–2015, space geodetic and Argo-based
OHC trends are similar (Fig. 6). Overall there is a fairly good spatial
coherence of the observed spatial structures as in the equatorial Pacific
Ocean and in the North Atlantic, but the amplitude of the signals is
systematically higher in the space geodetic OHC trend. In addition some
discrepancies are observed in the Indian Ocean where space geodetic OHC trends
are about 2 times the Argo-based estimates. Although input data are
similar, the OHC trends based on the various Argo datasets also show
differences at regional scales up to 2.6×10-3Wm-2 among
different Argo products. This is the same order of magnitude as the
difference with the regional MOHeaCAN trends (Fig. 6). These analyses on a
regional scale provide insights into the regional structure of the signal.
They remain preliminary and present several limitations. On the one hand,
the contribution of the regional halosteric signal is not taken into account
here in the calculation of the space geodetic OHC change. Ocean salinity
change may have a significant impact in some local regions (as in the
southeast Indian Ocean (Llovel and Lee, 2015), in the northwest Indian Ocean,
or close to the Arctic Ocean). On the other hand, the regional contribution
of the deep ocean in the Argo data (restricted to 0–2000 m) is not
considered. These limitations will be the subject of future work and may
lead to a better agreement between the OHC trends observed by space geodetic
data and Argo data.
Maps of ocean heat content trends from the space geodetic approach for
the period from January 2005 to December 2015 and at 3∘×3∘ resolution.
Earth energy imbalance: results and comparison
The space geodetic approach provides the mean EEI estimate and also the
temporal evolution of the EEI over the 15-year period from August 2002 to
August 2016 (Fig. 3). The mean EEI of +0.74±0.22Wm-2 is
obtained from the GOHC trend corrected to account for the energy uptake from
land, cryosphere, and atmosphere. This mean EEI value represents an enormous
amount of energy when it is integrated over the entire Earth's surface at
the top of the atmosphere. It represents a total energy uptake of the Earth
of about 350 TW (i.e. about 1000 times the power of the world's nuclear
power plants). Our EEI estimate indicates a positive trend of 0.02±0.05Wm-2yr-1, representing a non-significant acceleration of
the energy uptake by the ocean over 2002–2016 (see also Table C1 in Appendix C). Longer time series or more accurate data are needed to analyse this
acceleration. Our EEI estimate also shows large interannual variations in
EEI from -0.5 to 2.0 Wm-2 (Fig. 3) between 2002 and 2016 that are due
to climate-change variations in GOHC change or to internal variability.
Further studies are needed to determine the causes of these variations. At
3-year timescales the uncertainty of our EEI estimate varies from 0.8 to
1.0 Wm-2. These uncertainties are too high to enable the monitoring of
the EEI response to anthropogenic or natural forcing that requires an
accuracy below 0.1 Wm-2 (e.g. Meyssignac et al., 2019). Lower
uncertainties would be necessary to explore the EEI signal at shorter timescales.
A recent study applying the geodetic approach as well shows a value of
+0.77±0.27Wm-2 over the period 2005–2015 (Hakuba et al.,
2021). This result agrees very well with ours (+0.77±0.24Wm-2) despite significant differences in the input data, in particular
the EEH and the ocean mass.
Our space geodetic EEI is also compared at interannual timescales with
Argo-based and CERES-based EEI estimates (Fig. 7). Signals lower than 3 years are filtered out in all EEI time series. EEI means and trends are also
removed beforehand from each dataset to compare EEI variations at
interannual scales.
Interannual variations in Earth energy imbalance (EEI) time
series. Mean and trend values have been removed for each time series, and a
filter has been applied to remove signals lower than 3 years. Red lines
correspond to space geodetic estimates where estimates based on mascon ocean
mass are represented as dashed lines, and MOHeaCAN v2.1 is represented by the mean
value (solid red) and the uncertainty at 1-sigma (shaded areas). The green line
corresponds to CERES-based estimates and blue lines to the Argo-based
estimates.
The interannual signals are better correlated between the time series from
space geodetic and CERES data than with the Argo-based data. Although the
amplitude of the space geodetic EEI signal is slightly higher (up to 0.8 Wm-2), they appear to be fairly well phased between 2006 and 2013 (same
phase within a few months). In contrast, the Argo-based EEIs have similar
amplitudes to those of CERES, but are mostly out of phase. The short time
period of the in situ data in particular limits the analysis of these
signals. To date, the origin of the discrepancies between these different
EEI estimates remains under investigation. They are all impacted by internal
variability, in particular ENSO (e.g. mid-2007–mid 2009 (Loeb et al., 2012),
2011) and the high-frequency signals (monthly to biannual). Regional
signature of the internal variability may not be the same in the different
observing systems (owing to their different spatial and temporal resolution),
leading to discrepancies in EEI estimates. Observing systems with incomplete
coverage may miss some signals at specific spatial and temporal scales that
could have a major impact on the global estimate. Another source of
discrepancy among EEI estimates is that we assumed for the geodetic approach
and the in situ approach that 90 % of the excess of energy due to EEI is
captured by the ocean. While this assumption is reasonable at biannual and
longer timescales (Palmer and McNeall, 2014), it is probably not true at
smaller timescales when the atmosphere and to a smaller extent land and
cryosphere exchange larger portions of energy with the ocean. This too
simple assumption may explain some discrepancies between the CERES estimate
on one side and the geodetic and in situ estimates on the other side.
