Footprint Estimation Methodology

Pipeline

classify model (pinned registry)        -> model class (provider prefixes normalized)
resolve coefficients (with boundaries)  -> per-token Wh, uplifts, PUE, WUE, grid zone
token accounting                        -> fresh + cached input, output (reasoning is a
                                           reported subset of output, never re-added)
IT energy (accelerator boundary)        -> token terms summed, residual per-class spread
shared factors (applied exactly once)   -> x evidence-family factor (fully correlated
                                           across classes) x idle/reserve uplift
boundary normalization                  -> x PUE (IT -> facility)
water                                   -> on-site: IT-boundary kWh x WUE (Green Grid definition)
                                           off-site: facility kWh x grid water intensity
carbon                                  -> facility kWh x (per-zone grid intensity + embodied adder)
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.

Because that family-level disagreement affects every model class the same way, it is carried by a single shared evidence-family factor (central 1.0, 90 percent range 0.45 to 2.2) applied exactly once per estimate, fully correlated across classes; each per-token coefficient contributes only its residual, class-specific spread. Without this factoring, summing classes would treat the shared dispersion as independent noise and understate the tails. As measured on the 1.1.0 estimator, composed 90 percent intervals span roughly 10 to 12 fold for energy and carbon and roughly 20 to 27 fold for water (which stacks WUE and grid-water uncertainty on top). Every displayed figure carries its range.

All coefficients are modeled lognormal. Products propagate exactly; sums use Fenton-Wilkinson moment matching^{[8]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 modeled parameter distribution (P90) for every account: at credit prices this costs little and it buys deliberate conservatism headroom over the central estimate. The interval covers the methodology's stated parameter uncertainty only; structural uncertainty (model form, tokenizer differences, the treated-as-independent PUE/WUE pair, unregistered models, and the excluded scope) sits outside it by construction, which is why P90 accrual is described as a quantile of the modeled range and never as guaranteed coverage. 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 + 10 percent of cached input; reasoning is a subset of output and never counted twice), 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, and output tokens o (reported reasoning tokens are a subset of o and never add a separate term), 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 reasoning unreported]
E_raw  = E_raw · k_tier                    (batch or priority service tier, if any)
         per-class coefficients enter as residuals; the shared evidence-family
         factor F_family and the idle/reserve uplift then apply exactly once:
E_IT   = E_raw · F_family · 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) + A_embodied )          (gCO2e, location-based;
                                                              embodied is an adder in
                                                              gCO2e/kWh, not a multiplier)
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 = ( ln(p95/central) + ln(central/p05) ) / 2 / 1.6449   (balanced two-sided)
          if a physical floor exists: sigma = min( sigma, (mu - ln(floor)) / 1.6449 )
residual: for per-class coefficients, sigma_residual = sqrt( max(sigma^2 - sigma_family^2, 0) )
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^{[8]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 1.1.0). Every value is a lognormal coefficient; the table shows the MODELED quantiles (the median and the 90 percent range the estimator actually integrates over, after the balanced two-sided fit and any physical floor). 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.

Shared factors, uplifts, and token accounting

The evidence-family factor carries the shared top-down vs parametric dispersion and is applied exactly once per estimate, fully correlated across model classes; per-class coefficients contribute their residual spread. The hidden-reasoning multiplier applies to reasoning-class models whose APIs do not report reasoning token counts; the measured evidence is bimodal (roughly 1.5 to 2.6x on ordinary chat, roughly 11 to 13x on hard reasoning workloads), the single central sits between the modes because aggregate feeds cannot observe the mode, and it never defaults to 1.0. The embodied term is an ADDER in gCO2e per facility kWh, not a multiplier, because embodied share and grid intensity are anti-correlated.

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 below what a recognized mapping would produce for that location.

Water and carbon intensity

Grid carbon by zone (location-based annual average)

Basis note: eGRID zones are CO2e; Ember zones are CO2 only (understates CO2e by low single-digit percent, reflected in widened upper bounds), and both are generation-based direct emissions, not lifecycle. Deliberately unmapped pending primary zone data (conservative default applies): EM:CA-QC.

