Footprint Estimation Methodology

Pipeline

classify model (pinned registry)        -> model class
resolve coefficients (with boundaries)  -> per-token Wh, uplifts, PUE, WUE, grid
token accounting                        -> fresh + cached input, output, reasoning
IT energy (accelerator boundary)        -> token terms summed
boundary normalization                  -> x idle/reserve uplift (server folded in), then x PUE
water                                   -> on-site: IT-boundary kWh x WUE (Green Grid definition)
                                           off-site: facility kWh x grid water intensity
carbon                                  -> facility kWh x location-based grid intensity x embodied uplift
uncertainty                             -> closed-form lognormal propagation, P05/P50/P95
persist                                 -> estimate + every resolved coefficient + version

Estimates are pure functions of (metadata, version). Every stored estimate persists the resolved coefficients actually used, so any historical number is reproducible by reading, not re-deriving.

Uncertainty

Two families of evidence for per-token energy disagree by roughly an order of magnitude: top-down provider disclosures (Google's published median Gemini prompt figures^{[1]Elsworth et al. (Google), 2025. Measuring the environmental impact of delivering AI at Google: median Gemini Apps text prompt at 0.24 Wh comprehensive versus 0.10 Wh accelerator-only, the anchor of the top-down evidence family. arXiv:2508.15734.}; Epoch AI's GPT-4o estimate^{[2]Epoch AI, 2025. How much energy does ChatGPT use? Independent estimate of roughly 0.3 Wh for a typical GPT-4o query, corroborating the top-down family.}; Mistral's lifecycle report^{[4]Mistral AI, 2025. Lifecycle analysis of Mistral Large 2 (with Carbone 4 and ADEME): a provider-published per-response footprint used to sanity-check the evidence families.}) imply low values, while parametric per-token fits (EcoLogits-style^{[3]EcoLogits (GenAI Impact). Open parametric methodology estimating per-request LLM energy from modeled parameter counts and serving hardware; the high (parametric) evidence family in the per-token energy range.}) imply high ones. Batching, hardware generation, and mixture-of-experts serving explain most of the gap, but it is unresolved. Centrals sit nearer the top-down family; P95 reaches the parametric family. Composed 90 percent intervals for frontier traffic span roughly 25 to 35 fold. Every displayed figure carries its range.

All coefficients are modeled lognormal. Products propagate exactly; sums use Fenton-Wilkinson moment matching^{[7]Fenton, 1960. The Sum of Log-Normal Probability Distributions in Scatter Transmission Systems (IRE Transactions on Communications): the moment-matching approximation used to combine lognormal terms.}. A customer's monthly total is aggregated by summing token counts per coefficient group first and applying coefficient uncertainty once, because coefficient error is fully correlated across a customer's events and does not average out.

Retirement obligations accrue at the 90th percentile of the range (P90) for every account: at credit prices this costs little and it makes the retired quantity plausibly meet or exceed the estimate in nine cases out of ten. There is no lower election. Under token-tier pricing with retirements bundled, a lower quantile would not change the subscription price; it would only reduce the quantity retired and weaken the statement the certificate supports, so the option does not exist. The console's footprint bars rise to P90, the accrual basis, with a shade change marking the median (P50). Accrual at P90 is labeled as retiring against a quantile of the estimate range, never as guaranteed coverage. Subscription pricing keys on billable tokens (fresh input + output + reasoning + 10 percent of cached input), never on footprint magnitude. The 10 percent cached rate is a fixed billing rule defined in pricing, deliberately distinct from this methodology's cached-input coefficient, so no coefficient here can influence revenue.

Calculation

For a usage event with fresh input tokens i, cached input tokens c, output tokens o, and reported reasoning tokens r, in model class m on facility profile f:

E_raw  = i·e_in(m) + c·e_in(m)·k_cache + o·e_out(m)·[k_hidden if reasoning-class and r unreported] + r·e_out(m)
E_raw  = E_raw · k_tier                    (batch or priority service tier, if any)
E_IT   = E_raw · U_idle                    (accelerator -> IT-equipment boundary)
E_fac  = E_IT · PUE(f)                     (IT -> facility boundary)

Water  = E_IT[kWh] · WUE(f)  +  E_fac[kWh] · W_grid          (liters; reported in mL)
Carbon = E_fac[kWh] · I_grid(zone) · U_embodied              (gCO2e, location-based)
Energy = E_fac                                               (Wh, facility boundary)

