TOA EEI versus Surface Net Flux

By Andy May

Fasullo & Trenberth (2008) build a closed, observation‑based annual energy budget for Earth’s climate system, partitioned into the top of the atmosphere (TOA), atmosphere, land, and ocean. They combine satellite radiation measurements, weather reanalyses, a stand‑alone land model, and several ocean temperature products. Over the oceans, they diagnose the net surface flux as a residual of the TOA and atmospheric budgets and compare it to independently derived ocean heat content and its trend.

Their logic is:

1. The TOA imbalance is measured with satellite radiation data, after tuning.
   
2. Atmospheric storage and heat transfer are estimated with weather reanalysis models.
   
3. Ocean surface net energy flux (radiation + evaporation + sensible) is estimated as the difference of the change in total atmospheric heat content + atmospheric transport of heat minus the TOA net radiative flux.
   
4. Global ocean heat content and its trend are defined as the net surface energy flux integrated over the whole ocean.
   

Thus, if atmospheric and land storage are assumed to be small, over the study period, the global TOA imbalance is assumed to be equal to the global ocean heat (or thermal energy) uptake. All energy diagrams, like the NASA one shown in figure 1, make the same assumption. As shown in figure 1, over 60% of the thermal energy leaving Earth’s surface is in the form of latent heat (evaporation) and conduction of sensible heat, whereas all the energy leaving the TOA is in the form of radiation. Fasullo and Trenberth assume that these alternate forms of energy transfer are net zero (or close enough to it) and merely move heat about and are already accounted for at a global scale over their time period. While it is true that surface energy movements are net zero over some period of time, it is not true over all time periods due to nature’s tendency to reorganize local heat storage, the argument I present here.

To justify the simplifying assumption that Ocean Heat Content (OHC) thermal energy changes = net TOA radiation flux, they emphasize the law of energy conservation in the full atmospheric column, and they show that atmospheric and land thermal energy storage is small. However, when they compare OHC estimates from ocean measurements over a mean year to satellite-measured incoming and outgoing radiation they find substantial differences. Overall ocean temperature changes imply a substantially larger annual cycle of ocean heat content than can be accounted for by either TOA or surface radiation changes from satellite measurements. In simpler terms, the oceans are storing and releasing energy on their own time frame, independently of the TOA. The Fasullo and Trenberth dataset only covered the years 1985-1989 (ERBE) and 2000-2004 (CERES), and importantly, these ten years are much shorter than the natural AMO or PDO ocean oscillations.

PDO

The Atlantic Multidecadal Oscillation (AMO) is 60-70 years long, from trough to trough, and the Pacific Decadal Oscillation (PDO) is 20-30 years long. The oscillations each have a “warm” period when the respective oceans expel excess stored heat and a “cold” period when they store atmospheric heat. They accomplish this by moving heat up and down in the ocean column.

Fasullo and Trenberth, as well as later studies, (Johnson et al., 2016), (Loeb et al., 2009), and (Loeb et al., 2018), compute a variety of Earth Energy Imbalances (EEIs) that fall between 0.5 and 1.0 W/m². This is a range of 0.2 to 0.4 PW, which in terms of Ocean Heat Content (OHC) is 7 – 14 x 10²² Joules.

The observed magnitude of upper ocean heat content swings due to the PDO are 5-15 x 10²² Joules over a decade and some analyses show swings of 20 x 10²² Joules during strong shifts like 1976-77 and 1998-2013 (Meehl et al., 2011) and (England et al., 2014). Figure 4 of England et al. (2014) shows that intensified Pacific trade winds drove an additional ~8 × 10²² J of global 0–700 m ocean heat uptake between 1992 and 2011, with ~5–6 × 10²² J occurring in the Pacific and ~1–2 × 10²² J in the Indian Ocean. See the drop in the PDO over this period in figure 2.

A negative PDO phase is associated with surface cooling and a deeper ocean heat uptake. This phase leads to stronger trade winds which pump heat below 125 meters and cause surface cooling. England argues that this is heat redistribution and not a slowdown in planetary heat uptake.

