CarbonScaling: Quantitative Environmental Benchmarking

• CarbonScaling is a heterogeneous framework that employs explicit scaling laws to benchmark environmental impacts against system size.
• It spans applications from corporate emissions analysis and cloud autoscaling to neural network training, providing actionable metrics across domains.
• The framework enables optimized resource allocation and operational control while addressing trade-offs, assumptions, and real-world implementation challenges.

CarbonScaling is a heterogeneous research term used for a family of quantitative frameworks that connect environmental impact to scale, resource allocation, and control. In one line of work, it denotes allometric benchmarking: Mastrandrea et al. model corporate $\mathrm{CO_2e}$ emissions, primary energy use, water withdrawal, and waste production as power laws of firm size, $Y=\alpha S^\beta$, and use the fitted curve as a sector-specific benchmark of environmental performance (Mastrandrea et al., 2022). In computing systems, the term is used for carbon-aware autoscaling, scheduling, provisioning, and budgeting methods that adapt servers, containers, functions, or jobs to carbon intensity, renewable availability, deadlines, and SLOs (Hanafy et al., 2023). In LLMs, it has also been used for an analytical extension of neural scaling laws that incorporates operational and embodied carbon into training-time scaling analysis (Jiang et al., 2 Aug 2025). Across these uses, CarbonScaling is best understood as a methodological family rather than a single canonical model.

1. Intellectual lineage and recurrent mathematical structure

A central feature of CarbonScaling is the use of explicit scaling relations to compress complex environmental behavior into a small number of interpretable parameters. The corporate formulation uses a power law in firm size, while adjacent climate-economy research uses either power-law or proportional relations between emissions and system scale. In urban emissions analysis, the Urban Kaya Relation links city population $P$, GDP $G$, energy use $E$, and emissions $C$ through chained scaling laws such as $G\sim P^\beta$, $E\sim G^\alpha$, and $C\sim E^\gamma$, yielding $C\sim P^\theta$ with $Y=\alpha S^\beta$0 when the exponents are estimated consistently by Reduced Major Axis regression (Gudipudi et al., 2017). At the global macro scale, Garrett and coauthors report a persistent proportionality between current world primary energy consumption $Y=\alpha S^\beta$1 and cumulative historical inflation-adjusted production $Y=\alpha S^\beta$2, with $Y=\alpha S^\beta$3 Gigawatts per trillion 2010 US dollars, and then write carbon emissions as $Y=\alpha S^\beta$4 (Garrett et al., 2020).

These antecedents matter because later CarbonScaling formulations inherit the same formal strategy: they replace qualitative claims about “bigger systems emit more” with explicit parametric relations that can be estimated, benchmarked, or optimized. In the scaling-law variants, the main object is an exponent. In the control and scheduling variants, the main object is a constrained optimization or feedback policy, but the environmental signal still enters as a compact scalar—typically carbon intensity, power, or a carbon-weighted cost.

2. Power-law benchmarking of corporate environmental performance

In “Scaling laws in global corporations as a benchmarking approach to assess environmental performance,” Mastrandrea et al. study 6,529 publicly traded firms from 76 countries and 123 TRBC industries using 2018 Refinitiv EIKON data, and fit the log-log regression

$Y=\alpha S^\beta$5

for each environmental metric $Y=\alpha S^\beta$6 and firm-size proxy $Y=\alpha S^\beta$7 (Mastrandrea et al., 2022). Using annual revenue in € billion as the main size variable, they estimate for the global cross-sector sample: $Y=\alpha S^\beta$8 for $Y=\alpha S^\beta$9 emissions with $P$0 and $P$1; $P$2 for energy use with $P$3 and $P$4; $P$5 for water withdrawal with $P$6 and $P$7; and $P$8 for waste production with $P$9 and $G$0. All four global exponents are sublinear, implying that larger firms exhibit lower impact per unit revenue on average.

The framework converts these fitted laws into a benchmark. For a sector with parameters $G$1 and a firm of size $G$2, the expected impact is

$G$3

A firm above that curve is above the sectoral norm for its size, while a firm at or below it meets the sector-norm benchmark. The paper gives a numerical example for a hypothetical basic-materials company with annual revenue $G$4 billion €, using $G$5 and $G$6, which yields $G$7 million t $G$8 (Mastrandrea et al., 2022).

