Parameter definition

This page is generated from the auto-documentation in MESSAGE/parameter_def.gms.

This file contains the definition of all parameters used in MESSAGEix.

In MESSAGEix, all parameters are understood as yearly values, not as per (multi-year) period. This provides flexibility when changing the resolution of the model horizon (i.e., the set year).

Parameters written in italics are auxiliary parameters that are either generated automatically when exporting a MESSAGE-scheme ixmp.Scenario to gdx or that are computed during the pre-processing stage in GAMS.

General parameters of the MESSAGEix implementation

Parameter name Index dimensions Explanatory comments
duration_period (\(|y|\)) [1] year duration of multi-year period (in number of years) [2]
duration_time time duration of sub-annual time slices (relative to 1) [3]
duration_time_rel time | time relative duration between sub-annual time slices [4]
interestrate year economy-wide interest rate or social discount rate
discountfactor year cumulative discount factor over period duration [4]
[1]The short-hand notation \(|y|\) is used for the parameters \(duration\_period_y\) in the mathematical model documentation for exponents.
[2]The values for this parameter are computed automatically when exporting a MESSAGE-scheme ixmp.Scenario to gdx. Note that in MESSAGEix, the elements of the year set are understood to be the last year in a period, see this footnote.
[3]The element ‘year’ in the set of subannual time slices time has the value of 1. This value is assigned by default when creating a new ixmp.Scenario based on the MESSAGE scheme.
[4](1, 2) This parameter is computed during the GAMS execution.

Parameters of the Resources section

Parameter name Index dimensions
resource_volume node | commodity | grade
resource_cost node | commodity | grade | year
resource_remaining node | commodity | grade | year
bound_extraction_up node | commodity | level | year
commodity_stock [5] node | commodity | level | year
historical_extraction [6] node | commodity | grade | year
[5]This parameter allows (exogenous) additions to the commodity stock over the model horizon, e.g., precipitation that replenishes the water table.
[6](1, 2, 3, 4, 5) Historical values of new capacity and activity can be used for parametrising the vintage structure of existing capacity and implement dynamic constraints in the first model period.

Parameters of the Demand section

Parameter name Index dimensions
demand [demand_fixed] [7] node | commodity | level | year | time
peak_load_factor [8] node | commodity | year
[7]The parameter demand in a MESSAGE-scheme ixmp.Scenario is translated to the parameter demand_fixed in the MESSAGE implementation in GAMS. The variable DEMAND is introduced as an auxiliary reporting variable; it equals demand_fixed in a MESSAGE-standalone run and reports the final demand including the price response in an iterative MESSAGE-MACRO solution.
[8](1, 2) The parameters peak_load_factor and reliability_factor are based on the formulation proposed by Sullivan et al., 2013 [6]. It is used in Equation FIRM_CAPACITY_PROVISION.

Parameters of the Technology section

Input/output mapping, costs and engineering specifications

Parameter name Index names
input [9] node_loc | tec | year_vtg | year_act | mode | node_origin | commodity | level | time | time_origin
output [9] node_loc | tec | year_vtg | year_act | mode | node_dest | commodity | level | time | time_dest
inv_cost [9] node_loc | tec | year_vtg
fix_cost [9] node_loc | tec | year_vtg | year_act
var_cost [9] node_loc | tec | year_vtg | year_act | mode | time
levelized_cost [10] node_loc | tec | year_vtg | time
construction_time node_loc | tec | year_vtg
technical_lifetime node_loc | tec | year_vtg
capacity_factor [9] node_loc | tec | year_vtg | year_act | time
operation_factor [9] node_loc | tec | year_vtg | year_act
min_utilization_factor [9] node_loc | tec | year_vtg | year_act
rating_bin [12] node | technology | year_act | commodity | level | time | rating
reliability_factor [8] node | technology | year_act | commodity | level | time | rating
flexibility_factor node_loc | technology | year_vtg | year_act | mode | commodity | level | time | rating
renewable_capacity_factor node_loc | commodity | grade | level | year
renewable_potential node | commodity | grade | level | year
emission_factor node_loc | tec | year_vtg | year_act | mode | emission
[9](1, 2, 3, 4, 5, 6, 7, 8) Fixed and variable cost parameters and technical specifications are indexed over both the year of construction (vintage) and the year of operation (actual). This allows to represent changing technology characteristics depending on the age of the plant.
[10]The parameter levelized_cost is computed in the GAMS pre-processing under the assumption of full capacity utilization until the end of the technical lifetime.
[11]The construction time only has an effect on the investment costs; in MESSAGEix, each unit of new-built capacity is available instantaneously at the beginning of the model period.
[12]The upper bound of a contribution by any technology to the constraints on system reliability (Equation FIRM_CAPACITY_PROVISION) and flexibility (Equation OPERATING_RESERVE_CONSTRAINT) can depend on the share of the technology output in the total commodity use at a specific level.

Bounds on capacity and activity

The following parameters specify upper and lower bounds on new capacity, total installed capacity, and activity.

Parameter name Index names
bound_new_capacity_up node_loc | tec | year_vtg
bound_new_capacity_lo node_loc | tec | year_vtg
bound_total_capacity_up node_loc | tec | year_act
bound_total_capacity_lo node_loc | tec | year_act
bound_activity_up node_loc | tec | year_act | mode | time
bound_activity_lo node_loc | tec | year_act | mode | time

The bounds on activity are implemented as the aggregate over all vintages in a specific period (cf. Equation ACTIVITY_BOUND_UP and ACTIVITY_BOUND_LO).