England et al. (2014) show that intensified Pacific trade winds during the negative PDO phase caused a loss of −3.8 × 10²² J from the upper 125 m of the Indo‑Pacific, while simultaneously increasing subsurface heat content by +5.0 × 10²² J. This vertical redistribution produced a net gain of only 1.2 × 10²² J, illustrating that decadal PDO variability can generate large upper‑ocean heat content swings. However, only the ocean skin layer emits infrared radiation, evaporates, and conducts heat to the atmosphere. If thermal energy is redistributed deeper in the ocean column, it is not warming the atmosphere or detected by satellites. Furthermore, the ocean temperature measurements that are used to compute ocean heat content are highly dependent upon the depth where the readings are taken.

AMO

Robson et al. compute a time derivative of ocean heat content of a sudden AMO shift in the mid-1990s of over 1 x 10²² J/year. The entire AMO upswing extends from ~1975 to ~1998 (see figure 3), a period of 23 years, so the total change could be as much as 23 x 10²² Joules. Chen and Tung found that shifts in surface temperature and heat content in the Atlantic and the Southern Ocean are more extreme than found in the Pacific. They also present evidence that the major reorganization of OHC in the mid-1990s was global and helped to cause the pause in warming observed between 1998 and about 2014. The linearly detrended AMO region SST anomalies are shown in figure 3.

EEI (Earth Energy Imbalance)

Loeb et al.’s 2018 estimate of the TOA Earth Energy Imbalance is 0.71 W/m². When this is expressed in terms of Ocean Heat Content (OHC) it is roughly 8.9 x 10²² Joules. Loeb et al. assume that OHC can be used to set a TOA EEI absolute value, like Fasullo, Trenberth and others do, to calibrate their satellite incoming and outgoing radiation measurements. However, upper ocean heat content has more drivers than TOA EEI, especially over the long-term (>10 years). TOA EEI is just incoming and outgoing radiation flux, ocean surface flux is also a function of evaporation, wind speed, and direction. These latter factors manifest themselves as the major climate oscillations, especially the AMO and PDO. Table 1 shows the impact of AMO and PDO climate oscillations compared to Loeb et al.’s assumed TOA EEI of 0.71 W/m². Which is a function of OHC data, his “in-situ value” (Johnson et al., 2016):

“A one-time adjustment to shortwave (SW) and longwave (LW) TOA fluxes is made to ensure that global mean net TOA flux for July 2005–June 2015 is consistent with the in situ value of 0.71 W m⁻² (Loeb et al., 2018).”

Event	OHC Change (J)	Duration	Equivalent W/m²	Source
EEI (Loeb 2018)	8.9 x 1022 J	11 yr	0.71 W/m²	Loeb (2018)
PDO (England 2014)	8 x 1022 J (0–700 m anomaly)	20 yr	~0.32 W/m²	England et al. (2014)
AMO (Robson 2012)	10-20 x 1022 J	10–15 yr	~0.5–1.0 W/m²	Robson et al. (2012)

Table 1. A comparison of Loeb et al.’s OHC determined EEI values and changes due to the AMO and PDO.

Table 1 compares the Loeb et al. assumed EEI to the equivalent net flux at the ocean surface due to the extremes of the AMO and PDO in recent decades. Loeb’s period of measurement is roughly 2005-2015 and he used a variety of measurements, but his main source for the 0.71 W/m² value was the change in OHC (Johnson et al., 2016). During this period, the AMO was rising (see the undetrended AMO in figure 2 of May & Crok, 2024) and the PDO was falling (figure 2), these oscillations can produce an impact on shallow ocean OHC that is as large or larger than the anthropogenic greenhouse effect on EEI as estimated in AR6 (IPCC, 2021, p. 925) and (Li et al., 2024). His calculations may not reflect an anthropogenic greenhouse effect at all, just the net global ocean natural surface oscillation. We simply can’t tell with the data we have today, the data time period is too short.

The PDO and AMO contributions to OHC change in table 1 are redistributions of energy, not a planetary gain or loss of energy, like the TOA EEI. The problem is these, and other ocean oscillations, contaminate OHC-tuned EEI calculations and make the EEI calculation in figure 1 or in the other sources mentioned above inaccurate.

Loeb et al.’s methodology

As explained by Norman Loeb and colleagues (Loeb et al., 2009), the average global net radiation at the top of the atmosphere (TOA) is defined as the difference between the energy absorbed and emitted by the planet. If the planet is at equilibrium, the global net TOA radiation is zero. However, Earth is never at equilibrium, as attested to by the major long-term ocean oscillations like ENSO, the AMO, the PDO and so on. Earth’s oceans have an enormous heat capacity and the thermal energy content changes, especially the upper ocean heat content, over multidecadal periods.