Every symbol is a lognormal coefficient from the tables below except token counts, which are metered and exact. Uncertainty propagates in closed form:

fit:      mu = ln(central)    sigma = max( ln(p95/central), ln(central/p05) ) / 1.6449
product:  mu = sum(mu_i)      sigma = sqrt( sum(sigma_i^2) )
sum:      Fenton-Wilkinson moment matching:
            S_mean = sum(exp(mu_j + sigma_j^2/2))
            S_var  = sum((exp(sigma_j^2) - 1) · exp(2·mu_j + sigma_j^2))
            sigma_S = sqrt( ln(1 + S_var/S_mean^2) )
            mu_S    = ln(S_mean) - sigma_S^2/2
quantile: P_q = exp( mu + z_q·sigma )    (z_0.05 = -1.6449, z_0.5 = 0, z_0.9 = 1.2816, z_0.95 = 1.6449)

Monthly totals sum token counts per coefficient group first and apply coefficient uncertainty once (full correlation across a customer's events), then combine groups with Fenton-Wilkinson^{[7]Fenton, 1960. The Sum of Log-Normal Probability Distributions in Scatter Transmission Systems (IRE Transactions on Communications): the moment-matching approximation used to combine lognormal terms.}.

Constants

Generated from src/core/methodology/configV1.ts (methodology 1.0.0). Every value is a lognormal coefficient: central is the median, P05 and P95 bound the 90 percent plausible range. Boundary states what the value already includes (accelerator, server, or facility) so uplifts are applied exactly once. Full source citations accompany each value in the config file.

Per-token IT energy (accelerator boundary)

The unclassified class is deliberately the most conservative row: unknown models route there, and above 15 percent unclassified tokens in a period the certificate carries a disclosure.

Uplifts and token accounting

The hidden-reasoning multiplier applies to reasoning-class models whose APIs do not report reasoning token counts; it never defaults to 1.0.

Facility profiles (PUE and on-site WUE)

A request whose region is not a recognizable cloud region code uses the direct-api or unknown profile; a customer-supplied region can never reduce the obligation.

Water and carbon intensity

Grid carbon is location-based annual average. In 1.0.0 every zone uses the conservative default above; the region-to-zone mapping already covers 14 cloud regions (EPA eGRID subregions for US, Electricity Maps zones elsewhere) so the v1.1 per-zone rebuild with pinned vintages is a data change, not a code change.

Provenance

Per-token energy centrals sit nearer the top-down disclosures^{[1]Elsworth et al. (Google), 2025. Measuring the environmental impact of delivering AI at Google: median Gemini Apps text prompt at 0.24 Wh comprehensive versus 0.10 Wh accelerator-only, the anchor of the top-down evidence family. arXiv:2508.15734.[2]Epoch AI, 2025. How much energy does ChatGPT use? Independent estimate of roughly 0.3 Wh for a typical GPT-4o query, corroborating the top-down family.[4]Mistral AI, 2025. Lifecycle analysis of Mistral Large 2 (with Carbone 4 and ADEME): a provider-published per-response footprint used to sanity-check the evidence families.}, with P95 reaching the parametric family^{[3]EcoLogits (GenAI Impact). Open parametric methodology estimating per-request LLM energy from modeled parameter counts and serving hardware; the high (parametric) evidence family in the per-token energy range.}. Facility PUE and on-site WUE come from the operators' own fleet reporting^{[8]Google data center efficiency reporting. Fleet-wide trailing PUE reporting (about 1.10), the basis of the google-cloud facility profile.[9]Microsoft datacenter sustainability reporting. Regional fleet PUE and WUE fact sheets, the basis of the azure facility profile.[10]AWS sustainability reporting. Fleet water use efficiency reporting (about 0.18 L per kWh), the basis of the aws facility profile.}, applied under The Green Grid's WUE definition^{[11]The Green Grid, 2011. Water Usage Effectiveness (WUE): the metric definition this methodology follows, applied to IT-boundary energy.}. Off-site water uses generation water-intensity factors^{[12]Macknick et al. (NREL), 2011. A Review of Operational Water Consumption and Withdrawal Factors for Electricity Generating Technologies, NREL/TP-6A20-50900: the basis of off-site (grid) water intensity.}, with the on-site plus off-site framing following the AI water-footprint literature^{[13]Li et al., 2023. Making AI Less Thirsty: Uncovering and Addressing the Secret Water Footprint of AI Models: the framing for combining on-site cooling water with off-site electricity-embedded water. arXiv:2304.03271.}. The embodied-carbon uplift is grounded in architectural embodied-carbon accounting^{[14]Gupta et al., 2021-2022. Chasing Carbon (HPCA 2021) and ACT (ISCA 2022): architectural embodied-carbon accounting, the basis of the amortized embodied uplift.}, accelerator product carbon footprints^{[15]NVIDIA, 2024. HGX H100 product carbon footprint summary: manufacturing emissions for the dominant serving accelerator, an input to the embodied uplift range.}, and the Boavizta database^{[16]Boavizta. Open database and methodology for ICT hardware embodied impacts, cross-checking the embodied uplift.}. Grid carbon zone values for the v1.1 rebuild come from EPA eGRID (US)^{[17]EPA eGRID. US subregion grid emission factors: the pinned-vintage source for US zone carbon intensities in the v1.1 rebuild.} and Electricity Maps (elsewhere)^{[18]Electricity Maps / Ember. Zone-level location-based carbon intensities outside the US: the pinned-vintage source for non-US zones in the v1.1 rebuild.}.