The same study reports that sectoral disaggregation improves explanatory power: the mean $G$9 rises to $E$0 at the TRBC sector level and to $E$1–$E$2 at the industry level. It also notes that most sectors remain sublinear for $E$3 and water, whereas energy and waste can become superlinear in some highly competitive, energy-intensive industries such as airlines and petrochemicals. The proposed policy interpretation is explicitly benchmarking-oriented rather than absolute: mandating size- and sector-adjusted targets could cut global $E$4 emissions by roughly 15 percent, energy use by 11 percent, and water withdrawal by 10 percent if firms above the curve moved to the benchmark, although the authors emphasize self-reported data, OLS assumptions on log-log scales, intra-sector heterogeneity, and real-world implementation constraints.

3. Carbon-aware scaling in cloud, cluster, and hyperscale systems

In computing infrastructure, CarbonScaling usually denotes dynamic control of resources in response to time-varying carbon signals. CarbonScaler formalizes a single elastic batch job as a discrete allocation problem over time slots, where the schedule chooses server count $E$5 in each slot to minimize carbon subject to a total-work constraint, and then proves optimality of a greedy rule that allocates the next unit of server-time to the slot-server pair maximizing $E$6, where $E$7 is marginal work from the $E$8-th server and $E$9 is slot carbon intensity (Hanafy et al., 2023). Its Kubernetes prototype reports up to 51% carbon savings over carbon-agnostic execution, 37% over a suspend-resume policy, and 8% over the best static scaling policy.

Several later systems generalize that formulation to stronger uncertainty models or cluster-level control. LACS studies online carbon-aware resource scaling with unknown job length and switching costs, blends robust online policies with an ML prediction of job length, and empirically stays within 1.2% of an online baseline that assumes perfect job length information, within 16% of an offline baseline that also assumes accurate carbon forecasts, while reducing carbon footprint by 32% relative to deadline-aware carbon-agnostic execution (Bostandoost et al., 2024). CarbonFlex addresses the coupled provisioning-and-scheduling problem for many elastic batch jobs in a cloud cluster, learns runtime policies by case-based reasoning over historical traces and an offline oracle, integrates with AWS ParallelCluster, and decreases emissions by $C$0 compared to a carbon-agnostic baseline while performing within 2.1% of an oracle scheduler with perfect future knowledge (Hanafy et al., 23 May 2025).

At hyperscale, Google’s Carbon-Intelligent Compute Management performs day-ahead planning rather than per-job local scaling. It gathers next-48-hour carbon forecasts, predicts flexible and inflexible CPU demand, trains cluster-specific power models, and solves for hourly Virtual Capacity Curves that cap flexible-tier usage while preserving daily completion targets (Radovanovic et al., 2021). In operation, shaped clusters used 1–2% less power during the 3 hours of highest carbon intensity, while daily total flexible completion remained within SLO bounds more than 97% of the time. CASPER extends carbon-aware control to geo-distributed web services by jointly deciding per-region server counts and inter-region request routing via a mixed-integer linear program and an HTTP-layer scheduler, and reports up to 70% improvements over baseline methods with no latency performance degradation (Souza et al., 2024). For DAG-style data processing, PCAPS adds carbon-aware filtering to precedence-sensitive scheduling, explicitly using task importance induced by job precedence and time-varying carbon intensity; on a Spark-on-Kubernetes prototype, a moderate configuration reduces carbon footprint by up to 32.9% without significantly impacting the cluster’s total efficiency (Lechowicz et al., 13 Feb 2025).

A related architectural line exploits energy-source heterogeneity rather than only grid-time variation. ZCCloud colocates modular HPC containers with wind-farm substations and powers them only when stranded power is available, treating curtailed or zero/negative-price renewable generation as an intermittent resource (Yang et al., 2016). Under the reported cost model, the approach reduces total cost of ownership by 21–45% in baseline and high-power-price scenarios, and a 10 MW stranded-power extension yields an estimated annual reduction of approximately 39,420 t$C$1/yr.

