CCEM2023.pptx

Yves Caseau - CCEM : System Dynamics for Earth Model – December 2023 1/40
Coupling Coarse Earth Models(CCEM),
Global Warming and Social Cost of Carbon
Yves Caseau
National Academy of Technologies of France (NATF)
December 2023
2023 Wrap-up Presentation
Latest update : December 25th, 2023

Outline
1. Earth Models : SDEM vs IAM
 System Dynamics, Integrated Assessment Models
 Digital Twin and Simulation
2. CCEM Model Overview
 Coupling of 5 “coarse” models
 Known Unknowns as Parameters
3. Computational Results
 Preliminary Simulations
 Dependency to prior beliefs (the “Known Unknown”)
4. Next Steps
 Social Cost of Carbon (Impact of Global Warming)
 Geopolitics and Game Theory

Scope of Simulation : Earth’s Reaction to Global Warming (IPCC)
 We have the tools to adapt and mitigate (CO2 tax,
Energy source transition, …) but are slow to use them
 If we do not anticipate, adaptation will be forced upon us
 Redirection may cause irregular RCP
(representative carbon pathways)
fossil
clean
react anticipate
sobriety
redirection
BAU
warming

Integrated Assessment Models
 IAM: (Wikipedia Definition)
Integrated assessment modelling (IAM) or integrated modelling (IM) [a] is a term used for a type of scientific modelling that
tries to link main features of society and economy with the biosphere and atmosphere into one modelling framework.
William Nordhaus
(Wikipedia)
 Strengths (what it is useful for)
 Systemic view (more or less )
 What-if scenarios
 Global energy / economy /
climate coupling
 Limits
 Not a forecast engine
 Feedback loop:
 Policy is a parameter that get
optimized from “outside”
 Heavy use of time discount
(when used for optimization)
IAM examples
• DICE (Nordhaus & al)
• ISGM (MIT)
• ACCL (Banque de
France)
• IMACLIM (Cired)
• GIVE (Berkeley)

Similar Earth Models
ACCL (Banque de France)
GIVE (Greenhouse gas Impact Value Estimator)
MIT Integrated Global System
Modeling (IGSM) Framework
The IGSM framework consists primarily of
two interacting components—the
Economic Projection and Policy Analysis
(EPPA) model and the MIT Earth System
model (MESM). The EPPA model simulates
the evolution of economic, demographic,
trade and technological processes involved
in activities that affect the environment
at multiple scales, from regional to
global.
The Social Cost of Carbon Explorer is a
data tool that allows users to generate
updated estimates of the social cost of
carbon (SCC), which is the dollar
estimate of the economic damages from
emitting one additional ton of carbon
dioxide into the atmosphere. The SCC
Explorer is powered by the open-source
RFF-Berkeley Greenhouse Gas Impact
Value Estimator (GIVE) model which iis
based on Four modules: Socioeconomic,
Climate, Damages, Discounting (for SCC)
IMACLIM (Cired)
IMACLIM-R is a hybrid recursive general
equilibrium model of the world economy
that is split into 12 regions and 12
sectors. The base year of the model is
2001 and it is solved in a yearly time
step. IMACLIM-R is built on the GTAP-6
database that provides, for the year
2001, a balanced Social Accounting
Matrix (SAM) of the world economy. Like
any conventional general equilibrium
model, IMACLIM-R provides a consistent
macroeconomic framework to assess the
energy-economy relationship
It represents the interactions between
sectors and countries over time
through the clearing of commodities
markets
A tool to build climate change scenarios to
forecast Gross Domestic Product (GDP), modelling
both GDP damage due to climate change and the
GDP impact of mitigating measures. It adopts a
supply-side, long-term view, with 2060 and 2100
horizons. It is a global projection tool (30
countries / regions), with assumptions and results
both at the world and the country / regional level.
Five different types of energy inputs are taken
into account according to their CO2 emission
factors., Total Factor Productivity (TFP), which is
a major source of uncertainty on future growth
and hence on CO2 emissions, is endogenously
determined,

Limits to Growth – Club of Rome
 System Dynamic: (Wikipedia Definition)
System dynamics (SD) is an approach to understanding the nonlinear behavior of complex systems over time using
stocks, flows, internal feedback loops, table functions and time delays.
 Highlights from LtG (World3)
 The human economy is now using many critical resources and producing
wastes at rates that are not sustainable. Sources are being depleted. Sinks
are filling and, in some cases, overflowing.
 There is such an enormous amount of coal that we believe its use will be
limited by the atmospheric sink for carbon dioxide. Oil may be limited at
both ends
 World3 is a model designed to explore the behavior modes of an
interconnected, nonlinear, delayed-response, limited system. It is not
intended to spell out an exact prediction for the future or a detailed plan for
action
 Gaya Herington, “Five Insights for avoiding Global Collapse”
 Post-validation of LtG model, 30 years later …
 Earth for All: A Survival Guide for Humanity
 Two novelties included in the model are the Social Tension Index and the
Average Wellbeing Index.
Approximative difference between IAMs & SDEM
• IAMs are data-driven (calibrated from past data)
• Risk of overfitting when projected in the next century
• SDEM are designed from « first principles »
• Crude calibration / focus on orders of magnitude

Global Warming Impact : The Unknown Unknown
 A synthesis of hundreds of
published research articles
 Compared to the trajectory of economic
growth with no climate change, their
average projection is for a 23 percent loss
in per capita earning globally by the end
of this century
 Which means that if the planet is five
degrees warmer at the end of the century,
when projections suggest we may have
as many as 50 percent more people to
feed, we may also have 50 percent less
grain to give them
 We will, almost certainly, avoid eight
degrees of warming; in fact, several
recent papers have suggested the
climate is actually less sensitive to
emissions than we’d thought, and
that even the upper bound of a
business-as-usual path would bring
us to about five degrees, with a likely
destination around four.
Simplified categories of impacts
• Destruction of properties
• Health – loss of productive workforce
• Lack of water
• Loss of agricutural surface
• Loss of efficiency
Canicules
Droughts
Lack of
water
Floods
inc. coastal
Fires
Compassion
WW misery
Fear
Future
impact
Pain Job &
Property loss
Death & Severe Health
Issues
Population Displacements
Agriculture
Losses
Economy Hits
loss of assets &
workforce
M4: Loss of
productive
resources
M5:redirection

CCEM : Addressing Five “Known Unknowns”
« How much energy will be available in the
future ? At which costs? »
« How much energy is needed and acceptable
for the economy at a given cost ?»
Example:
At which speed can we add clean
energy in the next 30 years ?
EIA
« How fast can we substitute one form of
primary energy to another ? »
« What will be the economical and societal
consequences from the IPCCs predicted
global warming ?»
« which GDP growth can be expected from
investment, technology, energy
and workforce ? »
Example:
- How much energy subvention
must/can governments afford ?
Energy
To
GDP
Example:
What is the possible speed of
transition fossil>green for industry ?
2050
Eco
transition
Plan
Example:
Impact of reduced energy availability
on economical output ?
GDP
2050
Example:
- which damage to productive
resources ?
- Which redirection caused by fear ?
Temp
to GDP
loss