Data availability
Changes in OHC at global and regional scales and the EEI are gathered in
the “climate indicators from space product”, or “MOHeaCAN” product v2.1,
available online at 10.24400/527896/a01-2020.003 (Magellium/LEGOS, 2020) with the complete associated
documentation (product user manual and algorithm theoretical basis
document).
Conclusions and outlook
This study provides the first space geodetic estimate with a rigorous
uncertainty propagation algorithm of the Earth energy imbalance and changes
in ocean heat content at the global scale. It is based on the assumption that
monitoring heat accumulation in the ocean, with a combination of satellite
altimetry and gravimetry measurements, is representative of the vast
majority (∼90 %) of the energy imbalance observed at the
top of the atmosphere. The mean value of the EEI derived from this space
geodetic approach over the period from August 2002 to August 2016 is +0.74±0.22Wm-2. This figure is fully in agreement with data based
on in situ measurements (Argo network) within the confidence level of the
uncertainty. Furthermore, although this is a preliminary calculation, the
OHC change is also calculated for the first time at the regional scale thanks to
a set of expansion efficiency of heat coefficients estimated from in situ
Argo data. The spatial patterns retrieved in the OHC trends look similar to
climate mode fingerprints observed in steric anomalies (e.g. Pfeffer et al.,
2018). They also correlate well with regional OHC trends derived from in
situ Argo data, despite known limitations in these regional estimates (e.g.
deep ocean in Argo data and salinity ocean change not corrected in altimetry
and gravimetry approach).
The rigorous uncertainty estimate proposed here still has a few limitations.
It also does not account for the loss of spatial coverage imposed by the Argo
geographical mask in the computation of the expansion efficiency of heat. It
does not include the errors related to the estimation of the global
EEH value over the first 2000 m depth only (i.e. the effect of the deep
ocean on the EEH value is neglected). Furthermore, no error on the fraction
of energy entering the ocean α is included in the EEI uncertainty.
Finally, the approach depends on the knowledge of the GMSL and GMOM error
budget. These error budgets can be improved further. In particular, an
effort must be made to better describe the errors in spatial gravity
measurements, especially to include the uncertainties related to the
differences in the harmonic and mascon approaches in the error budget. The
consistency between the processing of altimetry and gravimetry data could
still be improved for instance by homogenising the GIA datasets used to
correct the gravimetry signals and the sea level from altimetry. Also,
atmospheric effects should be harmonised. Indeed, altimetry data are
currently processed with the dynamical atmospheric correction (Carrère
and Lyard, 2003) while only the inverse barometer correction is applied in
gravimetry processing (Blazquez et al., 2018). Another area for improvement
is the extension of the spatial and temporal scales of the OHC change
estimation. While altimetry and GRACE data are available together since
August 2002, the datasets provided in this study are limited in time (August
2002–August 2016) and space (Argo mask) as the objective of this study is to
demonstrate the feasibility of such an approach (proof of concept) using
reliable GRACE measurements and EEH/IEEH data over the Argo geographical
mask. However, in the future, the OHC change and EEI time series could be
extended in time using the GRACE-FO data already available from August 2018.
This requires managing issues related to the 11-month gap between GRACE and
GRACE-FO data (July 2017–June 2018) and the degradation of GRACE data
quality after August 2016. The OHC change could also be estimated outside
the current Argo mask by extrapolating the EEH coefficient grid to the full
ocean using ocean reanalyses. At this stage of the study, OHC changes and
EEI are retrieved in a conservative way. Altimetry and gravimetry grids are
resampled with a 3∘×3∘ spatial resolution, and the GOHC time series is
filtered at 3 years with the aim of mitigating the impact of high frequencies
from the input geodetic datasets and reducing signals related to internal
variability on the EEI. Additional studies are necessary to better apprehend
how geodetic data can be combined on both temporal and spatial dimensions so
as to investigate regional OHC changes.
This study emphasises that the synergy between spatial data (altimetry and
gravity) and in situ data (Argo network) is essential to obtain accurate
estimates of OHC change. The former contributes to observing the total OHC
variations over the entire water column and with a very good spatial and
temporal resolution since 2002, while the latter provides a quasi-global
coverage since 2005 and allows access to the vertical structure of the
thermal expansion of the ocean down to 2000 m depth. The capacity of both
observing systems to provide independent estimates of the EEI since 2005 is
absolutely essential. By pointing to discrepancies among different EEI
estimates from different observing systems, intercomparisons foster further
development to understand the causes for discrepancies. As we understand
these discrepancies, the different estimates will improve, and we can expect
significantly more precise and more robust estimates of the EEI in the
coming decade. It is crucial that the space geodetic observing system and
the Argo network continue the monitoring and improve their coverage and
accuracy in the years to come to support this effort.
