Functional Units And Allocation Methods For AESA Study Objectives

This note helps choose both the functional unit (fu_code) and the allocation method selectors used by:

• deterministic_asocc(...) and uncertainty_asocc(...)

• deterministic_acc(...) and uncertainty_acc(...)

• deterministic_asr(...) and uncertainty_asr(...)

• Only FU code: deterministic_io_lca(...) and uncertainty_io_lca(...)

The functional unit (FU) and allocation method tables of this file summarize methodological_notes/methodological_note__asocc_fus_allocation_methods.pdf. That appendix provides the definitions and mathematical expressions for each allocation method available in pyaesa.

Functional units

Choose first the functional unit according to the case study goal, scope, and system boundaries.

The accepted code syntax is the dot format shown below, for example fu_code="L2.c.b".

Symbols

Table 1. Sector and region selectors.

Symbol	Definition
s_p	Producing sector.
r_p	Producing region.
r_f	Final demand region where final demand occurs.
r_c	Total demand region where the studied outputs are first sold, whether the first sale is to intermediate demand or final demand.

The sector selector s_p is common to all level 2 (L2: sector level) FUs.

The region selectors (r_f, r_p, r_c) are specific per FU.

Table 2. Accounting boundary symbols.

Symbol	Definition
FD	Final demand.
TD	Total demand, i.e. final demand + intermediate demand/B2B.
CBA_FD	Consumption-based accounting of final demand -> Scopes 1, 2, 3.
CBA_TD	Consumption-based accounting of total demand -> Scopes 1, 2, 3
PBA	Production-based accounting -> Scope 1

Functional unit table

Table 3. Functional units available by study objective.

fu_code	Allocation level	Study objective represented by the FU	Accounting boundary	Required selectors
"L1.a"	L1	Final demand of goods and services in region(s) r_f in year t.	CBA_FD	r_f
"L1.b"	L1	Total production of goods and services by producing region(s) r_p in year t.	PBA	r_p
"L2.a.a"	L2	Total production of goods and services by sector s_p in producing region(s) r_p directly supplied to final demand worldwide in year t.	CBA_FD	s_p, r_p
"L2.a.b"	L2	Total production of goods and services by sector s_p in producing region(s) r_p in year t.	CBA_TD	s_p, r_p
"L2.a.c"	L2	Total production of goods and services by sector s_p in producing region(s) r_p in year t.	PBA	s_p, r_p
"L2.b.a"	L2	Total production of goods and services by sector s_p in producing region(s) r_p directly supplied to final demand in region(s) r_f in year t.	CBA_FD	s_p, r_p, r_f
"L2.b.b"	L2	Total production of goods and services by sector s_p in producing region(s) r_p directly supplied to total demand in region(s) r_c in year t.	CBA_TD	s_p, r_p, r_c
"L2.c.a"	L2	Final demand in region(s) r_f in year t of goods and services produced by sector s_p.	CBA_FD	s_p, r_f
"L2.c.b"	L2	Total demand in region(s) r_c in year t of goods and services produced by sector s_p.	CBA_TD	s_p, r_c

Reading L2 FU codes: Within L2, the middle letter describes how the sector and region scope is defined:

Table 4. L2 FU code sector and region scopes.

FU family	Scope represented
L2.a.*	Output of sector s_p produced in region(s) r_p, without selecting a demand region.
L2.b.*	Output of sector s_p produced in region(s) r_p and supplied to a selected demand region.
L2.c.*	Demand in a selected region for outputs of sector s_p, aggregated across producing regions.

The last letter describes the accounting boundary:

Table 5. L2 FU code accounting boundary suffixes.

Suffix	Boundary	Use when the ASR numerator (LCA) measures
.a	CBA_FD	Consumption-based accounting of outputs consumed by final demand (Scopes 1, 2, and 3).
.b	CBA_TD	Consumption-based accounting of outputs consumed by total demand, i.e. final demand and intermediate demand/B2B (Scopes 1, 2, and 3).
.c	PBA	Production-based accounting of direct burdens in the producing sector-region pair (Scope 1).

N.B., group_indices=True is not allowed for L2.a.b, L2.b.b, or L2.c.b because summing total demand CBA output rows can double count. For these FUs, define the upstream MRIO aggregation and disaggregation scope before running the study with process_mrio(...) arguments: agg_reg, agg_sec, and agg_version.

Allocation methods

The definitions and mathematical expressions for each allocation method are provided in methodological_notes/methodological_note__asocc_fus_allocation_methods.pdf. The allocation method labels below use the syntax accepted by pyaesa.

Allocation paths overview

Figure 1: Overview of UNCASExt/pyaesa allocation paths and methods across allocation levels and accounting system boundaries. The figure summarizes the allocation routes and method labels available across levels and accounting system boundaries.

^a UT(FDa) and UT(GVAa) are adjusted variants of UT(FD) and UT(GVA) designed to reflect overlapping supply-chain attributions of utility.

