Abstract
<title>Abstract</title> <p>Assessing the interactions between climate vulnerability and adaptive capacity requires measurement approaches that are conceptually rigorous, methodologically transparent, and empirically robust. This study proposes a methodological framework integrating the Livelihood Vulnerability Index (LVI), objective composite-indicator construction using the CRITIC-Entropy weighting method, and the Coupling Coordination Degree (CCD) model into a unified framework for quantifying vulnerability-adaptive capacity interactions at the household level. The framework is demonstrated using survey data from 316 rice-farming households across three agroecological typologies (irrigated lowland, rainfed upland, and coastal wetland) in Indonesia. Adaptive capacity is measured through five livelihood-capital dimensions and aggregated using objective weighting to reduce subjectivity, while the CCD model evaluates the coordination between adaptive capacity and climate vulnerability. The framework effectively distinguishes coordination patterns across agroecological systems, showing relatively coordinated conditions in irrigated lowlands, adaptive-capacity lag in rainfed uplands, and intermediate coordination in coastal wetlands. Gender-disaggregated analysis further reveals consistently lower coordination levels among female-headed households. Methodologically, this study extends the CCD model from regional and urban applications to household-level agricultural systems, demonstrating its suitability for integrated climate-risk assessment. The proposed framework provides a transparent, objective, and transferable approach for measuring climate vulnerability-adaptive capacity interactions and offers a replicable methodological framework for comparative vulnerability assessments across smallholder farming systems in the Global South.</p>