A p×n data matrix H containing modeled steric sea level or OHC data on p grid points and n monthly observations or model data, can be analyzed by finding the best fitting linear combination of defined base functions, which represent the data in its entirety using PCA ; also known as EOF decomposition. The data matrix, H, can be decomposed using singular value decomposition as follows H=USVT, where S is of size p×n and contains, at most m=min⁡(p,n), distinct singular values si on its main diagonal. The columns of U represent the time-invariant eigenvectors and are generally referred to as empirical orthogonal functions (EOF)s or “modes”. Corresponding principal components (PC)s, D, are then computed from D=SVT. These can be interpreted as the temporal evolution of scaling factors needed to reconstruct the input data, H, from the orthonormal basis, U, defined by the EOFs.

Model based steric sea level from the ORAS5 reanalysis is used as a basis for extracting leading EOFs for estimating sea level budgets as part of the fingerprint inversion. Similarly, in situ temperature and salinity profiles obtained from the Argo program are processed to global gridded products by various institutions using optimal interpolation techniques e.g.,. For both, model and in situ based datasets, steric sea level anomalies relative to a reference steric sea level are computed from the 4D temperature, T, and salinity, S, data as the integral of the ratio of density differences relative to the reference density, ρref, up to maximum depth, H, given by 1hsteric(λ,ϕ,t)=∫-H0ρref(Tref(λ,ϕ,z),Sref(λ,ϕ,z),p(λ,ϕ,z))-ρ(T(λ,ϕ,z,t),S(λ,ϕ,z,t),p(λ,ϕ,z,t))ρref(Tref(λ,ϕ,z),Sref(λ,ϕ,z),p(λ,ϕ,z))dz, where the density, ρ, is derived from temperature, salinity and pressure, p following the Thermodynamic Equation Of Seawater – 2010 TEOS-10,. In case of the ORAS5 model, H represents the maximum model depth of ∼6000 m, while when we analyze Argo data, a depth of 700 m is used. In other words, the integral limits are adapted depending on the utilized data, e.g. model or Argo, throughout the manuscript.

The global fingerprint inversion method fits spatial sea level patterns, so called “fingerprints”, to a combination of space-geodetic datasets from satellite altimetry and GRACE(-FO) gravity data in a forward modeling least-squares sense . The fingerprints refer to individual mass and steric contributions to sea level and are constructed based on a priori information. Here, we employ an updated inversion method , which is summarized in the following.

A possibility to validate the global-mean OHU rates from the Argo, model and space geodetic datasets is to compare against (globally averaged) data from the CERES project. However, it is known that due to radiometric calibration problems the long-term global mean from CERES original SYN dataset amounts to about 4 Wm-2 , several times bigger compared to all estimates derived from OHU simulations or in situ observations. The calibration stability of CERES satellite radiation measurements is thought to be at the 0.3 Wm-2 (or 0.1 % of the total in- or outgoing fluxes) level per decade, for 95 % confidence . Thus, before using the data for climate evaluations, the long-term mean flux in observed CERES data must be removed or restored from other measurements as it has been done in the CERES EBAF data set. This makes the CERES EBAF data not fully independent as they are tied to oceanic in situ, i.e. Argo, estimates of OHU in order to correct for biases.

EEI at the top of atmosphere (TOA) is extracted from CERES EBAF-TOA Ed4.2.1 data as the net flux by subtracting monthly outgoing longwave and shortwave fluxes from the incoming solar radiation at TOA. The gridded EEI is then globally averaged resulting in time series of EEI in Wm-2. For converting to CERES-OHU, we assume that 90 % of the excess heat at TOA is stored in the oceans .

In order to assess our results from the GAAMR method, we compare to a variety of published gridded datasets. The validation data can be roughly classified based on their origin: (1) gridded Argo profiles, (2) ocean model reanalysis data and (3) data from space geodetic approach, each denoted with the prefixed A, M and SG, respectively (Table ). Each dataset includes gridded temperature and salinity profiles, which are then directly converted to OHC utilizing the TEOS-10 Gibbs sea water toolbox as 10Qvali=Aoce∫-H0cpρ(T(z),S(z),p(z))(T(z)-Tref(z))dz, where cp and Aoce are the same as in Sect. . Density ρ at depth z is derived from temperature T, salinity S and pressure P. All utilized validation datasets are summarized in Table .

