A digraph permanent approach to evaluation and analysis of integrated watershed management system

- We developed a model based on graph theory for the management of watershed.
- Eight subsystems are identified which affect the watershed system.
- The matrix model is developed by considering all attributes along with interaction.
- The permanent index of the matrix represents the score of the system uniquely.
- The proposed methodology is also demonstrated by a suitable example.

SummaryIn the present study a deterministic quantitative model based on graph theory has been developed for the better development and management of watershed. Graph theory is an integrative systems approach to consider and model structural components of watershed management system along with the interrelationships between them concurrently and integratively. The factors responsible for the development of watershed system are identified. The degree of interaction between one subsystem with others are determined. The eigenvalue formulation is used to take care the inconsistencies arises due to inaccurate judgement in the degree of interaction between the subsystems. In this model the visual analysis is done to abstract the information using the directed graph or digraph. Then the matrix model is developed for computer processing. Variable permanent function in the form of multinomial represents the watershed system uniquely and completely by an index value. Different terms of the multinomial represent all possible subsystems of integrated watershed management system and thus different solutions for watershed management, leading to optimum solution. This index value is used to compare the suitability of the watershed with different alternatives available for its development. So the graph theory analysis presents a powerful tool to generate the optimum solutions for the decision maker for benefit of local people living in the watershed as well as the stakeholders. The proposed methodology is also demonstrated by a suitable example and is applied to the ecosystem and environment subsystem of the lake Qionghai watershed in China.