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^{[9]Google data center efficiency reporting. Fleet-wide trailing PUE reporting (about 1.10), the basis of the google-cloud facility profile.[10]Microsoft datacenter sustainability reporting. Regional fleet PUE and WUE fact sheets, the basis of the azure facility profile.[11]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^{[12]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^{[13]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^{[14]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 adder is grounded in architectural embodied-carbon accounting^{[15]Gupta et al., 2021-2022. Chasing Carbon (HPCA 2021) and ACT (ISCA 2022): architectural embodied-carbon accounting, the basis of the amortized embodied adder.}, accelerator product carbon footprints^{[16]NVIDIA, 2024. HGX H100 product carbon footprint summary: manufacturing emissions for the dominant serving accelerator, the anchor of the embodied adder range.}, and the Boavizta database^{[17]Boavizta. Open database and methodology for ICT hardware embodied impacts, cross-checking the embodied adder.}. Per-zone grid carbon values come from EPA eGRID subregion CO2e rates (US)^{[18]EPA eGRID. US subregion grid emission factors (eGRID2023 rev.2, CO2e output rates): the pinned-vintage source for US zone carbon intensities since methodology 1.1.0.} and Ember national generation CO2 (elsewhere)^{[19]Ember. National generation CO2 intensities (Ember Yearly Electricity Data, 2025 release): the pinned-vintage source for non-US zones since methodology 1.1.0. CO2-only, generation-based; the methodology widens upper bounds to reflect the missing CH4/N2O and lifecycle terms.}. The hidden-reasoning multiplier's range reflects measured bimodality in reasoning-model output volume^{[7]ML.ENERGY / Chung et al., 2025. The ML.ENERGY measurements behind the hidden-reasoning multiplier: reasoning models emit roughly 1.5 to 2.6x a non-reasoning model's output tokens on ordinary chat and roughly 11 to 13x on hard reasoning workloads, the bimodality the multiplier's wide interval reflects. arXiv:2505.06371.}.

Choices

• Location-based, not market-based, grid carbon (GHG Protocol Scope 2 vocabulary^{[20]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. The Green Software Foundation SCI specification (v1.1) permits short-run marginal, long-run marginal, or average grid intensity while excluding market-based measures; this methodology's location-based annual-average choice is consistent with that allowance^{[21]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, per zone since 1.1.0: mapped regions use primary-source annual averages with pinned vintages: EPA eGRID^{[18]EPA eGRID. US subregion grid emission factors (eGRID2023 rev.2, CO2e output rates): the pinned-vintage source for US zone carbon intensities since methodology 1.1.0.} subregion CO2e rates for US zones, and Ember^{[19]Ember. National generation CO2 intensities (Ember Yearly Electricity Data, 2025 release): the pinned-vintage source for non-US zones since methodology 1.1.0. CO2-only, generation-based; the methodology widens upper bounds to reflect the missing CH4/N2O and lifecycle terms.} national generation CO2 for non-US zones. The two bases differ: eGRID is CO2e; Ember is CO2 only (missing CH4 and N2O understates CO2e by low single-digit percent, reflected in widened upper bounds), and both are generation-based direct emissions, not lifecycle. Regions without a primary-source zone value (including hydro-heavy Quebec, where a defensible zone-level figure is not yet publicly pinned) deliberately stay on the conservative unknown-region default (central 450, range 250 to 700 gCO2e per kWh) rather than borrow a flattering national average.
• 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, modeled 90 percent range 1.1 to 14.6, with a physical floor of 1.0 since hidden reasoning cannot reduce compute). The underlying evidence is bimodal: measured ratios cluster around 1.5 to 2.6x for ordinary chat traffic and around 11 to 13x for hard reasoning workloads^{[7]ML.ENERGY / Chung et al., 2025. The ML.ENERGY measurements behind the hidden-reasoning multiplier: reasoning models emit roughly 1.5 to 2.6x a non-reasoning model's output tokens on ordinary chat and roughly 11 to 13x on hard reasoning workloads, the bimodality the multiplier's wide interval reflects. arXiv:2505.06371.}. Aggregate metering cannot observe which mode a given account's traffic is in, so the single central sits between the modes and the wide interval says so honestly.
• 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)^{[21]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^{[20]GHG Protocol, 2015. Scope 2 Guidance: the location-based accounting method this methodology follows for grid carbon.}; and The Green Grid's WUE definition^{[12]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 reports its market-based emissions as zero 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.