Part 2
 Preliminary Silulations
4. Next Steps

GWDG Dynamic System
Production
Consumption
Economy
Gaia
inventory
capacity
revenue
Conso
CO2 tax
Societal
Pressure
CO2
emissions
Unknown Model
IPCC Forecasts
Temperature
Water rise
GDP/
person
demography
+
+
-
-
Price
cost
needs
Equivalent
Consumption
Invest E
GDP
M4
World
Economy
Investments
Growth Invest
M1
supply
M2
demand
M3
Energy
transition
M5
Ecological
Redirection
delay
delay
delay
redistribution
renouncement
+
+
4 instances
• Oil
• Gas
• Coal
• Clean
4 instances:
• US
• Europe
• China
• Rest of
World
savings
cancel
Tech
Progress
substitution
Rate of CO2
catastrophies
crises
4 instances:
• US
• Europe
• China
• Rest of
World
Wheat
Steel
Food/`
person
Land Use
protectionism

Energy Resource Model (M1)
M1 captures the answer to the questions « How much fossil resources do we have ? At which costs? »
Four categories
 Oil
 Natural Gas
 Coal
 Clean (hydro/solar/wind/nuclear)
Each resource is defined through:
 For fossil energies, its inventory chart
(available Toe according to sell price)
 For clean energies, a growth potential curve
(max capacity in the future year, according to
manufacturing and resource constraints)
 A “max capacity” (max yearly output)
 A constraint about the speed at which this capacity
may evolve + a heuristic formula that adjusts the
capacity each year
GToe
Price : €/Toe
410$
242
Gtoe/y
Price : €/Toe
410$
Fossil Fuel Production = f(price)
Max capacity = min (c0 x In/I0,
cn-1 x min( maxGrowth,
expectedGrowth)
Local price elasticity
4 Gt
cmax
Gtoe/y
Price : €/Toe
$
Clean Energy Production = f(price)
Max capacity =
cn-1 x min( maxGrowth,
expectedGrowth)
unconstrained target price trends
follows world GDP

M1: Energy Production
Parameters
Equations (functions & differential state)
Data Model
Two kinds of sources of primary energy (e):
• FossilFuels :Oil, Goal, Gas
• One combined “Clean” (nuclear & renewable)
Energy sources are described through the max
capacity (that varies), the yearly output (depending on
supply-demand) and, for fossil fuels, the known
reserves
The main component of M1 is the Supply equation that
describes output as a function of price
Supply(e:Fossil,p,Cmax) = min(Cmax, max(0,Oe(1) * min(1,(Cmax / Ce(1))) *
(Pe(1) + (p – Pe(1)) * sensitivity(e)) / Pe(1))
State Variables:
• Oe(y): output (production) in Gtoe
for energy e at year y
• Ce(y): max capacity in Gtoe for energy e
• Ae(y): added capacity for energy e
through transfers (M3)
• tOe(y): total output in Gtoe from years 1 to y
• Pe(y): price in $ for 1 toe for energy e at year y
• UDz(y): demand (unconstrained consumption) for
zone z of energy e
• Gz(y): gdp for zone z on year y
• maxCapacityGrowth(e,y) : for clean energy y, expected max caoacity in Gtoe that may be added during
year y (yearly production)
• Inventory(e,p) : expected reserves (at year 1) for fossil fuel e with a market price p
• threshold(e) : part of current reserve when suppliers of e reduce their output to match reserves (strong
influence on PeakOil date)
• targetMaxRatio(e) : expected ratio between (max) capacity and output
• maxGrowthRate(e): percentage of capacity that can be added at most in a year for fossil e
• sensitivity(e) : price sensitivity factor for energy e
• co2perTon(e) : CO2 emissions to produce one toe of energy e
Supply(e:Green,p,Cmax) = min(Cmax,
(Cmax * targetMaxRatio(e) * (p / (Pe(1) * (1 + ( G(y-1) / G(1)) * sensitivity(e)))
Capacity(e:Fossil,y,p) =
min( min(expectedOutput(e,y), Ce(y – 1) * (1 + maxGrowthRate(e)) + Ae(y-)),
Ce(y – 1) * ( Inventory(e,p) - tOe(y – 1))/ threshold(e)))
Capacity(e:Green,y,p) =
min(expectedOutput(e,y), Ce(y – 1) + maxCapacityGrowthRate(e,y) + Ae(y-1)),
Belief: Known Unknowns
expectedOutput(e,y) =
[Sz in zone linearRegression(UDz(y-3), UDz(y-2) UDz(y-1)) ] * targetMaxRatio(e)
Data-Driven Parameters

Energy Consumption Model (M2)
M2 captures the answer to the question
« How much energy is needed for the economy at a given cost ?»
The heart of this model is (for each source & each zone)
a histogram of value production:
 Decomposition of value product (Y axis)
 Over “segments” of energy usage (X axis), sorted by energy
intensity
 This (virtual) decomposition is the base for telling how each world
zone will react to price increases
The net behavior is represented by four curves :
 Economy dematerialization trend (kW/$)
 Cancelation (% of activity that stops because price is too high)
 Economic loss due to cancelation (GDP impact of cancel)
 Margin reduction
In addition, we represent the expected efficiency gains:
 “Savings“ (energy efficiency) – reduction of consumption at iso-activity
 Savings are a “policy” (decision ahead of time that gets implemented)
 Substitution towards another form of energy (using the matrix provided by M3)
 The last two options triggers associated investments
Energy redistribution policy is a factor that lowers the pain of cancellation but
reduces the economic efficiency
Energy consumption for a given price
decreases according to cancelation
(upper histogram), energy savings and
substitution (M3: one energy source to
another)
Value (GDP) of each slice of
economy sorted by value/toe
Value
(T$)
100%
Current
Cost of
energy
Energy
consumption
Price / time
100%
p0
The loss of economic
value due to
Energy-based
cancellation follows
a convex law (lower
value creation
activities stop first)
Evolution of
distribution
represents the
dematerialization
of the zone economy
(kW/$)
Price / time
100%
Cancel Rate
100%
GDP
impact
Margins for
surviving
activities are
reduced by
increasing energy
prices

