From 1978 through 1999 the global average concentration of atmospheric carbon dioxide increased from 335 ppm to 368 ppm according to measurements of air samples collected at an array of ten stations extending from the Arctic to the South Pole. The global average rate of increase varied widely, however, with highest rates occurring in 1980, 1983, 1987, 1990, 1994, and 1998, all but the first of these calendar years near times of El Nin˜o events. The 13C/12C isotopic ratio of carbon dioxide, measured on the same air samples, varied in a similarly irregular manner, suggesting that exchange of atmospheric CO2 with terrestrial plants and soil is the dominant cause of both signals. Quantitative analysis of the data by a procedure called a "double deconvolution" supports this hypothesis but also suggests a variable exchange with the oceans, opposite in phase to the terrestrial exchange. This result may be in error, however, because it depends on an assumption that the global average isotopic discrimination of terrestrial plants has been constant. Allowing for a variation in discrimination of only about 1°/°° would eliminate the opposing fluctuations in oceanic flux, if its phasing has been opposite to that of the observed fluctuations in rate of change of CO2 concentration. In three companion articles that follow, we further deduce regional exchanges of CO2, making use of latitudinal gradients computed from the same atmospheric carbon dioxide data used in this global study.