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