Dynamic constraints on capacity and activity

The following parameters specify constraints on the growth of new capacity and activity, i.e., market penetration.

Parameter name Index names
initial_new_capacity_up node_loc | tec | year_vtg
growth_new_capacity_up [13] node_loc | tec | year_vtg
soft_new_capacity_up [13] node_loc | tec | year_vtg
initial_new_capacity_lo node_loc | tec | year_vtg
growth_new_capacity_lo [13] node_loc | tec_actual | year_vtg
soft_new_capacity_lo [13] node_loc | tec | year_vtg
initial_activity_up [14] node_loc | tec | year_act | time
growth_activity_up [13] [14] node_loc | tec | year_act | time
soft_activity_up [13] node_loc | tec | year_act | time
initial_activity_lo [14] node_loc | tec | year_act | time
growth_activity_lo [13] [14] node_loc | tec | year_act | time
soft_activity_lo [13] node_loc | tec | year_act | time
[13](1, 2, 3, 4, 5, 6, 7, 8) All parameters related to the dynamic constraints are understood as the bound on the rate of growth/decrease, not as in percentage points and not as (1+growth rate).
[14](1, 2, 3, 4) The dynamic constraints are not indexed over modes in the MESSAGEix implementation.

Cost parameters for ‘soft’ relaxations of dynamic constraints

The implementation of MESSAGEix includes the functionality for ‘soft’ relaxations of dynamic constraints on new-built capacity and activity (see Keppo and Strubegger, 2010 [3]). Refer to the section Dynamic constraints on market penetration.

Parameter name Index names
abs_cost_new_capacity_soft_up node_loc | tec | year_vtg
abs_cost_new_capacity_soft_lo node_loc | tec | year_vtg
level_cost_new_capacity_soft_up node_loc | tec | year_vtg
level_cost_new_capacity_soft_lo node_loc | tec | year_vtg
abs_cost_activity_soft_up node_loc | tec | year_act | time
abs_cost_activity_soft_lo node_loc | tec | year_act | time
level_cost_activity_soft_up node_loc | tec | year_act | time
level_cost_activity_soft_lo node_loc | tec | year_act | time

Historical capacity and activity values

Historical data on new capacity and activity levels are included in MESSAGEix for correct accounting of the vintage portfolio and a seamless implementation of dynamic constraints from historical years to model periods.

Parameter name Index names
historical_new_capacity [6] node_loc | tec | year_vtg
historical_activity [6] node_loc | tec | year_act | mode | time

Auxiliary investment cost parameters and multipliers

Documentation not yet included.

Parameters of the Emission section

The implementation of MESSAGEix includes a flexible and versatile accounting of emissions across different categories and species, with the option to define upper bounds and taxes on various (aggregates of) emissions and pollutants), (sets of) technologies, and (sets of) years.

Parameter name Index dimensions
historical_emission [6] node | emission | type_tec | year
emission_scaling [15] type_emission | emission
bound_emission node | type_emission | type_tec | type_year
tax_emission node | type_emission | type_tec | type_year
[15]The parameters emission_scaling allows to efficiently aggregate different emissions/pollutants and set bounds or taxes on various categories.

Parameters of the Land-Use model emulator section

The implementation of MESSAGEix includes a land-use model emulator, which draws on exogenous land-use scenarios (provided by another model) to derive supply of commodities (e.g., biomass) and emissions from agriculture and forestry.

Parameter name Index dimensions
historical_land [6] node | land_scenario | year
land_cost node | land_scenario | year
land_input node | land_scenario | year | commodity | level | time
land_output node | land_scenario | year | commodity | level | time
land_use node | land_scenario | year | land_type
land_emission node | land_scenario | year | emission
initial_land_scen_up node | land_scenario | year
growth_land_scen_up node | land_scenario | year
initial_land_scen_lo node | land_scenario | year
growth_land_scen_lo node | land_scenario | year
initial_land_up node | year | land_type
dynamic_land_up node | land_scenario | year | land_type
growth_land_up node | year | land_type
initial_land_lo node | year | land_type
dynamic_land_lo node | land_scenario | year | land_type
growth_land_lo node | year | land_type

Parameters of the Relations section

Generic linear relations are implemented in MESSAGEix. This feature is intended for development and testing only - all new features should be implemented as specific new mathematical formulations and associated sets & parameters.

Parameter name Index dimensions
relation_upper relation | node_rel | year_rel
relation_lower relation | node_rel | year_rel
relation_cost relation | node_rel | year_rel
relation_new_capacity relation | node_rel | year_rel | tec
relation_total_capacity relation | node_rel | year_rel | tec
relation_activity relation | node_rel | year_rel | node_loc | tec | year_act | mode

Fixed variable values

The following parameters allow to set variable values to a specific value. The value is usually taken from a solution of another model instance (e.g., scenarios where a shock sets in later to mimick imperfect foresight).

The fixed values do not override any upper or lower bounds that may be defined, so fixing variables to values outside of that range will yield an infeasible model.

Parameter name Index dimensions
fixed_extraction node | commodity | grade | year
fixed_stock node | commodity | level | year
fixed_new_capacity node | technology | year_vtg
fixed_capacity node | technology | year_vtg | year_act
fixed_activity node | technology | year_vtg | year_act | mode | time
fixed_land node | land_scenario | year

Note that the variable \(STOCK\_CHG\) is determined implicitly by the \(STOCK\) variable and therefore does not need to be explicitly fixed.