Abstract
Electricity consumed during robot-assisted radical prostatectomy (RARP) generates greenhouse-gas emissions that vary with local grid carbon intensity, yet existing environmental reports are mostly single-centre or single-country and therefore cannot separate procedure electricity demand from jurisdictional electricity context. In this cross-sectional modelling study, a standardised intraoperative plug-load model for RARP was linked to publicly available electricity carbon-intensity data from 208 jurisdictions. The base-case demand was 6.5 kW over a reference operative-time distribution with a median of 170 min (IQR 140–180), corresponding to 18.42 kWh per case, with uncertainty propagated to 12.24–20.48 kWh. Structural sensitivity analyses examined robot-only incremental load, low-resource, infrastructure-conditioning, and high plug-load upper-bound settings, together with counterfactual grid-decarbonisation scenarios. Electricity carbon intensity in the archived analytical extraction ranged from 23.8 to 738.8 gCO2eq/kWh, yielding 0.44–13.61 kgCO2eq per case in the base case (median 6.41; IQR 4.19–8.83). Across scenarios, power-demand assumptions changed absolute values, while jurisdictional grid carbon intensity remained the main source of cross-jurisdiction variation within this electricity-only model. Achieving an electricity-related footprint of < 1 kgCO2eq per case required a grid carbon intensity of < 54.3 gCO2eq/kWh and was achieved by 10 jurisdictions in the archived dataset. Within the defined intraoperative plug-load electricity boundary, using life-cycle grid-intensity factors, these results support location-specific reporting and indicate where electricity decarbonisation or operating-theatre energy management can reduce the electricity component of RARP. The analysis is not a full life-cycle assessment of RARP and should be interpreted alongside non-electricity sources such as consumables, sterilisation, anaesthesia, building services, and hospital stay.
Supplementary Information
The online version contains supplementary material available at 10.1038/s41598-026-56096-2.
Keywords: Prostatectomy, Robotic surgical procedures, Carbon footprint, Electricity, Greenhouse gases, Sustainable development
Subject terms: Energy science and technology, Engineering, Environmental sciences
Introduction
Climate change is increasingly recognised as a major determinant of population health, affecting heat-related morbidity and mortality, infectious-disease patterns, food and water security, and the frequency of extreme weather events1,2. Health systems also contribute to greenhouse-gas (GHG) emissions through direct energy use and upstream supply chains, creating a feedback loop in which the delivery of care contributes to the risks it seeks to mitigate3,4. In response, health systems and professional bodies have begun to adopt net‑zero targets and practical decarbonisation road maps that require more granular understanding of the emissions associated with infrastructure and clinical activity5–7. Recent reviews of hospital services and care pathways highlight both the rapid growth of procedure-level footprinting and substantial methodological heterogeneity, underscoring the value of transparent and reproducible modelling approaches8,9.
Surgery is a resource-intensive component of healthcare7,13. Operating theatres concentrate electricity demand and material throughput, and the perioperative pathway adds further emission sources such as sterilisation, procurement of single-use devices, and upstream manufacturing and transport7,13. Comprehensive life‑cycle assessment (LCA) is needed to capture the full footprint of a surgical episode8,13,18,20–23, but electricity is a particularly actionable component because it can be reduced through lower-carbon electricity procurement, on-site generation, and energy-efficiency interventions5–7,32. Moreover, the emissions consequence of a fixed electricity load depends on the emissions factor applied to electricity, which differs across jurisdictions and changes over time as grids decarbonise10–12,19.
Robot-assisted radical prostatectomy (RARP) is among the most common robotic procedures worldwide. Environmental analyses of robotic surgery are often institution-specific and frequently emphasise disposables and consumables, which can dominate overall procedure footprints13. For radical prostatectomy, a prospective multicentre study reported average intraoperative power draws of approximately 3.5 kW for the robot and 3.0 kW for the operating theatre, compared with approximately 0.6 kW for a laparoscopic column14. Even if electricity use is similar between centres, electricity-related GHG emissions will vary with the local electricity generation mix and net electricity imports10–12,19.
However, the existing literature remains dominated by single-centre or single-country studies that apply one local electricity factor13,14. This makes it difficult to distinguish whether differences between published carbon footprints reflect the procedure itself, local operating-theatre infrastructure, or simply the carbon intensity of the grid supplying the hospital. A cross-jurisdiction framework is therefore needed to quantify how much variation can arise from grid context alone under a common electricity-use model.
A cross-jurisdiction modelling study was conducted to link a standardised intraoperative electricity-use model for RARP to jurisdiction-level electricity carbon intensity. The purpose was not to propose a new carbon-accounting principle, but to quantify the magnitude of cross-jurisdiction variation that arises when a common electricity-use model is applied across heterogeneous electricity systems. The objectives of this study were to (i) quantify the distribution and extremes of electricity-related emissions per RARP case across all jurisdictions with available data; (ii) extend the framework with structural sensitivity analyses for power-demand assumptions, operating-theatre infrastructure scenarios, and grid-decarbonisation scenarios; (iii) provide a transparent scaling approach for translating per-case emissions into annual totals given local procedure volumes; and (iv) situate electricity-related results within broader hospital carbon accounting (Scope 2-aligned electricity accounting) and procedure-level footprinting literature without presenting the electricity-only model as a full life-cycle footprint of RARP.
Materials and methods
Study design and reporting
This was a cross-sectional modelling study based on publicly available, aggregated, jurisdiction-level data. No patient-level information was collected and no human participants were involved; therefore, institutional review board approval and informed consent were not required. Reporting follows the STROBE framework for observational studies, adapted for secondary-data modelling15,16.
Scope definition
The study quantifies electricity-related GHG emissions attributable to intraoperative electrical plug-load consumption during RARP (robotic platform and ancillary electrical equipment). The analysis does not include the full operating-theatre energy footprint (for example, heating, ventilation, and air conditioning), nor upstream emissions from disposables, instrument manufacture, sterilisation, or hospital stay. All GHG intensities are reported as life-cycle carbon dioxide equivalents (CO2eq) consistent with the source datasets and broader LCA/accounting frameworks17–23. Because the jurisdictional factors are life-cycle grid-intensity factors, these estimates should be interpreted as electricity-related life-cycle CO2eq estimates rather than as a formal GHG Protocol Scope 2 inventory unless institution-specific Scope 2 factors are substituted.
