Paris Agreement dodges cumulative effects | Brussels Blog

Paris Agreement dodges cumulative effects

posted by on 28th Aug 2020

This post uses a thermal model of the Earth, divided into two parts. Instant Earth that reacts immediately to greenhouse warming and Cumulative Earth that accumulates the effects of greenhouse warming.

Conclusion: The cumulative effects of global warming are not being taken seriously enough.


Earth’s Energy Imbalance

All the energy that enters or leaves the Earth does so via radiation at the top of the atmosphere. Before the industrial revolution, e.g. 1750, incoming radiation was balanced by outgoing radiation. Since then, triggered by emissions of greenhouse gases, less energy is leaving the Earth than entering, causing the Earth’s Energy Imbalance (EEI), which has been described as “the most fundamental metric defining the status of global climate change”.

Here, the extra energy stored in the Earth since 1750 will be referred to as ‘greenhouse heat’ as it is stored as heat (including latent heat from melted ice).


A simplified thermal model of the Earth

Here is the simplified thermal model of the Earth used in this note to explore climate policies. This model divides the Earth in two parts: Instant Earth and Cumulative Earth:

  • Instant Earth can receive and emit radiation to outer space. Its temperature reacts quickly to changes in EEI because it has low thermal capacity. It compromises the atmosphere plus the first few upper metres of ocean and land.
  • Cumulative Earth can only exchange heat with Instant Earth. The temperature of Cumulative Earth reacts slowly to heat from Instant Earth because it has much higher thermal capacity. Cumulative Earth is sub-surface ocean and sub-surface land. The sub-surface ocean dominates.

The surfaces of ice masses have characteristics of both Instant Earth and Cumulative Earth: Upper Earth because they can receive and emit radiation, but when they melt, they absorb energy, without much rise in temperature. A slow rise in temperature is a characteristic of Cumulative Earth. Also, the melt water joins the ocean. The vast bulk of the ocean is sub-surface, part of Cumulative Earth.


Global Mean Surface Temperature: Instant and cumulative effects.

The usual measure of the Earth’s surface temperature is called Global Mean Surface Temperature (GMST). To get a value for GMST at a specific time, temperatures from measuring stations are combined to form average values. There have been different schemes for averaging, complicated by the uneven geographical spread of the stations.

In the simplified thermal model, GMST can be identified as the temperature of the lowest part of Instant Earth, so it governs the rate of transfer of heat to Cumulative Earth. The greenhouse heat in Cumulative Earth is largely Ocean Heat Content. GMST is controlled by the concentrations of greenhouse gases in the atmosphere which create the Earth’s Energy Imbalance. In my thermal model the control is instantaneous.

The relationship between GMST and the greenhouse heat in Cumulative Earth is not instantaneous: This greenhouse heat in Cumulative Earth has been accumulated since 1750 from heat transfers from Instant Earth.


Instant and Cumulative Climate Effects

The climate effects in Instant Earth include heat waves, floods, droughts and storms. The most recognised climate effect of the heat in Cumulative Earth, is sea level rise. Cumulative warming of the ocean also plays an important part in melting sea ice and the edges of land-based ice masses as they extend into the ocean.


Storms and feedbacks

A less recognised Cumulative Effect is the intensification of tropical storms to become super hurricanes and super typhoons (2011), caused by the cumulative increase in ocean heat content. More recognition is coming as shown in Ocean heat as ‘fuel’ for hurricanes (2018):

Another less recognised Cumulative Effect is the warming of sub-surface permafrost in tundra and ocean floors. Some believe these may be the source of serious climate feedbacks, and important feedbacks are badly represented in climate models.

Judging from social media, mainstream media and scientific publications, Instant Effects get much more attention than Cumulative Effects. The most recognised Cumulative Effect is sea level rise, which is slow moving and less newsworthy than hurricanes or wildfires.


The instant becomes cumulative

In the scientific literature, the concern for instant effects is concentrated on a concern for peak GMST. This excludes or downplays effects that happen outside the time of the peak, which are below the peak but experienced over an extended period.

