[{"assumptions":["TCR is treated as a single representative scalar (best estimate 1.8\u00b0C, likely 1.2\u20132.4\u00b0C per AR6)","Instantaneous equilibration of forcing to temperature (ignores ocean heat uptake lag)","Log-linear forcing from CO\u2082 only; non-CO\u2082 forcings captured in scenario multipliers"],"category":"Climate","derived_from":["EQ-EMI-001"],"id":"EQ-CLM-001","last_reviewed":"2026-01-15","latex":"T(t) = \\mathrm{TCR} \\cdot \\frac{\\ln(C(t)/C_0)}{\\ln 2}","model_class":"Scenario","model_deps":["ClimateModelService","MonteCarloEngine"],"name":"Transient Climate Response (TCR) warming estimate","pages":["/run/<id>/step/2","/run/<id>/step/9"],"plain":"Warming above pre-industrial is proportional to TCR and the log ratio of current to pre-industrial CO\u2082 concentration.","review_status":"current","sensitivity":"critical","source":"IPCC AR6 WG1 Chapter 4; Matthews et al. 2009 Nature","uncertainty":"TCR uncertainty (\u00b10.6\u00b0C at 1\u03c3) dominates temperature pathway uncertainty up to 2050","units":"\u00b0C","variables":{"C(t)":"Atmospheric CO\u2082 concentration at time t (ppm)","C_0":"Pre-industrial CO\u2082 baseline (278 ppm)","T(t)":"Global mean surface temperature anomaly (\u00b0C)","TCR":"Transient Climate Response (\u00b0C per CO\u2082 doubling)"}},{"assumptions":["Linear interpolation of annual emissions between scenario waypoints","Non-CO\u2082 forcing converted to CO\u2082-equivalent using GWP100 from AR6","Permafrost carbon feedbacks partially included per AR6 Table SPM.2 footnotes"],"category":"Climate","derived_from":[],"id":"EQ-CLM-002","last_reviewed":"2026-01-15","latex":"B_{\\mathrm{rem}} = B_{\\mathrm{total}} - \\int_{t_0}^{t} E(\\tau)\\,d\\tau","model_class":"Scenario","model_deps":["ClimateModelService"],"name":"Carbon budget remaining (integrated emissions constraint)","pages":["/run/<id>/step/2","/run/<id>/step/7"],"plain":"Remaining carbon budget equals total IPCC-assessed budget minus cumulative emissions since the reference year.","review_status":"current","sensitivity":"critical","source":"IPCC AR6 WG1 Table SPM.2; Friedlingstein et al. 2022 ESSD","uncertainty":"Budget uncertainty \u00b1220 GtCO\u2082 at 1\u03c3 (IPCC AR6); dominated by TCRE distribution","units":"GtCO\u2082","variables":{"B_rem":"Remaining carbon budget (GtCO\u2082)","B_total":"Total IPCC SR1.5/AR6 budget from reference year (GtCO\u2082)","E(\u03c4)":"Annual net CO\u2082 emissions at time \u03c4 (GtCO\u2082/yr)","t_0":"Reference year (2020 for AR6 budgets)"}},{"assumptions":["Reference pathway is 'current policies' from UNEP EGR 2024 (57.4 GtCO\u2082e in 2025)","Linear ramp assumption for abatement deployment between waypoints","LULUCF net emissions treated separately from energy-system abatement"],"category":"Climate","derived_from":["EQ-CLM-002"],"id":"EQ-CLM-003","last_reviewed":"2026-02-01","latex":"A(t) = E_{\\mathrm{ref}}(t) - E_{\\mathrm{target}}(t)","model_class":"Scenario","model_deps":["ClimateModelService","GapAccountingEngine"],"name":"Emissions pathway abatement requirement","pages":["/run/<id>/step/7"],"plain":"Required abatement is the gap between the reference-policy emissions trajectory and the target pathway.","review_status":"current","sensitivity":"high","source":"UNEP Emissions Gap Report 2024; IEA World Energy Outlook 2024","uncertainty":"Reference pathway uncertainty \u00b13 GtCO\u2082e/yr; target pathway dependent on budget choice","units":"GtCO\u2082e/yr","variables":{"A(t)":"Required annual abatement at year t (GtCO\u2082e/yr)","E_ref(t)":"Reference policy emissions trajectory (GtCO\u2082e/yr)","E_target(t)":"Scenario target pathway (GtCO\u2082e/yr)"}},{"assumptions":["Damages are symmetric around global mean temperature (ignores distributional heterogeneity)","Quadratic form implies accelerating but bounded damage \u2014 challenged by