Electricity carbon intensity data
Jurisdiction-level electricity carbon intensity (gCO2eq/kWh) was obtained from the Low-Carbon Power carbon-intensity-of-electricity ranking/map and yearly export dataset, using the latest available yearly values or last-12-month values including net imports available at extraction10,11. Data were extracted on 11 January 2026. Low-Carbon Power reports life-cycle greenhouse-gas emissions in gCO2eq/kWh and provides public ranking/map pages and yearly CSV/JSON exports; the relevant access points are the ranking page (https://lowcarbonpower.org/ranking?metric=ci), the map page (https://lowcarbonpower.org/map-gCO2eq-kWh), and the yearly data export (https://lowcarbonpower.org/data-including-net-imports.csv and https://lowcarbonpower.org/data-including-net-imports.json)10,11. The dataset includes sovereign countries, selected subnational entities, and regional aggregates; throughout, these are referred to as “jurisdictions”, and summary statistics are reported across all entries. The exact extraction used for the analysis, including all 208 carbon-intensity values and derived outputs, is archived in Supplementary Table S1 and in the input CSV supplied with Supplementary Code 1. The live Low-Carbon Power dataset may be updated after the extraction date; consequently, Supplementary Table S1 is the version of record for reproducing the numerical values reported here, whereas a newly downloaded public extract can be used for updated analyses. The Sources_and_access worksheet of Supplementary Table S1 lists each dataset or file, variables used, access route, and restriction status, and the Data_dictionary worksheet defines variables, units, and derivations. For context, the Our World in Data compilation of life-cycle electricity intensities was also consulted; its data page provides downloadable CSV and metadata files (https://ourworldindata.org/grapher/carbon-intensity-electricity)12. No patient-level, proprietary, or access-controlled dataset was used.
Intraoperative electricity-use model
A standardised model of intraoperative plug-load electricity use was applied. Base-case plug-load power demand (P) was set to 6.5 kW, representing the combined electricity use of the robotic system and ancillary operating-theatre equipment during the procedure. This value aligns with reported average intraoperative power draws of approximately 3.5 kW for the robot and 3.0 kW for the operating theatre during radical prostatectomy14. The base-case parameter is interpreted as AC input power at the point of use, rather than as downstream device output power.
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1 |
Where E is per-case electricity use, P is real AC input power at the point of use, and t is operative duration in hours.
Structural sensitivity analyses varied P to reflect alternative attribution and configuration scenarios: (i) robot-only incremental load (P = 3.5 kW) to isolate electricity attributable to the robotic platform; (ii) low-resource ancillary baseline (P = 5.0 kW = 3.5 kW robot + 1.5 kW ancillary load) as an exploratory scenario for pared-down operating-theatre infrastructure; (iii) laparoscopic column context (P = 3.6 kW = 3.0 kW operating-theatre baseline + 0.6 kW laparoscopic column) for comparative context14; and (iv) a high plug-load upper-bound scenario (approximate P = 8.62 kVA/kW-equivalent) constructed by adding the 3.0-kW operating-theatre baseline to the nameplate apparent-power envelope reported for the da Vinci Xi system and optional equipment (Vision Cart 1500 VA, Surgeon Console 1000 VA, Patient Cart 1200 VA, optional second Surgeon Console 1000 VA, and ERBE VIO dV generator 920 VA)24. Because these manufacturer values are reported in VA rather than metered real kW, this scenario was treated as a conservative upper bound rather than as a direct measurement of real input power. The 3.0-kW ancillary baseline was retained in the base case because it is the only procedure-specific empirical operating-theatre estimate identified in the source study14; the 1.5-kW ancillary assumption was introduced only as a conservative exploratory low-resource counterfactual.
Jurisdictional electrical-infrastructure assumptions
Nominal mains voltage differences (for example, 110/120 V versus 220/230 V) were not modelled as separate modifiers of kWh because the model is formulated in real AC input power at the point of use; for a given real power and duty cycle, voltage alters current draw and circuit loading rather than watt-hours consumed. Most medical-device power supplies are designed to accept a range of input voltages and internally regulate downstream DC rails. Internal PSU conversion losses were therefore not parameterised separately in the base case because they are already embedded when power is measured or inferred on the input side. Separate transmission and distribution losses were not modelled as an additional parameter; the published jurisdictional CI factors were applied directly to metered plug-load electricity, consistent with the source-boundary convention. To represent jurisdictions in which additional external electrical conditioning may be required, an exploratory infrastructure-conditioning scenario was prespecified in which total plug-load demand was increased by 10% (P = 7.15 kW) to reflect plausible aggregate losses from UPS units, power conditioners, frequency converters, or transformers. This scenario, like the low-resource ancillary baseline, is intended as structural sensitivity analysis rather than direct measurement.
Operative-time reference distribution and uncertainty
Operative time was not estimated from patient-level data in this study. A pragmatic reference distribution, with a median of 170 min and an IQR of 140–180 min, was adopted using summary values reported in a contemporary RARP series25. This central estimate is also close to the pooled median operative time of 176 min reported in a recent systematic review of RARP series26. Because raw case-level times were unavailable, the 2.5th and 97.5th percentiles were approximated by piecewise-linear extrapolation of the quantile function, using the slopes between Q1-median and median-Q3. This yielded t2.5 = 113 min and t97.5 = 189 min. This was treated as a transparent quantile-anchored uncertainty distribution rather than as a parametric fit to raw operative-time data. The resulting quantile-defined uncertainty distribution was propagated via Monte Carlo sampling (10,000 draws) to obtain the median and 95% uncertainty intervals for electricity use and per-case emissions under each scenario. For the base case (P = 6.5 kW), this corresponds to E2.5 = 12.24 kWh and E97.5 = 20.48 kWh per case.
Emissions calculation
Electricity-related emissions per case were calculated as:
![]() |
2 |
Where GHG_case is electricity-related emissions per case and CI is the jurisdiction-specific life-cycle electricity carbon intensity applied to metered plug-load electricity.
Grid-decarbonisation sensitivity was evaluated using two counterfactual scenarios in which each jurisdiction’s carbon intensity was reduced by 50% and 90% relative to the extracted values (CI × 0.5 and CI × 0.1). These factors are intended for robustness testing rather than prediction. Because purchased electricity is commonly reported as Scope 2, interpretation under location-based versus market-based accounting is addressed in the Discussion, consistent with the GHG Protocol Scope 2 Guidance19.