The GRACE LEGOS ensemble V1.4
GRACE LEGOS V1.4 is an ensemble of 216 global water mass transfer solutions
derived from the GRACE and GRACE-FO mission covering the period from August 2002
to December 2020 at a monthly timescale and with a spatial resolution of 1∘. The total amount of water remains constant from one month to another
for each solution. The ensemble is based on L2 spherical harmonic solutions
from six different centres: COST-G RL1.2, CNES RL5.0, CSR RL06, GFZ RL06, JPL
RL06, and TUGRAZ ITSG2018. Atmosphere and ocean dealiasing models are
restored using AOD1B RL06 (Dobslaw et al., 2017) except for the CNES
solution where ERA-Interim and TUGO models were used. The ocean dealiasing
model is restored, and C0 coefficients are corrected in the spherical
harmonics to compensate for the total amount of water vapour in the
atmosphere expressed in C0 GAA (Chen et al., 2019). The ensemble also includes
a large variety of choices for post-processing corrections including three
geocentre motions (Lemoine and Reinquin, 2017; Uebbing et al., 2019; Sun
et al., 2016), three oblateness values of the Earth (Cheng et al., 2013; Lemoine and
Reinquin, 2017; Loomis et al., 2019), and two GIA corrections (ICE6G-D; Peltier
et al., 2018, and Caron et al., 2018). In order to reduce the anisotropic
noise, DDK filters are applied to the L2 solutions, including DDK5 and DDK6
(Kusche et al., 2009), except for the CNES solution where a truncated single-value decomposition scheme is used for the inversion instead of a classical
Cholesky inversion. This method reduces the noise drastically, but on the
other hand the coefficients of high degree where information is scarce are
normalised to the mean coefficients (Lemoine et al., 2016). Solid Earth
displacement due to the largest earthquakes (Sumatra 2004 and 2012,
Tohoku 2010, and Chile 2010) is corrected following (Tang et al., 2020).
Moreover, a new method to convert from spherical harmonics to equivalent
water height is applied. This method consists in
using high spatial a priori solutions to reduce leakage and Gibbs effects.
The spherical harmonics solution is separated in the a priori part using
external data such as land–ocean masks, glacier mass trends (Hugonnet et al.,
2021), and lake volume change (Crétaux et al., 2016) and the rest of the
harmonics solution which contains less signal and must be filtered.
Comparison of global mean ocean mass changes from satellite
gravimetry based on spherical harmonics solutions (LEGOS ensemble V1.4, in
grey) and mascon solutions over August 2002–August 2016 for the global
ocean. The mean of the full spherical harmonic ensemble is shown in red. The
mean of the spherical harmonic ensemble subset consistent with mascons is
shown in orange. The mean of the three mascon solutions considered in this
study is shown in blue.
Integrated expansion efficiency of heat (IEEH) dependence on in
situ temperature and absolute salinity at 1 atm in
mmJ-1.
Global mean sea level change components, global ocean heat content
changes, and Earth energy imbalance – trend and mean values and associated
uncertainties as estimated from the various datasets depicted in this paper.
Uncertainties are given within a 90 % CL.
Period 8/2002–8/20161/2005–12/2015Geocentric sea level+3.11±0.41+3.09±0.50change (mmyr-1)Sea level change+3.49±0.43+3.47±0.51(after GIA and GRDcorrections) (mmyr-1)Ocean mass change+1.83±0.21+1.80±0.21(mmyr-1)Steric sea level change+1.66±0.48+1.67±0.54(mmyr-1)Ocean heat content+0.70±0.20+0.71±0.23change (Wm-2)Earth energy imbalance+0.74±0.22+0.77±0.24(Wm-2; Wm-2yr-1)(mean)(mean)+0.02±0.05+0.08±0.09(trend)(trend)Author contributions
FM and MA led and designed the paper, which was edited by BM, AB, and
JP. AB and JP focused on the part related to gravimetry observations. FM,
RF, RJ, and AB developed the processing tools and performed the computations.
JC contributed to the gravimetry LEGOS ensemble. BM and MA led and designed
the study. GL, MR, and JB supervised the study. All the authors participated
in the discussions and revision of the paper.
Competing interests
The contact author has declared that neither they nor their co-authors have any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
We would like to thank all contributors of the MOHeaCAN product, and in particular Françoise Mertz, Laurent Soudarin, and Caroline Mercier for making the data available on the ODATIS portal and AVISO.
Financial support
This work has been supported by the ESA in the framework of the MOHeaCAN project (Monitoring Ocean Heat Content and Earth Energy ImbalANce from Space): https://eo4society.esa.int/projects/moheacan/ (last access: 19 January 2022). This work is also supported by the CNES for the dissemination of the products. Julia Pfeffer and Anne Barnoud are supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (GRACEFUL Synergy (grant no. 855677)). Jonathan Chenal was supported by the French Ministry of Ecological Transition.
Review statement
This paper was edited by Giuseppe M. R. Manzella and reviewed by two anonymous referees.
