Modeling the fields of thermokarst lakes in the permafrost based on the geo-simulation approach and satellite images

Based on the geo-simulation approach, a new model of the spatial structure of the fields of thermokarst lakes was developed which takes into account the lakes in the full range of their sizes (from 20 m$^2$ to 200 km$^2$) and the tortuosity of their coastal borders. The proposed model also enables us to take into account small lakes, which are considered to be intensive sources of methane and carbon dioxide emissions into the atmosphere from the thermokarst lakes. The structure of the model is determined as a set of flat figures with random locations of the lakes centers and random area and degree of tortuosity of their boundaries. It was established that the histogram of the tortuosity degree distribution obtained from the satellite measurements can be adopted, by the Pearson criterion, as corresponding to the lognormal law with high probability. Based on the use of satellite images of both medium and high spatial resolution, an empirical histogram of the size distribution of the lakes is developed for the permafrost of Western Siberia. The results of checking the correlating of the empirical histogram to the theoretical lognormal law showed the correspondence, according to the Pearson criterion, at the significance level of 0.99. For the software implementation of the geo-simulation model, it is proposed, within the framework of the Monte Carlo procedure, to generate sequences of four pseudorandom numbers, the first pair of which simulates the random coordinates of the centers of lakes and the second pair is for random degrees of tortuosity and areas of the lakes. We developed algorithms for generating sequences of pseudorandom numbers which make it possible to create software number sensors that display random degrees of tortuosity and areas of lakes distributed according to the lognormal law.