Procedure-volume scaling
Annual electricity-related emissions can be estimated by linear scaling:
![]() |
3 |
Where GHG_year is annual electricity-related emissions and N_cases is the annual number of RARP procedures.
When only total radical prostatectomy volume is available, N_cases can be treated as an upper bound for RARP-specific electricity emissions, with the caveat that approach mix varies across countries and time. Public administrative sources reporting radical-prostatectomy activity illustrate the heterogeneity of available national data structures, for example in Poland, England and Wales, Belgium, and France27–30.
Statistical analysis
Per-case results are presented as medians with interquartile ranges across jurisdictions, while time-driven uncertainty is expressed as 95% uncertainty intervals derived from Monte Carlo sampling. Structural sensitivity analyses (alternative plug-load power contexts, infrastructure scenarios, and grid-decarbonisation scenarios) are summarised in Table 4; Fig. 3, and Supplementary Table S1. Results for selected jurisdictions and standardised annual procedure volumes are presented in Tables 2 and 3; Figs. 1 and 2. The full jurisdiction-level results table, including the expanded exploratory infrastructure scenarios, is provided as Supplementary Table S1. All calculations and figures were generated from an explicit Python 3 implementation of Eqs. (1)-(3), using the scenario constants in Table 1 and the jurisdictional inputs archived in Supplementary Table S1. The reproducibility script is supplied as Supplementary Code 1 and was checked against the archived input CSV; exact reproduction of the published numerical values does not require internet access. Researchers can also rerun the script against an updated public carbon-intensity extract with the same variable structure, in which case numerical values may change with the source data.
Table 4.
Structural sensitivity to principal plug-load power assumptions and grid-decarbonisation scenarios (median operative time 170 min). Exploratory low-resource and infrastructure-conditioning scenarios are reported in Supplementary Table S1; the high plug-load column represents a conservative nameplate-derived upper bound.
| Jurisdiction | CI (gCO2eq/kWh) | Base-case (kg/case) | Robot-only (kg/case) | High plug-load upper bound (kg/case) | CI×0.5 (kg/case) | CI×0.1 (kg/case) |
|---|---|---|---|---|---|---|
| France | 33.3 | 0.613 | 0.330 | 0.813 | 0.306 | 0.061 |
| Sweden | 32.2 | 0.593 | 0.319 | 0.786 | 0.296 | 0.059 |
| EU | 193.4 | 3.562 | 1.918 | 4.723 | 1.781 | 0.356 |
| United Kingdom | 233.9 | 4.308 | 2.320 | 5.713 | 2.154 | 0.431 |
| Germany | 298.0 | 5.488 | 2.955 | 7.278 | 2.744 | 0.549 |
| United States | 347.7 | 6.403 | 3.448 | 8.492 | 3.201 | 0.640 |
| People’s Republic of China | 484.4 | 8.921 | 4.804 | 11.831 | 4.460 | 0.892 |
| Poland | 527.8 | 9.720 | 5.234 | 12.891 | 4.860 | 0.972 |
| India | 608.4 | 11.205 | 6.033 | 14.859 | 5.603 | 1.121 |
| South Africa | 683.5 | 12.588 | 6.778 | 16.693 | 6.294 | 1.259 |
| West Virginia | 738.8 | 13.606 | 7.326 | 18.044 | 6.803 | 1.361 |
| Median (all jurisdictions) | 347.9 | 6.408 | 3.451 | 8.498 | 3.204 | 0.641 |
Fig. 3.
Structural sensitivity to principal plug-load power assumptions and operative-time uncertainty. Straight lines show the linear relation between grid carbon intensity and per-case electricity-related emissions for the base case (P = 6.5 kW, t = 170 min), robot-only incremental load (P = 3.5 kW), and the high plug-load upper-bound configuration (approximate P = 8.62 kVA/kW-equivalent; nameplate-derived). The shaded band applies only to the base-case line and shows the 95% uncertainty interval due to operative-time uncertainty (t2.5 = 113 min; t97.5 = 189 min). For clarity, the exploratory low-resource and infrastructure-conditioning scenarios are reported in Supplementary Table S1 rather than plotted.
Table 2.
Electricity carbon intensity and modelled electricity-related emissions per RARP case for selected jurisdictions.
| Jurisdiction | Carbon intensity (gCO2eq/kWh) | Emissions per case, median (kgCO2eq) | 95% UI (kgCO2eq) |
|---|---|---|---|
| Ethiopia | 23.8 | 0.44 | 0.29–0.49 |
| Norway | 26.8 | 0.49 | 0.33–0.55 |
| Sweden | 32.2 | 0.59 | 0.39–0.66 |
| France | 33.3 | 0.61 | 0.41–0.68 |
| Switzerland | 38.6 | 0.71 | 0.47–0.79 |
| Brazil | 103.6 | 1.91 | 1.27–2.12 |
| Spain | 126.0 | 2.32 | 1.54–2.58 |
| Canada | 131.5 | 2.42 | 1.61–2.69 |
| Denmark | 138.8 | 2.56 | 1.70–2.84 |
| Belgium | 185.4 | 3.41 | 2.27–3.80 |
| EU | 193.4 | 3.56 | 2.37–3.96 |
| United Kingdom | 233.9 | 4.31 | 2.86–4.79 |
| Germany | 298.0 | 5.49 | 3.65–6.10 |
| Netherlands | 299.1 | 5.51 | 3.66–6.12 |
| Italy | 324.0 | 5.97 | 3.97–6.63 |
| United States | 347.7 | 6.40 | 4.26–7.12 |
| Japan | 436.9 | 8.05 | 5.35–8.95 |
| Australia | 453.1 | 8.34 | 5.55–9.28 |
| Iran | 464.4 | 8.55 | 5.69–9.51 |
| People’s Republic of China | 484.4 | 8.92 | 5.93–9.92 |
| Poland | 527.8 | 9.72 | 6.46–10.81 |
| Saudi Arabia | 543.1 | 10.00 | 6.65–11.12 |
| India | 608.4 | 11.20 | 7.45–12.46 |
| Indonesia | 624.5 | 11.50 | 7.64–12.79 |
| Mongolia | 669.2 | 12.32 | 8.19–13.70 |
| South Africa | 683.5 | 12.59 | 8.37–13.99 |
| The World | 418.3 | 7.70 | 5.12–8.56 |
| Ukraine | 230.5 | 4.25 | 2.82–4.72 |
| Turkey | 398.1 | 7.33 | 4.87–8.15 |
| Mexico | 415.5 | 7.65 | 5.09–8.51 |
Table 3.
