Entropy and climate. I: ERBE observations of the entropy production of the earth

This paper introduces an approximate method for estimating the global distributions of the entropy fluxed flowing through the upper boundary of the climate systems, and provides an estimate of the entropy exchange between the earth and space and the entropy production of the planet. The entropy fluxes are those associated with the exchange of radiation between the earth and space and a specific method is described to derive these entropy fluxes from available measurements of the earth's radiation budget. The distribution of these entropy fluxes and the entropy production derived from these fluxes differ in significant ways from those reported previously. The major source of these differences arises from the incorrect estimate of entropy exchange associated with reflected solar radiation in these earlier studies. This problem is overcome by the application of a simple physical model for the entropy exchange. Radiative‐transfer simulations of the entropy exchange demonstrate that this model reasonably approximates the entropy exchange associated with reflected solar radiation, and that the long‐wave fluxes of entropy are closely approximated by the equivalent black‐body entropy flux. Entropy fluxes calculated from the Earth Radiation Budget Experiment measurements show how the long‐wave entropy flux densities dominate the total entropy fluxes at all latitudes compared with the entropy flux densities associated with reflected sunlight, although the short‐wave flux densities are important in the context of clear sky‐cloudy sky net entropy flux differences. It appears from the analysis presented in this paper that the entropy production of the planet is both constant for the 36 months of data considered and very near its maximum possible value. The mean value of this production is 0.68 × 10 15 W K −1 and the amplitude of the annual cycle is approximately 1 to 2% of this value, which is within the uncertainty of our estimate. Climatic fluctuations of entropy production are shown to be less than about 2% of the total production and therefore cannot be detected using the method described in this paper. The production of global entropy is dominated entirely by radiative processes. It remains a considerable challenge to detect these climatic fluctuations above such a large background of entropy production.