# Model Documentation

### | Version 4.0

created with goxygen 0.21.1

# 56_ghg_policy

# Greenhouse gas policy (56_ghg_policy)

## Description

The module 56_ghg_policy connects emissions to costs which then enter the objective function of MAgPIE. Connecting emissions with costs in a cost minimization model like MAgPIE creates an incentive to reduce emissions. This can be interpreted as an internalization of the external costs by pollution, e.g. by policies that deincentivize polluting activity. Technically, every ton of emission is multiplied with an emission price to determine emission costs. Emission sources can be excluded from pricing by switches defined in config/default.cfg.

Please note that emissions that occur only once (e.g. CO2 emissions from deforestation) are handled differently than emissions that occur in every timestep (e.g. CH4 and N2O emissions from agricultural production).

## Interfaces

Interfaces to other modules

### Input

module inputs (A: price_sep16)
| Description | Unit | A
--- | --- | --- | ---
im_maccs_mitigation (t, i, emis_source, pollutants) | Technical mitigation of GHG emissions | \(1\) | x
vm_cdr_aff (j, co2_forestry) | Total CDR from afforestation (new and existing areas) between t+1 and t=s32_planing_horizon CO2-C | \(10^6 tC\) | x

### Output

module outputs
| Description | Unit
--- | --- | ---
im_pollutant_prices (t_all, i, pollutants) | Certificate prices for N2O-N CH4 CO2-C | \(USD_{05MER}/Mg\)
vm_btm_cell (j, emis_source, pollutants) | Cellular emissions before technical mitigation | \(Tg/yr\)
vm_btm_reg (i, emis_source, pollutants) | Regional emissions before technical mitigation | \(Tg/yr\)
vm_emission_costs (i) | Costs for emission rights for pollutants and greenhouse gases | \(10^6 USD_{05MER}/yr\)
vm_emissions_reg (i, emis_source, pollutants) | Regional emissions by source and gas after technical mitigation N CH4 C | \(Tg/yr\)
vm_reward_cdr_aff (i) | Regional revenues for carbon captured by afforestation | \(10^6 USD_{05MER}/yr\)

## Realizations

### (A) price_sep16

The price_sep16 realization applies pollutant prices to different emission types depending on the emission pricing policy defined in `f56_emis_policy`. In addition, carbon dioxide removal (CDR) from afforestation 32_forestry is rewarded depending on the afforestation incentive policy defined in `f56_aff_policy`. For CO2 emissions from land-use change and CDR from afforestation, the growth rate of the CO2 price is used to annuitize associated emission costs. If pollutant prices are zero, which is the default for reference scenarios without mitigation, total emission costs entering the objective function are zero.

`f56_emis_policy` contains scenarios determining for each gas and source whether it is priced or not. `f56_aff_policy` contains scenarios determining the incentive structure for afforestation.

Total regional GHG emissions `vm_emissions_reg` are the sum of emissions from different regional and cellular sources less the fraction `im_maccs_mitigation` that can be abated by technicial mitigation measures (see module 57_maccs). The emisssions before technical mitigation are calculated in the respective modules (51_nitrogen, 52_carbon, 53_methane) and delivered to this module through the interface variables `vm_btm_reg` and `vm_btm_cell`.

\[\begin{multline*} vm\_emissions\_reg(i2,emis\_source,pollutants) = vm\_btm\_reg(i2,emis\_source,pollutants) \cdot \left(1 - \sum\left(ct, im\_maccs\_mitigation(ct,i2,emis\_source,pollutants)\right)\right) \end{multline*}\] \[\begin{multline*} v56\_emis\_cell(j2,emis\_source,pollutants) = \sum_{cell(i2,j2)}\left( vm\_btm\_cell(j2,emis\_source,pollutants) \cdot \left(1 - \sum\left(ct, im\_maccs\_mitigation(ct,i2,emis\_source,pollutants)\right)\right)\right) \end{multline*}\] \[\begin{multline*} vm\_emissions\_reg(i2,emis\_source,pollutants) = \sum_{cell(i2,j2)}v56\_emis\_cell(j2,emis\_source,pollutants) \end{multline*}\]

Emission costs are calculated by multiplying regional and cellular emissions by the emission price `im_pollutant_prices` taking into account the price policy that was defined above in `f56_emis_policy`.