Scenario analysis: annual electricity-related emissions for a standardised volume of 10,000 RARP cases.
| Jurisdiction | Per-case emissions, median (kgCO2eq) | Annual emissions, median (tCO2eq) | Annual 95% UI (tCO2eq) |
|---|---|---|---|
| France | 0.61 | 6.1 | 4.1–6.8 |
| Sweden | 0.59 | 5.9 | 3.9–6.6 |
| EU | 3.56 | 35.6 | 23.7–39.6 |
| United Kingdom | 4.31 | 43.1 | 28.6–47.9 |
| Germany | 5.49 | 54.9 | 36.5–61.0 |
| United States | 6.40 | 64.0 | 42.6–71.2 |
| People’s Republic of China | 8.92 | 89.2 | 59.3–99.2 |
| Poland | 9.72 | 97.2 | 64.6–108.1 |
| India | 11.20 | 112.0 | 74.5–124.6 |
| South Africa | 12.59 | 125.9 | 83.7–139.9 |
Fig. 1.
Ranked distribution of electricity-related emissions per RARP case across 208 jurisdictions under the base-case plug-load model (P = 6.5 kW) and median operative time (t = 170 min). The blue line shows jurisdiction medians ordered by electricity carbon-intensity rank on the x-axis (1 = lowest-carbon grid); the shaded band shows the 95% uncertainty interval generated by operative-time uncertainty alone (113–189 min) and does not include alternative plug-load scenarios; annotations identify selected jurisdictions and aggregates.
Fig. 2.
Electricity-related emissions per RARP case for selected markets and regions under the base-case plug-load model. Bars denote median emissions and error bars denote the 95% uncertainty interval arising from operative-time uncertainty only; they do not include structural uncertainty from alternative plug-load assumptions. Jurisdictions are ordered by increasing median per-case emissions to highlight how the same electricity-use model maps to different emissions across clinically relevant settings.
Table 1.
Model parameters, technical assumptions, scenario definitions, and derived electricity use.
| Parameter | Value |
|---|---|
| Scope | Intraoperative electrical plug-load (robotic system + ancillary equipment); excludes HVAC and supply-chain components |
| Power demand (P) | Base case 6.5 kW; robot-only incremental 3.5 kW; low-resource ancillary baseline 5.0 kW; laparoscopic context 3.6 kW; infrastructure-conditioning overhead 7.15 kW; high plug-load upper-bound ~ 8.62 kVA/kW-equivalent (nameplate-derived structural sensitivity) |
| Electrical-infrastructure assumption | Point-of-use AC input power model; nominal 110/120 V versus 220/230 V supply changes current rather than kWh for a given measured power; internal PSU losses assumed embedded in input-side power draws; transmission/distribution losses not added separately because CI is applied per delivered kWh; additional external conditioning, UPS, converter, or transformer overhead represented only in the + 10% scenario |
| Operative time (t) | Median 170 min; IQR 140–180 min |
| Operative time uncertainty | t2.5 = 113 min; t97.5 = 189 min (piecewise-linear extrapolation) |
| Electricity use per case (E) | Base-case median 18.42 kWh (95% UI 12.24–20.48); robot-only 9.92 kWh; low-resource 14.17 kWh; laparoscopic 10.20 kWh; conditioning-overhead 20.26 kWh; high plug-load upper-bound 24.43 kWh (each at t = 170 min) |
| Electricity carbon intensity (CI) | Jurisdiction-level gCO2eq/kWh (Low-Carbon Power ranking; latest yearly values including net imports; extracted 11 Jan 2026) |
| Per-case emissions | GHG_case = E × CI/1000 (kgCO2eq) |
| Grid-decarbonisation sensitivity | CI × 0.5 and CI × 0.1 scenarios applied to jurisdiction-level CI values (robustness testing) |
Results
Electricity-use assumptions
Under the base case (P = 6.5 kW; median operative time t = 170 min), modelled electricity consumption was 18.42 kWh per case. Using the operative-time uncertainty bounds, electricity use ranged from 12.24 to 20.48 kWh (95% UI). Structural sensitivity shifted per-case electricity use proportionally: 9.92 kWh for a robot-only incremental load (P = 3.5 kW), 14.17 kWh for the low-resource ancillary baseline (P = 5.0 kW), 10.20 kWh for a laparoscopic column context (P = 3.6 kW), 20.26 kWh for the infrastructure-conditioning scenario (+ 10% overhead; P = 7.15 kW), and 24.43 kWh for the high plug-load upper-bound configuration (approximate P = 8.62 kVA/kW-equivalent), each evaluated at the same median operative time. Figure 3 provides a general conversion between grid carbon intensity and per-case emissions under the principal plug-load assumptions.
Electricity carbon intensity across jurisdictions
Across 208 jurisdictions with available data in the Low-Carbon Power ranking, electricity carbon intensity ranged from 23.8 gCO2eq/kWh (Ethiopia) to 738.8 gCO2eq/kWh (West Virginia). The median was 347.9 gCO2eq/kWh (IQR 227.5–479.5). In categorical terms, 17 jurisdictions had carbon intensity < 100 gCO2eq/kWh, 22 had 100–199, 41 had 200–299, 42 had 300–399, 43 had 400–499, 27 had 500–599, and 16 were ≥ 600 gCO2eq/kWh.
Per-case electricity-related emissions
Applying the standardised energy model, electricity-related emissions per RARP case ranged from 0.44 to 13.61 kgCO2eq (median 6.41; IQR 4.19–8.83). The five lowest-emitting jurisdictions were Ethiopia (0.44 kg/case), Central African Republic (0.44), Albania (0.45), Paraguay (0.46), and Norway (0.49). The five highest-emitting jurisdictions were West Virginia (13.61 kg/case), South Africa (12.59), Mongolia (12.32), Timor-Leste (12.06), and Gambia (12.06). Figure 1 depicts the full ranked distribution of per-case electricity-related emissions.