tipping-point literature","\u03b1 = 0.00267 from DICE-2023; alternative calibrations range 0.001\u20130.01","Does not capture catastrophic or non-linear tipping point damage"],"category":"Physical Damage","derived_from":["EQ-CLM-001"],"id":"EQ-DAM-001","last_reviewed":"2026-01-20","latex":"D(T) = \\frac{\\alpha T^2}{1 + \\alpha T^2}","model_class":"Scenario","model_deps":["DamageModelService"],"name":"DICE-style damage function (quadratic)","pages":["/run/<id>/step/9","/run/<id>/step/11"],"plain":"Fraction of GDP lost to climate damage as a quadratic function of temperature anomaly, calibrated to Nordhaus DICE-2023.","review_status":"current","sensitivity":"critical","source":"Nordhaus (2023) DICE model; Howard & Sterner (2017) meta-analysis","uncertainty":"Damage function specification is the single largest uncertainty in long-run economic cost; estimates vary by 10\u00d7 across literature","units":"fraction of GDP","variables":{"D(T)":"Fractional GDP damage","T":"Global mean temperature anomaly above pre-industrial (\u00b0C)","\u03b1":"Damage coefficient (0.00267 in DICE-2023 calibration)"}},{"assumptions":["Poisson process for event occurrence (memoryless, independent events)","Stationarity of hazard distribution (violated under climate change \u2014 CE applies non-stationarity adjustment)","Vulnerability functions are sector-constant within broad industry categories"],"category":"Physical Damage","derived_from":[],"id":"EQ-DAM-002","last_reviewed":"2026-01-20","latex":"\\mathrm{AAL} = \\int_0^{\\infty} L(p)\\,dp \\approx \\sum_i \\frac{L_i + L_{i+1}}{2} \\cdot (p_i - p_{i+1})","model_class":"Scenario","model_deps":["DamageModelService","CatastropheModel"],"name":"Annualised average loss (catastrophe actuarial)","pages":["/run/<id>/step/9","/run/<id>/step/12"],"plain":"Expected annual loss is the area under the exceedance probability curve \u2014 the actuarial integral over all loss-return-period combinations.","review_status":"current","sensitivity":"high","source":"RMS, AIR, catastrophe model industry standard; Guy Carpenter (2023)","uncertainty":"Model-to-model AAL variation \u00b130\u201350% across major cat model vendors for any given region/peril","units":"$bn/yr","variables":{"AAL":"Annualised average loss ($bn/yr)","L(p)":"Loss at exceedance probability p ($bn)","L_i":"Ground-up loss at return period i","p_i":"Exceedance probabilities at each return period level"}},{"assumptions":["Linear-quadratic form is a first-order approximation; non-linear tipping points not modelled","Adaptation (air conditioning, schedule shifting) is captured in a separate adaptation service","Sector labour shares from ILO 2023; outdoor exposure fractions from WHO"],"category":"Physical Damage","derived_from":["EQ-CLM-001"],"id":"EQ-DAM-003","last_reviewed":"2026-01-20","latex":"\\mathrm{LPL} = \\max\\!\\left(0,\\; \\beta_1 \\cdot (\\mathrm{WBGT} - \\mathrm{WBGT}_{\\mathrm{thresh}}) + \\beta_2 \\cdot (\\mathrm{WBGT} - \\mathrm{WBGT}_{\\mathrm{thresh}})^2\\right)","model_class":"Scenario","model_deps":["DamageModelService"],"name":"Labour productivity loss from heat stress (WBGT model)","pages":["/run/<id>/step/9"],"plain":"Labour productivity loss increases with wet-bulb globe temperature above a threshold, calibrated to sector-specific outdoor/indoor labour mix.","review_status":"current","sensitivity":"medium","source":"Kjellstrom et al. (2016) Lancet Planetary Health; Burke et al. (2015) Nature","uncertainty":"\u03b2 coefficient uncertainty \u00b140%; WBGT projection uncertainty from GCM spread dominates","units":"fraction of potential GDP","variables":{"LPL":"Labour productivity loss (fraction of potential output)","WBGT":"Wet-bulb globe temperature (\u00b0C)","WBGT_thresh":"Sector threshold (27\u00b0C outdoor heavy, 32\u00b0C indoor light)","\u03b2\u2081, \u03b2\u2082":"Sector-calibrated coefficients