This page is generated from inline documentation in MESSAGE/parameter_def.gms.

Parameter definition

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_ix.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
df_period year cumulative discount factor over period duration [4]
df_year year discount factor of the last year in the period [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, 3) These parameters are computed during the GAMS execution.

Parameters of the Resources section

In MESSAGEix, the volume of resources at the start of the model horizon is defined by resource_volume. The quantity of the resources that are extracted per year is dependent on two parameters. The first is bound_extraction_up, which constraints the maximum extraction of the resources (by grade) in a year. The second is resource_remaining, which is the maximum extraction of the remaining resources in a certain year, as a percentage. Extraction costs for resources are represented by resource_cost parameter.

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]Commodity stock refers to an exogenous (initial) quantity of commodity in stock. 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 MESSAGEix 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 (maximum peak load factor for reliability constraint of firm capacity) and reliability_factor (reliability of a technology (per rating)) are based on the formulation proposed by Sullivan et al., 2013 [sullivan_VRE_2013]. It is used in Reliability of installed capacity.

Parameters of the Technology section

Input/output mapping, costs and engineering specifications

Parameter name Index dimensions
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 [11] 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 [13] node_loc | technology | year_vtg | year_act | mode | commodity | level | time | rating
renewable_capacity_factor [14] node_loc | commodity | grade | level | year
renewable_potential [14] 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]Maximum share of technology in commodity use per rating. The upper bound of a contribution by any technology to the constraints on system reliability (Reliability of installed capacity) and flexibility (Equation SYSTEM_FLEXIBILITY_CONSTRAINT) can depend on the share of the technology output in the total commodity use at a specific level.
[13]Contribution of technologies towards operation flexibility constraint. It is used in Equation SYSTEM_FLEXIBILITY_CONSTRAINT.
[14](1, 2) renewable_capacity_factor refers to the quality of renewable potential by grade and renewable_potential refers to the size of the renewable potential per grade.

Bounds on capacity and activity

The following parameters specify upper and lower bounds on new capacity, total installed capacity, and activity. The bounds on activity are implemented as the aggregate over all vintages in a specific period (Equation ACTIVITY_BOUND_UP and Equation ACTIVITY_BOUND_LO).

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

Dynamic constraints on capacity and activity

The following parameters specify constraints on the growth of new capacity and activity, i.e., market penetration. The implementation of MESSAGEix includes the functionality for ‘soft’ relaxations of dynamic constraints on new-built capacity and activity (see Keppo and Strubegger, 2010 [keppo_short_2010]). For more information, please refer to the equations in section Dynamic constraints on market penetration of the mathematical formulation.

Parameter name Index names
initial_new_capacity_up node_loc | tec | year_vtg
growth_new_capacity_up [15] node_loc | tec | year_vtg
soft_new_capacity_up [15] node_loc | tec | year_vtg
initial_new_capacity_lo node_loc | tec | year_vtg
growth_new_capacity_lo [15] node_loc | tec_actual | year_vtg
soft_new_capacity_lo [15] node_loc | tec | year_vtg
initial_activity_up [16] node_loc | tec | year_act | time
growth_activity_up [15] [16] node_loc | tec | year_act | time
soft_activity_up [15] node_loc | tec | year_act | time
initial_activity_lo [16] node_loc | tec | year_act | time
growth_activity_lo [15] [16] node_loc | tec | year_act | time
soft_activity_lo [15] node_loc | tec | year_act | time
[15](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).
[16](1, 2, 3, 4) The dynamic constraints are not indexed over modes in the MESSAGEix implementation.

Parameters for the add-on technologies

The implementation of MESSAGEix includes the functionality to introduce “add-on technologies” that are specifically linked to parent technologies. This feature can be used to model mitigation options (scrubber, cooling). Upper and lower bounds of add-on technologies are defined relative to the parent: addon_up and addon_lo, respectively.


No default addon_conversion factor (conversion factor between add-on and parent technology activity) is set. This is to avoid default conversion factors of 1 being set for technologies with multiple modes, of which only a single mode should be linked to the add-on technology.

Parameter name Index names
addon_conversion node | tec | year_vtg | year_act | mode | time | type_addon
addon_up node | tec | vintage | year | mode | time | type_addon
addon_lo node | tec | vintage | year | mode | time | type_addon

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 [keppo_short_2010]). Refer to the section Dynamic constraints on market penetration. Absolute cost and levelized cost multipliers are used for the relaxation of upper and lower bounds.

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

Auxiliary investment cost parameters include the remaining technical lifetime at the end of model horizon (beyond_horizon_lifetime) in addition to the different scaling factors and multipliers as listed below. These factors account for remaining capacity (remaining_capacity) or construction time of new capacity (construction_time_factor), the value of investment at the end of model horizon (end_of_horizon_factor) or the discount factor of remaining lifetime beyond model horizon (beyond_horizon_factor).

Parameter name Index names
construction_time_factor node | tec | year_all
remaining_capacity node | tec | year_all
end_of_horizon_factor node | tec | year_all
beyond_horizon_lifetime node | tec | year_all
beyond_horizon_factor node | tec | year_all

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 [17] type_emission | emission
bound_emission node | type_emission | type_tec | type_year
tax_emission node | type_emission | type_tec | type_year
[17]The parameter emission_scaling is the scaling factor to harmonize bounds or taxes across types of emissions. It 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. The parameters listed below refer to the assigned land scenario.

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 Share Constraints section

Share constraints define the share of a given commodity/mode to be active on a certain level. For the mathematical formulation, refer to Constraints on shares of technologies and commodities.

Parameter name Index dimensions
share_commodity_up shares | node_share | year_act | time
share_commodity_lo shares | node | year_act | time
share_mode_up shares | node_loc | technology | mode | year_act | time
share_mode_lo shares | node_loc | technology | mode | year_act | time

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. For the formulation of the relations, refer to Section of generic relations (linear constraints).

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 mimic 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.