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Updated: Jun 27, 2025

Watershed Planning within a Quantitative Scenario Analysis Framework
Published on: July 24, 2016
Advances in Adjoint Functions of Connection Number in Water Resources Complex Systems: A Systematic Review
Liangguang Zhou1,2, Juliang Jin1, Rongxing Zhou1,3
1School of Civil Engineering, Hefei University of Technology, Hefei 230009, China.
The adjoint function of connection number enhances water resource analysis, but faces application challenges. Future research should focus on its exploration and application in complex systems.
Area of Science:
- Hydrology and Water Resources
- Complex Systems Analysis
- Mathematical Modeling
Background:
- The adjoint function of connection number is crucial for addressing uncertainty in complex water resource systems.
- Despite its advantages, limitations hinder the widespread application of the adjoint function in water resource research.
- Set pair analysis (SPA) has seen significant evolution, particularly with the integration of adjoint functions.
Purpose of the Study:
- To analyze the development, practical application issues, and future prospects of the adjoint function of connection number in water resource research.
- To identify key research directions and limitations within the evolution of the adjoint function of connection number.
- To provide insights for promoting the exploration and application of the adjoint function in complex systems.
Main Methods:
- Bibliometric analysis of the development of connection number in water resource set pair analysis.
- Review of the evolution and categorization of adjoint functions, including set pair potential and partial connection numbers.
- Identification of research gaps and limitations in current adjoint function methodologies.
Main Results:
- The development of the connection number of water resource set pair analysis shows three distinct stages: pre-2005 (sluggish), 2005-2017 (rapid advancement), and post-2018 (surge).
- Set pair potential and partial connection number are identified as crucial research directions, with subtractive set pair potential and semi-partial connection number showing rapid development.
- Research on connection entropy and adjacent connection number is comparatively limited, indicating areas for future focus.
Conclusions:
- The adjoint function of connection number has significantly advanced water resource set pair analysis, with specific potentials and partial connection numbers being key drivers.
- Limitations in consensus on total partial connection numbers and slow development of high-order versions necessitate further research.
- Future research should prioritize addressing current limitations and promoting the broader application of adjoint functions in water resources and other complex systems.
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