Operational Water Footprint

• Operational Water Footprint is a measure that quantifies both direct water use and embedded water in supply chains across various sectors.
• It employs quantitative models like the MEIO framework to decompose water flows, enabling precise attribution and system-wide benchmarking.
• Researchers utilize optimization and scheduling approaches to strategically reduce water consumption while balancing operational efficiency and sustainability.

The operational water footprint is a quantitative measure of water consumption attributable to the immediate activities, processes, and infrastructure operations of entities across industrial, digital, and utility domains. It captures not only direct water use––such as evaporative losses in cooling systems, process water in manufacturing, and irrigation––but also embedded water attributable to indirect consumption, including electricity generation and supply chain inputs. The measurement and management of operational water footprints have become increasingly essential due to mounting freshwater scarcity and regulatory as well as societal sustainability pressure, prompting complex modeling, benchmarking, and optimization approaches across sectors.

1. Conceptual Foundations and Mathematical Formulations

Operational water footprint quantification relies on both direct and indirect water flows. Mathematically, methods often decompose total footprint into:

• Direct water usage ($d$): Volumetric quantity consumed during core operations (e.g., manufacturing, cooling).
• Indirect (embedded) water: Water consumed in upstream activities or supply chain, traced via input-output relations or environmental multipliers.

The Multi-Entity Input-Output (MEIO) model defines a matrix-based framework:

$$\mathbf{WF} = (\mathbf{I} - \mathbf{A})^{-1} \cdot \mathbf{d}$$

where $\mathbf{A}$ is the matrix of inter-entity water exchange coefficients. This formulation aggregates all direct and indirect effects, supporting granular attribution of operational water footprint across ecosystem participants (Moghaddam et al., 2014).

In energy systems, operational footprint metrics comprise:

• Water withdrawal ($W_{withdrawal}$): Function of plant power output, cooling efficiency, and cooling mode:

$$W_{withdrawal} = f(P_{plant}, \eta_{cooling}, C_{tech})$$

• Water consumption ($W_{consumption}$): Predominantly evaporative losses:

$W_{consumption} = \beta \cdot P_{plant}$

(1908.10490)

For digital infrastructure, such as AI model operation, water footprint is computed using dynamic water usage effectiveness (WUE) and power usage effectiveness (PUE):

$$\mathrm{Water}_{operational} = \sum_t e_t \cdot [\rho_{s1,t} + \theta_t \cdot \rho_{s2,t}]$$

(Li et al., 2023), where $e_t$ is energy consumed at time $t$, $\rho_{s1,t}$ on-site WUE, and $\rho_{s2,t}$ off-site WUE due to grid mix.

2. Sector-Specific Operationalizations

Automotive and Telecommunications Production

The MEIO model demonstrates that indirect supply-chain contributions often dominate water footprints in complex manufacturing. In the automotive sector, water is embedded from raw material extraction through assembly; in Telco, facility cooling and equipment manufacture are notable (Moghaddam et al., 2014). Identifying system “hotspots” enables targeted interventions in both direct and indirect water use.

Power Generation and Grid Operation

For interconnected energy-water systems, modeling both withdrawal and consumption at plant-level resolution is crucial. The SGEM model parameterizes water footprint based on cooling technology, supply structure, and operational mode. Flexible scheduling of water-intensive resources can substantially reduce footprint––in the ISO New England case, coordinated dispatch scenarios yield reductions in water withdrawal by up to 25.6% (1908.10490).

AI Infrastructure and Data Centers

Operational water footprint in AI arises from cooling and electricity generation:

• On-site: Water evaporated in cooling towers—highly sensitive to ambient conditions.
• Off-site: Water used for grid electricity generation, varying with energy mix.

Training GPT-3 led to direct evaporation of 700,000 liters, with total consumption (training + inference) in data centers scaling to millions of liters per month. Projected global AI water withdrawals may reach 4.2–6.6 billion m³ in 2027, surpassing several national totals (Li et al., 2023, Jegham et al., 14 May 2025).