Choices

• Location-based, not market-based, grid carbon (GHG Protocol Scope 2 vocabulary^{[19]GHG Protocol, 2015. Scope 2 Guidance: the location-based accounting method this methodology follows for grid carbon.}): market-based figures would let provider REC matching drive obligations toward zero; location-based is more physically defensible.
• Average, not marginal, grid intensity: the metric attributes responsibility for existing load, it does not optimize placement. This deliberately diverges from the Green Software Foundation SCI preference for marginal signals^{[20]Green Software Foundation. Software Carbon Intensity specification (ISO/IEC 21031:2024): the metric shape this methodology is informed by, while deliberately diverging on marginal versus average intensity.}.
• Grid carbon values, 1.0.0: every region currently uses the conservative default (central 450, range 300 to 620 gCO2e per kWh). The region-to-zone mapping ships now; per-zone values from EPA eGRID^{[17]EPA eGRID. US subregion grid emission factors: the pinned-vintage source for US zone carbon intensities in the v1.1 rebuild.} and Ember/Electricity Maps^{[18]Electricity Maps / Ember. Zone-level location-based carbon intensities outside the US: the pinned-vintage source for non-US zones in the v1.1 rebuild.} with pinned vintage, plus a persisted live hourly signal, land in v1.1 as a data change.
• Unclassified models are estimated with the most conservative class in the table, because unknown models skew toward new frontier and reasoning models. Above 15 percent unclassified tokens in a period, certificates carry a disclosure and the console alerts.
• Hidden reasoning tokens: for reasoning-class models whose APIs do not report reasoning token counts, output tokens are scaled by a multiplier (central 4.0, range 1.5 to 20). The quantity is unobservable from outside; the interval says so.
• Tokenizer differences across providers (roughly 20 percent for English prose) are not normalized: each provider's coefficients apply to that provider's own counts; the effect is second order against the coefficient interval.
• PUE and WUE are negatively correlated (air cooling trades water for energy); they are treated as independent, which widens rather than narrows the interval, because a sourced joint distribution does not exist.
• Region honesty: requests whose region is not a recognizable cloud region code are estimated under conservative unknown-facility parameters. A customer-supplied region can never reduce an obligation unless it maps to a known code.

Standards

This methodology does not claim conformance to any standard. It is informed by: the Green Software Foundation SCI shape (ISO/IEC 21031:2024)^{[20]Green Software Foundation. Software Carbon Intensity specification (ISO/IEC 21031:2024): the metric shape this methodology is informed by, while deliberately diverging on marginal versus average intensity.}, including its embodied term, while deliberately diverging on marginal intensity; the GHG Protocol Scope 2 Guidance for the location-based method^{[19]GHG Protocol, 2015. Scope 2 Guidance: the location-based accounting method this methodology follows for grid carbon.}; and The Green Grid's WUE definition^{[11]The Green Grid, 2011. Water Usage Effectiveness (WUE): the metric definition this methodology follows, applied to IT-boundary energy.}. It does not meet ISO 14067 or the GHG Protocol Product Standard (cradle-to-grave) and does not reference them as a basis. ISO 14064-3 third-party review is the intended path before any strengthened claim.

Unknowables

Stated plainly because every competitor faces the same wall:

1. Active parameter counts, serving hardware, and datacenter regions for closed frontier models are undisclosed; those estimates carry the full interval width.
2. Hidden reasoning token volume where APIs do not report it.
3. Site-level WUE and grid mix for unidentifiable datacenters, which is most direct API traffic.
4. Whether the top-down or parametric energy evidence family is closer to right. Only direct measurement on open-weight models will narrow it.
5. Whether restoration in one basin meaningfully addresses water consumed in another. This is a scientific and ethical question accounting cannot resolve; water claims stay activity-framed and geographically qualified.

Changelog

Related

• Claim language and required disclosures: src/core/config/claims.ts, docs/TOS-SCHEDULES.md
• Known overlap disclosure: if a customer's model provider claims market-based zero emissions through annual REC matching and the customer separately retires RECs here, the same megawatt-hour is arguably claimed twice. The Terms require customers to disclose provider-level claims, and this document discloses the overlap.