M2: Energy Consumption
Parameters
Data Model
• Four Energy sources, Four zones : EU,US, CN, RoW
• M2 is based on analyzing the gdp production
through “homogeneous slices” to state 4 beliefs:
Energy density, cancel, GDP & margin impact
• M2 factors efficiency gains through technology
through the “saving” parameter for each zone
• M3 described the “energy transition” that transfers
some of the needs from one energy source to
another
Rz(e,y) = Uz(e,1) * economyRatio(z,y) * (1 – dematerialize(e,y))
* populationRatio(z,y) * (1 - GWz(y-1))
populationRatio(z,y) = 1 + (population(z,y) / population(z,1) – 1) * pop2energy(z)
State Variables:
• Rz(e,y): raw needs for energy e in Gtoe at year y
(before efficiency or transition is applied)
• Nz(e,y): needs for energy e in zone z during year y
once energy transition transfers are applied
• Tr(e1,e2,y): fraction of energy e1 demand that has
been transferred to energy source e2 at year y
• Uz(e,y): usage (constrained consumption) for zone z
of energy e
• Pe(y): Price for energy e ($/toe) at year y
• Sz(y): percentage of savings reached at year y
• GWz(y): percentage of capacity lost because of
global warming, cumulative to year y
• cancel(z,p) : share (percentage) of economy for zone z if the oil price equivalent reaches p
• impact(z,p) : associated impact on gdp (output of the remaining activities) when price is p
• population(z,y) : expected population of zone z at year y
• dematerialize(e,y) : expected decline in energy density (gdp/conso) for zone z
• savings(e,y) : share (percent) of energy that can be saved (efficiency) with iso-output
Nz(e,y) = Rz(e,y) + Se1<e Rz(e1,y) * Tr(e1,e,y) - Se<e2 Rz(e2,y) * Tr(e,e2,y)
Demand(e,z,y,p) = Nz(e,y) * (1 – Sz(y - 1) – cancel(z,p))
Demand(e,y,p) = Sz Demand(e,z,y,p)
Pe(y) = ! p | Demand(e,y,p) = Supply(e,y,p)
Belief
Ce(y) = max(Ce(y-1) , Capacity(e,y, Pe(y)))
Oe(y) = Sz Supply(e,z,y,p)
Data-driven
• economyRatio(z,y) : heuritiscs that combines the expected growth of the zone gdp (from the
amount of past investments) and the mutual influence of zones through global trade
• pop2energy(z): ratio between energy consumption growth and population growth

Energy Transition Model (M3)
M3 captures the answer to « How fast can we substitute one form of primary energy to another ? »
Substitution matrix
 Oil to Coal to Gas to Clean
 6 flows (N x N-1 / 2)
 A substitution matrix as 6 coefficients (share of
energy consumption that should be transitioned),
depending on year (policy)
 The matrix takes into account the “source to vector”
possible paths (cf. illustration) – It should also factor
the constraints from natural resources such as steel.
Mobile storage
electricity Industry
transportation
Heat
Oll & Natural Gas
Coal
Clean Energy
Static storage &
distributed
Vectors
The substitution matrix describes which substitution is feasible &
desirable from an energy policy viewpoint (on the demand side)
 Irreversible
 When acted (a given year), generate the associated Investment
(same for savings)
Note: Models M1 / M2 focus on primary energy sources, M3 takes
the energy vectors (electricity, hydrogen, …) into account to define
which transitions are feasible
Substitution
Matrix
Changes
Energy
Source
Demand
New
Capacities
and
transfer
Reflects the
Energy
Transition
policy
Speed of
changed is
capped (max
from M1)
Energy demand
(M2) is balanced
between 4 sources

M3: Energy Transition
Parameters
Data Model
Energy sources are ordered
• Oil < Coal < Gas < Clean
• Yielding 6 transitions (e1 -> e2)
The energy transition is a time-dependant
matrix that represent the possible transfer of
one primary source another (thanks to industrial
investments or the use of vectors such as
electricity)
Uz(e,y) = Nz(e,y) * (1 – savings(z,y - 1) – cancel(z, Pe(y)))
State Variables:
• Pe(y): price in $ for 1 toe for energy e at year y
• Uz(e,y): usage (constrained consumption) for zone z
of energy e
• Sz(y): percentage of savings reached at year y
• CNz(y): percentage of consommation canceled in
zone z at year y, because the price is too high
• IEz(y) : investments for new energy capacity for
energy source z at year y
• SP(y): steel price for year y
• transitionRate(z,e1,e2, y) : maximum transfer of energy needs from primary source e1 to e2
at year y, expressed as a percent
Sz(y) = max(Sz(y-1) , savings(z, Pe(y)))
CNz(y) = max(cancels(z, Pe(y))
Tr(e1,e2,y,) = max(Tr(e1,e2,y-1),
min(transitionRate(z,e1,e2,y), max(Tr(e1,e2,y-1) + maxGrowthRate(e))
IEz(y) = [ (Se max(0, Ce(y) - Ce(y-1)) * (Uz(e,y) / Sz1 Uz1(e,y)) +
Se (Nz(e,y) * max(0, S(y) - STr(e1,e2,y))) +
Se1<e2 Nz(e2,y) * max(0, (Tr(e1,e2,y) - (Tr(e1,e2,y-1))) ] *
investPrice(s) * (1 – sf(e) + (sf(e) * SP(y) / SP(1)) * (1 – ftech) y *
• techEfficiency(z) : yearly growth of tech efficiency (cost reduction in investment to build a
production capacity)
• investPrice(e) : investment that is necessary to build a capacity of 1Gtoe/y at year 1
• ftech(z) : expected yearly decline of investPrice in zone z (technology progress)
• steelFactor(e) : part of steel cost in total cost of investment for e
Belief
Data-driven

GDP Model (M4, World Economy)
M4 represents the question:
« which GDP is produced from investment, technology, energy and workforce ? »
Description
Economy is seen as a set of productive assets that
require energy and human capital to operate
Economy growth require investments that are a
fraction of results
We use a crude exponential growth model
• Output is linked to energy (cf. M2 + redistribution)
• Demography is factored through energy consumption
• Assets grow as a result of investments
• Energy transition investments are subtracted from total investments to
compute growth investments
• GW Crises are modeled two ways : a reduction of productive assets and as
”redirections of zone policies” (M5)
• The model computes the consumption without savings that drives the GDP and
the consumption with savings that drives CO2 emissions
• This model is applied to 4 “Blocks” : US, CN, EU, RoW
Productive
Assets
GDP
(Results)
Investments
Energy
Supply (Es)
population
Tech
Innovation
Energy transition
Growth
Invest
Global Warming
Natural Disasters
Loss of resources (people, land, factories …)
Energy
Demand
US
T$ 15
CN
T$ 6
EU
T$ 14.5
RoW
T$ 30
248
360
167 900 1080
1200
1300
90
2010 world economy crude decomposition (trade in G$)

M4: Physical versus Immaterial GDP
 The model uses “current dollars” as monetary unit (for GDP and energy price)
 “2100 dollars” is an abstract notion …
 High GDP growth in the past 30 years reflects the growing importance of “immaterial”
economy
 The “CCEM4” model (4th iteration) adds two outputs to evaluate the “material” side:
Steel production (proxy of material goods) Wheat production (proxy of Agriculture)
Energy
Resource
Energy
extraction
(M2)
Energy
Production
Iron
Resource
Ore
extraction
+ process
Iron
production
GDP
production
(M4’)
New
Energy
Capacity
Grain
Production
(M4’)
Agriculture
Land use
Catastrophes
Global
Warming
(M5)
Grain
production
/ inhabitant
GDP production
(M4)
Living
Health
Energy
Production
Agro
Efficiency
CO2
concentration
Global
Mood (M5)

