M5: Ecological Redirection

The M5 Model answers the question “What kind of consequences should we expect from the global warming forecasted by the IPCC models?”. There are three successive sub-questions:

·       What is the temperature elevation produced by the raise of CO2 (and other greenhouse gas)?

·       What are the economic consequences of this warming? (mostly, the SCC question)

·       How will the humanity react (from the population to the economy as a system)?

The first sub-question is addressed by abstracting the IPCC forecasts into a function that tells the temperature elevation as a function of the atmosphere CO2 concentration (cf. section 2.3). This is a coarse simplification and shows that CCEM does not attempt to be as precise as some other models such as IGSM (Sokolov, 2005). This function is extracted from the representative concentration pathways (RCP 4.5, RCP 6 and RCP 8.5) of the IPCC reports.


The second sub-question is more complex but there is a wealth of literature on the topic. CCEM lets the user represent her “belief” as a function that gives the percentage of GDP loss as a function of temperature elevation. This is a known unknown, as there is a wide variety of opinions on this topic, but it also fairly easy to decide if you want to use the output of Nordhaus model, or a more realistic output from ACCL, or come up with your own belief after reading a transverse study such as (Wade, 2016).


The third question is the more difficult one, and the reason for building the CCEM model. Without a feedback loop, it is easy to forecast a catastrophic ending, or a “business as usual” scenario, depending on your initial belief. But the reality of our “path towards catastrophe” will probably show some bifurcations, with some drastic reactions to some of the catastrophic events that global warming is bound to produce. This is where the concept of ecological redirection, following Bruno Latour and other research scientists (Bonnet, 2021) is quite useful. Instead of talking about “ecological transition” which makes little sense for a complex system with so many couplings (unless your beliefs are such that you think it will continue to operate “linearly” in the next century), it is better to assume that we have no idea of the final destination (“où atterrir?”, Bruno Latour, 2017). Redirection modeling may be seen as an oxymoron, it means to simply model the possibility of bifurcation along the path of global warming. In the current version of the model, we only consider three kinds of redirection:

·       Acceleration of CO2 taxes (which includes the globalization and forced adoption by all countries).

·       “Cancellation”, that is renouncing as some form of energy source for some usages. The example of banning non-electric cars in Europe starting 2035 is a perfect example.

·       Energy policy, which is the combination of accelerating the energy transition and modifying the “energy redistribution policy that is built into M3 thought the Alpha function). Redistribution here means distributing either the energy or the right to produce CO2 emissions according to a political rule, by opposition to market forces. The state subsidies of energy for citizens, that we saw as a consequence of the Russia-Ukraine war, is a perfect example.


The relation between CO2 emissions and CO2 concentration is kept very simple in CCEM, which is a known design limit. On the other hand, because we represent the temperature elevation as a function of CO2 concentration, we may capture some amplification loops which are present in the RCP scenarios, such as the fact that the loss of glacier and snow-covered area is amplifying solar forcing (reducing radiation) or the fact that additional methane may be released as a consequence of temperature elevation. With this respect, not taking methane concentration into consideration is a simplification that does not necessarily degrade the model relevance.


In the case of M5, the state variables are the following:

  AS(y): Agricultural surface on year y

      ES(y) : Areal that was transferred from Agriculture to Clean Energy Production

  WO(y): Wheat Output

      CO2(y): emission for year y in Gt

      CO2ppm(y): CO2 concentration reached on year y

  T(y): average globe temperature on year y

      PAINe(y): pain factor for zone z at year y

      TaxFz(y) :  intensification factor of CO2 tax for z

      CnFz(y): acceleration of cancel (factor) for zone z

      TrF(y): acceleration of energy transition (factor)


Each step of M5 simulation may be described as follows (the following equations represent the “logic of the model”). We compute the CO2 level from the emissions (minus the absorption capacity, a very crude abstraction). We then derive the temperature elevation from the “belief” table (IPCC(c)). For each of the four world regions (US, EU, China and RoW), we compute the associated pain level and the consequent “redirections” which are represented by coefficients (tax/cancel/redistribute) which are feedbacks to the other models.


Notice that ↑F(y) is a shorthand notation for the yearly increase ration F(y) / F(y – 1). These equations used additional parametric functions that represents the “known unknown” associated to M5:

      bioHealth(T,y): percentage of yield evolution, which declines when temperature raises but grows with worldwide diffusion of tech and best practices 

      agroEfficiency(p) : decline of productivity as energy price increases

      painProfile(z) : vector of 3 coefficients that define the global pain level

      painFromClimate(T): step function that sets a pain level as temperature rises.

      pain2Cancel(z,p) : policy that sets cancel acceleration (sobriety) as a function of pain

      pain2Transition(z,p) : policy linear function that links pain level p to Energy Transition acceleration

      co2Neutral : level of emissions that is approximately balanced by nature

      co2Energy: percentage of CO2 emission due to fossil energy

      co2Ratio: additional concentration in the atmosphere from additional CO2 emission (ratio)

      IPCC(c): temperature elevation caused by concentration c, extracted from IPCC RCPs

      satisfaction(z,dW,dG) : heuristics that defines satisfaction from WheatOutput change and GDP change