ReferencesAblain, M., Meyssignac, B., Zawadzki, L., Jugier, R., Ribes, A., Spada, G., Benveniste, J., Cazenave, A., and Picot, N.: Uncertainty in satellite estimates of global mean sea-level changes, trend and acceleration, Earth Syst. Sci. Data, 11, 1189–1202, 10.5194/essd-11-1189-2019, 2019.Anon: CERES_EBAF-TOA_Edition4.1,
https://doi.org/10.5067/TERRA-AQUA/CERES/EBAF-TOA_L3B004.1, 2019.Blazquez, A., Meyssignac, B., Lemoine, J., Berthier, E., Ribes, A., and Cazenave, A.: Exploring the uncertainty in GRACE estimates of the mass redistributions at the Earth surface: implications for the global water and sea level budgets, Geophys. J. Int., 215, 415–430, 10.1093/gji/ggy293, 2018.Boyer, T., Domingues, C. M., Good, S. A., Johnson, G. C., Lyman, J. M., Ishii, M., Gouretski, V., Willis, J. K., Antonov, J., Wijffels, S., Church, J. A., Cowley, R., and Bindoff, N. L.: Sensitivity of Global Upper-Ocean Heat Content Estimates to Mapping Methods, XBT Bias Corrections, and Baseline Climatologies, J. Climate, 29, 4817–4842, 10.1175/JCLI-D-15-0801.1, 2016.Caron, L., Ivins, E. R., Larour, E., Adhikari, S., Nilsson, J., and Blewitt, G.: GIA Model Statistics for GRACE Hydrology, Cryosphere, and Ocean Science, Geophys. Res. Lett., 45, 2203–2212, 10.1002/2017GL076644, 2018.Carrère, L. and Lyard, F.: Modeling the barotropic response of the global ocean to atmospheric wind and pressure forcing – comparisons with observations, Geophys. Res. Lett., 30, 1275, 10.1029/2002GL016473, 2003.Chen, J., Tapley, B., Seo, K.-W., Wilson, C., and Ries, J.: Improved Quantification of Global Mean Ocean Mass Change Using GRACE Satellite Gravimetry Measurements, Geophys. Res. Lett., 46, 13984–13991, 10.1029/2019GL085519, 2019.Chen, J., Tapley, B., Wilson, C., Cazenave, A., Seo, K.-W., and Kim, J.-S.: Global Ocean Mass Change From GRACE and GRACE Follow-On and Altimeter and Argo Measurements, Geophys. Res. Lett., 47, e2020GL090656, 10.1029/2020GL090656, 2020.Cheng, L., Abraham, J., Trenberth, K. E., Fasullo, J., Boyer, T., Locarnini, R., Zhang, B., Yu, F., Wan, L., Chen, X., Song, X., Liu, Y., Mann, M. E., Reseghetti, F., Simoncelli, S., Gouretski, V., Chen, G., Mishonov, A., Reagan, J., and Zhu, J.: Upper Ocean Temperatures Hit Record High in 2020, Adv. Atmos. Sci., 38, 523–530, 10.1007/s00376-021-0447-x, 2021.Cheng, M., Tapley, B. D., and Ries, J. C.: Deceleration
in the Earth's oblateness, J. Geophys. Res.-Sol. Ea., 118, 740–747, 10.1002/jgrb.50058, 2013.Church, J. A., White, N. J., Konikow, L. F., Domingues,
C. M., Cogley, J. G., Rignot, E., Gregory, J. M., van den Broeke,
M. R., Monaghan, A. J., and Velicogna, I.: Revisiting the Earth's
sea-level and energy budgets from 1961 to 2008, Geophys. Res. Lett.,
38, L18601, 10.1029/2011GL048794, 2011.Crétaux, J.-F., Abarca-del-Río, R., Bergé-Nguyen, M., Arsen, A., Drolon, V., Clos, G., and Maisongrande, P.: Lake Volume Monitoring from Space, Surv. Geophys., 37, 269–305, 10.1007/s10712-016-9362-6, 2016.Desbruyères, D. G., Purkey, S. G., McDonagh, E. L., Johnson, G. C., and King, B. A.: Deep and abyssal ocean warming from 35 years of repeat hydrography, Geophys. Res. Lett., 43, 10356–10365, 10.1002/2016GL070413, 2016.Dobslaw, H., Bergmann-Wolf, I., Dill, R., Poropat, L., Thomas, M., Dahle, C., Esselborn, S., König, R., and Flechtner, F.: A new high-resolution model of non-tidal atmosphere and ocean mass variability for de-aliasing of satellite gravity observations: AOD1B RL06, Geophys. J. Int., 211, 263–269, 10.1093/gji/ggx302, 2017.Enfield, D. B. and Mayer, D. A.: Tropical Atlantic sea surface temperature variability and its relation to El Niño-Southern Oscillation, J. Geophys. Res.-Oceans, 102, 929–945, 10.1029/96JC03296, 1997.Forget, G. and Ponte, R. M.: The partition of regional sea level variability, Prog. Oceanogr., 137, 173–195, 10.1016/j.pocean.2015.06.002, 2015.Frederikse, T., Riva, R. E. M., and King, M. A.: Ocean Bottom Deformation Due To Present-Day Mass Redistribution and Its Impact on Sea Level Observations, Geophys. Res. Lett., 44, 12306–12314, 10.1002/2017GL075419, 2017.Gaillard, F., Reynaud, T., Thierry, V., Kolodziejczyk,
N., and von Schuckmann, K.: In Situ–Based Reanalysis of the Global Ocean Temperature and Salinity with ISAS: Variability of the Heat Content and Steric Height, J. Climate, 29, 1305–1323, 10.1175/JCLI-D-15-0028.1, 2016.Good, S. A., Martin, M. J., and Rayner, N. A.: EN4: Quality controlled ocean temperature and salinity profiles and monthly objective analyses with uncertainty estimates, J. Geophys. Res.-Oceans, 118, 12, 6704–6716, 10.1002/2013JC009067, 2013.Gouretski, V. and Reseghetti, F.: On depth and
temperature biases in bathythermograph data: Development of a new