^b As the total direct and indirect GVA embodied in one unit of output equals that unit’s value, i.e. its FD, the one-step allocation paths UT(GVA) to UT(GVAa) and UT(FD) to UT(FDa) yield an identical result, here named one-step UT(TD). This one-step total demand approach is therefore neither consumption- nor production-anchored, analogously to one-step AR(E^{CBA_TD}).

L3 and L4 are not yet covered by pyaesa directly and can only be covered by doing “manual” postprocessing of pyaesa outputs. L3 and L4 require case study specific data. Examples include company revenues to scale a sector-level allocation to a firm-level allocation by comparing company turnover to total sector output in the MRIO, or activity data (e.g., passenger-kilometers delivered) benchmarked against corresponding totals at the relevant MRIO level. A future update of pyaesa will include the possibility to address these levels via user provided L3 and L4 datasets.

Method label syntax

Table 6. Allocation method label abbreviations.

Abbreviation	Meaning
SP	Sharing principle.
EM	Enacting metric.
UT	Utilitarian sharing principle.
EG	Egalitarian sharing principle.
PR	Prioritarian sharing principle.
HR	Historical responsibility.
AR	Acquired rights, also called grandfathering.
Pop	Population.
GDPcap	Gross domestic product per capita.
E	Environmental pressure.
Ecap	Per capita environmental pressure.
cum	Cumulative value over the responsibility period.
FD	Final demand.
TD	Total demand, i.e. final demand + intermediate demand/B2B.
FDa	Adjusted final demand, propagated through downstream supply chains with the Ghosh inverse.
GVA	Gross value added.
GVAa	Adjusted gross value added, propagated through upstream supply chains with the Leontief inverse.

Method selection arguments

Use method_plan="default" unless the study intentionally constrains the method set and provides justifications to do so. For L1 functional units, select subset of methods with l1_methods. For L2 functional units, select subsets of one-step methods with one_step_methods, two-step L2 methods with two_step_methods, and explicit L1 to L2 pairs of two-step methods with l1_l2_pairs.

Table 7. Accepted method_plan values.

Value	Meaning
"default"	Use all methods available for the selected FU.
"one_step"	Use only selected one-step L2 methods.
"two_steps"	Use only selected two-step L2 methods combined with compatible L1 methods.
"pairs"	Use only explicit l1_l2_pairs entries of two-step methods.
"one_step_pairs"	Use selected one-step L2 methods plus explicit l1_l2_pairs entries.

Explicit pair strings use the syntax L1METHOD::L2METHOD, for example EG(Pop)::UT(FDa). The part before :: is the L1 method and the part after :: is the L2 method. Method labels must match the registry labels exactly.

L1 allocation methods by FU

Table 8. L1 allocation methods available by FU.

fu_code	L1 methods
L1.a	EG(Pop), PR(GDPcap), PR-HR(Ecap,cum^{CBA_FD}), AR(E^{CBA_FD}), AR(Ecap^{CBA_FD})
L1.b	EG(Pop), PR(GDPcap), PR-HR(Ecap,cum^{PBA}), AR(E^{PBA}), AR(Ecap^{PBA})

L2 allocation methods by FU

One-step methods allocate the L2 FU directly against the global carrying capacity.

Two-step methods first allocate an L1 share against the global carrying capacity, then allocate the selected L2 FU inside that L1 share. When the L2 in L1 weight is consumption-based, the L1 vs global weight uses L1.a. When the L2 in L1 weight is production-based, the L1 vs global weight uses L1.b.

Table 9. L2 allocation route equations.

Route	Allocation structure
one-step	L2_aSoCC = L2 vs global
two-step	L2_aSoCC = L1 vs global * L2 in L1

Table 10. L2 allocation methods available by FU.

fu_code	one-step L2 vs global methods	L2 in L1 methods for two-step allocation	L1 vs global FU used for two-step methods
L2.a.a	UT(FD), AR(E^{CBA_FD})	UT(FD), AR(E^{CBA_FD})	L1.a
L2.a.b	UT(TD), AR(E^{CBA_TD})	UT(FDa) with L1.a; UT(GVAa) with L1.b	UT(FDa) uses L1.a; UT(GVAa) uses L1.b
L2.a.c	UT(GVA), AR(E^{PBA})	UT(GVA), AR(E^{PBA})	L1.b
L2.b.a	UT(FD), AR(E^{CBA_FD})	UT(FD), AR(E^{CBA_FD})	L1.a
L2.b.b	UT(TD), AR(E^{CBA_TD})	UT(FDa) with L1.a; UT(GVAa) with L1.b	UT(FDa) uses L1.a; UT(GVAa) uses L1.b
L2.c.a	UT(FD), AR(E^{CBA_FD})	UT(FD), AR(E^{CBA_FD})	L1.a
L2.c.b	UT(TD), AR(E^{CBA_TD})	UT(FDa) with L1.a; UT(GVAa) with L1.b	UT(FDa) uses L1.a; UT(GVAa) uses L1.b

What to do next

Now that you have been through tutorials/study_objectives/0_study_objectives.md and tutorials/study_objectives/1_functional_units_and_allocation_methods.md, go to the tutorial corresponding to your study end objective. The available study objective notebooks are listed in tutorials/study_objectives/0_study_objectives.md.