Constraining the Global Ocean Heat Content Through Assimilation of CERES-Derived TOA Energy Imbalance Estimates

1 Introduction

The accuracy of integrated quantities in ocean reanalyses is fundamental for understanding the change of the global climate, although its correct determination is nontrivial due to the spatially and temporally inhomogeneous observation sampling (Wunsch, 2016). Net radiative fluxes at the top of the atmosphere (TOA) balance the absorbed solar minus the outgoing longwave radiations. Greenhouse gases entrapping heat in atmosphere cause global warming of the Earth and lead to long-term positive downward energy imbalance at the top of the atmosphere, emerging from combined observational and modeling studies (e.g., Trenberth et al., 2014). The TOA net radiative flux thus represents a unique diagnostics to monitor the Earth system energy change.

This energy imbalance is mostly absorbed by the global ocean and is visible in terms of long-term ocean heat content increase. The Argo float observing network has provided since early 2000s an unprecedented sampling of the subsurface temperature, contributing to estimating the percentage of Earth's energy imbalance (EEI) stored in the oceans to be more than 90% (Riser et al., 2016), the remaining part being taken by atmosphere, land, and cryosphere and being about an order of magnitude smaller than the ocean heat uptake (Trenberth et al., 2016). A variety of processes, with generally different timescales, influence the TOA net radiation variability, ranging from slowly varying climate modes (mostly El Niño–Southern Oscillation and Pacific Decadal Oscillation), volcanic eruptions, and anthropogenic emissions, till month-scale phenomena like the Madden-Julian Oscillation and fast-varying weather regimes affecting the cloud cover at global scale (e.g., Brown et al., 2014; von Schuckmann et al., 2016).

Estimates of the Earth's energy imbalance at TOA can be measured by the Clouds and the Earth's Radiant Energy System (CERES, Wielicki et al., 1996) instruments on board the Terra, Aqua, and Suomi National Polar-orbiting Partnership (NPP) satellites. CERES measures solar-reflected and Earth-emitted radiation from the TOA to the Earth's surface. Together with cloud properties retrieved by the Moderate Resolution Imaging Spectroradiometer and total solar irradiance data from the Solar Radiation and Climate Experiment mission, CERES data can be combined to estimate the TOA energy imbalance. CERES data are acknowledged to be crucial in estimating the Earth's energy variability and the global warming. Actual estimates of this imbalance are compiled by CERES Energy Balanced and Filled (EBAF) products, which preserve the closure of the radiation budget by means of using concurrent estimates of energy components (Loeb et al., 2009); for instance, Argo based heat content variation estimates are taken into account to calibrate the EBAF TOA net radiation.

In spite of the good observational sampling of the subsurface temperature by Argo floats since approximately mid-2000s, many statistical objective analyses and ocean reanalyses of subsurface temperature fail in capturing the ocean heat content tendencies measured by CERES EBAF data (Smith et al., 2015; Trenberth et al., 2016). This is in general due to lack of uniform global observational coverage, suboptimal assumptions in mapping procedures and data assimilation schemes (Boyer et al., 2016). In reanalyses that use a dynamical ocean general circulation model (OGCM), systematic or random errors in the atmospheric forcing (Valdivieso et al., 2015) and vertical physics (Palmer et al., 2017) may also affect the warming rate accuracy. Data assimilation procedures are generally found able to correctly constrain regional ocean heat tendencies (Storto, Masina, et al., 2016) or long-term averaged tendencies (Storto, Yang, et al., 2016), while barely capture the inter-annual variability of the heat content tendencies themselves.

Achieving realistic energy budget variability within Earth system simulations is also crucial in the context of ocean model long-term simulations (e.g., OMIP, Danabasoglu et al., 2014) and coordinated climate change experiments (e.g., CMIP5, Taylor et al., 2012) that aim at reconstructing and projecting the past and future climate of the Earth system through coupled model simulations forced by realistic greenhouse gas concentrations. In this context, recent estimates of TOA energy imbalance may be incorporated in ocean or Earth system simulations to realistically constrain the total energy budget, preventing Earth system climate simulations from providing realistic estimates of the energy imbalance (Smith et al., 2015).

Variational data assimilation schemes can be derived from the Bayesian analysis equation (e.g., Lorenc, 1986) and offer a straightforward mathematical framework to ingest observation types with sophisticated observation operators, including, for instance, CERES-derived TOA net radiation fluxes. Aim of this paper is to act as a proof-of-concept for constraining ocean heat content tendencies through global TOA energy imbalance data. The structure of the present work consists of section 1, section 2 describing the data used and the experimental ocean reanalysis system, section 6 reporting the results from the assimilation experiments, and section 7 summarizing and discussing the main achievements.

