Evaluation of heavy metal pollution with uneven spatial sampling distribution based on Voronoi area density

Ecological risk index and Voronoi diagram have been extensively used as a diagnostic guide for heavy metal pollution to support people in-depth analysis of the possibility of various contamination sources causing damage to social production, life, and the ecological environment. However, under the condition of uneven distribution of detection points, there are often situations where the Voronoi polygon area corresponding to a large degree of pollution is small or the area of the Voronoi polygon is great with a low level of pollution, and using the Voronoi area weighting or the Voronoi area density may ignore heavily polluted local areas. This study proposes the Voronoi density-weighted summation to accurately measure the concentration and diffusion of heavy metal pollution in the target area for the above issues. Then, we propose a contribution value method based on k-means to determine the number of divisions to ensure the prediction accuracy and computational cost at the same time. Moreover, applying local entropy deepens the understanding of local regional and overall system situations. Through four representative regions, the results show that the proposed whole scheme based on Voronoi diagram can effectively predict and evaluate the spatial distribution of heavy metal pollution, which provides a theoretical basis for comprehending and exploring the complex pollution environment.