M4: World Economy
Parameters
Data Model
Computes two trajectories
- expected gdp (maxout) without energy constraints
- gdp = constrained growth because of cancellation
GDP is produced from assets that grows according to
investments but require energy
Investments are a share of GDP that is reduced two
ways
- when energy price goes up, margins reduce
- activities that are cancelled require social
management which impairs the ability to invest
Mz(y) = Mz(y - 1) * (population(z,y) / population(z,y - 1)) * dGWz (y) + IGz(y - 1) * roi(z,y)
State Variables:
• Mz(y): theoretiocal “maxoutput” for zone z = gdp that
would have occurred if all necessary energy was
here
• Gz(y): gdp for zone z on year y (G(y) = Sz Gz(y)
• Iz(y): amounts of investments
• IGz(y): amounts of investments
• SCz(y): steel consummation for zone z at year y
• SP(y): steel price for year y
• IRatio(z) : part of gdp that zone z attributes to investments
• iRevenue(z): share of revenue that is invested
• Energy4steel(y) : energy needed to produce one ton of steel in year y
Gz(y) = Mz(y ) * (1 - impactCancel(z,p))
Iz(y) = Gz(y) * iRevenue(z) * (1 – margin(z,oilEquivent(y)) * (1 - impactCancel(z,p))
IGz (y) = Iz(y) - IEz(y)
oilEquivalent(y) = (SePe(y) * Poil(1) * Oe(y) / Pe(1)) / = (Sc Oe(y))
SCz(y) = Gz(y) / ironDensity(z,y)
Belief
SP(y) = SP(1) * (oilEquivalent(y) * energy4steel(y))/ (oilEquivalent(1)) * energy4steel(1))
Policy
• impact(z,p) : impact of cancel on gdp n zone z when oil-equivalent price is p
• margin(z,p) : impact on profits for remaining activities of zone z when oil-equivalent price is p
• roi(z,y) : expected return on investment (R/I) = additional gdp expected R for investment I
in future year y for zone z
• disasterLoss(z,T) : loss of gdp (%) when temperature raises to T
• ironDensity(z,y): density of iron in z economy (gdp / Gt of steel)
impactCancel(z,p) = alpha(z,y) * (CNz(y) / Uz(y) + Sz(y) + CNz(y) +
(1 – alpha(z,y)) * impact(z,OPe(y))
• Alpha(z,t) : fraction of energy that is “redistributed” with subsidy (versus free market)
dGWz(y) = (1 - GWz(y)) / (1 - GWz(y - 1))
GWz(y) = disasterLoss(T(y – 1))

Ecological Redirection (M5)
M5 answers the question « What kinds of redirection should we
expect from the IPCCs global warming consequences ?»
Bruno Latour’s redirection concept tells that this is a non-
linear coupling.
There is no “point A to point B” trajectory, but reactions along
the way, based on the catastrophic events that will unfold
M5 is made of three components:
 A simple projection from IPCC to link CO2 output (from M2-M3) to
expected temperature rise (using RCP 4.5, 6 and 8.5)
 A random, discrete function that define “pain thresholds” as CO2 &
temperature rise
 A redirection model (very naïve) with three components
 Increase into energy redistribution (feedback to M2)
 Increase CO2 tax (versus planned trajectory)
 Economic crisis (feedback to M4)
 Production capability damaged by warming
(e.g. agriculture)
 Workforce disruption (from strikes to massive death tolls of
natural catastrophes and wars)
IPCC model extraction T = f(CO2)
CO2 concentration
« pains » : weather
catastrophes and
cost of living
« Redirection »
Energy
Redistribution
& cancel
acceleration
Economy
Damage
(loss of resource)
CO2 Tax
Acceleration
Transition
to Green
acceleration
time
CO2(PPM)
Close Economy Branches
Température (C°)
catastrophe
catastrophe
Three drivers : fear (of future production loss), pain (less
revenue) and compassion (disaster happening elsewhere)

M5: Ecological Redirection
Parameters
Data Model
We compute multiple impacts of CO2 emissions:
• Average temperature elevation
• Total Area used for agriculture
• Wheat Output (a proxy of agriculture output)
• Reduction of gdp due to global warming
• Pain due to global warming
From the zone level of pain, we compute ecological
redirection according to each zone policies, impacting
CO2 tax, sobriety (cancel) and energy transition
acceleration
CO2(y) = (Se Oe(y) * co2perTon(e)) / co2Energy
CO2ppm(y) = CO2ppm(y-1) + (CO2(y) – co2Neutral) * eCO2Ratio
State Variables:
• 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)
• co2Neutral : level of emissions that is approximately balanced by nature
• co2Energy: percentage of CO2 emission due to fossile 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
Belief Policy
• pain2Tax(z,p) : Policy for zone z that links elevated pain level p to a percentage CO2 tax
• 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
T(y) = T(1) + (IPCC(CO2(y)) – IPCC(CO2(1)))
PAINz(y) = painProfile(z) . (painFromClimate(T(y)) ,
(Cnz(y) x (1 – Alpha(z)),
satisfaction(z, WO(y) – WO(y-1), (Gz(y) - Gz(y-1)) / Popz(y)))
TaxFz(y) = pain2Tax(z, PAINz(y))
CnFz(y) = pain2cancel(z, PAINz(y))
TrFz(y) = pain2transition(z, PAINz(y))
ES(y) = ES(y – 1) + DCclean(y) * landEImpact(y)
AS(y) = (AS(y1) – ES(y)) * (1 – landLossWarming(T(y)))
WO(y) = WO(1) * ↑AS(y) * ↑aggroEfficiency(oilEquivalent(y)) * bioHealth(y,T(y))
• 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
↑F(y) = F(y)/F(1)

M5: Ecological Redirection Feedback
 3 loops (one large aggregation)
CO2 ↗ T (C°) ↗
M2
Less energy
available
Loop 1: T to ”pain” to reaction
M4 Loss of
productive
resources Loop 2: T to ”destruction”
to economy loss
M4 M2
CO2
tax ↗
cancel
renunciation
↗
Transition to
clean energy
↗
Composite Pain
Loop 3: Economy contraction
to pain to reaction canicules
droughts
floods
fires
Compassion
WW misery
Fear
Future impact
Pain Job &
Property loss
Death
Displacements
Agriculture
Losses
Economy
Hits
Aggregated into “T to pain” abstraction

Part 3
4. Next Steps

CCEM : Simulation Model
 Each model M1 to M5 represents a discrete one-year difference equation
 Inputs: some of the state variables (at year n – 1)
 Outputs: some of state variables (M1 to M5 partitioning)
 10 to 30 lines of code (each)
2010
State of the
world
Energy
Sources
Zones World
Earth N = 40,90, … times
2050 / 2100 / …
State(i) = ƒ (state(i-1),*)
M1 M2 M3 M4 M5
Outcome = time-series
GDP
CO2
Energy

