# Increased energy use for adaptation significantly impacts mitigation pathways | Panda Anku

### The IAM approach

WITCH is a dynamic global model that fully integrates a simplified representation of the economy, the energy system, and the climate system. The economy is modeled through an intertemporal optimal growth model. A representative agent chooses consumption to maximize regional welfare, and consumption decisions are related to investment choices. The energy sector is hard-linked with the rest of the economy. Energy investments and resources are chosen optimally together with the other macroeconomic variables. Energy demand and, in particular, fuel and technology choices are optimized intertemporally, under a set of constraints, including carbon and other energy prices. A climate model (MAGICC) computes the future changes in the global average temperature on the basis of the GHG emissions generated by economic activities and the energy system. A fully-integrated module translates regional GHG emissions into global temperature through atmospheric concentrations. Another module links the global average temperature increase to changes in regional average temperature based on the linear statistical downscaling model of country-level mean temperature estimated by using future warming scenarios (Representative Concentration Pathways, RCPs, see Section 1 in the Supplementary Methods). WITCH integrates an air pollution module, FASST(R). It is a source-receptor model based on the TM5-FASST model developed by JRC-Ispra, that computes the annual concentrations of several pollutants, namely Sulfur Dioxide (SO2), Nitrogen Oxides (NOx), fine Particulate Matter (PM 2.5), and ground-level Ozone (O3). The fine PM 2.5 concentrations include Particulate Organic Matter (POM), secondary inorganic PM, dust, and sea salt. The FASST(R) model produces concentrations on a world spatial grid of resolution of one degree by one degree and has previously been used to assess premature death from air pollution exposure62,63.

Regarding the adaptation–energy feedback loop, a set of equations links the occurrence of extreme temperatures to energy demand. We match the energy demand shocks in WITCH to the available empirical evidence from ref. 31 and therefore use Extreme Temperature Indicators (ETIs) defined as the yearly count of days in which average temperatures fall above the threshold of 27.5 °C and below the threshold of 12.5 °C, respectively. We exclude the moderate temperature intervals and aggregate adjacent extreme bins, and focus on the two temperature intervals of exposure to extreme heat and cold (T < 12.5 °C and T > 27.5 °C).

The heterogeneous relationship between the vector of ETIs (ηi,t) and temperature across climate conditions is captured by grouping countries in clusters (Supplementary Methods). We use a polynomial function (f) of yearly mean temperatures (Ti,t). We estimate a panel, fixed-effect model with ordinary least square (OLS) on yearly, country-level observations for 180 countries from 1970 to 2010 (Supplementary Methods). The regional future realizations of the ETIs are then determined endogenously within the model and defined for climatic clusters as follows, c, as:

$${{{{{{{{boldsymbol{eta }}}}}}}}}_{i,t}=f({T}_{cin i,t},{T}_{cin i,t}^{2})$$

(1)

where

i regions (17 regions)

c clusters (4 clusters)

t 5-year time step in the model from 2005 to 2100

Sector-specific, semi-elasticities are used to link energy demand and ηi,t. They are calibrated after the estimates published by31, which model the long-term relationship between energy demand, weather, income, and prices as a dynamic adjustment process. Semi-elasticities indicate the percentage by which demand shifts relative to its conditional mean level in consequence of an additional day occurring in a given interval (j) with respect to the reference temperature interval. The semi-elasticities are specific to two macro-regional groups: temperate and tropical countries. In both macro-groups, the number of days falling within the extreme temperature intervals lies in the tails of the daily temperature distribution (Supplementary Fig. 2 presents a stylized representation of the energy demand shock based on the two extreme temperature bins in tropical and temperate countries). The semi-elasticities provided by ref. 31 capture how energy responds to long-term weather shocks, allowing us to project future energy demand shocks that account for extensive margin adjustments (e.g., purchase of air conditioners, improvements in energy efficiency). Other appealing features of the analysis developed in ref. 31 are that it captures the potential nonlinearity in the demand responses to weather and climate, provides asymmetric responses in temperate and tropical countries, and separates the influence of humidity and temperature on demand. The lack of empirical evidence providing alternative demand response functions for multiple fuels, sectors of the economy, and climate areas limits the scope for assessing the robustness of the results based on ref. 31. The transmission of the climate shock in the commercial and industrial sectors in tropical economies reflects the extensive use of distributed petroleum-fired generators to satisfy final electricity demand.

