Research on the Model Improvement of a DLA Fractal River Network

Computer simulations are introduced into the river dynamics field to provide a basis for studying fractal river networks. This paper improved on the defects of particle aggregation and growth methods in the standard diffusion-limited aggregation (DLA) model and proposed a fractal algorithm for simulating the evolution of the river network. To correct these defects, this model used watershed geomorphology as the entry point and analyzed the characteristics of runoff classification, aspect probability and contour lines. Thus, the unit-gradient growth calculation method, anisotropic Brownian motion and other related parameter optimization mechanisms (such as probability-position and step size) were established. In addition, the 2D fractal river network was simulated under different conditions. These simulations calculated the bifurcation ratio of the rendering based on Horton's law, and its value was bounded between the values of natural river channels (3 ~ 5). The standard DLA algorithm was used for simulation, but the bifurcation ratio (±5.2) of the aggregate was higher than the value of the natural river network. Therefore, the improved model can reflect the structural characteristics of the river network more realistically based on quantitative indicators. The evolution mechanism of the natural watershed was evaluated by the cyber-physical systems theory, providing a model base to study the growth and evolution of river networks. The fractal dimension of the water system fitted with each simulated subgraph was based on the box counting method. The value boundary was between 1.457 and 1.747, providing a division standard for the development degree of the watershed geomorphology. Further, according to the relationship between the number of particles and the fractal dimension, the sensitivity test of the model was also analyzed and evaluated, and its sensitivity coefficient gradually increased from 2.75 to 8.38 based on a suitable data-set, which will make the predicted watershed water system closer to its development level. Finally, use of the improved DLA model was suggested for modeling river networks.