CCEM : Six KNUs (Key kNown Unknowns)
 These 6 KPI provide the best characterization of the CCEM “known unknowns”
 what creates the heavier debate, for instance speed of Clean energy growth vs fossil reserve
 These KPI can be compared with other published values from prospective institutes 
 When looking at a simulated forecast, one should always ask for these 6 hypotheses
Clean Energy Growth Rate
KPI1: PWh added in 10 years
Default value : 13 PWh
IRINA 1.5C scenario: 25 PWh
Energy Intensity
KPI2: CAGR decrease of E/GDP
Default value : 1.2% (2010-2050)
1.4% between 1990 and 2022
IRINA 1.5C scenario: 2.7%
Energy to price elasticity
KPI3: long-term elasticity demand to price
Default value : -0.3
Values from Reed : -0.05 short-
term and -0.3 long-term
Electrification of Energy
KPI4: electricity(TWh) / total energy
Default value : 48% in 2050
16% in 2020
IRINA 1.5C scenario: 80%
Return on Investment
KPI5: world average of RoI
(yearly GDP increase / investment)
Default value : 9.3% (2010-2050)
Calibrated from past + guess 
Global Warming Impact
KPI6: GW damages, as % of GDP for +3C
Default value : -6.7% at +2.6C
approximate SCC at 270$/t
Values picked from Schroders: 8% at 3C

“Yves Belief” Scenario (WIP)
Beware of
“immaterial
” dollars
Inertia of
non-electric
fossil energy
Growth of
immaterial
service
economy
Reflects
latest
forecasts
6.6 7.3 7.8 8.4 9 9.1 9.2 9.3 9.4 9.3 9.2
240 238.5
232.3
223
211.8
204.9
196.8
184
172.6
160.6
144.8
319.9
220.1
189.5
164.7
144.1
119.6
108.2
96
85.2
75.1
65
51
91.2
118.4
151.5
181.4
199.8
212.9
223.7
241.9
263.1
284.6
0
50
100
150
200
250
300
350
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Kaya Identity
Pop (G) gCO2/KWh e-intensity (kWh/$) / 10 GDP/p (100$)
33.8
66
86
110
132
145 155 163
176
192
207
389.2
527
589
656
687
628
605
564
542
519
486
14.5 14.6 14.8 15.1 15.5 15.8 16.1 16.3 16.4 16.4 16.4
25 34 38.3 41 40.7 36 33.3 29 26.1 23.3 19.7
0
100
200
300
400
500
600
700
800
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Median Scenario
GDP (T$) Energy (EJ) Temperature(C) CO2(Gt/y)
CO2 @
595ppm

Sensitivity Analysis for Key Beliefs
Fossil
Energy
Influence of estimated
reserve @ price
Open or limit the
growth of Coal
Very strong influence both on final GDP and CO2 RCP
Large influence on China, important to curtain CO2
Transition
to clean
energy
Rate of possible clean
TW.h additions
Speed of Energy
transition (move to e)
Heavily debated, strong influence on GDP if serious about CO2 reduction
(versus Coal) – Breakthrough (fusion) impact is dominated by transition …
Strong inertial factor, that makes “Accord de Paris” unrealistic, but for a
major loss of GDP (order of magnitude : -50%, not -3%)
Efficiency and
Sobriety
(cancel)
Technology capacity to
increase efficiency
Sensibility of the
cancellation model
Large influence, but not major (unless a complete breakthrough happens …
but large diversity of use cases)
Important but not major – still one of the difficult “known unknown” to
forecast over the 21st century
Growth &
Price sensitivity
Sensibility of growth
model
Impact of price
elasticity parameters
Very large influence of projected GDP, less on CO2 emissions
Moderate influence since energy price is mostly a signal in CCEM to adjust
supply and demand (feedback loop on steel price)

Sensitivity Analysis : Fossil Fuel Reserves The amount of fossil energy
is a key driver to the global
warming
The impact is high for US and
Europe, less for China who
rely on coal and green energy
The speed at which green
energy capabilities can be
added (belief) is critical in
the low fossil fuel scenario
The other critical belief is
the speed of the possible
energy transition (switching
“primary sources”) since
fossil energies is close to 80%
today
33.8
66
86
108
119
131 140
152
166
181
199
389.2
527
588
634
615
567
554
544 536
517
499
14.5 14.6 14.8 15.1 15.5 15.7 15.9 16.1 16.3 16.4 16.4
25 34 38.3 39.4 36.3 32.3 30.2 28.3 26.4 23.8 21.4
0
100
200
300
400
500
600
700
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Low Fossile Reserves
33.8
66
86
113
143
171
194
209
227
243
263
389.2
527
589
681
776 778
801
769
743
692
652
14.5 14.6 14.8 15.2 15.6 16 16.3 16.5 16.6 16.7 16.7
25 34 38.3 42.7 46.3 44.9 45.1 41.5 38.2 33.5 29.6
0
100
200
300
400
500
600
700
800
900
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
High Fossile Reserves

Sensitivity Analysis : Carbon Tax Carbon tax works to reduce
the output of fossil energy,
resulting in improved
warming …
At a strong cost on GDP
growth …
T$ 224 -> T$ 209 -> T$ 175
(2100 GDP)
Because of its energy density,
the Chinese economy would
be the most impacted:
T$ 69 -> T$ 52 -> T$ 20
This simulation with a
homogeneous Carbon tax
throughout the world is
probably unrealistic
The relative positioning of
Zone economies (without
taxes and with energy) is a
belief (input parameter)
33.8
66
83
106
125
142
152
164
176
190
209
389.2
527
550
618
632
602
582
564
538
506
487
14.5 14.6 14.8 15.1 15.4 15.7 15.9 16.2 16.3 16.4 16.4
25
34 35.5 38.3 37.5 34.2 31.7 29.3 26.1 22.5 19.8
0
100
200
300
400
500
600
700
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Low Carbon Tax (80$/t)
33.8
66
78
95 102
126
140
148
156
167
179
389.2
527
499
523
483
512
523
489
455
427
395
14.5 14.6 14.7 15 15.2 15.4 15.5 15.7 15.8 15.9 15.9
25
34 32 32 27.1 29 28.5 25 21.5 18.4 15.1
0
100
200
300
400
500
600
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
High Carbon Tax (400 to 600 $/t)

Exploring beliefs (without redirection)
 These are the outcome associated to three ”typical” sets of “beliefs”.
High estimates of fossil reserves
Goal production constant growth allowed
Moderate transition efforts
More efficiency gains and accelerated
cost of technology decline
Accelerated energy transition
Moderate CO2 tax (300)
Block Coal production growth,
sets a high CO2 tax at 400+$/t
accelerate green transition
promotes sobriety through regulation
33.8
66
86
112
140
172
188 197 206
223 227
389.2
527
599
700
797
843 848
816
777 769
695
14.5 14.6 14.8 15.2 15.6 16.1 16.4 16.6 16.7 16.8 16.9
25 34 39.2 44.6 48.9 50.8 50.3 46.4 41.7 39.8 33.8
0
100
200
300
400
500
600
700
800
900
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Energy-Rich Scenario (+3 C°)
33.8
66
86 93
108
127 135 145
160
179
203
389.2
527
576
502 507 495
469
436
423
409 409
14.5 14.6 14.8 15 15.2 15.4 15.5 15.6 15.6 15.6 15.6
25 34 37.2 29.8 27.6 25.9 22.7 19 16.4 14.1 12.6
0
100
200
300
400
500
600
700
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
"Stick to Paris Agreement" (+1.7C°)
33.8
66
87
101
120
142
160
183
207
234
267
389.2
527
578
540 548
530 522 525 513
485
459
14.5 14.6 14.8 15 15.3 15.5 15.6 15.8 15.9 15.9 15.9
25 34 37.3 32 29.4 27.9 25.7 24.2 21.5 18.4 15.5
0
100
200
300
400
500
600
700
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Exponential Technologies Scenario
(+2C°)