\[\begin{multline*} v56\_emission\_costs\_reg\_yearly(i2,emis\_reg\_yr56) = \sum_{pollutants}\left( vm\_emissions\_reg(i2,emis\_reg\_yr56,pollutants) \cdot f56\_emis\_policy\left("\%c56\_emis\_policy\%",pollutants,emis\_reg\_yr56\right) \cdot \sum_{ct} im\_pollutant\_prices(ct,i2,pollutants)\right) \end{multline*}\] \[\begin{multline*} v56\_emission\_costs\_cell\_yearly(j2,emis\_cell\_yr56) = \sum_{pollutants}\left( v56\_emis\_cell(j2,emis\_cell\_yr56,pollutants) \cdot f56\_emis\_policy\left("\%c56\_emis\_policy\%",pollutants,emis\_cell\_yr56\right) \cdot \sum_{ct,cell(i2,j2)}im\_pollutant\_prices(ct,i2,pollutants)\right) \end{multline*}\]

As MAgPIE is a recursive dynamic model, within the optimization of the current time step it does not account for benefits or costs in future time steps. This can be problematic for the treatment of emissions that occur only once under continuous management (such as deforestation, where the forest has been cut down the cropland can be continuously cultivated without further deforestation emissions) versus emissions that occur continously (such as fertilization emissions, that will re-occur every year for continuously management). We therefore distinguish one-off and yearly emissions, and discount one-off emissions assuming an infinite time-horizon to level them with yearly emissions. Since one-off emissions are delivered by the 52_carbon module as annual emissions they are multiplied here by the timestep length `m_timestep_length` to obtain emissions for the entire timestep and are then transformed back into annual costs by multiplying by the emission price and a discount factor `p56_ghg_price_growth_rate` that is equal to the growth rate of the emissions price.

\[\begin{multline*} v56\_emission\_costs\_reg\_oneoff(i2,emis\_reg\_one56) \geq \sum_{pollutants}\left( vm\_emissions\_reg(i2,emis\_reg\_one56,pollutants) \cdot m\_timestep\_length \cdot f56\_emis\_policy\left("\%c56\_emis\_policy\%",pollutants,emis\_reg\_one56\right) \cdot \sum_{ct}\left( im\_pollutant\_prices(ct,i2,pollutants) \cdot \frac{ p56\_ghg\_price\_growth\_rate(ct,i2,pollutants)}{\left(1+p56\_ghg\_price\_growth\_rate(ct,i2,pollutants)\right)}\right) \right) \end{multline*}\] \[\begin{multline*} v56\_emission\_costs\_cell\_oneoff(j2,emis\_cell\_one56) \geq \sum_{pollutants}\left( v56\_emis\_cell(j2,emis\_cell\_one56,pollutants) \cdot m\_timestep\_length \cdot f56\_emis\_policy\left("\%c56\_emis\_policy\%",pollutants,emis\_cell\_one56\right) \cdot \sum_{ct,cell(i2,j2)}\left( im\_pollutant\_prices(ct,i2,pollutants) \cdot \frac{ p56\_ghg\_price\_growth\_rate(ct,i2,pollutants)}{\left(1+p56\_ghg\_price\_growth\_rate(ct,i2,pollutants)\right)}\right) \right) \end{multline*}\]

Total regional emission costs consist of costs from yearly and one-off emissions occuring in this region and its cells.

\[\begin{multline*} vm\_emission\_costs(i2) = \sum_{emis\_reg\_yr56} v56\_emission\_costs\_reg\_yearly(i2,emis\_reg\_yr56) + \sum_{emis\_reg\_one56} v56\_emission\_costs\_reg\_oneoff(i2,emis\_reg\_one56) + \sum_{emis\_cell\_yr56, cell(i2,j2)} v56\_emission\_costs\_cell\_yearly(j2,emis\_cell\_yr56) + \sum_{emis\_cell\_one56, cell(i2,j2)} v56\_emission\_costs\_cell\_oneoff(j2,emis\_cell\_one56) \end{multline*}\]

Benefits from carbon removal (from afforestation) are also calculated in this module taking into account the policy that was defined above in `f56_aff_policy`. Cost and benefits are however not summed here but in 11_costs.

\[\begin{multline*} vm\_reward\_cdr\_aff(i2) = \sum_{co2\_forestry,cell(i2,j2)}\left( v56\_reward\_cdr\_aff(j2,co2\_forestry) \right) \end{multline*}\] \[\begin{multline*} v56\_reward\_cdr\_aff(j2,co2\_forestry) = vm\_cdr\_aff(j2,co2\_forestry) \cdot f56\_aff\_policy\left(co2\_forestry,"\%c56\_aff\_policy\%"\right) \cdot \sum_{ct,cell(i2,j2)}\left( im\_pollutant\_prices(ct,i2,"co2\_c") \cdot \frac{ p56\_ghg\_price\_growth\_rate(ct,i2,"co2\_c")}{\left(1+p56\_ghg\_price\_growth\_rate(ct,i2,"co2\_c")\right) }\right) \end{multline*}\]

> Limitations There are no known limitations.