3. Optimization, Decision Support, and Scheduling Approaches

Industrial water management increasingly utilizes integrated optimization frameworks:

• MINLP/MILP Models: Formulations encompass conservation, quality, capacity, and blending constraints. Linearization and discretization strategies enable real-time computation for large networks (Vatikiotis et al., 24 Apr 2025).
• Metaheuristics and ML-Driven Scheduling: Frameworks such as SLIT and WaterWise embed water use equations into multi-objective job or resource scheduling algorithms (MILP for WaterWise (Jiang et al., 29 Jan 2025), ML-guided evolutionary search for SLIT (Moore et al., 29 May 2025)). These consider both local cooling efficiency and grid water intensity, with delay tolerance and capacity constraints. Empirical deployments demonstrate 14–99% reductions in operational water footprint compared to naive schedulers.

4. Comparative Analysis and Integrative Strategies

Comparison to Scope 3 and Life Cycle Assessment (LCA) reveals important distinctions:

Model	Direct Water	Indirect Water	Interaction Modeling	Granularity
Scope 3	Yes	Yes	Aggregated	Low
LCA	Yes	Yes	Static Factors	Moderate
MEIO	Yes	Yes	Dynamic Matrix	High

MEIO and optimization-based approaches allow granular, network-aware allocations, supporting provider and end-user accounting with minimal leakage and handling scale efficiently (Moghaddam et al., 2014, Jiang et al., 29 Jan 2025). A key insight is the frequent tradeoff between carbon and water sustainability: renewable deployment (hydropower, grid-mix) or delay-based load shifting may reduce one impact at the expense of the other (Jiang et al., 29 Jan 2025, Li et al., 2023).

5. Data, Benchmarking, and Predictive Modeling

Comprehensive datasets now support operational water analysis at high spatial and temporal resolution. One five-year dataset (2019–2023) provides hourly water efficiency for US cities and electricity sources; the key direct cooling tower models use:

$$W_{direct}^{FixedApproach} = \lambda \cdot \left(-0.0001896 T_w^2 + 0.03095 T_w + 0.4442\right)$$

$$W_{indirect}(t) = \frac{\sum_k e_k(t) w_k}{\sum_k e_k(t)}$$

where $T_w$ is wet-bulb temperature and $w_k$ water intensity for generation source $k$ (Gupta et al., 24 May 2024). These data support operational scheduling for buildings, EV charging, and data center load balancing.

Benchmarking LLM inference at scale uses cross-efficiency DEA and infrastructural multipliers (PUE, on-site/off-site WUE) to estimate prompt-level and annual consumption. Models vary by >70x in per-query water footprint, highlighting the value of infrastructure-aware deployment (Jegham et al., 14 May 2025).

6. Implications for Sustainability, Policy, and Strategic Planning

Precision in operational water footprint accounting enables:

• Targeted reduction strategies for supply chains, utilities, and digital infrastructure.
• Policy formulation and compliance benchmarking for water usage, supporting eco-labeling and transparency in AI model cards (Li et al., 2023).
• Intervention in water-scarce regions via geospatial load balancing, substitution frameworks for food and resource selection, and adoption of water-free or minimal water cooling technologies.
• Integrative co-optimization, balancing water, carbon, energy costs, and service quality. Trade-offs demand optimization frameworks capable of multi-objective scheduling under dynamic constraints (Jiang et al., 29 Jan 2025, Moore et al., 29 May 2025).

A plausible implication is that scalable, matrix-based and optimization-driven approaches will be essential for operational sustainability as resource demands intensify and regulatory thresholds become more stringent.

7. Future Directions and Research Needs

Further granularity in temporal and spatial footprint modeling, unified datasets, and continued algorithmic advances are needed for real-time optimization. Integrating water scarcity indices and downstream ecosystem impacts is pivotal for next-generation operational water footprint frameworks. The sectoral convergence of manufacturing, utilities, cloud computing, and AI highlights the necessity of robust, generalizable models capable of dynamic adaptation across diverse environmental and operational contexts.