# Marginal abatement cost curve module (57_maccs)¶

**Table of contents**- Marginal abatement cost curve module (57_maccs)

## Description¶

The module 57_maccs has two functions:

a) it connects emissions to costs that enter MAgPIEs goal function.

When emissions are connected to costs, the optimization leads to an outcome with lower emissions. It 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. Emissions costs are calculated in every realization.

Note that emissions that occur only once (e.g. deforestation emissions) are handled differently than emissions that occur every timestep (e.g. fertilization emissions). For the emissions from land use change it can be decided which emission sources (land pools) are considered in the GHG emission pricing policy.

b) it allows to reduce emissions by technical mitigation measures in exchange for additional mitigation costs

Technical mitigation activity includes for example better spreader maintenance, feed additives or investments into animal waste facilities. In simplification, these activities are assumed to have solely an effect on costs and emissions, while no consequences on biophysical values like yields or water requirements are directly modeled.

Mitigation costs are estimated using marginal abatement cost (MAC) curves. The curves allow to reduce emissions before technical mitigation by a certain share in exchange for additional costs. The MAC curves are based on the data of Lucas et al^{1} (2007).

Note that the data quality of mitigation cost curves is still very poor. However, currently no better data is available. Origin data contains the integral of Lucas MAC-Curves aggregated over regions and interpolated between 10er time steps. Exponential curves are then fitted into the points. If only one data point exists, a linear line was taken from the origin (0,0). Finally, an upper limit was included to avoid excessive extrapolation of the fitted curves. The upper limit is represented by the most costly technology in the Lucas data set.

## Interfaces¶

### Input¶

Name Description Unit A B $sm\_years$ length of current time step years x x $pm\_annuity\_due(i)$ annuity-due annual cash flows over n years in each region - x x $vm\_btm\_cell(j,emis\_cell)$ annual emissions by emission source categories Tg N2O-N CH4 and CO2-C x x $vm\_exp\_emis\_affore(j,emis\_co2\_forestry)$ total additional CO2_C emissions beyond current time step according to $sm\_invest\_horizon$ Tg CO2-C x x $fcm\_ghg\_prices(i,ghg)$ current ghg prices US$ 2004 per Mg N2O-N CH4 and CO2-C x x

_{The last columns of the table indicate the usage in the different realizations (numbered with capital letters)}

### Output¶

Name Description Unit $vm\_btm\_reg(i,emis\_reg)$ emissions before technical mitigation Tg N2O-N CH4 and CO2-C $vm\_emissions\_reg(i,ghg)$ endogenous emissions Tg N2O-N CH4 and CO2-C $vm\_emission\_costs(i)$ costs for emission pollution rights mio US$2004 $vm\_maccs\_costs(i)$ costs of technical mitigation of GHG emissions mio US$2004

### Interface plot¶

Figure 0: Information exchange among modules

## Realizations¶

### (A) off_cell¶

The module reports regional emissions for main GHG categories based on different emission sources and calculates associated emission cost (rights, permits). Technical mitigation is not considered in this realization. Therefore, the main feature of this module is that the cost of technical mitigation of the GHG emissions is set to zero:

Equation 1:

\begin{equation*}

vm\_maccs\_costs.fx(i)=0

\end{equation*}

Total regional GHG emissions are obtained as a sum of emissions from different regional emission sources:

Equation 2:

\begin{equation*}

vm\_emissions\_reg(i,ghg) = \sum \limits_{ghg\_to\_emis(ghg,emis)} v57\_emis\_reg(i,emis)

\end{equation*}

Regional emissions for different source categories are calculated in the respective modules (carbon, nitrogen, methane) and delivered through the interface variable $vm\_btm\_reg(i,emis)$:

Equation 3:

\begin{equation*}

v57\_emis\_reg(i,emis\_reg) = vm\_btm\_reg(i,emis\_reg)

\end{equation*}

Equation 4:

\begin{equation*}

v57\_emis\_cell(j,emis\_cell) = vm\_btm\_cell(j,emis\_cell)

\end{equation*}

Equation 5:

\begin{equation*}

v57\_emis\_reg(i,emis\_cell) = \sum \limits_{cell(i,j)} vm\_btm\_cell(j,emis\_cell)

\end{equation*}

Emission pricing:

Calculation of total regional costs for pollution rights (i.e. emission costs, since the emission prices come from a MAgPIE-ReMIND coupled run with a mitigation target, and the carbon price is calculated with respect to the carbon budget defined by a mitigation target) is performed as a sum of regional emission costs for the emissions that occur annually ($N_2O$ soil emissions, animal waste management etc.) and the emissions that are off set once in a lifetime (carbon emission from land use change LUC), all reduced by the benefits from carbon removal from land afforestation:

Equation 6:

\begin{align*}

vm\_emission\_costs(i) = \sum \limits_{emis\_co2\_forestry} \sum \limits_{cell(i,j)} & v57\_exp\_emission\_costs\_co2(j,emis\_co2\_forestry) +\\