from Kjellstrom et al. 2016"}},{"assumptions":["Smooth, convex MAC curve \u2014 in practice, MAC curves have discontinuities at technology step changes","Perfect competition in carbon markets (no market power, no transaction costs)","MAC curve calibrated to IEA NZE scenario technology cost projections"],"category":"Economics","derived_from":["EQ-CLM-003"],"id":"EQ-ECO-001","last_reviewed":"2026-02-01","latex":"C^* = \\frac{\\partial \\mathrm{TC}}{\\partial A}\\bigg|_{A = A^*}","model_class":"Scenario","model_deps":["EconomicModelService","GapAccountingEngine"],"name":"Marginal abatement cost curve (MAC) \u2014 carbon price equilibrium","pages":["/run/<id>/step/5","/run/<id>/step/11"],"plain":"The equilibrium carbon price equals the marginal abatement cost at the policy-target abatement level.","review_status":"current","sensitivity":"critical","source":"IPCC AR6 WG3 Chapter 3; IEA Net Zero 2050 (2021)","uncertainty":"Carbon price range for 1.5\u00b0C: $50\u2013250/t by 2030 (IPCC AR6 Table 13.SM.2)","units":"$/tCO\u2082e","variables":{"A":"Annual abatement (GtCO\u2082e/yr)","A*":"Policy-target abatement level","C*":"Equilibrium carbon price ($/tCO\u2082e)","TC":"Total transition cost function ($tn)"}},{"assumptions":["Constant returns to scale in K and L","Capital income share \u03b1 = 0.35 (OECD average; varies significantly across developing economies)","Climate damage enters multiplicatively (not additively) \u2014 implies no threshold catastrophe"],"category":"Economics","derived_from":["EQ-DAM-001"],"id":"EQ-ECO-002","last_reviewed":"2026-02-01","latex":"Y(t) = A(t) \\cdot K(t)^\\alpha \\cdot L(t)^{1-\\alpha} \\cdot \\Omega(T,P)","model_class":"Scenario","model_deps":["EconomicModelService","DSGEModel"],"name":"Structural growth with climate adjustment (augmented Solow)","pages":["/run/<id>/step/11"],"plain":"Output is an augmented Cobb-Douglas production function where \u03a9(T,P) is a climate-policy multiplier reducing productivity under both physical damage and transition costs.","review_status":"current","sensitivity":"high","source":"Solow (1956); Dietz & Stern (2015) DICE extension; Burke et al. (2015)","uncertainty":"\u03a9 specification drives long-run GDP uncertainty; \u03b1 uncertainty \u00b10.05 has minor near-term impact","units":"USD (real)","variables":{"A(t)":"Total factor productivity","K(t)":"Capital stock","L(t)":"Effective labour","Y(t)":"Real GDP","\u03a9(T,P)":"Climate-policy damage multiplier (0\u20131)","\u03b1":"Capital income share (~0.35)"}},{"assumptions":["Ramsey utility discounting with CRRA utility function","SCC range driven almost entirely by choice of \u03c1: Nordhaus \u2248$20, Stern \u2248$200, EPA 2023 \u2248$190","Damage function specification second-largest driver (see EQ-DAM-001)"],"category":"Economics","derived_from":["EQ-DAM-001","EQ-ECO-002"],"id":"EQ-ECO-003","last_reviewed":"2026-02-01","latex":"\\mathrm{SCC} = \\int_t^{\\infty} \\frac{\\partial D(\\tau)}{\\partial E_t} \\cdot e^{-\\rho(\\tau - t)}\\,d\\tau","model_class":"Scenario","model_deps":["EconomicModelService"],"name":"Social Cost of Carbon (Ramsey discounting)","pages":["/run/<id>/step/5","/run/<id>/step/11"],"plain":"The SCC is the present value of all future marginal damages from one additional tonne of CO\u2082 emitted today, discounted at the pure rate of time preference \u03c1.","review_status":"current","sensitivity":"critical","source":"Nordhaus (2017) AER; Stern (2006); US EPA (2023) revised SCC","uncertainty":"SCC values range $15\u2013$400 in mainstream literature; discount rate choice is fundamentally an ethical/political decision","units":"$/tCO\u2082","variables":{"D(\u03c4)":"Climate damage at time \u03c4","E_t":"Emissions at time t","SCC":"Social cost of carbon ($/tCO\u2082)","\u03c1":"Pure rate of time preference (Nordhaus: 1.5%; Stern: 0.1%)"}},{"assumptions":["100% pass-through