2 Data and Methods

2.3 Assimilation of Global Heat Content Tendency

In order to assimilate CERES EBAF-TOA data (y_EBAF) into the ocean analyses, the variational data assimilation cost function J in incremental form (i.e., with minimization performed over =x − x_b, with x the ocean state, that is the analysis at the minimum of J, and x_b the background state) has been reformulated as follows:

(1)

Where B is the background-error covariance matrix, H is the tangent linear version of the observation operator, and d is vector of misfits calculated using the nonlinear observation operator. The third right-hand-side term corresponds to the CERES EBAF-TOA penalty term: δEEI is the increment of δx in TOA net radiation space, and d^EEI is the misfit between CERES EBAF-TOA observation and the background-equivalent, respectively given by

(2)

and

(3)

Where T indicates temperature in the 3-D computational grid of volume V, which is one of the state parameters included in x along with the 3-D salinity and sea surface height. ρ c_p is the product of the reference density (1020 kg m⁻³) and the seawater heat capacity (4000 J kg⁻¹  °C⁻¹), Δt is the assimilation time window (here 15 days, in seconds), and and are background temperature at the beginning (t1) and end (t2) of the assimilation time window. The coefficient β determines the fraction of the EEI absorbed by the global ocean, and it is currently assumed to be equal to 0.93, according to Allan et al. (2014). However, this value makes sense for long-term (multiannual) timescales, while it is questionable for the monthly timescale of the EEI data used here, due to subseasonal processes that may vary the percentage of EEI absorbed by the ocean on short timescales (von Schuckmann et al., 2016). We take this into account by considering the representativeness error for the CERES derived estimates.

Indeed, the observational error R_EEI shapes how much the analysis heat content tendency approaches the satellite-derived estimate. We have used 0.4 W m⁻² for R_EEI as the approximate squared sum of the variances of the representation and instrumental errors. Here the representation error quantifies the uncertainty in assuming that a constant fraction of the CERES EBAF-TOA data explains the global ocean heat content tendencies, namely, the uncertainty of the observation operator and, in particular, the uncertainty of the β coefficient. Such an error is assumed equal to 0.3 W m⁻², corresponding to the EEI monthly global anomaly for nonocean components, as suggested by Trenberth et al. (2016). The instrumental error is assumed equal to 0.3 W m⁻², estimated by Loeb et al. (2016) as standard deviation of the differences of CERES measurements from different satellite platforms.

Note that the CERES EBAF-TOA penalty term involves scalars, as both observations, background and increments are globally averaged values. The formalism of 1 separates for the sake of clarity the EEI penalty term from the usual variational cost function observational term, although the former can be absorbed in the latter as EEI is in fact an observation as much as any other, in spite of the observation operator involving global averages and temporal differences. A similar framework has recently been introduced by Takacs et al. (2016) to include an atmospheric mass conservation penalty term in the GEOS atmospheric variational data assimilation system used for the Modern-Era Retrospective Analysis for Research and Applications atmospheric reanalysis production. Ocean state estimations also include averaging observation operators, for instance in order to constrain the 4-D ocean state toward an external climatology (e.g., in ECCO, Forget et al., 2015).

The variational analysis equation 1 is solved iteratively by using the L-BFGS-B minimizer (Zhu et al., 1997), which requires the calculation of the gradient of 1 for quick convergence. The adjoint of the operator in 3 spreads the gradient of the CERES EBAF-TOA penalty term onto the 3-D temperature adjoint. The specification of the background-error covariances is crucial here, because it determines where locally the gradient is spread, implying that a misspecification of them leads to wrong CERES observations driven increments (e.g., areas with overestimated errors will be much too subject to the EEI correction, and conversely for areas with underestimated errors).

It can be noted that extending the assimilation scheme to strong or weak constraint, four-dimensional data assimilation is straightforward, requiring equation 2 to be replaced by.

(4)

where δT_t1 and δT_t2 are the increments valid at the beginning and end of the assimilation time-window (i.e., the variation of the OHCT implied by data assimilation), although here for simplicity we focus on 3DVAR experiments.

3 Results

We present the results of our implementation by comparing different metrics from four experiments: INS refers to the reference experiment with assimilation of temperature and salinity from in situ profiles; INS&OHCT assimilates also CERES EBAF data, further to the in situ ocean observing network; NOASS is a control experiment without data assimilation; finally, OHCT assimilates only CERES EBAF data. These four experiments are conceived specifically to assess the impact of the global ocean heat content tendency constraint either in synergy or not with conventional observations. All experiments span the period 2000–2013 and share the same initial conditions, coming from a long-term integration with the INS experiment setup. Additionally, we report results from the CMCC C-GLORSv5 ocean reanalysis (1980–2015, Storto & Masina, 2016), representing a realization of a global ocean reanalyses at eddy-permitting resolution, with the additional assimilation of satellite observations (sea surface temperature, sea level anomalies, and sea ice concentrations), representing a state-of-the-art modern global ocean reanalysis.