Sectorial semi-elasticities (βi,f,s,j) are aggregated with the share of the final energy demand of each sector over the total final energy demand as weights (λi,f,s,t), for each fuel and for each time step of the model. The share is computed from the baseline model projections in each 5-year time step. The aggregation yields a set of semi-elasticities ({overline{beta }}_{i,f,t,j}) specific to each region (i), energy vector (f), and year (t).

$${overline{beta }}_{i,f,t,j}=mathop{sum}limits_{s}{lambda }_{i,f,s,t}{beta }_{i,f,s,j}$$

(2)

where

i regions (17 regions)

t time step in the model, 2005–2100

f energy vector (electricity EL, nonelectric energy GAS, and OIL)

s sectors (residential, commercial, and industrial)

j average daily temperature interval

Climate-induced shocks on energy demand, (Φf,i,t), combine historical and future realizations of the ETIs with average sectorial semi-elasticities aggregated over the two temperature intervals (j):

$${{{Phi }}}_{i,f,t}=frac{exp ({sum }_{j};{overline{beta }}_{i,f,t,j}{{{{{{{{boldsymbol{eta }}}}}}}}}_{{{{{{{{boldsymbol{i,t}}}}}}}}})}{exp ({sum }_{j};{overline{beta }}_{i,f,j}{{{{{{{{boldsymbol{eta }}}}}}}}}_{{{{{{{{boldsymbol{i,t}}}}}}}}})}-1$$

(3)

where

i regions (17 regions)

t time step in the model, 2005–2100

f energy vector (electricity EL, nonelectric energy GAS, and OIL)

j average daily temperature interval

We follow ref. 64 and assume that the climate-induced energy demand shocks affect the productivity of the energy inputs entering into the aggregate production function. If climate-induced shocks increase energy demand, it is as if the economic systems needed more energy to produce output. Climate-related positive shocks (i.e., increase in energy demand) are therefore modeled as technological retrogression, requiring more inputs to generate a given output. In the WITCH model, energy (EN) is a combination of electricity (EL) and nonelectric energy (NEL), which includes coal, gas, and oil. Electricity and nonelectric energy can be substituted with an elasticity of substitution, ρEN:

$${{{{{{{{rm{EN}}}}}}}}}_{i,t}={[{tilde{alpha }}_{{{{{{{{rm{EL}}}}}}}},i}{{{{{{{{rm{EL}}}}}}}}}_{i,t}^{{rho }_{{{{{{{{rm{EN}}}}}}}}}}+{tilde{alpha }}_{{{{{{{{rm{NEL}}}}}}}},i}{{{{{{{rm{NEL}}}}}}}}{i,t}^{{rho }_{{{{{{{{rm{EN}}}}}}}}}}]}^{frac{1}{{rho }_{{{{{{{{rm{EN}}}}}}}}}}}$$

(4)

In this formulation, the productivities of electricity and nonelectricity are endogenous functions of climate shocks:

$${tilde{alpha }}_{{{{{{mathrm{EL}}}}}},i,t}={alpha }_{{{{{{mathrm{EL}}}}}},i}frac{{{{Phi }}}_{{{{{{mathrm{EL}}}}}},i,t}{Q}_{{{{{{mathrm{EL}}}}}},i,t}}{{sum }_{f}{Q}_{f,i,t}}$$

(5)

$${tilde{alpha }}_{{{{{{mathrm{NEL}}}}}},i,t}={alpha }_{{{{{{mathrm{NEL}}}}}},i}left[frac{{{{Phi }}}_{{{{{{mathrm{GAS}}}}}},i,t};{Q}_{{{{{{mathrm{GAS}}}}}},i,t}}{{sum }_{f};{Q}_{f,i,t}}+frac{{{{Phi }}}_{{{{{{mathrm{OIL}}}}}},i,t};{Q}_{{{{{{mathrm{OIL}}}}}},i,t}}{{sum }_{f};{Q}_{f,i,t}}right]$$

(6)

### Quantification of additional new capacity

In the WITCH model, investments in new power generation plants to fulfill electricity demand depend on: (i) the cost of electricity generation of the different technologies, which combines capital costs, Operation and Maintenance (O&M) expenditure, and the costs for fuels in an endogenous way; (ii) the lifetime power plants; (iii) a constraint on the flexibility of the power generation fleet to accommodate the integration of renewables; (iv) an installed capacity constraint on the power generation fleet to guarantee that sufficient capacity is built to meet the instantaneous peak electricity demand (for further details see ref. 37).