As well as the effects of greenhouse heat in Cumulative Earth there are the ‘instant effects’ that are properties of Instant Earth, which take place an extended period. E.g.

  1. Cumulative death toll.
  2. Cumulative economic damage.
  3. Cumulative loss of ‘human happiness’.
  4. Cumulative biodiversity destruction.
  5. Cumulative climate feedbacks such as albedo changes.

Using one moment in time, the time when GMST reaches a peak value, to frame climate policy ignores cumulative damage and the dangers of a prolonged period of increased Earth’s Energy Imbalance.

The Paris Agreement has framed policy on climate change based on Instant Effects at a moment in time by choosing a limit to GMST to a maximum value. The time is the time of peak temperature.


The Paris Agreement

The target of the Paris Agreement specifies that GMST should not rise past a certain limit, during this century. It says:

The Paris Agreement central aim is to strengthen the global response to the threat of climate change by keeping a global temperature rise this century well below 2 degrees Celsius above pre-industrial levels and to pursue efforts to limit the temperature increase even further to 1.5 degrees Celsius.

The Paris limit to GMST is set in relation to ‘pre-industrial’ GMST. Like GMST itself, the ‘pre-industrial’ reference temperature has had different interpretations. There is also room for interpretation in the meaning of ‘well below 2 degrees Celsius’.

There are these three uncertainties in the Paris Agreement:

1. The definition of GMST.
2. The meaning of pre-industrial temperature.
3. The meaning of ‘well below 2 degrees Celsius’

There is another aspect of the Paris Agreement that is unclear. This concerns how the ‘Paris limit’ might be exceeded. For the following example, assume the limit is 2.0°C. Consider these two scenarios:

  • Scenario 1 Earth’s Energy Imbalance keeps GMST at 1.9°C for the rest of the century starting now.
  • Scenario 2 Earth’s Energy Imbalance keeps GMST at 1.1°C until 2090, then 1.9 for the final decade.

Both scenarios will be compliant with the Paris Agreement, but the differences are:

  • 1 With Scenario 1, GMST is significantly higher than Scenario 2, for the years 2021 to 2090. For these years the worse effects associated with Instant Earth will occur (droughts, floods, heat waves & etc).
  • 2 With Scenario 1, the heat in the Cumulative Earth is much higher.
  • 3 During the years 2021 to 2090, in Scenario 1, climate feedbacks will increase the Earth’s Energy Imbalance. These feedbacks include carbon-cycle feedbacks such as increased fires, decomposing organic matter in thawed permafrost. There will also be non-carbon feedbacks such as albedo change due to reduced ice cover. Several of these feedbacks are poorly represented in climate models.

Scenario 2 is clearly preferable to scenario 1 but both are compliant with the Paris Agreement. This has important implications for policies on short term climate pollutants, such as methane or CO2 when Carbon Capture and Storage is used (see below).


Short-Lived Climate Pollutants and Earth’s surface temperature.

When CO2 is released into the atmosphere from burning fossil fuels, approximately 50% remains in the atmosphere, while 25% is absorbed by land plants and trees. The other 25% is absorbed into areas of the ocean (See NOAA: Ocean-Atmosphere CO2 Exchange). The proportion that remains stays in the atmosphere for centuries (unless there are deliberate actions to remove it). Once the atmospheric concentration of CO2 has been increased by one year’s emissions, it takes a very long time to fall by natural processes, so each year’s increase builds on top of previous years. It accumulates in the atmosphere.

The 50% of CO2 emissions that accumulates in the in the atmosphere limits the energy that is leaving the Earth and increases the Earth’s Energy Imbalance. This, in turn, controls the Earth’s surface temperature and the Instant Effects of climate change.

Other greenhouse gases affect the Earth’s Energy Imbalance. The most important of the other greenhouse gases are methane (CH4), F-gases and nitrous oxide (N20) (EPA: Overview of Greenhouse Gasses). At the present, the warming caused by methane is 58% of CO2’s warming. F-gases are 11% and N20 is 10% (Real Climate: The evolution of radiative forcing bar-charts).