Global heat content results are presented in Figure 1, with the corresponding statistics in Table 1, and are relative to the 2001–2013 period. CERES EBAF data indicate an ocean-absorbed EEI imbalance equal to 0.67 W m⁻² (using the beta coefficient discussed in section 2). Without assimilation the model results indicate an overestimated heat content tendency (2.12 W m⁻²), due to the overestimation of net heat flux by ERA-Interim (see Valdivieso et al., 2015), while with the assimilation of in situ only the tendency is underestimated (0.38 W m⁻²). Only the assimilation of CERES data (experiments INS&OHCT and OHCT) leads to values close to the observed ones, although the assimilation of only CERES data still leads to a much too large warming. Largely negative peaks in the annual signal occur during 2004, 2011, and 2012 when only in situ profiles are assimilated, opposed to the positive values of CERES during those years. The correlation between CERES estimate is significant for all experiments at monthly timescale, with largest score provided as expected by INS&OHCT. In contrast, the correlation of the data with the mean seasonal cycle removed highlights the benefits of the CERES data assimilation. Note that correlations are larger without in situ data assimilation (i.e., in the OHCT experiment), suggesting that the latter may introduce some spurious variability. C-GLORSv5 has a mean value very close to CERES data, but with a very low (nonsignificant) correlation, suggesting that its mean ocean heat content tendency is not linked to possibly better reproduced variability. This apparent paradox is probably due to the more sophisticated data assimilation scheme (surface nudging, sea ice and altimetry data assimilation, and large-scale bias correction). Compensation of errors may also occur on long timescales.

Figure 1 (top row, right column) also indicates the increased warming rate variability of the reanalyses without global heat content constraint with respect to CERES data, suggesting that the experiments may be characterized by spurious high-frequency variability, as also noted by Trenberth et al. (2016). This higher than CERES variability is especially visible INS, and it is significantly reduced by means of CERES data assimilation, both at monthly and yearly timescales. Related to that, the monthly climatology (Figure 1, middle row, left column) also suggests a larger seasonal cycle in the experiments without CERES data, quantified by the seasonal amplitude (Table 1) greater than 10 W m⁻², opposed to the 8.41 W m⁻² found for CERES EBAF data. Furthermore, the assimilation of CERES EEI data leads to a power spectrum with generally less energy at the scales shorter than 1 year or greater than 3 years, in accordance with the estimates from CERES.

In terms of global ocean heat content (temporally integrated heat content tendency, Figure 1, bottom row), differences are amplified. Importantly, the warming hiatus present in INS and NOASS for the first half of 2000s is largely mitigated in INS&OHCT, suggesting that the joint assimilation of conventional observations and CERES may prevent the reanalysis system to show this warming decrease, which as many authors suggest may be due to the vertical redistribution of the global ocean heat content (e.g., Balmaseda et al., 2013). Finally, also the monthly climatology of the global ocean heat content shows an amplified seasonal cycle when the CERES EBAF data are not accounted for.

Table 1 also reports RMSE scores for the four experiments and C-GLORSv5 calculated against monthly maps of AVISO altimetry data (Le Traon et al., 1998), NOAA SST analyses (Reynolds et al., 2007), and in situ misfits (from EN4 before their assimilation). Note that the first two are completely independent verifying datasets within the experiments, except in C-GLORSv5 that assimilates them. In-situ profiles may be considered independent if the temporal correlation of the observation errors is neglected. RMSE scores are meant to show that the assimilation of CERES is at least not degrading the accuracy of the reanalyses. We found for all parameters a non-significant impact of CERES data assimilation: neutral impact when also in situ data are assimilated (INS&OHCT with respect to INS), and slightly positive (but nonsignificant) impact when in situ are not assimilated (OHCT with respect to NOASS) for sea level and surface temperature.

Figure 2 focuses on the difference of OHC trend and seasonal amplitude of INS&OHCT minus INS for the study period. Most of warming difference is found in the Atlantic Ocean and, to a lesser extent, in the Pacific Ocean midlatitudes and eastern Indian Ocean. This distribution is linked to both the background-error covariances (the larger they are, the bigger is the correction borne by CERES data) and the geographical sampling of in situ observations: note that the assimilation of well sampled TAO/TRITON tropical moorings may anchor the warming in the Tropical Pacific Ocean, thus preventing a significant change in that region when CERES data are assimilated. The seasonal amplitude map difference suggests that the decrease in the Southern Hemisphere leads to the globally averaged decrease. The Northern Hemisphere on the contrary is characterized by an increase of amplitude in the Atlantic sector, while the Pacific sector exhibits a decrease and an increase in the western and eastern regions, respectively. The difference between OHCT and NOASS (not shown) emphasizes only the cooling effect of CERES data assimilation due to the overestimation of net heat flux.