\sum \limits_{emis\_reg\_yearly57} & v57\_emission\_costs\_reg\_yearly(i,emis\_reg\_yearly57) + \\

\sum \limits_{emis\_reg\_oneoff57} & v57\_emission\_costs\_reg\_oneoff(i,emis\_reg\_oneoff57) + \\

\sum \limits_{emis\_cell\_yearly57} \sum \limits_{cell(i,j)} & v57\_emission\_costs\_cell\_yearly(j,emis\_cell\_yearly57) + \\

\sum \limits_{emis\_cell\_oneoff57} \sum \limits_{cell(i,j)} & v57\_emission\_costs\_cell\_oneoff(i,emis\_cell\_oneoff57)

\end{align*}

Note that two addends in the equation 6 are redundant: currently there are no cellular emissions that occur yearly and there are no modeled regional emissions that occur only once in a lifetime ("oneoff"). The implementation of the equation 6 (also equation 8 and 9 which are defined over an empty set and thus not active constraints) is such that allows flexibility in further module development.

Cost of the emissions that are off-set just once in a lifetime (carbon) are related with the land use change (LUC), and specifically here to deforestation. Since the "carbon" module calculates emissions from LUC and reports it at annual level, these emissions are multiplied here with the length of the time step period and the emission cost is discounted by the annuity rate. The application of the emission price with respect to different emission sources is determined in the parameter matrix $f57\_policy\_emis\_integration(emis\_yearly57)$. Expected additional reduction in carbon emissions from afforestation is calculated in the forestry module (forestry).

In particular, all of the components of emission costs are obtained from the following:

Equation 7:

\begin{align*}

v57\_emission\_costs\_reg\_yearly(i,emis\_reg\_yearly57) &= \sum \limits_{ghg\_to\_emis(ghg,emis\_reg\_yearly57)} [v57\_emis\_reg(i,emis\_reg\_yearly57) \\

&* f57\_policy\_emis\_integration(emis\_reg\_yearly57) * fcm\_ghg\_prices(i,ghg)]

\end{align*}

Equation 8 (not active):

\begin{align*}

v57\_emission\_costs\_reg\_oneoff(i,emis\_reg\_oneoff57) & \ge \sum \limits_{ghg\_to\_emis(ghg,emis\_reg\_oneoff57)} [v57\_emis\_reg(i,emis\_reg\_oneoff57) \\

&* sm\_years * f57\_policy\_emis\_integration(emis\_reg\_oneoff57) \\

&* fcm\_ghg\_prices(i, ghg) / pm\_annuity\_due(i)] \\

\end{align*}

Equation 9 (not active):

\begin{align*}

v57\_emission\_costs\_cell\_yearly(i,emis\_cell\_yearly57) &= \sum \limits_{ghg\_to\_emis(ghg,emis\_cell\_yearly57)} [v57\_emis\_cell(i,emis\_cell\_yearly57) \\

&* f57\_policy\_emis\_integration(emis\_cell\_yearly57) * \sum \limits_{cell(i,j)} fcm\_ghg\_prices(i,ghg)]

\end{align*}

Equation 10:

\begin{align*}

v57\_emission\_costs\_cell\_oneoff(i,emis\_cell\_oneoff57) & \ge \sum \limits_{ghg\_to\_emis(ghg,emis\_cell\_oneoff57)} [v57\_emis\_cell(i,emis\_cell\_oneoff57) \\

&* sm\_years * f57\_policy\_emis\_integration(emis\_cell\_oneoff57) \\

&* \sum \limits_{cell(i,j)} (fcm\_ghg\_prices(i, ghg) / pm\_annuity\_due(i))] \\

\end{align*}

Equation 11:

\begin{align*}

v57\_exp\_emission\_costs\_co2(j,emis\_co2\_forestry) & \ge vm\_exp\_emis\_affore(j,emis\_co2\_forestry) \\

&* f57\_policy\_emis\_integration(emis\_co2\_forestry) \\

&* \sum \limits_{cell(i,j)} fcm\_ghg\_prices(i,\text{"$co2\_c$"}) / \sum \limits_{cell(i,j)} pm\_annuity\_due(i) \\

\end{align*}

Limitations

No technical mitigation allowed

### (B) on_cell (default)¶

In this implementation, emissions can be reduced by technical mitigation at additional costs.

The module realization is the same as the *off_cell* realization with the following differences:

Equation 3 and 4 now contain a reduction factor $v57\_maccs\_mitigation$.

Equation 3':

\begin{align*}

v57\_emis\_reg(i,emis\_reg) &= \sum_{emis\_to\_mcats57(emis\_reg,mcats57)} (vm\_btm\_reg(i,emis\_reg) \\

&*(1 - v57\_maccs\_mitigation(i,mcats57))

\end{align*}

Equation 4':

\begin{align*}

v57\_emis\_cell(j,emis\_cell) &= \sum_{cell(i,j), emis\_to\_mcats57(emis\_cell,mcats57)} (vm\_btm\_reg(j,emis\_cell) \\

&*(1 - v57\_maccs\_mitigation(i,mcats57))

\end{align*}

Equation 12 estimates the mitigation costs (which enters the core cost objective function) as the product of emissions before technical mitigation and the unit cost of mitigation derived in equation 13.

