Data Fusion and Aggregation Methods to Develop Composite Indexes for a Sustainable Future

Research on environmental risk modeling relies on numerous indicators to quantify the magnitude and frequency of extreme climate events, their ecological, economic, and social impacts, and the coping mechanisms that can reduce or mitigate their adverse effects. Index-based approaches significantly simplify the process of quantifying, comparing, and monitoring risks associated with other natural hazards, as a large set of indicators can be condensed into a few key performance indicators. Data fusion techniques are often used in conjunction with expert opinions to develop key performance indicators. This paper discusses alternative methods to combine data from multiple indicators, with an emphasis on their use-case scenarios, underlying assumptions, data requirements, advantages, and limitations. The paper demonstrates the application of these data fusion methods through examples from current risk and resilience models and simplified datasets. Simulations are conducted to identify their strengths and weaknesses under various scenarios. Finally, a real-life example illustrates how these data fusion techniques can be applied to inform policy recommendations in the context of drought resilience and sustainability.

💡 Research Summary

The paper addresses a fundamental challenge in environmental risk modeling: how to condense a large set of heterogeneous indicators into a small number of composite indexes that can be used for monitoring, comparison, and policy guidance. After outlining the evolution of drought risk assessment—from hazard‑only approaches to the modern “exposure‑sensitivity‑adaptive capacity” framework—the authors focus on the two essential steps of index construction: indicator selection and the choice of aggregation and weighting method. While many studies rely on expert‑driven (subjective) weights, this work systematically evaluates five objective weighting schemes that have been applied in other fields but are rarely compared side‑by‑side in the context of climate‑related risk indices.

The five methods examined are:

1. Variance‑based weighting – assigns each indicator a weight proportional to the inverse of its variance, thereby giving more influence to statistically stable indicators.
2. Entropy‑based weighting – uses information theory; indicators with higher entropy (greater uncertainty) receive lower weights, while low‑entropy, information‑rich indicators are emphasized.
3. Principal Component Analysis (PCA) – transforms correlated indicators into orthogonal principal components, then derives weights from the loadings and eigenvalues of the selected components. This reduces redundancy but introduces dependence on the number of components retained.
4. CRITIC (Criteria Importance Through Inter‑criteria Correlation) – combines each indicator’s standard deviation (a measure of contrast) with a conflict factor derived from pairwise Pearson correlations. The product yields an “information measure” that balances variability and independence.
5. Data Envelopment Analysis (DEA) – a non‑parametric efficiency‑benchmarking technique. Each region or community is treated as a Decision‑Making Unit (DMU); all indicators are modeled as outputs, a dummy input of one is used, and the linear program maximizes each DMU’s efficiency subject to the constraint that no DMU exceeds an efficiency of one. Optimal weights are obtained for each DMU and then averaged to produce a global weight set. DEA therefore provides system‑specific, policy‑relevant weights while preserving comparability across units.

To assess the behavior of these methods under controlled conditions, the authors conduct Monte‑Carlo simulations with 20 synthetic systems and five indicators. Four scenarios are generated: (a) independent normal distributions, (b) mixed variances, (c) high correlation among the first three indicators, and (d) a “systemic correlated” case where means follow a triangular ordering and multivariate dependence is imposed. All indicator values are min‑max normalized to