Selected jurisdictions relevant to robotic prostatectomy
Among selected large economies and regions, per-case electricity-related emissions (median) were 0.61 kgCO2eq in France (rank 7), 0.59 in Sweden (rank 6), 3.56 in the EU aggregate (rank 38), 4.31 in the United Kingdom (rank 57), 5.49 in Germany (rank 78), 6.40 in the United States (rank 104), 8.92 in the People’s Republic of China (rank 158), 9.72 in Poland (rank 173), 11.20 in India (rank 194), and 12.59 in South Africa (rank 207). Operative-time uncertainty produced relatively narrow within-jurisdiction intervals compared with between-jurisdiction differences; for example, Poland was 9.72 kg/case (95% UI 6.46–10.81) versus France 0.61 (95% UI 0.41–0.68). Table 2 summarises selected jurisdictions and Fig. 2 contrasts key markets.
Structural sensitivity to power-demand assumptions and grid decarbonisation
Scenario analyses confirmed that jurisdictional grid carbon intensity remained the main source of cross-jurisdiction differences within the electricity-only boundary, whereas power-demand assumptions primarily scaled absolute emissions. Across all jurisdictions, the median per-case emission was 3.45 kgCO2eq under the robot-only incremental load (P = 3.5 kW), 4.93 kgCO2eq under the low-resource ancillary baseline (P = 5.0 kW), 7.05 kgCO2eq under the infrastructure-conditioning scenario (+ 10% overhead), and 8.50 kgCO2eq under the high plug-load upper-bound scenario (approximate P = 8.62 kVA/kW-equivalent), compared with 6.41 kgCO2eq in the base case (P = 6.5 kW). Applying a CI x 0.5 scenario halved the median per-case emissions to 3.20 kgCO2eq; CI × 0.1 reduced the median to 0.64 kgCO2eq. The principal scenarios are summarised in Table 4 and illustrated in Fig. 3, and the expanded jurisdiction-level sensitivity outputs are reported in Supplementary Table S1. A pragmatic emissions-intensity threshold can be derived for local benchmarking. Under base-case energy use (18.42 kWh per case), achieving < 1 kgCO2eq of electricity-related emissions requires a grid carbon intensity of < 54.3 gCO2eq/kWh. Ten jurisdictions met this threshold in the archived dataset, whereas jurisdictions with carbon intensity ≥ 600 gCO2eq/kWh exceeded 11 kgCO2eq per case under the same electricity-use model.
Scaling to annual totals
Because electricity-related emissions scale linearly with procedure volume, per-case differences translate directly into programme-level totals. As a standardised example, a programme performing 10,000 RARP cases annually would have electricity-related emissions of approximately 6.1 tCO2eq in France and 97.2 tCO2eq in Poland under the same assumptions (Table 3). Supplementary Table S1 provides per-case estimates for all 208 jurisdictions, including the expanded infrastructure sensitivities.
Discussion
Principal findings
Under the base-case model, electricity-related emissions varied > 30-fold across jurisdictions (0.44–13.61 kgCO2eq per case). This spread arises primarily from differences in grid carbon intensity rather than from plausible variability in operative duration, ancillary baseline, or plug-load configuration. For example, varying plug-load power from 3.5 kW (robot-only incremental) to 8.62 kVA/kW-equivalent (high configuration) scales absolute emissions by about 2.5-fold, and the exploratory low-resource and conditioning scenarios shift the all-jurisdiction median from 4.93 to 7.05 kgCO2eq per case, whereas jurisdictional grid carbon intensity varies > 30-fold across the archived dataset. Consequently, the jurisdictional ranking and the central electricity-only conclusion - that grid carbon intensity is the main determinant of cross-jurisdiction variation under a fixed plug-load model - remain robust across structural sensitivity scenarios (Table 4; Fig. 3, and Supplementary Table S1).
An actionable benchmark threshold was also derived: at base-case energy use (18.42 kWh), a grid carbon intensity below 54.3 gCO2eq/kWh is required to keep electricity-related emissions below 1 kgCO2eq per case. Only 10 jurisdictions met this threshold, illustrating that most settings would need substantially cleaner electricity and/or additional energy reductions to reach sub-kilogram electricity footprints for RARP.
Interpretation and relation to existing sustainability frameworks
Using jurisdiction-appropriate emission factors is already standard good practice in carbon accounting17,19,22,23. The contribution of the present study is therefore not to restate that principle, but to quantify how large the resulting differences become for a standardised RARP electricity load across 208 jurisdictions and to provide a transparent framework that others can update with local measurements. Purchased electricity is typically reported as Scope 2, and the GHG Protocol recommends both a location-based method (grid-average emission factors) and a market-based method reflecting contractual instruments such as green tariffs, renewable power purchase agreements, or energy attribute certificates19. Recent literature emphasises that pathway- and procedure-level footprints can complement organisational inventories by identifying high-leverage hotspots and enabling benchmarking across sites when emission factors and boundaries are standardised8,13,31. This study contributes a simple, transparent approach for the intraoperative electricity component, designed to be integrated into broader accounting exercises rather than to stand in for full LCA. In practical hospital carbon accounting, the kWh estimate used here can be multiplied by the institution’s Scope 2 emission factors to populate annual inventories and support internal governance mechanisms such as service-line benchmarking, carbon budgets, or an internal carbon price17,19,32. Hospital carbon-footprint tools show that Scope 2 can remain a material category and a practical target for action, even though its relative contribution varies by institution and jurisdiction5–7,32.
Clinical and operational implications
The large cross-jurisdiction spread has immediate implications for interpretation of single-centre studies and for cross-country benchmarking. First, comparisons of “the carbon footprint of RARP” without reporting the electricity emissions factor (and whether it is direct versus life-cycle, annual-average versus time-varying, and location-based versus market-based) can yield misleading conclusions about the procedure itself19. Second, because the relationship between carbon intensity and electricity-related emissions is linear, decarbonising electricity (through system-level grid changes or hospital-level market-based procurement) yields proportionate reductions19; CI × 0.5 and CI × 0.1 scenarios illustrate the scale of potential improvement. Third, within a fixed grid, operational energy management remains relevant: reducing avoidable delays, avoiding unnecessary equipment standby, and minimising plug-load where clinically safe can each reduce electricity-related emissions by the same proportion6,7,32. In principle, in settings with high temporal variability in grid intensity, aligning elective scheduling with lower-carbon periods could offer additional reductions, although this was not evaluated here and would require local marginal or hourly emissions data and operational flexibility.