of carbon price to covered emitters","Coverage rate: 40% global average (current); 75% in ambitious policy scenario","Carbon revenue recycling mechanism does not affect macro growth in this model (first-order only)"],"category":"Fiscal","derived_from":["EQ-ECO-001"],"id":"EQ-FIS-001","last_reviewed":"2026-02-01","latex":"R_c = \\tau_c \\cdot E_{\\mathrm{covered}} \\cdot \\frac{1}{\\mathrm{GDP}}","model_class":"Scenario","model_deps":["FiscalModelService"],"name":"Carbon revenue as fraction of GDP","pages":["/run/<id>/step/12"],"plain":"Carbon revenue (as share of GDP) equals the carbon tax/ETS price times covered emissions divided by GDP.","review_status":"current","sensitivity":"medium","source":"IMF Fiscal Monitor 2023; World Bank Carbon Pricing Dashboard","uncertainty":"Coverage rate uncertainty \u00b120 percentage points; pass-through uncertainty \u00b130%","units":"% of GDP","variables":{"E_covered":"Covered emissions under the carbon pricing scheme (GtCO\u2082e/yr)","GDP":"Nominal GDP ($tn)","R_c":"Carbon revenue (% GDP)","\u03c4_c":"Carbon price ($/tCO\u2082e)"}},{"assumptions":["Climate risk premium is additive to baseline WACC","Physical risk premium calibrated to cat bond spreads and TCFD disclosures","Transition risk premium calibrated to fossil fuel stranded asset write-down scenarios"],"category":"Finance","derived_from":["EQ-ECO-002","EQ-DAM-001"],"id":"EQ-FIN-001","last_reviewed":"2026-02-10","latex":"\\mathrm{WACC} = \\frac{E}{V} R_e + \\frac{D}{V} R_d (1-T_c) + \\Delta_{\\mathrm{climate}}","model_class":"Scenario","model_deps":["FinancialStressService"],"name":"Weighted average cost of capital (WACC) \u2014 climate-adjusted","pages":["/run/<id>/step/13"],"plain":"Climate-adjusted WACC adds a climate risk premium to the standard WACC formula, reflecting higher physical and transition risk in the cost of equity and debt.","review_status":"current","sensitivity":"high","source":"Modigliani-Miller (1958); IPCC AR6 WG3 Chapter 15; GFANZ (2023)","uncertainty":"Climate risk premium estimates vary 0\u2013300bps across methodologies; sector-specific calibration adds \u00b1100bps","units":"%","variables":{"D/V":"Debt share of capital structure","E/V":"Equity share of capital structure","R_d":"Cost of debt (pre-tax)","R_e":"Cost of equity (CAPM-derived)","T_c":"Corporate tax rate","\u0394_climate":"Climate risk premium addition (0\u2013200bps depending on scenario)"}},{"assumptions":["N=2000 samples sufficient for stable P5/P95 estimates (verified by convergence test)","Parameter distributions are independent (covariance structure partially captured via \u03b4 factor)","Normal/triangular/uniform distributions \u2014 tails may be heavier in reality"],"category":"Uncertainty","derived_from":[],"id":"EQ-UNC-001","last_reviewed":"2026-01-10","latex":"\\hat{\\mu} = \\frac{1}{N}\\sum_{i=1}^{N} f(\\theta_i), \\quad \\mathrm{CI}_{90} = [P_{5}(f), P_{95}(f)]","model_class":"Diagnostic","model_deps":["MonteCarloEngine"],"name":"Monte Carlo expected value and confidence interval","pages":["/run/<id>/step/8"],"plain":"Monte Carlo mean and 90% confidence interval estimated from N=2000 samples drawn from parameter distributions.","review_status":"current","sensitivity":"medium","source":"Metropolis & Ulam (1949); IPCC AR6 uncertainty guidance; CE internal calibration","uncertainty":"Sampling error in P5/P95 ~\u00b12% at N=2000; parameter distribution assumptions dominate","units":"depends on output variable","variables":{"N":"Number of Monte Carlo samples (2000 in CE)","P_5, P_95":"5th and 95th percentiles of output distribution","\u03b8_i":"Parameter vector drawn from joint distribution","\u03bc\u0302":"Sample mean of output f"}},{"assumptions":["\u03b4 = 0.22 is a central estimate; empirically poorly constrained","Covariance structure: \u03c1_elec = 0.21 for energy