correction scheme based on analysis of a global ocean database,
Deep-Sea Res. Pt. I, 57, 812–833, 10.1016/j.dsr.2010.03.011, 2010.Gregory, J. M. and Lowe, J. A.: Predictions of global and regional sea-level rise using AOGCMs with and without flux adjustment, Geophys. Res. Lett., 27, 3069–3072, 10.1029/1999GL011228, 2000.Gregory, J. M., Griffies, S. M., Hughes, C. W., Lowe, J. A., Church, J. A., Fukimori, I., Gomez, N., Kopp, R. E., Landerer, F., Cozannet, G. L., Ponte, R. M., Stammer, D., Tamisiea, M. E., and van de Wal, R. S. W.: Concepts and Terminology for Sea Level: Mean, Variability and Change, Both Local and Global, Surv. Geophys., 40, 1251–1289, 10.1007/s10712-019-09525-z, 2019.Hakuba, M. Z., Frederikse, T., and Landerer, F. W.: Earth's Energy Imbalance From the Ocean Perspective (2005–2019), Geophys. Res. Lett., 48, e2021GL093624, 10.1029/2021GL093624, 2021.Hansen, J., Sato, M., Kharecha, P., and von Schuckmann, K.: Earth's energy imbalance and implications, Atmos. Chem. Phys., 11, 13421–13449, 10.5194/acp-11-13421-2011, 2011.Hosoda, S., Ohira, T., Sato, K., and Suga, T.: Improved description of global mixed-layer depth using Argo profiling floats, J. Oceanogr., 66, 773–787, 10.1007/s10872-010-0063-3, 2010.Huang, B., Thorne, P. W., Banzon, V. F., Boyer, T., Chepurin, G., Lawrimore, J. H., Menne, M. J., Smith, T. M., Vose, R. S., and Zhang, H.-M.: Extended Reconstructed Sea Surface Temperature, Version 5 (ERSSTv5): Upgrades, Validations, and Intercomparisons, J. Climate, 30, 8179–8205, 10.1175/JCLI-D-16-0836.1, 2017.Hugonnet, R., McNabb, R., Berthier, E., Menounos, B., Nuth, C., Girod, L., Farinotti, D., Huss, M., Dussaillant, I., Brun, F., and Kääb, A.: Accelerated global glacier mass loss in the early twenty-first century, Nature, 592, 726–731, 10.1038/s41586-021-03436-z, 2021. IOC, SCOR, and IAPSO: The international thermodynamic equation of seawater – 2010: Calculation and use of thermodynamic properties, Intergovernmental Oceanographic Commission, Manuals and Guides no. 56, UNESCO (English), 196 pp., 2010.Ishii, M., Fukuda, Y., Hirahara, S., Yasui, S., Suzuki, T., and Sato, K.: Accuracy of Global Upper Ocean Heat Content Estimation Expected from Present Observational Data Sets, Sola, 13, 163–167, 10.2151/sola.2017-030, 2017.Kato, S., Rose, F. G., Rutan, D. A., Thorsen, T. J., Loeb, N. G., Doelling, D. R., Huang, X., Smith, W. L., Su, W., and Ham, S.-H.: Surface Irradiances of Edition 4.0 Clouds and the Earth's Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) Data Product, J. Climate, 31, 4501–4527, 10.1175/JCLI-D-17-0523.1, 2018.Kolodziejczyk, N., Prigent-Mazella, A., and Gaillard, F.: ISAS-15 temperature and salinity gridded fields, SEANOE [data set], 10.17882/52367, 2017.Kuhlbrodt, T. and Gregory, J. M.: Ocean heat uptake and its consequences for the magnitude of sea level rise and climate change, Geophys. Res. Lett., 39, L18608, 10.1029/2012GL052952, 2012.Kusche, J., Schmidt, R., Petrovic, S., and Rietbroek, R.: Decorrelated GRACE time-variable gravity solutions by GFZ, and their validation using a hydrological model, J. Geodesy, 83, 903–913, 10.1007/s00190-009-0308-3, 2009.Landerer, F. W., Flechtner, F. M., Save, H., Webb, F. H., Bandikova, T., Bertiger, W. I., Bettadpur, S. V., Byun, S. H., Dahle, C., Dobslaw, H., Fahnestock, E., Harvey, N., Kang, Z., Kruizinga, G. L. H., Loomis, B. D., McCullough, C., Murböck, M., Nagel, P., Paik, M., Pie, N., Poole, S., Strekalov, D., Tamisiea, M. E., Wang, F., Watkins, M. M., Wen, H.-Y., Wiese, D. N., and Yuan, D.-N.: Extending the Global Mass Change Data Record: GRACE Follow-On Instrument and Science Data Performance, Geophys. Res. Lett., 47, e2020GL088306, 10.1029/2020GL088306, 2020.L'Ecuyer, T. S., Beaudoing, H. K., Rodell, M., Olson, W., Lin, B., Kato, S., Clayson, C. A., Wood, E., Sheffield, J., Adler, R., Huffman, G., Bosilovich, M., Gu, G., Robertson, F., Houser, P. R., Chambers, D., Famiglietti, J. S., Fetzer, E., Liu, W. T., Gao, X., Schlosser, C. A., Clark, E., Lettenmaier, D. P., and Hilburn, K.: The Observed State of the Energy Budget in the Early Twenty-First Century, J. Climate, 28, 8319–8346, 10.1175/JCLI-D-14-00556.1, 2015.Lee, S.-K., Park, W., Baringer, M. O., Gordon, A. L., Huber, B., and Liu, Y.: Pacific origin of the abrupt increase in Indian Ocean heat content during the warming hiatus, Nat. Geosci., 8, 445–449, 10.1038/ngeo2438, 2015.Legeais, J.-F., Meyssignac, B., Faugère, Y., Guerou, A., Ablain, M., Pujol, M.-I., Dufau, C., and Dibarboure, G.: Copernicus sea level space observations: a basis for assessing mitigation and developing adaptation strategies to sea level rises, Front. Mar. Sci., 8, 704721, 10.3389/fmars.2021.704721, 2021.
