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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. 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. Although this is indeed a “coarse” abstraction, 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 (cf. discussion in Section 5.1).
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 one of the key reasons 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. 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, or the zone-differentiated form of CBAM).
· “Cancellation”, that is renouncing to some form of energy source for some usages (may be defined as “forced sobriety”). 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.
In the case of M5, the state variables are the following:
• AS(y): Agricultural surface on year y
• ES(y) : Area 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:
(1) We compute the CO2 level from the emissions, using an absorption ration (roughly, 50% is absorbed by the ocean and the earth surface, while the other half is added in the atmosphere).
(2) We then derive the temperature elevation from the “belief” table (IPCC(c)).
(3) We compute the wheat production according to the model presented in Figure 7. The first step is to compute ES(y), the estimated cultivable land attributed to energy production (such as solar farms or biofuels). The second step is to reduce the total “arable land” according to the losses caused by global warming. Last we compute the wheat output according to four factors: the total surface used for agriculture AS(y), the expected gain in yield (productivity through better practices and technology), the reduced efficiency because of energy scarcity – expressed as a function of price, in the same spirit as the cancel function of M2, and a bioHealth factor that represents the expected impact of warming on wheat agriculture.
(4) For each of the five world regions (US, EU, China, India and RoW), we compute the associated pain level using a weighted sum (painProfile(z) is a weight vector) of three factors: global warming, energy scarcity and combined loss of GDP/person and food/person.
(5) Once the pain level is known, we compute the “ecological redirection”, represented by a tuple of factors (TaxFz(y), CnFz(y), TrFz(y), SvFz(y), PrFz(y)). Each factor is a percentage that is used in the previous equations from M1 to M4, and that represents respectively the acceleration of carbon taxation, an increased in forced sobriety, an acceleration of energy transition, an acceleration of energy saving investments and, last, an increase in protectionism (similar to the CBAM – Carbon Border Adjustment Mechanism that Europe is trying to setup).
(6) Once the “protectionism factor” PrFz(y) is set for zone z, the actual trade barriers are set for each other zone z2 according to the difference both in CO2 emissions (per unit of energy consumed) and in the CO2 taxes. The heuristic of equation (6) sets a trade protection of up to TaxFz(y) for those zone z2 which higher emissions and lower carbon taxes.
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
• cropYield(y) : increase of productivity in year y due to propagation of best practices and improvement in agriculture science
• 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
• 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
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