Abstract:Watersheds, as fundamental units of terrestrial ecosystems, hold representative significance in ecological sustainability research. This study conceptualizes the watershed as a self-organizing and dynamic system, aiming to quantitatively analyze the complexity of landscape patterns and accurately assess its ecological sustainability. The study innovatively proposes an enhanced Boltzmann entropy model for land use data, comprehensively considering the components and spatial configuration characteristics of different land use types. This model has been applied to quantitatively assess landscape pattern complexity in the Yanhe watershed from 1980 to 2020, exploring ecological sustainability from the perspectives of "pattern" and "dynamics". The results reveal several key findings: (1) The complexity of landscape patterns within the Yanhe watershed exhibits significant spatial heterogeneity. Specifically, the upper-middle reaches of the basin exhibit the highest landscape complexity, followed by the middle-lower reaches, whereas the upper reaches display an intertwined distribution of complexity, and the lower reaches exhibit the lowest complexity. Among different land use types, reservoirs and ponds have the highest average landscape complexity, while natural woodland, high- coverage grassland and shrublands have the lowest. (2) The landscape complexity of the Yanhe watershed has undergone significant changes over the past four decades. Between 2000 and 2010, 75% of landscape units experienced an increase in complexity, particularly as agricultural land was converted to forested and grassland areas. From 2010 to 2020, although land use did not change much, the overall landscape complexity showed a clear downward trend before stabilizing. The reduction in complexity suggests a trend toward greater landscape orderliness and enhanced ecological system stability within the watershed. The method for calculating landscape pattern complexity and analyzing ecological sustainability based on Boltzmann entropy is applicable to other watersheds or landscape types, providing a novel perspective and approach for ecological protection and management.