Lemoine, J.-M. and Reinquin, F.: Processing of SLR observations at CNES, Newsletter EGSIEM, October, p. 3, 2017.
Lemoine, J.-M., Bourgogne, S., Biancale, R., Bruinsma, S., and Gégout, P.: CNES/GRGS solutions Focus on the inversion process, in Paper presented at the GRACE Science Team Meeting, A1-02, Berlin, Germany, 2016.Levitus, S., Antonov, J. I., Boyer, T. P., Baranova, O. K., Garcia, H. E., Locarnini, R. A., Mishonov, A. V., Reagan, J. R., Seidov, D., Yarosh, E. S., and Zweng, M. M.: World ocean heat content and thermosteric sea level change (0–2000 m), 1955–2010, Geophys. Res. Lett., 39, L10603, 10.1029/2012GL051106, 2012.Llovel, W. and Lee, T.: Importance and origin of halosteric contribution to sea level change in the southeast Indian Ocean during 2005–2013, Geophys. Res. Lett., 42, 1148–1157, 10.1002/2014GL062611, 2015.Llovel, W., Purkey, S., Meyssignac, B., Blazquez, A., Kolodziejczyk, N., and Bamber, J.: Global ocean freshening, ocean mass increase and global mean sea level rise over 2005–2015, Sci. Rep., 9, 17717, 10.1038/s41598-019-54239-2, 2019.Loeb, N. G., Lyman, J. M., Johnson, G. C., Allan, R. P., Doelling, D. R., Wong, T., Soden, B. J., and Stephens, G. L.: Observed changes in top-of-the-atmosphere radiation and upper-ocean heating consistent within uncertainty, Nat. Geosci., 5, 110–113, 10.1038/ngeo1375, 2012.Loeb, N. G., Thorsen, T. J., Norris, J. R., Wang, H., and Su, W.: Changes in Earth's Energy Budget during and after the “Pause” in Global Warming: An Observational Perspective, Climate, 6, 62, 10.3390/cli6030062, 2018a.Loeb, N. G., Doelling, D. R., Wang, H., Su, W., Nguyen, C., Corbett, J. G., Liang, L., Mitrescu, C., Rose, F. G., and Kato, S.: Clouds and the Earth's Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) Top-of-Atmosphere (TOA) Edition-4.0 Data Product, J. Climate, 31, 895–918, 10.1175/JCLI-D-17-0208.1, 2018b.Loomis, B. D., Rachlin, K. E., and Luthcke, S. B.: Improved Earth Oblateness Rate Reveals Increased Ice Sheet Losses and Mass-Driven Sea Level Rise, Geophys. Res. Lett., 46, 6910–6917, 10.1029/2019GL082929, 2019.Magellium/LEGOS: Climate indicators from space: Ocean heat content and Earth energy imbalance, AVISO [data set], 10.24400/527896/a01-2020.003, 2020.Mantua, N. J. and Hare, S. R.: The Pacific Decadal Oscillation, J. Oceanogr., 58, 35–44, 10.1023/A:1015820616384, 2002.McDougall, T. J. and Barker, P. M.: Getting started with TEOS-10 and the Gibbs Seawater (GSW) Oceanographic Toolbox, 28 pp., SCOR/IAPSO WG127, ISBN 978-0-646-55621-5, available at: http://www.teos-10.org/pubs/Getting_Started.pdf (last access: 19 January 2022), 2011.Melet, A. and Meyssignac, B.: Explaining the Spread in Global Mean Thermosteric Sea Level Rise in CMIP5 Climate Models∗, J. Climate, 28, 9918–9940, 10.1175/JCLI-D-15-0200.1, 2015.Meyssignac, B., Piecuch, C. G., Merchant, C. J., Racault, M.-F., Palanisamy, H., MacIntosh, C., Sathyendranath, S., and Brewin, R.: Causes of the Regional Variability in Observed Sea Level, Sea Surface Temperature and Ocean Colour Over the Period 1993–2011, Surv. Geophys., 38, 187–215, 10.1007/s10712-016-9383-1, 2017.Meyssignac, B., Boyer, T., Zhao, Z., Hakuba, M. Z.,
Landerer, F. W., Stammer, D., Köhl, A., Kato, S., L'Ecuyer, T.,
Ablain, M., Abraham, J. P., Blazquez, A., Cazenave, A., Church,
J. A., Cowley, R., Cheng, L., Domingues, C. M., Giglio, D.,
Gouretski, V., Ishii, M., Johnson, G. C., Killick, R. E., Legler,
D., Llovel, W., Lyman, J., Palmer, M. D., Piotrowicz, S., Purkey,