## Definitions

### Objects

module-internal objects (A: price_sep16)
| Description | Unit | A
--- | --- | --- | ---
f56_aff_policy (co2_forestry, aff56) | afforestation policy scenarios | \(1\) | x
f56_emis_policy (scen56, pollutants_all, emis_source) | emission policy scenarios | \(1\) | x
f56_pollutant_prices (t_all, i, pollutants, ghgscen56) | ghg certificate prices for N2O-N CH4 CO2-C | \(USD_{05MER}/t\) | x
p56_ghg_price_growth_rate_avg (i, pollutants) | Average over time of growth rate of certificate price | \(\%/yr\) | x
p56_ghg_price_growth_rate (t, i, pollutants) | Growth rate of certificate price | \(\%/yr\) | x
q56_cell_to_reg (i, pollutants, emis_source) | Aggregation to regional emissions | \(Tg/yr\) | x
q56_emission_costs_cell_oneoff (j, emis_cell_one56) | Calculation of cellular costs for emissions occuring only once in time | \(10^6 USD_{05MER}/yr\) | x
q56_emission_costs_cell_yearly (j, emis_cell_yr56) | Calculation of cellular costs for annual emissions | \(10^6 USD_{05MER}/yr\) | x
q56_emission_costs (i) | Calculation of total emission costs | \(10^6 USD_{05MER}/yr\) | x
q56_emission_costs_reg_oneoff (i, emis_reg_one56) | Calculation of regional costs for emissions occuring only once in time | \(10^6 USD_{05MER}/yr\) | x
q56_emission_costs_reg_yearly (i, emis_reg_yr56) | Calculation of regional costs for annual emissions | \(10^6 USD_{05MER}/yr\) | x
q56_reward_cdr_aff (j, co2_forestry) | Cellular revenues for carbon captured by afforestation | \(10^6 USD_{05MER}/yr\) | x
q56_reward_cdr_aff_reg (i) | Regional revenues for carbon captured by afforestation | \(10^6 USD_{05MER}/yr\) | x
q56_technical_mitigation_cell (j, pollutants, emis_source) | Application of maccs on emissions | \(Tg/yr\) | x
q56_technical_mitigation_reg (i, pollutants, emis_source) | Application of maccs on emissions | \(Tg/yr\) | x
s56_limit_ch4_n2o_price | upper limit for CH4 and N2O GHG prices | \(USD_{05MER}/tC\) | x
s56_reward_neg_emis | reward CDR from all sources (-Inf) or only from afforestation (0) | \(1\) | x
v56_emis_cell (j, emis_source, pollutants) | Cellular emissions by source and gas after technical mitigation N CH4 C | \(Tg/yr\) | x
v56_emission_costs_cell_oneoff (j, emis_cell_one56) | Costs for emissions occuring only once in time | \(10^6 USD_{05MER}/yr\) | x
v56_emission_costs_cell_yearly (j, emis_cell_yr56) | Costs for emissions occuring yearly | \(10^6 USD_{05MER}/yr\) | x
v56_emission_costs_reg_oneoff (i, emis_reg_one56) | Costs for emissions occuring only once in time | \(10^6 USD_{05MER}/yr\) | x
v56_emission_costs_reg_yearly (i, emis_reg_yr56) | Costs for emissions occuring yearly | \(10^6 USD_{05MER}/yr\) | x
v56_reward_cdr_aff (j, co2_forestry) | Cellular revenues for carbon captured by afforestation | \(10^6 USD_{05MER}/yr\) | x

### Sets

sets in use
| description
--- | ---
aff56 | afforestation policy scenarios
co2_forestry(emis_source_cell) | Sources of forestry land CO2 emissions
emis_cell_one56(emis_source_cell) | cellular oneoff emission sources
emis_cell_yr56(emis_source_cell) | cellular yearly emission sources
emis_reg_one56(emis_source_reg) | regional oneoff emission sources
emis_reg_yr56(emis_source_reg) | regional yearly emission sources
emis_source | Emission sources
ghgscen56 | ghg price scenarios
i | World regions
pollutants_all | all pollutants
pollutants(pollutants_all) | subset of pollutants_all that can be taxed
scen56 | emission policy scenarios
t_all | 5-year time periods
t(t_all) | Simulated time periods

## Authors

Benjamin Bodirsky, Florian Humpenoeder

## See Also

11_costs, 32_forestry, 51_nitrogen, 52_carbon, 53_methane, 56_ghg_policy, 57_maccs

## References