4. Autoscaling in microservices, serverless, and FaaS platforms

Another major CarbonScaling usage centers on microservice and serverless autoscaling under SLO constraints. Full Scaling Automation (FSA) is an end-to-end predictive horizontal autoscaling system for large cloud clusters that combines multi-scale time-series representation learning, a representation-enhanced deep autoregressive forecasting model, and task-conditioned Bayesian regression for mapping workload to per-Pod CPU utilization (Wang et al., 2023). Deployed on 3,000+ microservices in Ant Group data centers, it runs every 5 minutes and, on real-world datasets, reports forecasting MAE/RMSE of 1.257/22.76 versus 1.427/26.76 for the best baseline, regression MAE/RMSE of 0.365/0.799 versus approximately 0.63/1.24 for XGBoost, and autoscaling resource consumption about 15–20% lower than FIRM or Autopilot while preserving SLOs. During the Double 11 shopping festival of 2022, the deployment saved 1,538,000 kWh and reduced 947 tons of $C$2, as certified by the China Environmental United Certification Center.

CASA addresses serverless cloud computing through a bi-objective formulation that jointly minimizes cumulative operational carbon and average SLO violation rate over a planning horizon, using a two-phase local-search algorithm per epoch and a real-time autoscaler for CPU and DRAM adjustments (Qi et al., 2024). In the reported experiments, CASA reduces the operational carbon footprint of a FaaS cluster by up to 2.6x while also reducing the SLO violation rate by up to 1.4x relative to the state of the art. SFCM extends the objective set by adding wastewater generation to carbon and SLO metrics, producing Pareto fronts over $C$3 triples for 15-minute epochs on Azure serverless traces (Qi et al., 2024). Compared to the best baseline SCORE, SFCM-SLO reduces SLO violation rate by up to 22%, SFCM-Carbon reduces carbon emissions by up to 35%, and SFCM-Water reduces water usage by up to 37%; the balanced variant achieves 45% lower SLO violation rate, 25% lower carbon emissions, and 26% lower wastewater than HYBRID, and 14% carbon reduction plus 20% water reduction versus SCORE at the cost of less than 1% higher SLO violation.

Platform-level serverless routing introduces additional carbon-aware mechanisms. GreenWhisk extends Apache OpenWhisk with an Energy Interface, weighted consistent hashing, and a Retry Queue for deferral under high-carbon or low-energy conditions (Serenari et al., 2024). In grid-connected mode it avoids roughly 20–30% of $C$4 while adding less than 5% latency overhead; in grid-isolated mode it halves average server downtime and reduces instances of battery level below 20% by approximately 60%. GreenScale broadens the scope to edge-cloud applications across mobile devices, edge datacenters, routers, and hyperscale datacenters, and shows that optimizing directly for carbon yields scheduling decisions distinct from energy- or performance-optimal ones, with up to 29.1% carbon reduction and an annual saving of 232.7 t$C$5 per million users; intelligent battery charging reduces mobile carbon footprint by up to 61.2% (Kim et al., 2023). NeuroScaler adds model-predictive control over replica counts using multi-tier telemetry from PDUs, servers, and containers, and reduces energy consumption by 34.68% relative to the Kubernetes Horizontal Pod Autoscaler while maintaining target latency (Chaves et al., 9 Feb 2026).

5. Accounting, budgeting, and analytical extensions

CarbonScaling also appears in work that does not directly schedule jobs but instead measures, allocates, or budgets emissions. Google’s cloud carbon-accounting methodology allocates shared machine energy by decomposing machine power into idle and dynamic components, assigning idle power using a reservation-based physical allocation and dynamic power using measured usage, then reallocating shared-service footprints to final users and multiplying by per-hour PUE and location-specific carbon intensity (Schneider et al., 2024). The resulting framework is an allocation pipeline from machine telemetry to per-customer $C$6, and it explicitly emphasizes physical factors favored by the GHG Protocol’s Scope 3 Reporting Standard.