Global net radiation at the TOA should be in phase with, and of similar magnitude, as global ocean heat storage. However, ocean heat content (OHC) responds to changes in the energy imbalance at the ocean surface and not necessarily to the energy imbalance at the TOA. The ocean surface is separated from the TOA by the atmosphere and its thick convective troposphere.

The TOA and ocean surface fluxes are not equal and are only partially connected to one another. All thermal energy fluxes at the TOA are via radiation and in figure 1, only 36% of surface heat transfer is via radiation. The heat transfer mechanisms are different, and the atmosphere has heat capacity, whereas space does not. Even so, Loeb and NASA assume that the energy imbalance at the surface is the same as the energy imbalance at the TOA over very short time periods.

Energy conservation requires that over long enough periods, where internal variability is not a factor, that the surface energy fluxes should approximately equal the fluxes at the TOA. I don’t argue this point, only that given the periods of the AMO and PDO, the time period used in these recent studies is too short, 20 years of data is not enough.

CERES Data

Loeb et al. 2018 write that without adjustments to the CERES shortwave (SW) and longwave (LW) data the TOA net imbalance is about 4.3 W/m², much larger than expected and probably not possible. This is a known calibration issue and not a measurement of the true TOA radiation imbalance. They then go on to explain that to avoid this problem they adjust the SW and LW fluxes within their ranges of uncertainty to force the satellite measurements to reflect the imbalance calculated using ocean heat content. As mentioned above, in CERES EBAF (“Energy Balanced and Filled”) version 4, the global annual mean values are adjusted such that the July 2005– June 2015 mean net TOA flux is 0.71 ± 0.10 W/m², which is from Johnson et al. (2016) and an update from the previous value of 0.58 W/m².

We used the CERES EBAF data to map the TOA net radiation trend from 2001-2024 for the globe, the map is shown in figure 4. Much of the map is near zero (light yellow), but there are areas, in the Pacific and over the continents where the trend is negative, that is more outgoing radiation than incoming. All the energy transfer at the TOA is via radiation, none is stored or transferred via other mechanisms.

Figure 5 shows the EBAF surface net radiation (SW + LW) trend map for the same years. Although this data is corrected using the assumption that the Earth Energy Imbalance at the ocean surface is the same as the Earth Energy Imbalance at the TOA, the resulting trends are different. This is expected since the atmosphere intervenes in several ways as shown in figure 1. It absorbs or reflects (154.1 W/m² or 45%) of the incoming sunlight, and it cools the surface through evaporation (latent heat, 86.4 W/m² or 36%) and by absorbing some of the surface heat via conduction (18.4 W/m² or 8%). Only about 58 W/m² of surface infrared emissions are sent to space, the rest are recycled via the atmosphere. Due to all the interference from the atmosphere, as well as changing heat storage, the cooling and warming areas are different, and the surface is showing more warming than at the TOA.

Figure 6 plots the latitude corrected means of both the TOA EEI and the net surface radiation (SW + LW) over the 2001-2024 period with CERES EBAF data after converting the net radiation flux values to anomalies from the respective means. I converted the net energy fluxes to anomalies because the magnitudes of the raw radiation fluxes are different due to the atmosphere.

Conclusions

Using variations in upper ocean heat content to calibrate the satellite measured TOA EEI is a good idea, but unfortunately, ocean heat content has many more drivers than just radiation-in minus radiation-out. Upper‑ocean heat content is strongly influenced by multidecadal internal variability, and because CERES absolute fluxes are tuned to OHC, current EEI estimates may reflect a mixture of forced and internal variability. Longer, more stable OHC records are needed before EEI can be used as a robust indicator of anthropogenic forcing.

This does not eliminate the possibility of a long-term human-caused imbalance, it just makes detecting it very difficult or impossible over short periods of time. We need to understand the ocean oscillations better than we do or wait until we have enough data to account for their swings in thermal energy storage.

We have decent data for this calculation since about 2005, but the ocean cycles contaminating the EEI calculation are not related to greenhouse gas emissions or other possible anthropogenic drivers of climate change since the oscillations pre-date any possible anthropogenic influence (Gray et al., 2004). Therefore, attributing any portion of EEI to anthropogenic forcing is premature. Longer, more stable OHC datasets are required to cleanly separate anthropogenic forcing and interval variability.

Download the bibliography here.

Download the CERES R code used to make some of the figures here.