To Assess The Impact Of Global Warming By Random Graphs Of Temperature Data

Global warming has become a topical issue in recent years. This study assesses the impact of global warming via evolution process of climate relevance networks comparing with lots of random graphs. This framework consider climate for different sites in a region as a whole and focus on their relationships, so we can get overall properties of the region and capture the big picture.The data used in this paper is monthly average temperature and precipitation data for 828 climate stations in America, date range from 1906 to 2005.We purposed a new method to measure the correlation of time series data for measuring the correlation of different climate stations. This method do Discrete Hartley Transform to time series data and the Euclidean distance between Hartley coefficient vectors got from transformation is considered as the correlation of the time series data. After measuring correlation of different climate stations, we employ permutation test to test the significance of the correlation, only statistically significant correlations are chosen to construct climate relevance network. Network constructed by this framework is rigorous and reliable.When analyzing the networks, we generate lots of random graphs with prescribed degree sequence to estimate the significance of statistics or score we studied. This makes the statistics or score we used in this paper conform to one standard, and good for comparing to them in different networks.After studying node degree distribution, common networks and clustering coefficient of climate relevance networks, we focus on four-node sub-graph in networks. We found that 3 kinds of four-node sub-graph structure, which contain three-node complete graph in it, are network motifs of climate relevance network. Sub-graph ration profile of all ten climate relevance networks have little difference between each other. We measured relevance between each two of relative sub-graph ratio curve for four-node complete graph, average temperature curve and average geographical distance curve for all linked stations in networks. Then we get the conclusion that (1) number of complex or highly connected sub-graph structures in climate relevance networks decreases as average temperature raises in first 50 years, means climate relevance network is becoming similar to random graphs, and the trend reverse in the next 50 years, means number of complex sub-graph structures increases as average temperature raises, more characteristic structures appear in climate relevance networks. (2) average geographical distance for all linked stations in networks decreases when number of highly connected sub-graph structures in climate relevance networks increases, which means new complex sub-graph structures are formed by climate stations close to each other in geography. (3) average temperature and average geographical distance for all linked stations in networks have no distinct relevance relationship, it denies a conjecture that raising temperature will enhance correlation of climates of areas far in geography.At last, by exploring community structure in climate relevance networks, we found three meaningful climate station clustering, which can represent three different climatic regions. Based on knowledge of America climate, we added with another two climate station clustering, and get five sub-networks from them. With the same treatment for whole climate relevance network, we get some local evolution features.