The cumulative additional new capacity added in response to the variation in electricity demand required for adaptation that we report (Γh,i,t) for each technology h in region i at time t is computed as follows:

$${{{Gamma }}}_{h,i,t}=mathop{sum }limits_{t=2005}^{t}left({K}_{h,i,t}^{{{{{{mathrm{Ada}}}}}}}-{K}_{h,i,t}^{{{{{{mathrm{NoAda}}}}}}}right)$$

(7)

$${K}_{h,i,t+1}={K}_{h,i,t}{((1-{delta }_{h,i,t+1}))}^{{{{Delta }}}_{t}}+{{{Delta }}}_{t}frac{{I}_{h,i,t}}{S{C}_{h,i,t}}$$

(8)

Where δh,i,t+1 is a depreciation rate based on a finite lifetime of the power plant, Ih,i,t are the annual investments, and SCh,i,t the investment cost.

### Quantification of energy costs

Power generation costs (C_GEN), include the investments in generation capacity (I), R&D investments in power generation technologies (I_RD), O&M costs (OM), and fuel expenditures for power generation (E_FUEL):

$${{{{{{{{rm{CGEN}}}}}}}}}_{{{{{{{{rm{i,t}}}}}}}}}=mathop{sum}limits_{h}({{{{{{{{rm{I}}}}}}}}}_{{{{{{{{rm{h,i,t}}}}}}}}}+{{{{{{{{rm{I}}}}}}}}_{{{{{{{rm{RD}}}}}}}}}_{{{{{{{{rm{h,i,t}}}}}}}}}+{{{{{{{{rm{OM}}}}}}}}}_{{{{{{{{rm{h,i,t}}}}}}}}}+{{{{{{{{rm{E}}}}}}}}_{{{{{{{rm{FUEL}}}}}}}}}_{{{{{{{{rm{h,i,t}}}}}}}}})$$

(9)

where

i regions (17 regions)

t time step in the model, 2005–2100

j power generation technology

Fuel costs (C_FUEL) include the investments and O&M costs in fossil-fuel extraction (OM_ex) and the expenses associated with liquids and gas consumption (EXP_ff), excluding the expenses related to fuel consumption in the power sector:

$${{{{{{{{rm{C}}}}}}}}_{{{{{{{rm{FUEL}}}}}}}}}_{{{{{{{{rm{i,t}}}}}}}}}=mathop{sum}limits_{f}({{{{{{{{rm{OM}}}}}}}}_{{{{{{{rm{ex}}}}}}}}}_{{{{{{{{rm{i,t,f}}}}}}}}}+{{{{{{{{rm{EXP}}}}}}}}_{{{{{{{rm{ff}}}}}}}}}_{{{{{{{{rm{i,t,f}}}}}}}}})$$

(10)

where

i regions (17 regions)

t time step in the model, 2005–2100

f fuel

Investments in the electrical grid (I_GRID) are computed based on grid capital. The grid capital stock is adjusted by taking into account a linear relationship between grid capacity and the capacity of traditional power generation technologies and the investments for integrating the generation of variable renewables. A detailed description is available in ref. 37.

### Scenarios

In the current policy scenario, GHG emission targets extrapolate beyond 2020 the implied ambition levels of current climate policies until 2020. Overall, the current policy scenario with no energy-adaptation feedback leads to cumulative carbon emissions of about 5000 GtCO2eq, from 2018 until 2100 Table 5. More stringent mitigation scenarios keep the increase in global mean temperature in 2100 at 2.5 °C and well below 2 °C, resulting in cumulative GHG emissions from 2018 until 2100 of 3600, and 1500 GtCO2eq, respectively. Non-CO2 greenhouse gases in these scenarios are priced equivalently to the implied CO2 prices, by using 100-year global warming potentials for conversion. We use explicit GHG pricing, and climate stabilization targets are achieved in a global cost-optimal way, with no international compensation scheme or carbon emission trading.

Population65 and country-level GDP projections implemented by using Purchasing Power Parities (PPP)66 are based on the basic and extended SSPs40. The main results use the Shared Socio-Economic Pathway Middle-of-the-Road (SSP2), which is a continuation of the historical trends, while the SI presents some results across SSPs. For more information on the implementation of key aspects, such as energy productivity, land-use and power technologies, and fossil-fuel resources, see ref. 37.