The mitigation levers also differ in actionability. Lower-carbon electricity procurement or on-site renewable supply can offer the largest absolute reduction5–7,19,32, but it often depends on hospital estates teams, purchasing authorities, or national policy rather than the surgical team alone. By contrast, avoiding unnecessary standby, switching off optional components when not needed, and removing non-value-adding workflow delays are more directly actionable at theatre level7,32. Importantly, any attempt to reduce operative time should be understood as removal of avoidable delay and improved workflow reliability - not speed for its own sake - and must not compromise patient safety, training, or oncological quality. Manufacturers may also have an important role: lower-idle-power architecture, automatic sleep or standby protocols, higher-efficiency internal power supplies, modular shutdown of unused carts or consoles, and transparent kWh metering could reduce emissions regardless of grid context. Embedding such requirements into green operating-theatre programmes and procurement specifications would help translate procedure-level modelling into organisational action7,32.
Context within the total procedure footprint
Electricity is only one component of the environmental impact of RARP. Systematic reviews of surgical footprints report wide ranges across procedures and identify consumables, anaesthesia-related sources, and supply chains as dominant contributors in many contexts13. For contextualisation of the electricity-only results, the component data reported by Fuschi et al. were re-examined14. In that study, the plug-load components most comparable to the present boundary are approximately 4.1 kgCO2eq for the robot and 4.2 kgCO2eq for ancillary operating-theatre equipment, yielding approximately 8.3 kgCO2eq per case. The same table also reports building-conditioning values of 13 kgCO2eq for winter heating and 16 kgCO2eq for summer cooling. Because heating and cooling represent alternative seasonal conditions rather than simultaneous contributors, they should not be summed within a single case total. A seasonal-average conditioning term of approximately 14.5 kgCO2eq therefore yields a corrected energy subtotal of approximately 22.8 kgCO2eq per robotic case, with seasonal alternatives of approximately 21.4 kgCO2eq in winter and 24.4 kgCO2eq in summer. Adding the reported instrument production, disposal, and sterilisation component (approximately 9.5 kgCO2eq) places the contextual total in the low-30-kgCO2eq range. This component-based reconstruction is lower than the larger total obtained when winter and summer conditioning terms are effectively combined, and it reinforces that the present model should be interpreted only as the intraoperative plug-load component rather than as a full life-cycle total. The present model should therefore not be used to rank the total environmental performance of robotic, laparoscopic, or open prostatectomy; overall conclusions could change when consumables, instrument manufacture, sterilisation, anaesthesia, HVAC, transport, and hospital stay are included. Across the modelled base-case range (0.44–13.61 kgCO2eq), intraoperative plug-load electricity would represent only a minor contributor to the corrected contextual total in very low-carbon grids, but could become a major contributor in high-carbon grids. This supports the narrower claim that the electricity component is highly context sensitive; it does not justify a single, jurisdiction-invariant percentage contribution for RARP as a whole.
Importantly, the system boundary excludes building services such as ventilation, heating, and cooling. Operating theatres have high air-change requirements and can be energy intensive7,13; depending on facility design and climate, HVAC electricity may rival or exceed plug-load electricity. Therefore, absolute electricity-related emissions for the surgical environment will be larger when facility energy is included, and the same grid-intensity dependence applies to both plug-load and building electricity.
Strengths
This study links an openly accessible jurisdiction-level carbon-intensity dataset to an explicit, reproducible electricity-use model for RARP. By adding structural sensitivity analyses for plug-load power assumptions, infrastructure scenarios, and grid-decarbonisation scenarios, it shows that the central conclusion (grid intensity drives cross-jurisdiction variation) is robust while providing practical scenario ranges for local planning. The model can be updated as carbon-intensity factors change and can be extended to other robotic procedures by substituting operative time and power-demand assumptions. A full jurisdiction-level supplementary table is provided to support local use and benchmarking. Because the framework is algebraic and scenario-based, institutions can readily adapt it by substituting local measurements of plug-load electricity, incorporating building electricity where available, or integrating the kWh estimate into broader pathway LCAs that include consumables and upstream supply-chain processes8,13.
Limitations
Several limitations remain. First, the model isolates intraoperative plug-load electricity and does not quantify full pathway emissions. It excludes HVAC and building services in the base case, along with consumables, instrument manufacture, sterilisation, anaesthesia-related emissions, transport, and hospital stay. Concerns about operating-theatre infrastructure were addressed by adding explicit low-resource and conditioning-overhead sensitivities, but globally harmonised metered datasets for RARP suites are still lacking, so these scenarios should be interpreted as structured bounds rather than direct measurements. The high plug-load upper-bound scenario was derived from manufacturer nameplate ratings rather than from metered real power and should therefore be interpreted conservatively. Second, operative time and power demand can vary with surgeon experience, case complexity, equipment configuration, and local theatre practice; the reference distribution was therefore derived from published summary data rather than raw case-level observations, and the modelled power-demand scenarios do not replace site-specific metering. Third, carbon-intensity values represent jurisdiction-level annual averages that may not reflect a specific hospital’s electricity contract, local marginal generation, or hourly variation. Fourth, the CI x 0.5 and CI x 0.1 counterfactuals are stylised scenario tests rather than forecasts of how specific jurisdictions will decarbonise. Fifth, the primary carbon-intensity source is a live public dataset. The exact extraction used here is preserved in Supplementary Table S1 and the archived input CSV in Supplementary Code 1 and should be used for verification; users who update the analysis with later source data should document the new extraction date and should expect numerical values to change if the source dataset has been revised. Sixth, the model applies published annual-average life cycle grid-intensity factors and does not evaluate market-based contracts, hourly or marginal grid intensity, or embodied emissions of electrical infrastructure. Finally, this electricity-only model should not be interpreted as a full life-cycle carbon footprint of RARP or as evidence that one operative approach is environmentally preferable overall.
