Flood regulation is increasingly recognized as a complex, multivariate challenge in the Anthropocene due to accelerated floodplain urban sprawl and changing hydroclimatic conditions. However, existing research lacks a unified quantitative framework to describe the multivariate processes of flood regulation. In this study, we introduce the FRAMES framework (i.e., Flood Regulation Assessment as a MultivariatE System), in which we conceptualize the flood regulation as the responses of water infrastructures to keep floodplain settlement under certain flood exposure levels (ELs) under diverse hydroclimatic conditions. To explicitly model the interactions, we introduce (i) ELs of floodplain settlements, calculated using the cumulative distribution of the height above nearest drainage for urban pixels, (ii) flood return periods to represent hydroclimatic factors, and (iii) operational load (OL) of water infrastructures to describe the capacity allocated for flood control. Additionally, a flood regulation surface is introduced to synthesize the three-variable interactions in a continuous manner. To demonstrate our method, we apply it to the Ganjiang River Basin in China to study the interactions of Ji’An city and the upstream Wan’An Dam under various flood levels. We find a general intensification of the OL of Wan’An Dam (e.g., from 14.1% to 26.6% at a 10% EL under 100-year floods) due to the urban expansion of Ji’An city between 1985 and 2015. Moreover, the flood regulation surface reveals that due to the sparsely distributed settlements closest to the river, there is a disproportionate increase in the OL per unit decrease in EL. This indicates diminishing returns from dam-centered flood regulation strategies and suggests a critical threshold where alternative measures (e.g. local embankments, floodplain restoration) may be needed. Our study establishes a quantitative and extensible framework to describe the multivariate flood regulation processes, offering a promising tool to inform flood management tailored to the regional interplay of flood regulation.

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