To Explore The Impact Of Global Warming By Analysis Temperature Change Correlation Networks And Matrices

All the signs indicate that global temperatures are gradually increasing. Global warming has become an indisputable fact, and this problem has been growing concern. In academia, global warming has become a hot issue among scientists all over the world. The purpose of this article is not only to verify the hypothesis that as time goes on the climatic similarities between different regions are increasing and the climate is losing its diversity but also to provide a new perspective for predicting the future of global temperature trend and understanding the manifestations of global climate. In order to achieve the objective, we use two models, correlation network and correlation matrix, to experiment and analyze temperature data with the theories in mathematic, computer science and bioinformatics.As the positioning of this article is an academic research paper, the framework of this article will be theories introduction, algorithms chosen and amendment, experiment on the data and draw the conclusion. The main research steps and the overall research ideas are summarized below.Firstly, we pretreated and divided the a-century data, which consist of monthly average temperature of 802 weather stations in American, into ten groups with the interval of ten year. And we use the Euclidean distance of pairwise vectors, which are formed by the coefficients of the temperature curve doing the discrete Hartley transform, to represent the correlation between weather stations.Secondly, with the consideration of time complexity, we apply Monte Carlo algorithm to permutation test in order to enhance the statistical significance of the correlation between pairwise weather stations. And based on it, we construct reliable correlation networks and correlation matrices with statistical significance for each group.Moreover, we made some basic analysis to the networks using degree distribution, common graphs and clustering coefficient and so on. From the subgraph point of view, we made comparison among the networks and their random graphs, and results nicely support the research need and previous hypothesis. We also identify the community structure in the networks, and along with some geographical characteristic, by constructing three climate station clusterings. We made some analysis and comparison on the three climate station clusterings from subgraph point of view and then get some local evolution feature.Last but not least, we make some analysis and comparison on the correlation P-value matrices. We use two methods to inspect the similarities of pairwise correlation matrices: do principle component analysis by eigenvalue and eigenvector; to represent the differences of pairwise matrices directly by the cosine of angle between matrices.From the results we found that the statistic to measure the number of complex subgraphs in the networks change in opposite trends against temperature. In another word, the appearance probability of complex subgraphs in the networks reduces when the temperature rises. It indicates that from the topology structure point of view, the correlation networks are becoming more and more random as temperature go up. The difference among subgraph appearance probability of three climate-station clusterings, which constructed according to the territory characteristic of American, coincides with some official weather reports.At the same time, the result of correlation matrices, which was represented by the Euclidean distance, root mean square deviation, cosine of angle of matrices, shows that with time goes on the difference between correlation matrices has an downward trend. This conclusion also confirmed our article's assumption from another angle. Namely, global warming cause the loss of climate diversity and the relevance of the overall global temperature changes have become relatively chaotic.