Conclusion
Using a standardised intraoperative plug-load model, the electricity-related component of robot-assisted radical prostatectomy varied by more than 30-fold across jurisdictions and was most strongly shaped by the local grid carbon intensity applied to each jurisdiction, across operative-time, infrastructure, and plug-load sensitivity analyses. The practical implication is that cross-site comparisons of RARP electricity emissions are only interpretable when both the local electricity emission factor and the electricity-use assumptions are reported transparently. In high-carbon grids, cleaner electricity procurement and operating-theatre energy management can reduce this operational component; in low-carbon grids, the main residual mitigation opportunities may lie more often in non-electricity parts of the surgical pathway. The contribution of the present study is therefore quantitative and comparative within a defined intraoperative electricity-use boundary, using life-cycle grid-intensity factors, rather than a replacement for full pathway life-cycle assessment.
Supplementary Information
Below is the link to the electronic supplementary material.
Author contributions
Conceptualization: R.B.D.; methodology: R.B.D.; software: R.B.D.; validation: R.B.D; formal analysis: R.B.D.; investigation: R.B.D.; resources: R.B.D.; data curation: R.B.D.; writing—original draft preparation: R.B.D.; writing—review and editing: R.B.D.; visualization: R.B.D.; supervision: R.B.D.; project administration: R.B.D.; funding acquisition: R.B.D.
Data availability
All data generated or analysed during this study are included in this article and its Supplementary Information files or are available from the public sources identified below. The primary analytical input was the Low-Carbon Power carbon-intensity-of-electricity ranking/export dataset (life-cycle gCO2eq/kWh; latest available yearly or last-12-month values including net imports), accessed on 11 January 2026 from the public ranking/map pages and downloadable yearly CSV/JSON exports10,11. The exact analytical extraction used in the manuscript, including the carbon-intensity values for all 208 jurisdictions and all derived scenario outputs, is provided in Supplementary Table S1 and in the archived input CSV supplied with Supplementary Code 1. Supplementary Table S1 contains the Table S1, Sources_and_access, and Data_dictionary worksheets, which document the source datasets, access routes, variables, units, derivations, and restriction status. Supplementary Table S1 should be used to verify the published numerical results because the live web dataset may be updated after extraction. Public contextual data were obtained from Our World in Data’s carbon-intensity-of-electricity data page and associated downloadable CSV/metadata files12. No patient-level, proprietary, restricted, or access-controlled datasets were used. No access restrictions, payment, permission, or data-use agreement applies to the archived analytical data. Figure source data for Figs. 1, 2 and 3 are provided in Supplementary Table S1 and can be regenerated using Supplementary Code 1.
Code availability
The custom Python 3 code used to generate the jurisdiction-level calculations, structural sensitivity outputs, annual-scaling tables, figures, and summary statistics is provided as Supplementary Code 1 (Supplementary_Code_1_RARP_electricity_model.zip). The package contains RARP_electricity_reproducibility.py, README_Supplementary_Code_1.txt, requirements.txt, and input_ci_dataset.csv exported from Supplementary Table S1. The code implements Eqs. (1)-(3), the scenario constants in Table 1, and the output routines for the manuscript tables and figures. It runs offline using the archived input CSV, so the published numerical values can be reproduced even if the public web dataset changes. It can also be run with an updated public carbon-intensity extract with the columns Jurisdiction and CI_gCO2e_kWh for future updates. No proprietary software, private dataset, or access-controlled algorithm is required, and no access restrictions apply to the code.
Declarations
Competing interests
The author declares no competing interests.
Ethics
Not applicable. This study used publicly available, aggregated jurisdiction-level data and did not involve human participants or identifiable patient data.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
- 1.Intergovernmental Panel on Climate Change. Climate change 2023: synthesis report (IPCC, 2023). 10.59327/IPCC/AR6-9789291691647. [Google Scholar]
- 2.World Health Organization. Climate change and health. https://www.who.int/news-room/fact-sheets/detail/climate-change-and-health (accessed 11 January 2026).
- 3.Karliner, J., Slotterback, S., Boyd, R., Ashby, B. & Steele, K. Health care’s climate footprint: how the health sector contributes to the global climate crisis and opportunities for action. Health Care Without Harm and Arup (2019). https://healthcareclimateaction.org/report/health-cares-climate-footprint/ (accessed 11 January 2026).
- 4.Eckelman, M. J. & Sherman, J. D. Environmental impacts of the U.S. health care system and effects on public health. PLoS One11, e0157014. 10.1371/journal.pone.0157014 (2016). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 5.Health Care Without Harm. Global road map for health care decarbonization. https://healthcareclimateaction.org/climate-smart-healthcare/global-road-map-health-care-decarbonization (accessed 11 January 2026).
- 6.NHS England. Delivering a ‘net zero’ national health service. https://www.england.nhs.uk/greenernhs/publication/delivering-a-net-zero-national-health-service/ (accessed 11 January 2026).
- 7.Brighton and Sussex Medical School, Centre for Sustainable Healthcare & UK Health Alliance on Climate Change. Green surgery: reducing the environmental impact of surgical care. UK Health Alliance on Climate Change, London. (2023). https://ukhealthalliance.org/wp-content/uploads/2023/04/GreenSurgeryReport_v2.pdf (accessed 11 January 2026).
- 8.Kouwenberg, L. H. J. A. et al. The carbon footprint of hospital services and care pathways: A state-of-the-science review. Environ. Health Perspect.132, 126002. 10.1289/EHP14754 (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 9.Mirow, J., Venne, J. & Brand, A. Green health: how to decarbonise global healthcare systems. Sustain. Earth Rev.7, 28. 10.1186/s42055-024-00098-3 (2024). [Google Scholar]
- 10.Low-Carbon Power. Carbon intensity of electricity (gCO2eq/kWh): ranking by country/region. https://lowcarbonpower.org/ranking?metric=ci (accessed 11 January 2026).
- 11.Low-Carbon Power. Where do our emissions numbers come from? https://lowcarbonpower.org/blog/emissions (accessed 11 January 2026).
- 12.Our World in Data. Carbon intensity of electricity. https://ourworldindata.org/grapher/carbon-intensity-electricity?tab=chart (accessed 11 January 2026).