Earth Model : A Digital Twin to Question your Mental Model
From Beliefs to Simulation to Outcomes
Beliefs
• Energy assets
• Savings roadmap
• GDP Energy-
elasticity
• Global Warming
impacts
• Expected growth if
resources
Foundations
• CO2 -> temperature (IPCC)
• Assets x Energy -> GDP -> investments -> delta(assets)
• Production to Demand adjust through prices
What you
Give as
An input
Do not use
CCEM if you
disagree
Levers
• Energy Transition roadmap
• CO2 Tax
• Redistribution
Outcome
N
iterations
What you
Play with during
simulation
True value : revisit your beliefs from observing outcomes
GTES
Game-Theory
Evolutionary Simulation
Use the Digital Twin:
• To challenge your beliefs
• To experience feedback loops
• To play with policies
A ”coarse” model does not make
you smarter, but less stupid 

Part 4
4. Next Steps

Global Warming Impact : The Unknown Unknown
 A synthesis of hundreds of published research articles
 Compared to the trajectory of economic growth with no climate change, their average projection is for a 23 percent
loss in per capita earning globally by the end of this century
 Warmer oceans can absorb less heat, which means more stays in the air, and contain less oxygen, which is doom
for phytoplankton—which does for the ocean what plants do on land, eating carbon and producing oxygen—which
leaves us with more carbon, which heats the planet further. And so on. These are the systems climate scientists call
“feedbacks”; there are more
 Which means that if the planet is five degrees warmer at the end of the century, when projections suggest we may
have as many as 50 percent more people to feed, we may also have 50 percent less grain to give them
 We will, almost certainly, avoid eight degrees of warming; in fact, several recent papers have suggested the
climate is actually less sensitive to emissions than we’d thought, and that even the upper bound of a business-
as-usual path would bring us to about five degrees, with a likely destination around four.
 “Climate tipping points - too risky to bet against”
 Lenton & al, Nature 2019
 Main reference for Stern, Stiglitz & Taylor
 Politicians, economists and even some natural scientists have tended to assume that tipping points in the Earth
system — such as the loss of the Amazon rainforest or the West Antarctic ice sheet — are of low probability and
little understood. Yet evidence is mounting that these events could be more likely than was thought ….
 Models suggest that the Greenland ice sheet could be doomed at 1.5 °C of warming, which could happen as soon
as 2030. Thus, we might already have committed future generations to living with sea-level rises of around 10 m
over thousands of years. …. At 1.5 °C, it could take 10,000 years to unfold3; above 2 °C it could take less than
1,000 years

IPCC AR6 (2023) Climate Change & its Working Group
WG2 & WG3: full of surprising beliefs …
Scenarios & RPC
• P127 : Shared Socio-Economic Pathways
summary in box SPM1 page 10
• 50-55 GtCO2-eq in 2030 – iso 2015, to be confirmed 
Impact (WG II)
• Close to zero « dollar impact figures » - cf page 14.
Why the world listen to « crazy optimistic IAM »
simulations  ….
Mitigation
• Solar and Wind Mitigation potential for 2030 seems over-estimated (CCEM Belief #2)
page 27 : 8 GtC02 saved in 2030 => remove 2.7 Gtep fossil (average)
=> 10 times the capacity added from 2010 to 2020 (all clean energies combined)
• Page 54 : simplistic view of energy costs (without vector or storage impact)
• Zero recommendation of CO2 tax (same comment about IAMs)

Global Warming Impact and SCC (Social Cost of Carbon)
 Social Cost of Carbon
 Wikipedia: The social cost of carbon (SCC) is the marginal cost of the impacts
caused by emitting one extra ton of carbon emissions at any point in time.
The purpose of putting a price on a ton of emitted CO2 is to aid people in
evaluating whether adjustments to curb climate change are justified.
 Range of price : 50$ to 500$/t (100-200$/t is the current preferred estimate)
 Link with companies “benchmark price” of CO2
 ”Comprehensive evidence implies a higher social cost of CO2”
 Rennert & al, Nature 2022
 SCC at 185$/t, mostly agriculture and mortality
 Very wide dispersion of agro-impact (FUND model,
from Canada to Southeast Asia)
 SCC is computed by Monte-Carlo (naïve) simulation
 Simulations are based on GIVE model
 Damages (simple interpolation of published tables )
– Health (Cromar et al), Agriculture (Moore et al),
Energy dropdown (Clark et al),
Coastal impacts (small, cf Diaz)

Social Cost of Carbon (SCC) and IAMs
 “The economics of immense risk, urgent action and radical change:
towards new approaches to the economics of climate change”
 Stern, Stiglitz and Taylor, 2022
 Our first task in this paper is to argue that, as a methodological approach, the optimization framework embodied in
IAMs is inadequate to capture deep uncertainty and extreme risk, involving potential loss of lives and livelihoods
on immense scale and fundamental transformation and destruction of our natural environment
 Damage functions, where impacts can be immense and there are large irreversibilities (the importance of which is
limited in the absence of uncertainty), non-linearities, and complex feedback effects, giving rise to tipping points
 The absence of a scientific basis to estimate probabilities of outcomes associated, say with climate change of 3.5
degrees Celsius, well beyond anything experienced, combined with the sensitivity of IAM analyses to those
probabilities, in turn has profound implications for the policy relevance of IAMs: they provide no guidance on how
to resolve differences in key judgements around risk and uncertainty
 The conservative/incomplete nature of impact assessment in IAM
is well-documented
 Swiss Re Institute
 -11% in 2050 at +2C, -14% at +2.6C, -18% at +3.2C
 Rule of thumb applied to Moody’s model : x 10 
 Moody’s “The Economic Implication of Climate Change”, 2019
 For US, equivalent to Nordhaus’s finding !
+1.5C : 0.7% impact on GDP, 2C: 1.3%,4C:3.6%
 The world map is interesting

CBAM (Carbon Border Adjustment Mechanism)
and Game Theory
 a policy tool designed by the European Union to mitigate the risk of carbon
leakage, where companies might move carbon-intensive production to
countries with looser emission constraints, or where imported goods are
cheaper because they are produced with higher carbon emissions, compared
to goods made within the EU. Here's a breakdown of how CBAM works:
 CBAM requires importers of certain goods into the EU to pay a carbon price. This price is intended to be equivalent to the carbon price that
would have been paid if the goods were produced under the EU's carbon pricing rules
 The mechanism calculates the carbon cost based on the greenhouse gas emissions embedded in the imported good
 During the initial phase, companies importing goods into the EU will need to start reporting emissions for these goods. Eventually, they will
have to comply by purchasing carbon certificates corresponding to those emissions
 Critical for Michelin, especially because of the two steps process (raw materials
before finished goods) which receiving heavy criticism (CBAM is not adopted yet)
 How can players influence each others ? To promote cleaner energy sources ?
 Positive (part of model) : Balance of Trade export economy growth
 Protectionism and trade barriers : key, but hard to evaluate (2024 goal for CCEM v5)
 CBAM : better (more specific) but difficult to implement