technologies; \u03c1_CDR = 0.25 for carbon removal","Linear scaling of overlap with portfolio size \u2014 likely underestimates overlap at high ambition levels"],"category":"Uncertainty","derived_from":[],"id":"EQ-UNC-002","last_reviewed":"2026-02-01","latex":"A_{\\mathrm{net}} = A_{\\mathrm{gross}} \\cdot (1 - \\delta)","model_class":"Scenario","model_deps":["GapAccountingEngine"],"name":"Portfolio abatement de-duplication factor (overlap discount)","pages":["/run/<id>/step/6","/run/<id>/step/7"],"plain":"Net abatement equals gross portfolio abatement discounted by factor \u03b4 to account for double-counting of overlapping mitigation pathways (e.g. electrification + grid decarbonisation).","review_status":"current","sensitivity":"high","source":"IEA NZE 2023 scenario accounting; Luderer et al. (2019) Nature Climate Change","uncertainty":"\u03b4 range 0.10\u20130.35 translates to \u00b15\u20137 GtCO\u2082e/yr uncertainty in net abatement at 30 Gt gross","units":"fraction","variables":{"A_gross":"Sum of all individual technology/policy abatement claims","A_net":"Net unique abatement (GtCO\u2082e/yr)","\u03b4":"De-duplication factor (default 0.22; range 0.10\u20130.35)"}},{"assumptions":["Additively separable drivers \u2014 in reality, population, income, and technology co-evolve","Non-CO\u2082 GHGs expressed as CO\u2082-equivalent using GWP100 (AR6 values)","LULUCF emissions accounted separately"],"category":"Emissions","derived_from":[],"id":"EQ-EMI-001","last_reviewed":"2026-01-15","latex":"E = P \\cdot \\frac{G}{P} \\cdot \\frac{E_{\\mathrm{prim}}}{G} \\cdot \\frac{E_{\\mathrm{CO_2}}}{E_{\\mathrm{prim}}}","model_class":"Reference","model_deps":["ClimateModelService","EconomicModelService"],"name":"Kaya identity \u2014 CO\u2082 emissions decomposition","pages":["/run/<id>/step/7"],"plain":"Total CO\u2082 emissions equal population \u00d7 per-capita GDP \u00d7 energy intensity of GDP \u00d7 carbon intensity of energy.","review_status":"current","sensitivity":"medium","source":"Kaya (1990); IPCC AR6 WG3 Figure SPM.4","uncertainty":"Identity is exact; uncertainty enters through projection of each driver","units":"GtCO\u2082/yr","variables":{"E":"CO\u2082 emissions (GtCO\u2082/yr)","E_CO\u2082/E_prim":"Carbon intensity of energy (GtCO\u2082/EJ)","E_prim/G":"Primary energy intensity (EJ/$tn GDP)","G/P":"Per-capita GDP ($/person)","P":"Population (billions)"}},{"assumptions":["Weights w_1\u2013w_4 are expert-calibrated, not empirically estimated","Linear combination \u2014 assumes no interaction effects between pathway and policy","Score normalisation maps to qualitative risk tiers: Low <0.4, Medium 0.4\u20130.7, High >0.7"],"category":"Emissions","derived_from":[],"id":"EQ-EMI-002","last_reviewed":"2026-02-10","latex":"P_{\\mathrm{trans}} = w_1 \\cdot s_{\\mathrm{path}} + w_2 \\cdot s_{\\mathrm{policy}} + w_3 \\cdot s_{\\mathrm{emission}} + w_4 \\cdot s_{\\mathrm{shock}}","model_class":"Diagnostic","model_deps":["ClimateModelService"],"name":"Transition pressure composite index","pages":["/scenarios","/run/<id>/step/2"],"plain":"CE's internal transition pressure score is a weighted composite of pathway intensity, policy regime stringency, sector emissions profile, and shock overlay.","review_status":"current","sensitivity":"medium","source":"CE internal calibration against NGFS Phase IV scenario outputs","uncertainty":"Weight uncertainty \u00b10.1 per component translates to \u00b10.15 composite score uncertainty","units":"dimensionless (0\u20131)","variables":{"P_trans":"Transition pressure score (0\u20131 normalised)","s_emission":"Sector emissions intensity score","s_path":"Scenario pathway score (SSP1.9=1.0 \u2026 SSP5.8.5=0.1)","s_policy":"Policy regime score (net-zero=1.0 \u2026 delayed=0.1)","s_shock":"Active shock overlay score","w_1\u2013w_4":"Calibrated weights (0.40, 0.30, 0.20, 0.10)"}}]