S. G., Roemmich, D., Roca, R., Savita, A., von Schuckmann, K., Speich, S., Stephens, G., Wang, G., Wijffels, S. E., and Zilberman, N.: Measuring Global Ocean Heat Content to Estimate the Earth Energy Imbalance, Front. Mar. Sci., 6, 432, 10.3389/fmars.2019.00432, 2019.Munk, W.: Ocean Freshening, Sea Level Rising, Science, 300, 2041–2043, 10.1126/science.1085534, 2003.Palmer, M. D. and McNeall, D. J.: Internal variability of Earth's energy budget simulated by CMIP5 climate models, Environ. Res. Lett., 9, 034016, 10.1088/1748-9326/9/3/034016, 2014.Palmer, M. D., Roberts, C. D., Balmaseda, M., Chang, Y.-S., Chepurin, G., Ferry, N., Fujii, Y., Good, S. A., Guinehut, S., Haines, K., Hernandez, F., Köhl, A., Lee, T., Martin, M. J., Masina, S., Masuda, S., Peterson, K. A., Storto, A., Toyoda, T., Valdivieso, M., Vernieres, G., Wang, O., and Xue, Y.: Ocean heat content variability and change in an ensemble of ocean reanalyses, Clim. Dynam., 49, 909–930, 10.1007/s00382-015-2801-0, 2017.Peltier, W. R., Argus, D. F., and Drummond, R.: Comment on “An Assessment of the ICE-6G_C (VM5a) Glacial Isostatic Adjustment Model” by Purcell et al., J. Geophys. Res.-Sol. Ea., 123, 2019–2028, 10.1002/2016JB013844, 2018.Pfeffer, J., Tregoning, P., Purcell, A., and Sambridge, M.: Multitechnique Assessment of the Interannual to Multidecadal Variability in Steric Sea Levels: A Comparative Analysis of Climate Mode Fingerprints, J. Climate, 31, 7583–7597, 10.1175/JCLI-D-17-0679.1, 2018.Piecuch, C. G. and Ponte, R. M.: Mechanisms of interannual steric sea level variability, Geophys. Res. Lett., 38, L15605, 10.1029/2011GL048440, 2011.Piecuch, C. G., Quinn, K. J., and Ponte, R. M.: Satellite-derived interannual ocean bottom pressure variability and its relation to sea level, Geophys. Res. Lett., 40, 3106–3110, 10.1002/grl.50549, 2013.Ponte, R. M., Sun, Q., Liu, C., and Liang, X.: How Salty Is the Global Ocean: Weighing It All or Tasting It a Sip at a Time?, Geophys. Res. Lett., 48, e2021GL092935, 10.1029/2021GL092935, 2021.Prandi, P., Meyssignac, B., Ablain, M., Spada, G., Ribes, A., and Benveniste, J.: Local sea level trends, accelerations and uncertainties over 1993–2019, Sci. Data, 8, 1, 10.1038/s41597-020-00786-7, 2021.Purkey, S. G. and Johnson, G. C.: Warming of Global Abyssal and Deep Southern Ocean Waters between the 1990s and 2000s: Contributions to Global Heat and Sea Level Rise Budgets, J. Climate, 23, 6336–6351, 10.1175/2010JCLI3682.1, 2010.Rao, S. A., Dhakate, A. R., Saha, S. K., Mahapatra, S., Chaudhari, H. S., Pokhrel, S., and Sahu, S. K.: Why is Indian Ocean warming consistently?, Climatic Change, 110, 709–719, 10.1007/s10584-011-0121-x, 2012.Roemmich, D. and Gilson, J.: The 2004–2008 mean and annual cycle of temperature, salinity, and steric height in the global ocean from the Argo Program, Prog. Oceanogr., 82, 81–100, 10.1016/j.pocean.2009.03.004, 2009.Ruiz-Barradas, A., Chafik, Lé., Nigam, S., and Häkkinen, S.: Recent subsurface North Atlantic cooling trend in context of Atlantic decadal-to-multidecadal variability, Tellus A, 70, 1–19, 10.1080/16000870.2018.1481688, 2018.Russell, G. L., Gornitz, V., and Miller, J. R.: Regional sea level changes projected by the NASA/GISS Atmosphere-Ocean Model, Clim. Dynam., 16, 789–797, 10.1007/s003820000090, 2000.Spada, G. and Melini, D.: On Some Properties of the Glacial Isostatic Adjustment Fingerprints, Water, 11, 1844, 10.3390/w11091844, 2019.Stammer, D., Balmaseda, M., Heimbach, P., Köhl, A., and Weaver, A.: Ocean Data Assimilation in Support of Climate Applications: Status and Perspectives, Annu. Rev. Mar. Sci., 8, 491–518, 10.1146/annurev-marine-122414-034113, 2016.Sun, Y., Riva, R., and Ditmar, P.: Optimizing estimates of annual variations and trends in geocenter motion and J2 from a combination of GRACE data and geophysical models, J. Geophys. Res.-Sol. Ea., 121, 8352–8370, 10.1002/2016JB013073, 2016.Taburet, G., Sanchez-Roman, A., Ballarotta, M., Pujol, M.-I., Legeais, J.-F., Fournier, F., Faugere, Y., and Dibarboure, G.: DUACS DT2018: 25 years of reprocessed sea level altimetry products, Ocean Sci., 15, 1207–1224, 10.5194/os-15-1207-2019, 2019.Tang, L., Li, J., Chen, J., Wang, S.