Embodied Water Footprint: Methods & Applications

• Embodied Water Footprint is a comprehensive metric that quantifies both direct and indirect water usage across stages like extraction, production, and consumption.
• The methodology employs MEIO models, nonlinear optimization, and machine learning to allocate water use among entities and achieve precise green-blue partitioning.
• Applications span industry, agriculture, and cloud computing, where spatial-temporal and scarcity adjustments optimize water intensity and sustainability.

The embodied water footprint quantifies the total water resources consumed—both directly and indirectly—in the lifecycle of products and services. This metric incorporates water withdrawals and consumption at upstream production stages, operational processes, and infrastructure provisioning, embedding both visible and hidden flows across industrial, agricultural, and computing ecosystems. Recent literature establishes rigorous frameworks and models for analyzing and optimizing the embodied water footprint at multiple scales, linking economic, environmental, and regional resource constraints.

1. Foundations and Definitions

The embodied water footprint measures aggregate water usage that is absorbed (withdrawn or consumed) at every stage of a product’s value chain, including upstream material extraction, intermediate manufacture, logistics, and final operation. This system-level metric is not limited to direct water withdrawals, but encompasses indirect water embedded in feedstocks, electricity, cooling, and the manufacture of infrastructure components (e.g., computing hardware).

MEIO (Multi-Entity Input–Output) modeling provides a formalism for attributing both direct and indirect water use among interconnected actors. The MEIO water footprint vector for final consumption can be expressed as:

$W = (I – A)^{-1} \cdot F$

where $I$ is the identity matrix, $A$ encodes water usage coefficients (transfers between entities), and $F$ lists immediate water footprints for each usage channel (Moghaddam et al., 2014). Partitioning is not symmetric across land-use regimes: global hydrological data reveals that green water (evapotranspiration, $ET$) dominates over blue water (runoff, $R$), with $ET/P \approx 0.62$ and $R/P \approx 0.38$ as representative area-weighted ratios (Althoff et al., 2023).

2. Analytical Frameworks and Computational Models

Rigorous modeling of the embodied water footprint leverages input–output analysis, nonlinear optimization, machine learning, and spatial-temporal aggregation frameworks.

• Input–Output Models: MEIO generalizes the classic Leontief economic IO approach, but tracks water flows, re-allocating responsibility for direct and indirect use among producers, utilities, and consumers (Moghaddam et al., 2014). Allocation coefficients ($\alpha_{ij}$) quantify each entity’s contribution to the system-wide footprint.
• Feedstock Import Optimization: Minimizes total cost and embodied water impact of commodity supply, incorporating both unit water footprints ($\mu_i$) and weighted scarcity ($W_i$):

$$\text{Water Impact} = \sum_{i=1}^{N} \left( \frac{W_i}{W_i - \mu_i x_i} \mu_i x_i \right)$$

with nonlinear constraints incorporating both production targets and environmental limits (Frittelli et al., 2020).

• Machine Learning Partitioning: Cubist regression is used to predict green-blue water partitioning in 3,614 catchments, based on climate, land use, and topography, with a mean absolute error of 0.07 for blue fluxes (Althoff et al., 2023).
• Computing/AI Operational Metrics:
  • On-site and off-site Water Usage Effectiveness (WUE) are measured per energy unit; operational ($\rho_{s1,t}$) and scope-2 ($\rho_{s2,t}$) WUE are time-dependent, capturing real-time spatial and temperature effects (Li et al., 2023, Jegham et al., 14 May 2025).
  • The total water footprint for a period $T$ and effective infrastructure lifetime $T_0$ is:

$$\text{Water}_{\text{Total}} = \sum_t e_t \left[\rho_{s1,t} + \theta_t \rho_{s2,t}\right] + \frac{T \cdot W}{T_0}$$

• Adjusted Water Impact (AWI): SCARF introduces spatial-temporal water stress correction. AWI = (Total water) × (local stress factor), with water stress aggregated across relevant periods with discounting (Wu et al., 28 Jun 2025).

3. Sectoral and Use-case Applications

Industry and Manufacturing

Automotive and telecommunications applications of MEIO demonstrate allocation of embodied water footprint across raw material extraction, component assembly, infrastructure operation, and end-user service deployment. Disaggregation traces water at each manufacturing stage; responsibility is shared based on action graphs and transaction flows (Moghaddam et al., 2014).