Argo data were collected and made freely available by the International Argo Program and the national programs that contribute to it (https://argo.ucsd.edu, last access: 16 September 2026, https://www.ocean-ops.org, last access: 16 September 2026). The Argo Program is part of the Global Ocean Observing System. The Argo-only validation products are limited by the coverage of the Argo program and do not cover large parts of the polar oceans, which limits the validation in these regions (Fig. ). In contrast, model products and the space geodetic data from MOHeaCAN are available for all ocean sub-regions investigated below. In order to better manage the number of datasets used here for validation and visualization, we computed ensemble means and corresponding spread for each of the three sub-categories. For this we also included prior MOHeaCAN versions 2.1, 3.0 and 4.0 (Table ). All datasets provide data during the period January 2005 till December 2015, the “golden age” of ocean sampling , which will be the basis for validation comparisons in the following.

Space geodetic approaches for computing ocean heat content (OHC) and it's rate, i.e. ocean heat uptake (OHU), generally require information on steric sea level change by computing a sea level budget. Here, we utilize a global fingerprint inversion method driven by satellite altimetry, satellite gravity and in situ profile data from the Argo program (Sect. ). For the period January 2005 till December 2015, we find a global steric sea level rate of 1.24 ± 0.16 mmyr-1, which together with a mass driven relative sea level change of 1.94 ± 0.16 mmyr-1 closes the total sea level rise (3.18 ± 0.22 mmyr-1) within a residual to observed altimetry sea level of 0.04 ± 0.08 mmyr-1 (see Table  for the full budget). Note that while the mass, steric and total sea level changes are derived from gridded values covering the whole ocean with a resolution of 0.25°, the residual is computed directly at the 1 Hz along-track input altimetry data positions.

Total sea level from our inversion matches well with sea level estimated from using globally gridded monthly sea level of 3.15 mmyr-1. If we evaluate total sea level change directly at the along-track altimetry locations our inversion estimate is found to be 3.41 mmyr-1, which fits well to the 3.42 mmyr-1 derived from sea level data based on . Similarly, inversion based mass sea level also corresponds well to independently processing the GRACE(-FO) data following resulting in 1.85 mmyr-1. These sea level budget estimates, especially the steric sea level contribution, are in good agreement with published estimates e.g.,. With our inversion approach we can further split the steric contribution into a thermo- (1.22 ± 0.16 mmyr-1) and halosteric (0.02 ± 0.02 mmyr-1) components, where the former clearly dominates the estimate on global scales and is directly linked to OHC change, while the latter can have significant regional impact.

Regionally, we find good agreement between our trend maps for January 2005 till December 2015 (Fig. ) and recent publications . When comparing to results by we find similarities between the patterns of total sea level change and Argo-based steric sea level and our results (Fig. ), despite utilizing a slightly different time period for the derived trends. However, for the ocean mass change component report significant trend anomalies in the North Atlantic ocean, also been mentioned by , where the same region is also found to exhibit large residual trends, when subtracting the sum of all components from the total sea level observed by altimetry. From our fingerprint approach (Fig. C), we can not confirm these residual trend signals, similar to , who do not see these North Atlantic trend signals in the majority of their investigated products, including fingerprints, mascons and spherical harmonic solutions, except for the CSR spherical harmonic solution which shows slightly negative trends. EOF decomposition of our residual sea level (not shown here) reveals that there are no major trend signals left within our residual trends (Fig. G), as these are dominated by the major current regions (Gulf stream, Aghulas current, etc.), which are not modeled as part of our fingerprint approach. Similarly, we do not find significant positive residual trends in the Indian ocean as have been observed over the 2005–2015 period by others their supplement Fig. 5.

On global scales, we compare OHC from our GAAMR approach (Sect. ) to OHC derived from various publicly available observational and model-based datasets (Sect. ), as well as published estimates. In addition, one can directly compare to independently observed estimates derived from the CERES project. Monthly CERES EBAF-TOA Ed4.2.1 data have been globally averaged in order to derive an estimate of EEI, which is then further converted to OHU and OHC.