Global Warming, Geopolitics and Game-Theory
Sampling
Monte-Carlo
Search for Nash
Equilibriums
Machine Learning
Local
optimization
GTES
parametric analysis
Global
Parameterized
Optimization
Problem
Parameters
Strategy
External
Tactical
Non-cooperative
Repeated
Game
Strategic analysis of the
player’s goals
Classification
Taking the uncertainty of the
model into account
Actors
Context
GTES (game-theoretical evolutionary simulation) is a proven framework:
 For complex systems with “known unknowns”
 To look for possible Nash equilibriums …
 … to explore the interplay of beliefs
An approach inspired by Robert Axelrod pioneering work on Agent-based models of
cooperation & competition
 E.g.; experimental/evolutionary validation of TIT-for-TAT strategy in a repeated prisoner dilemma game
 Developed for Telco market competition simulation (3G, 4G, Free) and other complex SD models
Yves Caseau – 2014 – Serious Games as a Tool to Understand Complexity in Market Competition 9/42
Game Theoretical Evolutionary Simulation (GTES)
GTES is a tool for looking at a complex
model with too many unknowns
Problem
(fuzzy,
complex,
…)
Abstrac-
tions
Model:
Set of
equations with
too many
unknown
parameters !
Split
parameters
« Players »
Environment
(DIP)
Strategy (DDP)
Tactical (DV)
“tactical” may
be derived from
“strategy”
(local
optimization)
Parameters which
describe the
player’s goals
eParameters
sParameters
Parameters which are
meaningful (e.g., oil
price future)
Scenario-defined
Obscure &
unknown
randomize
Game Theoretical
Approach
Player’s degrees of
freedom
Wolter
Fabrycky:
DDP/DIP/DV
Part
II
:
GTES
(
Game
Theoretical
Evolutionary
Simulation
)

Playing the « Warming Game »
 Policies (tactical parameters for GTES = BR in game theory)
 Linear function from pain to two percentages [min%,max%]
 Strategy = goals for each zone
 GDP, Pain level, World temperature (vector of weight that defines the goals of zones)
 GTES will look for a Nash Equilibrium between the four players that maximizes the
weighted goals
Example of Questions :
 What is the benefit of an “EU green policy” facing D. Trump and Xi Jinping ?
 Is there an anticipation benefit (“suffer earlier, suffer less”) ?
 What are the levers for player to influence each others (trade barriers, CBAM, …) ?
 Leverage GTES framework to randomize beliefs (from curves to « trapeze » areas)
E CO2 DT pain react
Cancel acceleration
CO2 tax
Energy Transition
Zone policies
GTES
Game-Theory
Evolutionary
Simulation

Conclusion
 A tool to explore beliefs (mental models) and
their combined effects
 A fine-line between over-complexity (hence overfitting)
and naiveté (irrelevant)
 If, and only if, CCEM shows relevance,
move to game-theoretical analysis
WARMING/ ADAPTATION
CARBON-NEUTRAL
Finite World
Radical Change
Open World
Continuous Change
Temperature
rises
Technology changes the game
W. Nordhaus
Adjust to GW
moderate GDP effects
P. Diamandis
Abundance
JM Jancovici
Carbon Shift
P.Sevigne
Collapse
Personal insights from simulation
(people & companies)
• Get ready for (major) energy price
increases
• Get ready for warming
• Home insulation
• Plants substitution
• Improve your resilience
• Distributed utilities (energy, water)
• Expect redirections
Global insights from simulation
• China strategy (Coal + Green + slow
transition) is robust ...
• Carbon tax will not be adopted uniformly
• CBAM tools will be required
• (climate) Crisis will occur and are
necessary to change
• Energy transition is a critical factor,
• Thus a “2050 carbon-neutral ambition”
is a sound goal for enterprises

Appendix
Mental
Model
Equations
Code
Specification
Validation
System Dynamics
CCEM presentations
This appendix ...
Full paper coming

GitHub repo
Javascript version
coming 

Fossil Energy Input Parameters (Oil, Gas, Coal)
// inventory : use 2020 numbers + 2010_2020 consumption (40Gtep)
// in 2010 : inventory at 193, 2020 : 242 (+45 +40 consumption)
// key design : inventory at current price in 2010 = 70% of reserves ?
// we add +50GTep if price go very high (hard case = conservative)
Oil :: FiniteSupplier( index = 1,
inventory = affine(list(400,193.0), list(600, 290.0),
list(1600, 350), list(5000, 450.0)),
capacityGrowth = 6%, // adding capacity takes time/effort
threshold = 193.0 * 90%,
price = 410.0, // 60$ a baril -> 410$ a ton
capacityMax = Oil2010 * 110%, // a little elasticity
horizonFactor = 120%, // steers the capacity growth
sensitivity = 40%, // +25% price -> + 20% prod
production = Oil2010,
co2Factor = 3.15, // 1 Tep -> 3.15 T C02
co2Kwh = 270.0, // each kWh yields 270g of CO2
investPrice = 1.5, // same as gas ?
steelFactor = 10%) // part of investment that is linked to steel
Major Open Questions
1. Inventory (Reserves = f(price))
• Growth of Coal is unclear
• Reserves’ estimates seem to stabilize
2. Price sensitivity parameters
• Define the energy selling policies
• Price is only a signal in CCEM
3. Known knowns 
• Second eye is welcome to check for
mistakes
• Google + Web as the source

Clean Energy (Nuclear, Hydro, Solar, Wind)
// 2010 : 35% of 21500TWh, from 7500 to 10400 in 2020 (0.64 to 0.89)
// Clean: 1500$ / kW -> 1.6Mwh -> 10.9 B$ / GToe (low end) to
Clean :: InfiniteSupplier( index = 4,
// this line reflect current capacity to add (GTep/y), grows with
biofuels
growthPotential = affine(list(200,0.02),list(500,0.11),
list(1000,0.15),list(6000,0.3)),
horizonFactor = 110%, // steers the capacity growth
production = Clean2010,
capacityMax = Clean2010 * 110%,
sensitivity = 50%, // expected price growth expressed
as % of GDP growth
investPrice = 11.0, // nuclear =
1000e/(MWh/y), green = 800-1500e/MWh (will go down)
price = 550.0, // 50e/MWh (nuc/ charbon) -> 80e in 2020
co2Factor = 0.0, // What clean means :)
co2Kwh = 0.0,
steelFactor = 40%) // typical for 1MW wind: 3.2Me cost,
// 460T steel, 1.7Me cost of steel
1. Growth capacity ( = f(price))
• Disputed topic
• Question of steel / raw materials
• But price of solar is going down …
• Shared with other energies
• Influence on price trajectory
3. Known knowns 

