Correlation Dimensions of Climate Sub-Systems and Their Geographic Variability

The correlation dimension D₂ of precipitation (Canada and Africa), air temperature (Canada, New Zealand and Southern Hemisphere), geo-potential height (Canada) and un-regulated streamflow (Canada, USA and Africa) were estimated using the Hill procedure of Mikosch and Wang (1995) and the bias correction of Wang and Gan (1998). After bias correction, it seems that D₂ is distinct between climate sub-systems, such that for precipitation it is between 8 and 9, for streamflow between 7 and 9, for temperature between 10 and 11, and for geo-potential heights between 12 and 14. The results seem to suggest that climate might be viewed as a loosely coupled set of fairly high dimensional, sub-systems and different selected variables can yield different estimates of D₂. Further, results also suggest that D₂ of the climate sub-systems studied generally have low geographic variability, as found between precipitation of Western Canada and Uganda, between streamflow data of basins representing wide range climate and scales from Canada, USA and Africa; between temperature data of Western Canada, New Zealand, and southern hemisphere; and the original D₂ analyzed from Canadian geo-potential heights are similar to that of the Western Europe, eastern North America and Germany. There is at most a weak relationship between basin physical characteristics, or location or basin scale and streamflow D₂, while climatic influence is more obvious, as shown by drier basins having slightly higher D2 than basins of wetter climate, basins from temperate climate having higher D₂ than those from cold or hot climates, and comparable D₂ between precipitation and streamflow data.