The hydraulic characteristics of artificial waterfalls constitute an important research area for both academia and industry.As yet,the hydraulic parameters used in the hydraulic design of landscape waterfalls are not well understood for use in qualitative and quantitative analyses.Due to their complicated shapes and appearances,it remains a challenging problem to design or simulate realistic waterfall scenes.In this paper,we present a hybrid model and an efficient numerical method for simulating the hydraulic characteristics of waterfalls and investigate the critical flow in waterfall design and the adherent flow phenomenon.We fit empirical equations to predict the size and shape of different waterfall flow patterns to provide a basis for the design and construction of waterscapes in the real world.We then apply our work to an artificial waterfall in Kraal Jiang River and the results demonstrate that our model achieves desirable control qualities and good agreement in a real-world application. The hydraulic characteristics of artificial waterfalls constitute an important research area for both academia and industry. As yet, the hydraulic parameters used in the hydraulic design of landscape waterfalls are not well understood for use in qualitative and quantitative analyzes. Due to their complicated shapes and appearances , it remains a challenging problem to design or simulate realistic waterfall scenes. In this paper, we present a hybrid model and an efficient numerical method for simulating the hydraulic characteristics of waterfalls and investigate the critical flow in waterfall design and the adherent flow phenomenon. fit empirical equations to predict the size and shape of different waterfall flow patterns to provide a basis for the design and construction of waterscapes in the real world. We then apply our work to an artificial waterfall in Kraal Jiang River and the results demonstrate that our model achieves desirable control qualities and good agreement in a real-world appl ication.