Agriculture and Food

Dietary consumption recommendations leverage knowledge graphs, machine learning, and detailed ingredient data to quantify and minimize the embodied water footprint per meal. Ingredient substitutions allow users to reduce the water intensity from over 20,000 m³/ton to less than 5,300 m³/ton. The underlying models predict water footprint via neural networks trained with MSE loss on integrated food and water datasets (Joshi et al., 26 Mar 2024).

Computing and Cloud Services

Operational water footprint in computing is dominated by data center cooling and regional electricity generation. Batch scheduling frameworks (e.g., WaterWise) co-optimize carbon and water footprints:

$$f(j, r) = \lambda_{CO_2} \cdot \frac{CO_2(j, r)}{CO_{2,j}^{max}} + \lambda_{H_2O} \cdot \frac{H_2O(j, r)}{H_{2O,j}^{max}}$$

Capacity and delay tolerance constraints enable environmentally aware workload placement, reducing both operational and embodied water footprints depending on grid mix (carbon intensity, EWIF) and water scarcity (Jiang et al., 29 Jan 2025). Benchmarking frameworks reveal wide per-query water intensity for LLMs, ranging from ~2 ml (efficient models) to >150 ml (large, poorly optimized deployments). Aggregated annual consumption may fill hundreds of Olympic pools, with substantial societal implications (Jegham et al., 14 May 2025).

4. Spatial, Temporal, and Scarcity Adjustments

Water stress (ratio of demand to supply) introduces spatial-temporal granularity in footprint assessment:

• SCARF’s AWI metric multiplies raw consumption by watershed-specific stress factors (WSF), calculated for short-lived or long-term deployments with discounting (Wu et al., 28 Jun 2025):

$AWI = (W_{\text{on}} + W_{\text{off}}) \cdot WSF_b$

• Facility location (mapped via Aqueduct API to hydrological basins) and timing (seasonal variation, future projections) significantly affect environmental impact. For example, datacenter and fab rankings may reverse depending on present vs. future water stress weighting.

A plausible implication is that infrastructure siting and operation scheduling can reduce embodied water footprint by orders of magnitude simply by taking spatial-stress and temporal dynamic factors into account.

5. Integration with Life Cycle and Scope-3 Methodologies

MEIO and associated models are compatible with Scope-3 (indirect) accounting and Life Cycle Assessment (LCA). This enables comprehensive tracing of water use from raw material extraction, production, operation, and end-of-life management across extended supply chains (Moghaddam et al., 2014). Integration informs hotspot identification for targeted interventions, as well as criteria for sustainable procurement, technology adoption (e.g., efficient cooling), and transnational feedstock trade optimization (Frittelli et al., 2020).

6. Datasets, Benchmarking, and Optimization Opportunities

Recent efforts have produced open-access datasets comprising hourly operational water usage and water embedded in electricity generation for 58 major U.S. cities over 5 years. These datasets enable analysis of daily, seasonal, and regional variability, model validation, and benchmarking for applications such as EV charging, building load management, and geographical load balancing in data centers (Gupta et al., 24 May 2024).

Standardized frameworks now deploy empirical benchmarking (e.g., DEA cross-efficiency for LLMs) to rank models by eco-efficiency, correlating energy drawn, carbon emissions, and water footprint at deployment scale (Jegham et al., 14 May 2025).

Optimization strategies—e.g., location selection, temporal scheduling, batching (for hardware efficiency), and tech stack choices (e.g. liquid vs. evaporative cooling)—are recognized as primary levers for embodied water footprint reduction. Their efficacy is context-dependent and must account for complex trade-offs between carbon and water efficiency, which at times are conflicting (Jiang et al., 29 Jan 2025, Li et al., 2023).

7. Future Directions and Challenges

Major challenges persist regarding data quality, scope, and model complexity. Interdependencies across entities, regions, and time introduce substantial analytical and computational overhead. Incorporating dynamic evolution (climate change, trade patterns), improving transparency (real-time reporting for AI models, open dataset development), and extending models to multi-objective frameworks for environmental trade-off balancing remain active research areas.

A plausible implication is that future sustainability standards will increasingly require both carbon and spatially-weighted water impact metrics for operational and embodied footprint disclosures, thereby driving industry behavior toward more resilient and environmentally conscious practices in production, consumption, and cloud computing.