On global scales, OHC change is mainly driven by seasonal changes as well as long term trends and accelerations (Fig. A). Considering CERES-OHC as independent reference, the seasonal signal from all other approaches generally agree well in phase, but show some larger amplitudes and variations in trend and acceleration. The latter becomes obvious after removing those aforementioned signals, computed over the reference period January 2005 till December 2015, from the individual datasets and comparing the residuals (Fig. B). During the computation period, the OHC estimates from different methods agree well, albeit being more noisy compared to the CERES-OHC. It becomes immediately clear that the variation in acceleration leads to significant disagreement, especially for the model ensemble after 2016. Estimates from our GAAMR method and based on converting inversion-derived steric sea level to OHC using a constant factor of 0.52 Wm-2(mmyr-1)-1 agree quite well with the CERES-OHC also outside of the computation period after 2016; before 2005 we find also our estimates to be influenced by model deficiencies, likely stemming from non-global Argo data coverage being assimilated into the ORAS5 model, which is the basis for our steric fingerprints. In addition, inversion-based results (GAAMR and direct steric sea level conversions) show lower quality towards the end of the GRACE mission lifetime (after mid 2016), whereas results derived after the launch of the GRACE-FO mission in 2018 are again close to the CERES-OHC.

From our GAAMR method we find an overall increase of 1.34×1022 ± 0.12×1022 Jyr-1 for the period January 2005 till December 2015, which fits well into the range of OHC trend values reported by based on several published estimates. When further separating OHC into contributions from the Northern and Southern hemispheres, we derive OHC rates of 0.52×1022 ± 0.11×1022 Jyr-1 and 0.82×1022 ± 0.14×1022 Jyr-1, respectively. The estimate for the Southern hemisphere compares well to and is in agreement with the findings reported in . Our estimate for the Northern hemisphere is found to be slightly above the reported spread of results by but also in agreement with .

Expressing the trends in OHC in terms of global OHU allows for further comparison between the individual datasets considered and our proposed GAAMR method (Fig. A, Table ). We find OHU of 0.58 ± 0.14 Wm-2 from GAAMR with an OHU trend, i.e. OHC acceleration, of 0.20 ± 0.24 Wm-2 per decade (Fig. A, Table ). While the OHU estimate shows the overall best agreement with that derived from the CERES project (0.67 Wm-2 per decade), the OHU trend derived from CERES is about double (0.41 Wm-2 per decade) what we find from GAAMR (Fig. B, Table ). The difference in OHU trend likely results from a strong negative residual during 2007 and 2008 (Fig. B), which is driven by a significant scaling factor associated with the steric fingerprint representing the majority of the ENSO signal. While the CERES result does not seem to be strongly influenced by the La Niña event, similar negative residuals are found from the other datasets as well, albeit not as pronounced as in GAAMR (Fig. B). Considering all investigated datasets, we find a general spread of OHU between about 0.30–0.70 Wm-2 with some outliers exceeding these bounds (minimum: 0.08 ± 0.60 Wm-2 from A-SCRIPPS and maximum: 1.09 ± 0.12 Wm-2 from the ORAS5 reanalysis model). For the OHU trends, we find roughly 3 clusters of trend estimates (1) around 0.15–0.25 Wm-2 per decade (2) around 0.40 Wm-2 per decade and (3) around 0.55 Wm-2 per decade with some individual results exceeding these ranges up to 0.93 ± 1.04 Wm-2 per decade from A-SCRIPPS and even negative OHU trends (-0.26 ± 0.32 Wm-2 per decade and -0.39 ± 1.0 Wm-2 per decade for M-ORAS5 and M-Glorys2v4, respectively).

Our estimated OHU fits well within the reported range of 0.53–0.74 Wm-2 by for the period 2006 till 2015 extracted from in situ data, ocean reanalysis and converting steric sea level using a constant conversion factor. When we convert the reported ensemble mean (thermo-)steric sea level change of 1.31 ± 0.4 mmyr-1 from for 2005–2015 to 0.68 ± 0.21 Wm-2 using the constant factor 0.52 Wm-2(mmyr-1)-1, the estimated OHU is higher than those estimated above. This can be explained by the constant factor not accounting for acceleration, which influences the estimated OHU. In other words, when directly converting the steric sea level trend to OHU, we find estimates more in line with considering only linear change as given in Table .

On regional scales, comparison between individual datasets on ocean basin scales reveals significant differences (Fig. ). Note that some datasets introduced in Sect.  are provided as global time series only and, thus, we include here only those datasets that can be evaluated in these sub-basins.