Figure 2 (right) shows the globally averaged trends by vertical levels (accumulated from the top as lines and in different vertical regions as bars, along with uncertainty estimates using bootstrapping). The sketch indicates that most of CERES data-induced warming occurs below 1,500 m, consistently with the fact that in situ profiles well constraint the upper ocean, and with the common speculation that the missing energy seen by CERES but not by most ocean heat content estimates during the hiatus period stems from the unmeasured deep ocean warming.

Finally, Figure 3 shows the temperature climatology difference between the two pairs of experiments (OHCT minus NOASS and INS&OHCT minus INS, left and right columns, respectively), as a function of the month of the year and latitude (for the surface to bottom temperature, top row) and as a function of depth and latitude (for the yearly climatology, bottom row). When no in situ data are assimilated, CERES data lead to a year-round cooling confined to the low and middle latitudes and the top 3,000 m, peaking in the subtropics at about 200 m of depth. When they are assimilated, the temperature increase peaks in July and August (for both hemispheres, at around 20°S and 20°N). The warming also peaks in the subtropics and at around 200 m of depth, with the Southern Ocean having a slightly deeper penetration of the warming, in accordance with recent findings (Stephens & L'Ecuyer, 2015).

4 Summary and Discussion

Most of data assimilation schemes used for ocean reanalyses are not conservative schemes, implying that global ocean integrals, crucially important for climate monitoring, may spuriously vary along time. An exception is represented by ocean state estimations performed with adjoint methods (Wunsch & Heimbach, 2013). Adding global constraints in modern data assimilation systems is thus attracting increasing attention of atmospheric and oceanic reanalysis communities dealing with both variational and ensemble data assimilation methods (e.g., Takacs et al., 2016, and Barth et al., 2016, respectively), although conservation laws in the latter are perhaps harder to maintain due to the purely statistical nature of the error covariances (Lorenc, 2003). Note also variational schemes provide global analysis solutions, thus representing a straightforward mathematical framework to introduce global constraints.

Here we show that global EEI estimates derived by the Clouds and the Earth's Radiant Energy System can be successfully ingested in an ocean reanalysis system to constrain the global ocean heat content. In particular, spurious variability in CERES blind experiments (larger seasonal and interannual variability, underestimated ocean heat content tendency, and poor temporal correlation) is recovered by the assimilation of CERES-derived estimates of ocean heat content tendencies, without affecting the accuracy of the reanalysis. Compared to nonassimilative simulation, the only ingestion of EEI data also reduces the biases of the atmospheric forcing that, within our modeling configuration, leads to an unrealistically large over-estimation of the OHCT.

The assimilation of CERES data helps in closing the global energy budget. There exist emerging consensus that the recent surface warming slowdown is an apparent feature associated with the poor sampling of deep ocean temperature (see Balmaseda et al., 2013; England et al., 2014; Trenberth & Fasullo, 2013). The debate on the hiatus is still open, with recent works pointing out that uncertainties in the energy budget terms may prevent the full understanding of the hiatus (Hedermann et al., 2017). The present study suggests that the additional assimilation of CERES data, which do not show any apparent warming hiatus, induces a warming below 1,500 m of depth. However, this feature might be also affected by the structure of the background-error covariances and the lack of observations below 1,500 m and thus should be taken cautiously. Nevertheless, it represents a successful proof-of-concept for using TOA EEI data in ocean models. The ocean heat uptake appears larger in the Southern Ocean, consistently with many recent studies (Stephens & L'Ecuyer, 2015), suggesting that also the geographical changes induced by the CERES data assimilation are realistic.

Furthermore, efforts devoted for homogenizing EEI time series and merging multiplatform datasets, as achieved by Allan et al. (2014) for the 1985–2012 period can be used by reanalysis applications and emphasize the potential of global constraint methods, allowing for instance for a 30 year reanalysis time series with energy budget globally constrained. A natural long-term perspective is the inclusion of sophisticated energy optimization method, as the ones proposed for instance by L'Ecuyer et al. (2015) in data assimilation systems for climate reanalyses; for instance, strongly coupled data assimilation methods currently under development in many institutes (e.g., Laloyaux et al., 2015) are the complementary ingredient that will enable climate reanalyses to follow the observed energy budget at both local and global scales.

The approach presented here may also be applied to historical ocean reanalyses (e.g., Yang et al., 2017) or long-term ocean-only (e.g., Danabasoglu et al., 2014) or air-sea coupled (Taylor et al., 2012) simulations, where the temporally varying value of EEI may be substituted to a climatological one, with an associated larger observational error that spans the actual interannual variability of the EEI. This strategy might ensure that the energy budget of the ocean component is not unrealistically broken, thus limiting the negative effect of wrong external forcing.