Equation 12:

\begin{align*}

vm\_maccs\_costs(i) &\ge \sum_{emis\_to\_mcats57(emis\_reg,maccs57)} (vm\_btm\_reg(i,emis\_reg) \\

&* v57\_maccs\_unitcost(i,maccs57)) \\

&+ \sum_{cell(i,j)} \sum_{emis\_to\_mcats(emis\_cell,maccs57)} (vm\_btm\_cell(j,emis\_cell) \\

&* v57\_maccs\_unitcost(i,maccs57))

\end{align*}

Equation 13 calculates the costs per unit of reduction. The unit-costs rise with higher mitigation shares. The linear and exponential equations for the curve fitting are simply added, as for one of the two the parameters are always 0.

Equation 13:

\begin{align*}

v57\_maccs\_unitcost(i, maccs57) &= ic57\_maccs\_param(i, maccs,\text{"$linear$"})*v57\_maccs\_mitigation(i, maccs57) \\

&+ (ic57\_maccs\_param(i,maccs57,\text{"$exponential$"}) \\

&*v57\_maccs\_mitigation(i,maccs57) + 1)^{1/ic57\_maccs\_param(i,maccs57,\text{"$exponent$"})} - 1

\end{align*}

Finally, the maximum mitigation is constrained by bounds:

Equation 14

$v57\_maccs\_mitigation.up(i,maccs57) = ic57_maccs\_param(i,maccs57,"bound\_x")$

Equation 15

$v57\_maccs\_unitcost.up(i,maccs57) = ic57\_maccs\_param(i,maccs57,"bound\_y")$

For emission categories without MACC curves, no technical mitigation is allowed.

Equation 16

$v57\_maccs\_mitigation.fx(i,nomaccs57) = 0$

Limitations

There are no known limitations of this module realization

Name Description Unit A B $v57\_emis\_reg(i,emis)$ regional emissions by emission source category after technical mitigation Tg N, CH4 and C x x $v57\_emis\_cell(j,emis)$ cellular emissions by emission source category after technical mitigation Tg N, CH4 and C x x $v57\_exp\_emission\_costs\_co2(i,emis\_co2\_forestry)$ expected costs for co2_c emission pollution rights from afforestation mio US$ x x $v57\_emission\_costs\_reg\_yearly(i,emis\_yearly57)$ costs for pollution from emissions occurring yearly mio US$ x x $v57\_emission\_costs\_reg\_oneoff(i,emis\_oneoff57)$ costs for pollution from emissions occurring only once mio US$ x x $v57\_emission\_costs\_cell\_yearly(j,emis\_yearly57)$ costs for pollution from emissions occurring yearly mio US$ x x $v57\_emission\_costs\_cell\_oneoff(j,emis\_oneoff57)$ costs for pollution from emissions occurring only once mio US$ x x $v57\_maccs\_mitigation(i,mcats)$ intermediate calculations of mitigation costs % x $v57\_maccs\_unitcost(i, maccs)$ costs for the desired mitigation level per unit source emission US$/t x $f57\_policy\_emis\_integration(emis\_yearly57)$ application of CO2 price on land pools - x x $f57_maccs\_param(t\_all,i,maccs57,maccs\_param57)$ emission factors for N excreted on pasture land - x $ic57\_maccs\_param(i, maccs, maccs\_param)$ mac curve parameters - x $emis\_reg\_oneoff57$ regional oneoff emission sources - x x $emis\_cell\_oneoff57$ cellular oneoff emission sources - x x $emis\_pricing\_allland57$ cellular emission pricing all land pools - x x $emis\_pricing\_forestry57$ cellular emission pricing forestry land pool - x x $emis\_reg\_yearly57$ regional yearly emission sources - x x $emis\_cell\_yearly57$ cellular yearly emission sources - x x $mcats57$ mitigation categories - x $maccs57$ mitigation categories with MACCS - x $nomaccs57$ mitigation categories without MACCS - x $maccs\_param57$ parameters of MAC-curve - x $emis\_to\_mcats57$ set mapping from $emis$ to $mcats57$ - x $emis\_to\_maccs57$ set mapping from $emis$ to $maccs57$ - x

_{The last columns of the table indicate the usage in the different realizations (numbered with capital letters)}

## Developer(s)¶

Benjamin Leon Bodirsky

## See Also¶

Overview, 51_nitrogen, 52_carbon, 53_methane

## References¶

^{1} Lucas, P. L., D.P. Van Vuuren, J. G. J. Olivier, and M. Den Elzen. 2007. Long-term reduction potential of non-CO2 greenhouse gases.