N2O has an average lifetime in the atmosphere of 114 years, so over several decades it accumulates in the atmosphere in a similar way to CO2. F-gases also accumulate in the atmosphere as their lifetimes are thousands of years.

However, methane does not accumulate in the same way. When methane is emitted, it stays in the atmosphere for a decade or so before being removed by natural chemical reactions. After 9.1 years half of it has gone [9]. This means atmospheric concentration of methane falls quickly unless replenished.

The decay of methane causes a fall in the Earth’s Energy Imbalance causing a decrease in the Earth’s surface temperature (GMST). This decrease would happen almost as quickly as methane decays, but currently the decay is more than offset by increased emissions of methane.

Some argue for a policy of sharply reducing methane emissions because it would have an immediate effect on reducing Earth’s Energy Imbalance and Earth’s surface temperature. Shindell et al. argue this in Simultaneously Mitigating Near-Term Climate Change and Improving Human Health and Food Security.

Others, particularly Professor Myles Allen, are wary of this view. They seem to imply that efforts to curb methane emissions means allowing more emissions of CO2. In the Oxford Martin Policy Paper, Short-Lived Promise? Myles Allen wrote

early action on SLCP mitigation could affect the temperatures and climate impacts experienced by the generation of today’s decision-makers but will have little impact on the warming experienced by future generations. Unless it is accompanied by ambitious reductions in CO2 emissions, early SLCP mitigation will also have very little impact on eventual peak warming.

In another publication from the Oxford Martin School, Dr Michelle Cain, quotes Myles Allen:

“We don’t actually need to give up eating meat to stabilise global temperatures,” says Professor Myles Allen who led the study (meat production is a major source of methane). “We just need to stop increasing our collective meat consumption.”

Of course, a lower amount meat consumption would give stability at a lower temperature.

Professor Allen’s views have given this impression: “Don’t worry much about short term climate heating from methane until peak temperature is close because the extra surface heating will have dissipated before the peak.”

This seemed to be the meaning that Professor David MacKay took. This is an extract from notes I made from a conversation I had with him in 2009:

3) By the time peak temperature occurs any methane released now will have been removed from the atmosphere by natural processes so it will not affect global warming at the all-important peak.

I confirmed these notes with Professor MacKay. At that time, he was Chief Scientist at the Department of Energy ad Climate Change. Put more crudely this view appears to be: “Don’t worry about methane emissions for the time being.”

This view highlights the damage from climate change at one moment in  time, the time of peak temperature. This is misleading: It downplays the cumulative effects of sea-level rise and accumulating feedbacks. It also downplays the continuing disaster of the effects on economies, human lives and nature.


Carbon Capture and Storage

A policy of Carbon Capture is sometimes promoted as a solution to climate change. This entails removing CO2 from the atmosphere some time after it is emitted. This changes CO2 from a long-lived greenhouse gas into a short-lived greenhouse gas.

Correctly timed this may help to keep GMST within a specific limit but GMST will be raised during the time between emission and extraction, causing the cumulative problems described above. To account for climates feedbacks more CO2 must be extracted than emitted.



A policy which simply limits Earth’s surface temperature at a specific time has imited use. It can hide serious issues.

The Paris Agreement hides serious issues.


Postscript 7th September 2020

The paper Revised estimates of ocean-atmosphere CO2 flux are consistent with ocean carbon inventory by Watson et al. provides increased estimates for the the size of the CO2 sink in the Earth’s oceans. The increase seems enough to account for the carbon imbalance reported in the Global Carbon Project.

The paper says this about the ocean surface layer:

Furthermore, the MBL [ mass boundary layer] is embedded within the ocean’s thermal skin, the uppermost ~1000 µm which is cooler than the underlying water because the ocean surface is a net emitter of heat, both via latent heat and longwave radiative fluxes, to the atmosphere.

1000 um is one millimetre supporting the idea that the “ocean’s thermal skin” is a shallow part of the surface of the ocean, and is part of “Instant Earth” as described above.


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