For the Pacific Ocean we find the residual curves from all datasets to agree relatively well during the analysis period with the space geodetic methods exhibiting a slightly lower noise level compared to the Argo and model-based ensembles (Fig. ). Regarding OHU (Fig. A and Table ), we find the Argo based methods on the lower end with estimates between -0.12 ± 0.16 Wm-2 and 0.06 ± 0.26 Wm-2. In contrast, the space geodetic approaches, including our GAAMR solution, provide slightly larger OHU estimates around 0.1 Wm-2, whereas the model-based estimates can differ significantly based on the model (-0.22 to 0.17 Wm-2). Regarding OHU-trends, we find positive decadal trends from all datasets mostly concentrated in the range 0.25–0.50 Wm-2 per decade with some model based values exceeding these limits (Fig. B and Table ). If we do not consider OHC accelerations, i.e. OHU trends, during estimation (Table ), our OHU estimates for the Pacific Ocean are found to be larger compared to published Argo based estimates of 0.15 Wm-2 by . In contrast, it becomes significantly smaller when considering an OHU trend during estimation with only estimates from GAAMR (0.12 Wm-2) and the Glorsys2v4 model (0.17 Wm-2) showing good agreement.

For the Atlantic ocean, we find a generally higher spread and larger noise in the residual Argo and model ensembles compared to the Pacific ocean, while the space geodetic based residuals show a similar level around zero (Fig. ). In terms of OHU, we find a similar level as for the Pacific ocean with our GAAMR estimate of 0.06 ± 0.04 Wm-2 located roughly in the middle of all individual estimates. Argo-based OHU is found to be smaller with most ensemble members even indicating negative OHU in the Atlantic, whereas space geodetic and all, but one, model OHU estimates are found to be positive (Fig. A and Table ). For OHU trends we generally find significantly larger estimates for the Argo-based results above 0.3 Wm-2 per decade, while model estimates are found around 0.1 Wm-2 per decade (Fig. B and Table ). Our GAAMR estimate (0.20 ± 0.08 Wm-2 per decade) lies between those two data groups. Similar to the Pacific Ocean, estimates for the Atlantic Ocean when not considering OHU trends (Table ), are found to be roughly in line with the reported estimates around 0.17 Wm-2 by and , whereas estimates are systematically smaller in our normal processing, which considers OHU trends.

The residuals from the Indian Ocean (Fig. ) show significant discrepancies between individual data groups. During the estimation period we, again, find space geodetic methods to exhibit the lowest noise level and relatively good agreement with model derived OHC residuals, while those from Argo are found to be noisier. In 2016, we find an artifact occurring for all Argo and all model data and to a much smaller extend also in the space geodetic data (Fig. ). The reasons for this are currently unknown. Afterwards, a steep increase in OHC residuals can be observed from all model data, while Argo-based OHC-residuals increase at a significantly smaller rate. In contrast space geodetic results see no such significant increases in OHC residuals (Fig. ). This data discrepancy is also reflected in the OHU estimates. On the one hand, we find a moderate OHU of 0.30 ± 0.04 Wm-2 from our GAAMR method, while most other datasets indicate stronger OHU estimates of 0.4–0.5 Wm-2 (Fig. A and Table ). On the other hand, the same large OHU values are connected to strongly negative OHU trends of -0.40– -0.20 Wm-2 per decade, while we find only -0.14 ± 0.08 Wm-2 per decade from GAAMR and only -0.03 ± 0.10 Wm-2 per decade from the MOHeaCANv5 dataset (Fig. B and Table ). Nonetheless, our estimates of Indian Ocean OHU significantly exceed the 0.17 Wm-2 reported in . If we do not consider an OHU trend during estimation, estimates are closer, albeit still slightly larger (Table ).

While most datasets provide results in the Arctic and Southern oceans, for Argo datasets these are generally based on only a few grid cells as Argo provides only a very limited coverage of these high-latitude regions (see Fig. ). This is also evident from the significant noise level in the OHC residuals for these two regions and a large ensemble spread after our analysis period (Fig. ). Space geodetic and model estimates are less affected due to high latitude observation coverage and the model domains including these ocean regions. For the inversion, the fingerprint spatial patterns are assumed to be static over time, the global rescaling from the combined GRACE, altimetry and Argo observations nevertheless does provide “predicted” sea level change, budget and derived OHC from GAAMR in these high latitude regions. However, these still need to be interpreted with caution. While space geodetic missions show only very small residuals, model results show a larger noise level, albeit smaller as that found from Argo data. This is also reflected in the OHU and OHU trend estimates. For the GAAMR and MOHeaCAN space geodetic approaches we find OHU and OHU trends close to zero, while model estimates, especially for the Southern Ocean, can reach values of up to ±0.1 Wm-2 (Fig. A and Table ) and an OHU trend range of -0.07–0.1 Wm-2 per decade (Fig. B and Table ). While we report the estimated Argo values, we do not consider those representative considering the very limited Argo coverage in these regions and the significantly different number of provided grid cells from each Argo product. report a very large contribution of 0.24 Wm-2 based on Argo for the Southern Ocean, which we cannot confirm here.