Budget-based control replaces instantaneous caps with cumulative constraints. “Using Budgets to Reduce Application Emissions” defines an emissions budget $C$7 over lifetime $C$8, tracks per-second emissions as $C$9, updates the remaining budget by $G\sim P^\beta$0, and uses a MAPE-K loop to choose between scale up, scale down, migrate, or no action so as to maximize performance while respecting the long-run budget (Lierse et al., 13 Apr 2026). With six weeks of real-world carbon intensity data from Germany, France, and Poland, the budget-based policy improves task fulfillment by up to 36% in variable grids relative to fixed per-second rates, while achieving parity in stable grids. The banking-and-spending logic is the key analytical innovation: low-carbon intervals preserve budget slack that can later be spent in high-carbon periods without violating the hard cumulative constraint.

The 2025 LLM paper titled “CarbonScaling” extends neural scaling laws by incorporating operational and embodied carbon into model-training analysis (Jiang et al., 2 Aug 2025). Its core decomposition is

$G\sim P^\beta$1

with GPU operational carbon modeled as a function of number of GPUs, duration, PUE, carbon intensity, static power, dynamic power, and utilization, and embodied carbon tied to chip area, carbon per unit area, and hardware lifetime. The paper preserves the neural-scaling intuition that loss decreases as a power law of compute, but links that to carbon via an accuracy-carbon scaling law with exponent $G\sim P^\beta$2. It further reports that real-world training curves lie 2–5$G\sim P^\beta$3 to the right of the ideal case because of utilization losses and embodied cost, and that aggressive critical batch size scaling can yield up to approximately 20% carbon savings at extreme scale.

6. Trade-offs, assumptions, and open questions

A persistent misconception in this literature is that carbon-aware scaling is equivalent to energy minimization. The cited studies repeatedly reject that equivalence. GreenScale explicitly states that optimizing for carbon, compared to performance and energy efficiency, yields unique scheduling solutions (Kim et al., 2023). SFCM finds that SLO-focused FaaS scheduling can exacerbate water use, so a carbon-only or latency-only objective can be environmentally incomplete (Qi et al., 2024). The LLM CarbonScaling paper likewise shows that better hardware energy efficiency does not remove carbon inefficiency at extreme scale, because communication overhead and underutilized GPUs create diminishing returns (Jiang et al., 2 Aug 2025).

The main assumptions and limitations vary by domain but are structurally similar. Corporate benchmarking depends on self-reported EIKON data, OLS on log-transformed observations, and sector-level averaging that can hide technologically important heterogeneity (Mastrandrea et al., 2022). Cloud schedulers depend on carbon forecasts, workload forecasts, profiling of marginal scaling curves, or measured switching costs; CarbonScaler explicitly notes dependence on carbon-intensity forecasts and profiled marginal-capacity curves (Hanafy et al., 2023), while Google’s fleet-wide system uses average rather than marginal grid carbon intensity and limits shaping to temporal rather than inter-datacenter spatial shifting (Radovanovic et al., 2021). Serverless and edge frameworks often assume simplified carbon, power, or cooling models and may omit network or cooling-plant dynamics; SFCM, for example, assumes a single datacenter and simplified carbon and water models (Qi et al., 2024). Budget-based schemes assume reliable telemetry and enforceability of long-run budgets, while predictive autoscalers such as FSA and NeuroScaler require sufficiently stable observability and retraining pipelines (Wang et al., 2023).

A broader interpretive issue is whether simple scaling relations should be read as descriptive regularities, benchmarking tools, or optimization targets. In the corporate literature, scaling laws mainly function as descriptive and comparative baselines. In cloud and serverless systems, the same style of formalization becomes prescriptive: carbon intensity enters an objective, a threshold, or a control loop, and the system actively changes scale or placement. In LLM training, CarbonScaling is analytic again, but with an explicitly design-oriented interpretation: it converts a target loss or accuracy into a carbon footprint estimate under ideal and non-ideal hardware regimes (Jiang et al., 2 Aug 2025). The term therefore spans at least three research modes—measurement, control, and theory—even though each mode retains the same underlying ambition: to make carbon consequences scale-aware, quantitatively explicit, and operationally actionable.