Nomenclature#
The mathematical symbols used in the models.
Symbol |
Description |
|---|---|
\(o\) |
Delay output variable |
\(i\) |
Delay input variable |
\(\tau\) |
Delay-time (time constant) |
\(D\) |
Aggregate demand |
\(Pop\) |
Population |
\(I\) |
Per-capita income |
\(p\) |
Ticket price |
\(\epsilon_{\upsilon}\) |
Elasticity of demand to variable \(\upsilon\) |
\(\sigma\) |
Calibration constant |
\(RPKpc_{trend}\) |
Trend per-capita Revenue Passenger Kilometers |
\(L\) |
Left asymptote (propensity to travel at zero income) |
\(R\) |
Right asymptote (propensity to travel at infinite income) |
\(\iota\) |
Income per capita at the inflection point |
\(B\) |
Logistic growth rate |
\(C\) |
Logistic control of the transition between asymptotes |
\(\nu\) |
Logistic control of maximum growth |
\(RPKpc_{story}\) |
Storyline-adjusted per-capita Revenue Passenger Kilometers |
\(F_{SSP}\) |
Storyline multiplier factor |
\(RPK_{trend}\) |
Trend total Revenue Passenger Kilometers |
\(ASK_{trend}\) |
Trend Available Seat Kilometers |
\(LF\) |
Load factor (RPK/ASK) |
\(ASK\) |
Total Available Seat Kilometers |
\(ASK_m\) |
Available Seat Kilometers for market \(m\) |
\(S_m\) |
Share of trend supply for market \(m\) |
\(SR_m\) |
Supply-shift ratio for market \(m\) |
\(\epsilon_p\) |
Price elasticity of demand |
\(p_{cap}\) |
Capped ticket price |
\(p_{trend}\) |
Trend ticket price |
\(D_{cap}\) |
Capped demand |
\(D_{trend}\) |
Trend demand |
\(\theta_{avoidance}\) |
Annual burden associated with demand aversion |
\(d_f\) |
Social discount rate |
\(\Theta_{avoidance}\) |
Present valuation of future policy burdens |
\(S^{\max}_{a}\) |
Maximum market share of aircraft \(a\) |
\(t_{ramp}\) |
Ramp duration for fleet replacement |
\(\tau_{fleet}\) |
Fleet replacement time constant |
\(ASK_{aircraft}\) |
ASK covered by a specific aircraft type |
\(EC_{aircraft}\) |
Energy consumption per ASK for an aircraft type |
\(C_{aircraft}\) |
Total energy consumed by an aircraft type |
\(C^{direct}_{energy}\) |
Direct embarked consumption of each energy carrier |
\(IF_{pathway}\) |
Impact factor per unitary production for a pathway |
\(IF^{direct}_{pathway}\) |
Direct impact generated at production for a pathway |
\(CF_{p,i}\) |
Consumption of input \(i\) per unitary production of pathway \(p\) |
\(IF_{energy}\) |
Energy mean impacts weighted by pathway shares |
\(S_p\) |
Share of production for pathway \(p\) |
\(P_{energy}\) |
Total production of an energy type |
\(P_{pathway}\) |
Production of a specific pathway |
\(C_{pathway,input}\) |
Input consumption of a pathway |
\(C_{energy,input}\) |
Aggregated input consumption by energy type |
\(C_{resource}\) |
Total consumption of a resource |
\(s_{resource}\) |
Allocation share for a resource |
\(P_{resource}\) |
Total production of a resource |
\(B_{CO_2}\) |
Target carbon budget |
\(s_{CO_2}\) |
Fair share of carbon budget for aviation |
\(CO_2\) |
Carbon dioxide emissions |