Despite covering only 3 % of the ocean area, the contribution of the remaining ocean, which includes warming of e.g., the Mediterranean Sea, the Baltic Sea and the Asian Seas, including the Indonesian Throughflow, is found at levels of to 10 % of the global OHU. We find a general good agreement between OHU and OHU trend estimates from all products with our GAAMR results fairly in the middle with a contribution of about 0.1 Wm-2 OHU and -0.15 Wm-2 per decade OHU trend (Fig.  and Tables  and ). Most of these regions represent shallow seas where sea level changes are dominated by water mass changes and transports resulting from remote steric effects. For the Southeast Asian seas this remote steric effect in combination with steric variability in non-shallow regions, such as the South China Sea e.g., drive the majority of the OHU. In other words, the heat in this region rather acts as a compensation for missing signal outside of these regions. Furthermore In addition, local thermo- and halo-steric effects in the Mediterranean Sea also contribute on a smaller scale.

In the following we present results for an extended data period, i.e. January 2005 till December 2024. However, not all of the data products are available until end of 2024 and thus, we limit our presented results to three Argo products, one model result, as well as our own computations based on converting steric sea level directly and our GAAMR approach.

The global OHC residuals, after removing mean, trend, acceleration and seasonal signals, (Fig. A), show a good agreement between independent data from the CERES project and our space geodetic results, similar to the above analysis period. This is also reflected in the OHU (Fig. B and Table ), where we find 0.57 Wm-2 and 0.61 ± 0.10 Wm-2 from the CERES project and GAAMR, respectively. While OHU estimates from Argo also agree within error bounds, that from the ORAS5 model is significantly larger (0.82 ± 0.12 Wm-2). Global trends in OHU (Fig. C and Table ) derived from the CERES project are found to be almost double of what has been found from the other data products (0.41 Wm-2 per decade). Argo and model OHU trends are found generally smaller compared to that from GAAMR, which appears to be mainly driven by OHU trend differences in the Pacific and Indian oceans (Fig. C and Table ).

Regional OHU over the extended period in the Pacific and Atlantic oceans is found to be similar to the analysis period (2005 till 2015) reported above (Fig. ) around 0.1 Wm-2 for both with all estimates agreeing within error bounds. Only the Argo solution from SCRIPPS shows a significantly smaller OHU. In contrast, estimates for the Indian ocean are found to be significantly smaller (0.2–0.25 Wm-2) over the extended estimation period (Fig. B) compared to the shorter period (Fig. A). At the same time corresponding trends in OHU, which have been negative for the shorter period (Fig. B) are found to be closer to zero (Fig. C). Similar to the shorter analysis period, we find OHU and OHU trend values close to zero for the Artic and Antarctic oceans. OHU from the remaining part of the ocean is also found to be close to zero, whereas it accounted for about 0.1 Wm-2 for the shorter analysis period.

We compare the spatial patterns of OHU (Fig. ) and OHU trends (Fig. ) on grid level. We generally find good agreement with respect to the distribution of larger regions of positive and negative OHU (and OHU trends). OHU from ORAS5 is generally very similar to that from converting steric sea level using a temporally constant factor and our GAAMR method due to ORAS5 representing the basis for our steric fingerprints used within the inversion approach. However, spatial patterns are not identical, but rather differ in details, e.g. in the northern and equatorial Atlantic ocean, the central Indian ocean or the Southern ocean (Figs.  and ). We find negative OHU in the northern Atlantic, which have been linked to a weakening of the Atlantic meridional overturning circulation , where a collapse would significantly increase ocean warming . In contrast, the patterns derived from EN4 appear more generalized with less detail, which is mainly due to the lower grid resolution compared to the other results (1.0 vs. 0.25°). Furthermore, this results from the covariance lengths used in the objective analysis which have length of 300–400 km at the equator, which can be increased exponentially to 1500 km towards the poles . In addition, we find differences in OHU and corresponding trends in the northern Atlantic and the southern Pacific oceans, as well as around southern Australia, where the Argo data suggests significant positive OHU, while model and space geodetic results point to a region of significant negative OHU. While the global oceans are mostly warming , there has also been regional cooling, e.g., in the (sub-)tropical Pacific (Fig. ), which have been linked to a general “La Niña-like” strengthening of the zonal ocean heat gradients . Changes in the Indian Ocean Walker circulation leading to a general warming in the Arabian Sea and the northern part of the Indian Ocean. These transports from the Indian Ocean equatorial region have been linked to El Niño-Southern Oscillation and Indian Ocean Dipole signals in the past .

