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General structure

The MIMOSA model consists of several sub-modules, called model components. Each component is made up of multiple variables (global or regional), parameters and equations (called constraints).

  • Economics

    Cobb-Douglas production function, investments, consumption and capital stock

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  • Welfare

    Welfare and the utility function

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  • Emissions and temperature

    • Baseline emissions, regional mitigated emissions and cumulative emissions
    • Temperature module
    • Constraints on emissions like inertia

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  • Mitigation

    Mitigation costs and Marginal Abatement Cost curve

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  • Sea-level rise

    Determines the level of global sea-level rise

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  • Damages

    Temperature related damages and sea-level rise related damages

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  • Effort-sharing

    Optional Various effort-sharing regimes to distribute the mitigation (and sometimes damage) costs

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  • Emission trading

    Optional Allows for global trade of emission reductions

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  • Financial transfers

    Optional Financial transfer schemes like a global damage cost pool

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Building the abstract model

Builds the abstract model for MIMOSA by combining all components. Some components are optional. In the parameters, different variants of some components can be chosen. The components are:

  • damage_module: The damage module to use
  • emissiontrade_module: The emission trading module to use
  • financialtransfer_module: The financial transfer module to use
  • welfare_module: The welfare module to use
  • objective_module: The objective module to use
Source code in mimosa/abstract_model.py 
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def create_abstract_model(
    damage_module: str,
    emissiontrade_module: str,
    financialtransfer_module: str,
    welfare_module: str,
    objective_module: str,
) -> AbstractModel:
    """
    ## Building the abstract model

    Builds the abstract model for MIMOSA by combining all components. Some components are optional. In the
    parameters, different variants of some components can be chosen. The components are:

    - `damage_module`: The damage module to use
    - `emissiontrade_module`: The emission trading module to use
    - `financialtransfer_module`: The financial transfer module to use
    - `welfare_module`: The welfare module to use
    - `objective_module`: The objective module to use

    """
    m = AbstractModel()

    ## Constraints
    # Each constraint will be put in this list,
    # then added to the model at the end of this file.
    constraints = []

    ## Time and region
    m.beginyear = Param()
    m.dt = Param()
    m.tf = Param()
    m.t = Set()
    m.year = None  # Initialised with concrete instance
    m.year2100 = Param()

    m.regions = Set(ordered=True)

    ######################
    # Create data functions
    # Will be initialised when creating a concrete instance of the model
    ######################

    m.baseline_emissions = lambda year, region: None
    m.population = lambda year, region: None
    m.TFP = lambda year, region: None
    m.GDP = lambda year, region: None
    m.carbon_intensity = lambda year, region: None

    def baseline_cumulative(year_start, year_end, region):
        years = np.linspace(year_start, year_end, 100)
        return np.trapz(m.baseline_emissions(years, region), x=years)

    m.baseline_cumulative = baseline_cumulative
    m.baseline_cumulative_global = lambda m, year_start, year_end: sum(
        baseline_cumulative(year_start, year_end, r) for r in m.regions
    )

    ######################
    # Components
    ######################

    # Emissions and temperature equations
    constraints.extend(emissions.get_constraints(m))

    # Sea level rise
    constraints.extend(sealevelrise.get_constraints(m))

    # Damage costs
    if damage_module == "RICE2010":
        constraints.extend(damages.ad_rice2010.get_constraints(m))
    elif damage_module == "WITCH":
        constraints.extend(damages.ad_witch.get_constraints(m))
    elif damage_module == "RICE2012":
        constraints.extend(damages.ad_rice2012.get_constraints(m))
    elif damage_module == "COACCH":
        constraints.extend(damages.coacch.get_constraints(m))
    elif damage_module == "nodamage":
        constraints.extend(damages.nodamage.get_constraints(m))
    else:
        raise NotImplementedError

    # Abatement costs
    constraints.extend(mitigation.get_constraints(m))

    # Emission trading
    if emissiontrade_module == "notrade":
        constraints.extend(emissiontrade.notrade.get_constraints(m))
    elif emissiontrade_module == "globalcostpool":
        constraints.extend(emissiontrade.globalcostpool.get_constraints(m))
    elif emissiontrade_module == "emissiontrade":
        constraints.extend(emissiontrade.emissiontrade.get_constraints(m))
    else:
        raise NotImplementedError(
            f"Emission trading module `{emissiontrade_module}` not implemented"
        )

    # Financial transfer
    if financialtransfer_module == "notransfer":
        constraints.extend(financialtransfer.notransfer.get_constraints(m))
    elif financialtransfer_module == "globaldamagepool":
        constraints.extend(financialtransfer.globaldamagepool.get_constraints(m))
    else:
        raise NotImplementedError(
            f"Financial transfer module `{financialtransfer_module}` not implemented"
        )

    # Burden sharing regime
    constraints.extend(burdensharing.get_constraints(m))

    # Cobb-Douglas and economics
    constraints.extend(cobbdouglas.get_constraints(m))

    # Utility and welfare
    if welfare_module == "welfare_loss_minimising":
        constraints.extend(welfare.welfare_loss_minimising.get_constraints(m))
    elif welfare_module == "cost_minimising":
        constraints.extend(welfare.cost_minimising.get_constraints(m))
    elif welfare_module == "inequal_aversion_general":
        constraints.extend(welfare.inequal_aversion_general.get_constraints(m))
    else:
        raise NotImplementedError(f"Welfare module `{welfare_module}` not implemented")

    # Objective of optimisation
    if objective_module == "utility":
        objective_rule, objective_constraints = objective.utility.get_constraints(m)
    elif objective_module == "globalcosts":
        objective_rule, objective_constraints = objective.globalcosts.get_constraints(m)
    else:
        raise NotImplementedError

    constraints.extend(objective_constraints)

    ######################
    # Add constraints to abstract model
    ######################

    for constraint in constraints:
        add_constraint(m, constraint.to_pyomo_constraint(m), constraint.name)

    m.obj = objective_rule

    return m