- 13.Robinson, P. N., Surendran, K. S. B., Lim, S. J. & Robinson, M. The carbon footprint of surgical operations: A systematic review update. Ann. R. Coll. Surg. Engl.105, 692–708. 10.1308/rcsann.2023.0057 (2023). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 14.Fuschi, A. et al. The impact of radical prostatectomy on global climate: A prospective multicentre study comparing laparoscopic versus robotic surgery. Prostate Cancer Prostatic Dis.27, 272–278. 10.1038/s41391-023-00672-4 (2024). [DOI] [PubMed] [Google Scholar]
- 15.von Elm, E. et al. The Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement: Guidelines for reporting observational studies. PLoS Med.4, e296. 10.1371/journal.pmed.0040296 (2007). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 16.EQUATOR Network. STROBE statement. https://www.equator-network.org/reporting-guidelines/strobe/ (accessed 11 January 2026).
- 17.World Resources Institute & World Business Council for Sustainable Development. The greenhouse gas protocol: a corporate accounting and reporting standard. Revised edn. (2004). https://ghgprotocol.org/sites/default/files/standards/ghg-protocol-revised.pdf (accessed 11 January 2026).
- 18.World Resources Institute & World Business Council for Sustainable Development. Product life cycle accounting and reporting standard. (2011). https://ghgprotocol.org/standards/product-standard (accessed 11 January 2026).
- 19.World Resources Institute & World Business Council for Sustainable Development. Scope 2 guidance: an amendment to the GHG Protocol corporate standard. (2015). https://ghgprotocol.org/scope-2-guidance (accessed 11 January 2026).
- 20.International Organization for Standardization. ISO 14040:2006 environmental management—life cycle assessment—principles and framework (ISO, 2006). [Google Scholar]
- 21.International Organization for Standardization. ISO 14044:2006 environmental management—life cycle assessment—requirements and guidelines (ISO, 2006). [Google Scholar]
- 22.International Organization for Standardization. ISO 14064-1:2018 greenhouse gases—part 1: specification with guidance at the organization level for quantification and reporting of greenhouse gas emissions and removals (ISO, 2018). [Google Scholar]
- 23.International Organization for Standardization. ISO 14067:2018 greenhouse gases—carbon footprint of products—requirements and guidelines for quantification (ISO, 2018). [Google Scholar]
- 24.Intuitive Surgical. da Vinci Xi system readiness guide. https://www.intuitive.com/-/media/project/intuitive-corporate/website/products/da-vinci-xi/system/readiness-guide/davinci_xi_readiness_guide.pdf (accessed 11 January 2026).
- 25.Bravi, C. A. et al. Robot-assisted radical prostatectomy with the novel Hugo robotic system: Initial experience and optimal surgical set-up at a tertiary referral robotic center. Eur. Urol.82, 233–237. 10.1016/j.eururo.2022.04.029 (2022). [DOI] [PubMed] [Google Scholar]
- 26.Marino, F. et al. Robot-assisted radical prostatectomy performed with the novel Hugo™ RAS system: A systematic review and pooled analysis of surgical, oncological, and functional outcomes. J. Clin. Med.13, 2551. 10.3390/jcm13092551 (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 27.Centrum e-Zdrowia. Prostatektomia radykalna – porównanie metod zabiegu. https://ezdrowie.gov.pl/portal/home/badania-i-dane/zdrowe-dane/raporty/prostatektomia-radykalna-porownanie-metod-zabiegu-2025 (accessed 11 January 2026).
- 28.National Prostate Cancer Audit. State of the nation report. (2023). https://www.npca.org.uk/resources/state-of-the-nation-report-2023/ (accessed 11 January 2026).
- 29.Institut National d’Assurance Maladie-Invalidité. Prostatectomie radicale (hommes): variations de pratiques médicales. https://www.healthybelgium.be/fr/variation-de-pratiques-medicales/prostatectomie-radicale (accessed 11 January 2026).
- 30.Institut national du cancer. Programme de médicalisation des systèmes d’information (PMSI). https://www.cancer.fr/professionnels-de-sante/ressources-et-outils/les-bases-de-donnees/pmsi (accessed 11 January 2026).
- 31.Watts, N. et al. The Lancet MedZero: Carbon analytics for health care, by health care, at scale. Lancet407, 205–207. 10.1016/S0140-6736(25)02280-9 (2026). [DOI] [PubMed] [Google Scholar]
- 32.Quitmann, C. et al. Assessing greenhouse gas emissions in hospitals: The development of an open-access calculator and its application to a German case-study. Cleaner Environ. Syst.16, 100262. 10.1016/j.cesys.2025.100262 (2025). [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
All data generated or analysed during this study are included in this article and its Supplementary Information files or are available from the public sources identified below. The primary analytical input was the Low-Carbon Power carbon-intensity-of-electricity ranking/export dataset (life-cycle gCO2eq/kWh; latest available yearly or last-12-month values including net imports), accessed on 11 January 2026 from the public ranking/map pages and downloadable yearly CSV/JSON exports10,11. The exact analytical extraction used in the manuscript, including the carbon-intensity values for all 208 jurisdictions and all derived scenario outputs, is provided in Supplementary Table S1 and in the archived input CSV supplied with Supplementary Code 1. Supplementary Table S1 contains the Table S1, Sources_and_access, and Data_dictionary worksheets, which document the source datasets, access routes, variables, units, derivations, and restriction status. Supplementary Table S1 should be used to verify the published numerical results because the live web dataset may be updated after extraction. Public contextual data were obtained from Our World in Data’s carbon-intensity-of-electricity data page and associated downloadable CSV/metadata files12. No patient-level, proprietary, restricted, or access-controlled datasets were used. No access restrictions, payment, permission, or data-use agreement applies to the archived analytical data. Figure source data for Figs. 1, 2 and 3 are provided in Supplementary Table S1 and can be regenerated using Supplementary Code 1.
The custom Python 3 code used to generate the jurisdiction-level calculations, structural sensitivity outputs, annual-scaling tables, figures, and summary statistics is provided as Supplementary Code 1 (Supplementary_Code_1_RARP_electricity_model.zip). The package contains RARP_electricity_reproducibility.py, README_Supplementary_Code_1.txt, requirements.txt, and input_ci_dataset.csv exported from Supplementary Table S1. The code implements Eqs. (1)-(3), the scenario constants in Table 1, and the output routines for the manuscript tables and figures. It runs offline using the archived input CSV, so the published numerical values can be reproduced even if the public web dataset changes. It can also be run with an updated public carbon-intensity extract with the columns Jurisdiction and CI_gCO2e_kWh for future updates. No proprietary software, private dataset, or access-controlled algorithm is required, and no access restrictions apply to the code.