Energy Transition Matrix &
Energy Savings/ Cancellation
EnergyTransition :: list<Affine>(
// Oil moves Gas (already done mostly, transport), to Coal (CTL ?) and Clean
affine(list(2010,0.0),list(2100,0.0)), // oil -> Coal (CTL) - none by default
affine(list(2010,0.0),list(2020,0.0),list(2040,0.05),list(2100,0.08)), // oil->Gas
affine(list(2010,0.0),list(2020,0.0),list(2040,0.05),list(2100,0.1)), // oil-> Clean
// Coal is abundant, moving to Clean forms takes longer, Coal to Gas happened in the US
affine(list(2010,0.0),list(2020,0.0),list(2040,0.05),list(2100,0.1)), // Goal to Gas
(US specific)
affine(list(2010,0.0),list(2020,0.02),list(2040,0.1),list(2100,0.2)), //Coal->Clean
// Gas moves to clean will start after Ukraine war :)
affine(list(2010,0.0),list(2020,0.05),list(2040,0.1),list(2100,0.3))) // Gas->Clean
// energy saving policy (expressed as a % that can be saved through new tech/process)
USSaving ::
affine(list(2010,0),list(2020,10%),list(2030,18%),list(2050,25%),list(2100,35%))
// we define here four cancellation vectors
UScancel ::
affine(list(410,0.0),list(800,0.05),list(1600,0.15),list(3200,0.4),list(6000,0.8),
list(10000,1.0))
1. Energy Transition Matrix
• A key parameter ! Defines which
energy transition is feasible
• Must be realistic about the
change of energy vector …
2. Energy Efficiency in the future is
a belief …
3. Cancellation AND sobriety
• Key belief / key driver for LT
energy price
Mobile storage
electricity Industry
transportation
Heat
Oll & Natural Gas
Coal
Clean Energy
Static storage &
distributed
Vectors

One Zone (Europe, US, China, RestOfWorld)
US :: Consumer(
index = 1,
consumes = list<Energy>(Oil2010 * 23%, Coal2010 * 11%,
Gas2010 * 20%, Clean2010 * 21%),
popEnergy = 0.4, // mature economy
cancel = UScancel,
cancelImpact = CancelImpact,
marginImpact = improve(UScancel,-30%),
// high value companies are less sensitive to enery price
saving = USSaving,
subMatrix = tune(EnergyTransition,Coal,Gas,
affine(list(2010,0.1),list(2020,0.6),
list(2040,0.7),list(2100,0.8))),
dematerialize =affine(list(2010,0),list(2020,22%),list(2030,30%),
list(2050,40%),list(2100,50%)),
roI = affine(list(2000,18%), list(2020,18%),
list(2050, 16%), list(2100,15%)),
carbonTax = affine(list(380,0.0),list(6000,0.0)),
// default is without carbon tax
1. Important Known Known :
Energy Consumption Matrix (4 x 4)
3. Dematerialization &
Return on Investment
• Should be moved (cf. next slide)
• A true belief, hard to get a consensus

Four « Blocks » : Economy for One Zone
USgdp :: 15.0 // moves to 21.4 in 2019
USir :: 20% // investment as a fraction of revenue
USeco :: Block(
describes = US,
population = affine(list(2010,0.311),
list(2040,0.365),list(2100,0.394)),
gdp = USgdp,
investG = (USgdp * USir), // T$
investE = 0.05,
// amount of energy in green energies + Nuke in 2010 ...
iRevenue = USir, // part of revenue that is invested
ironDriver = affine(list(2010,122),list(2020,156),
list(2050,200),list(2100,300))
)
1. Economy data
• GDP / investments (harder)
• Balance of Trade between 4
Blocks
2. Energy Investments
• Not so easy to consolidate …
• And to forecast (cf. previous)
3. Iron density of GDP growth
• Very hard to find a consensus
between Economists
• To be discussed with O. Vidal

World
World :: WorldEconomy(
wheatProduction = 0.66, // in giga tons
techFactor = 1%, // improvement of techno, annual rate
(different from savings) - 5% gain every 10 years
steelPrice = 3800.0, // $/tonne
energy4steel = affine(list(2000,0.5),list(2020,0.45),
list(2050,0.6),list(2100,1)),
agroLand = 17.6, // millions of km2
landImpact = affine(list(2000,8.0), list(2020,10.0),
list(2050,20.0), list(2100,15.0)),
// land needed to produce 1 MWh of clean energy
lossLandWarming = affine(list(0.0,100%),list(2.0,96%),
list(4,90%)),
agroEfficiency = affine(list(400,100%),list(600,96%), list(1000,92%),
list(2000, 85%), list(5000,75%)),
bioHealth = affine(list(0.0,100%),list(1.0,98%),
list(2.0,96%),list(4.0,90%)),
cropYield = affine(list(2000,100%),list(2020,115%),
list(2050,130%),list(2100,150%))
)
1. World Global parameters
• Wheat production
• Tech progress
2. Steel Production Model
3. Wheat Production model
• Impact of new energy on land
• Impact of global worming
• Yield is expected tech progress
while bioHealth is the negative
consequence of warming

Gaia (Earth Model M5)
// warming: IPCC input => temperature increase = f(CO2 concentrartion) - based on RPC
4.5, 6 and 8.5
// disasterLoss : Nordhaus hypothesis about GDP loss = f(temperature)
// This calibration proposed here is more pessimistic than Nordhaus, based on Schroders.
Gaia :: Earth(
co2PPM = 388.0, // qty of CO2 in atmosphere in 2010 (ppm)
co2Add = 34.0, // billions T CO2
co2Ratio = 0.13, // + 2.5 ppm at 19 Gtep/y
co2Neutral = 15.0, // level (GT CO2/y) which is "harmless" (managed by
atmosphere)
warming = affine(list(200,0),list(400,0.7),list(560,2.4),list(680,2.8),list(1200,4.3)),
avgTemp = 14.63, // 2010 data "0.62°C (1.12°F) above the 20th century
average of 13.9°C"
avgCentury = 13.9, // reference IPCC
// M5 new slots
disasterLoss = affine(list(1.0,0),list(1.5,1.5%),list(2,4%),list(3,8%),list(4,15%),list(5,25%)),
painClimate = step(list(1.0,0),list(1.5,1%),list(2,10%), list(3,20%), list(4,30%)),
painGrowth = step(list(-20%,20%),list(-
5%,10%),list(0%,5%),list(1%,1%),list(2%,1%),list(3%,0)),
painCancel = step(list(0,0),list(5%,2%), list(10%,5%), list(20%,10%),
list(30%,20%),list(50%,30%)))
painProfile = list<Percent>(40%,30%,30%), // not used yet
1. CO2 accumulation model
• Naïve but sufficient
• Warming from CO2 extracted
from IPCC
2. Impact from Warming
• A key hot topic with no consensus,
hence a key belief
• My average of various papers
3. Pain from Warming impact
• Computed but not used yet for
retroaction
• Hence the sensitivity is arbitrary

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