By propagating the formal errors of thermosteric sea level from our inversion output throughout our GAAMR method and also assuming a 5 % ORAS5 reanalysis error level during conversion to OHC, regional errors of OHU and OHU trends are shown in Fig. . These represent the errors corresponding to the GAAMR results in Figs.  and . Largest errors are detected in major current regions, including the Gulf steam, the Aghulas current and the Kuroshio current. This is expected as thermosteric variability in these regions is large due to eddy and gyre presence.

The Hovmöller diagram in Fig.  shows the inter-annual spatial ocean heat distribution for the major ocean basins of the Pacific, Atlantic and Indian Oceans, derived from GAAMR and ORAS5, with sea surface temperature (SST) from the ERA5 reanalysis for comparison . For computing the inter-annual signal, we remove the monthly climatology (January 2005 till December 2024) as well as the OHC trend and acceleration signal (Figs.  and ). Generally, we find the GAAMR signal to be lower compared to the ORAS5 reanalysis, similar to our results on regional OHC reported above.

At inter-annual timescales in the equatorial Pacific Ocean, we observe alternating patterns of warming and cooling that correspond to the ENSO signal (Fig. ). From the GAAMR results, transport of ocean heat is observed in the tropical and sub-tropical Pacific Ocean (Fig. ). Warm water is concentrated around 30° N until about 2005 and then slowly propagates southward toward the equator until about 2010. Afterwards, warm water is propagating northward again until about 2014. After 2014, a relatively large warming region is observed in the sub-tropic zone. A similar but less pronounced transport is found in the tropical zone of the Southern hemisphere. These transport periods align well with the Pacific Decadal Oscillation (PDO, Fig. ), which has been found to be linked to variability in EEI at the top of atmosphere . Towards the polar regions, we generally find decreasing OHC, which is different to SST. SST clearly also shows effects from the marine heat wave “blob” . Indeed we find the same pattern, albeit much less pronounced, also in whole-water-column OHC from GAAMR (Fig. ).

Differences in the details of the inter-annual spatio-temporal signal structure are observed between GAAMR and ORAS5, e.g. in the (sub-)tropical southern part of the Atlantic in 2011 and 2012 (Fig. ). This again highlights the ability of GAAMR to adapt not only to variations in amplitude, but also spatial signal variations. We observe a clear signal in SST between 30 and 40° N, which is, albeit significantly less pronounced, visible also in OHC distribution from GAAMR as well as ORAS5. From GAAMR we observe reduced heat variability in the tropical zone and even after the large ENSO event in 2010 the corresponding heating over the entire water column is less pronounced and slightly lagging behind the SST signal.

In the Indian Ocean, we find the inter-annual signals in the northern part and the tropical zone exhibiting a distinctive pattern of North-South stripes in the SST spatial distribution (Fig. ), which can be linked to ENSO periods (Fig. ). Here, we find a more lagged response with warm and cold water being transported northward driven by a change in the Indian Ocean Walker circulation leading to a general warming in the Arabian Sea . These transports from the Indian Ocean equatorial region have been linked to ENSO and Indian Ocean Dipole (IOD, Fig. ) signals in the past . After 2018, we find generally larger levels of heat transport from the equatorial Indian ocean towards the North and, to a smaller extent, to the South. This indicates an explanation for the lower OHU levels observed for the 20 year period compared to the shorter analysis period (Figs.  and ).

We finally investigate the connection between our GAAMR results and well defined major climate indices (Fig. ). We find strong correlation of 0.82 between the principal component of the second mode of the GAAMR approach and the Multivariate ENSO Index MEIv2, index. Similarly, the PC of the second mode is also closely linked to the Pacific Decadal Oscillation PDO, index, where we find a correlation of 0.71. Thus, the second mode within GAAMR represents, both, the ENSO variability and the PDO variability, e.g. following the general trend into the negative seen in PDO after 2016 while having the MEI variability superimposed. Our correlation results are in line with those reported by who compared sea surface temperature (SST) anomalies to indices for ENSO and PDO, which has been linked to variability in EEI before . Other indices, such as the Indian Ocean Dipole IOD, index, can not be directly linked to a single mode in GAAMR, but are rather spread over multiple modes. In order to achieve a clear signal separation for these weaker signals from EOF decomposition, one would need more data, i.e. a significantly longer time series.