-Y., Wang, R., and Hu, X.: Seismic Impact of Large Earthquakes on Estimating Global Mean Ocean Mass Change from GRACE, Remote Sens., 12, 935, 10.3390/rs12060935, 2020.Tapley, B. D., Bettadpur, S., Ries, J. C., Thompson, P. F., and Watkins, M. M.: GRACE Measurements of Mass Variability in the Earth System, Science, 305, 503–505, 10.1126/science.1099192, 2004. Taylor, J. R.: An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2nd edn., University Science Books, Sausalito, California, 344 pp., 1997.Trenberth, K. E., Fasullo, J. T., and Balmaseda, M. A.: Earth's Energy Imbalance, J. Climate, 27, 3129–3144, 10.1175/JCLI-D-13-00294.1, 2014.Uebbing, B., Kusche, J., Rietbroek, R., and Landerer, F. W.: Processing Choices Affect Ocean Mass Estimates From GRACE, J. Geophys. Res.-Oceans, 124, 1029–1044, 10.1029/2018JC014341, 2019. von Schuckmann, K., Palmer, M. D., Trenberth, K. E., Cazenave, A., Chambers, D., Champollion, N., Hansen, J., Josey, S. A., Loeb, N., Mathieu, P.-P., Meyssignac, B., and Wild, M.: An imperative to monitor Earth's energy imbalance, Nat. Clim. Change, 6, 138, 2016.von Schuckmann, K., Le Traon, P.-Y., Smith, N., Pascual, A., Djavidnia, S., Gattuso, J.-P., Grégoire, M., Nolan, G., Aaboe, S., Fanjul, E. Á., Aouf, L., Aznar, R., Badewien, T. H., Behrens, A., Berta, M., Bertino, L., Blackford, J., Bolzon, G., Borile, F., Bretagnon, M., Brewin, R. J. W., Canu, D., Cessi, P., Ciavatta, S., Chapron, B., Trang Chau, T. T., Chevallier, F., Chtirkova, B., Ciliberti, S., Clark, J. R., Clementi, E., Combot, C., Comerma, E., Conchon, A., Coppini, G., Corgnati, L., Cossarini, G., Cravatte, S., de Alfonso, M., de Boyer Montégut, C., De Lera Fernández, C., de los Santos, F. J., Denvil-Sommer, A., de Pascual Collar, Á., Dias Nunes, P. A. L., Di Biagio, V., Drudi, M., Embury, O., Falco, P., d'Andon, O. F., Ferrer, L., Ford, D., Freund, H., León, M. G., Sotillo, M. G., García-Valdecasas, J. M., Garnesson, P., Garric, G., Gasparin, F., Gehlen, M., Genua-Olmedo, A., Geyer, G., Ghermandi, A., Good, S. A., Gourrion, J., Greiner, E., Griffa, A., González, M., Griffa, A., Hernández-Carrasco, I., Isoard, S., Kennedy, J. J., Kay, S., Korosov, A., Laanemäe, K., Land, P. E., Lavergne, T., Lazzari, P., Legeais, J.-F., Lemieux, B., Levier, B., Llovel, W., Lyubartsev, V., Le Traon, P.-Y., Lien, V. S., Lima, L., Lorente, P., Mader, J., Magaldi, M. G., Maljutenko, I., Mangin, A., Mantovani, C., Marinova, V., Masina, S., Mauri, E., Meyerjürgens, J., Mignot, A., McEwan, R., Mejia, C., et al.: Copernicus Marine Service Ocean State Report, Issue 4, J. Oper. Oceanogr., 13, S1–S172, 10.1080/1755876X.2020.1785097, 2020a.von Schuckmann, K., Cheng, L., Palmer, M. D., Hansen, J., Tassone, C., Aich, V., Adusumilli, S., Beltrami, H., Boyer, T., Cuesta-Valero, F. J., Desbruyères, D., Domingues, C., García-García, A., Gentine, P., Gilson, J., Gorfer, M., Haimberger, L., Ishii, M., Johnson, G. C., Killick, R., King, B. A., Kirchengast, G., Kolodziejczyk, N., Lyman, J., Marzeion, B., Mayer, M., Monier, M., Monselesan, D. P., Purkey, S., Roemmich, D., Schweiger, A., Seneviratne, S. I., Shepherd, A., Slater, D. A., Steiner, A. K., Straneo, F., Timmermans, M.-L., and Wijffels, S. E.: Heat stored in the Earth system: where does the energy go?, Earth Syst. Sci. Data, 12, 2013–2041, 10.5194/essd-12-2013-2020, 2020b.Watson, C. S., White, N. J., Church, J. A., King, M. A., Burgette, R. J., and Legresy, B.: Unabated global mean sea-level rise over the satellite altimeter era, Nat. Clim. Change, 5, 565–568, 10.1038/nclimate2635, 2015.WCRP Global Sea Level Budget Group: Global sea-level budget 1993–present, Earth Syst. Sci. Data, 10, 1551–1590, 10.5194/essd-10-1551-2018, 2018.Weller, E., Min, S.-K., Cai, W., Zwiers, F. W., Kim, Y.-H., and Lee, D.: Human-caused Indo-Pacific warm pool expansion, Sci. Adv., 2, e1501719, 10.1126/sciadv.1501719, 2016.
Wouters, B., Bonin, J. A., Chambers, D. P., Riva, R. E. M., Sasgen, I., and Wahr, J.: GRACE, time-varying gravity, Earth system dynamics and climate change, Rep. Prog. Phys., 77, 116801, 10.1088/0034-4885/77/11/116801, 2014.