Sampling the diurnal and annual cycles of the Earth’s energy imbalance with constellations of satellite-borne radiometers

Abstract. The Earth's energy imbalance, i.e. the difference between incoming solar radiation and outgoing reflected and emitted radiation, is the one quantity that ultimately controls the evolution of our climate system. Despite its importance, the exact magnitude of the energy imbalance is not well known, and because it is a small net difference of about 1 Wm^-2 between two large fluxes (approximately 340 Wm^-2), it is challenging to measure directly. There has recently been a renewed interest in applying wide-field-of-view radiometers onboard satellites to measure the outgoing radiation, and hence deduce the global annual mean energy imbalance. Here we investigate how to sample, using a limited number of satellites, in order to correctly determine the global annual mean imbalance. We simulate satellites in polar (90° inclination), sun-synchronous (98°) and precessing orbits (73°, 82°), as well as constellations of these types of satellite orbits. We find that no single satellite provides sufficient sampling, both globally and of the diurnal and annual cycles, to reliably determine the global annual mean. If sun-synchronous satellites are used, at least six satellites are required for an uncertainty below 1 Wm^-2. One precessing satellite combined with one polar satellite results in an uncertainty of 0.07 to 0.08 Wm^-2, and a combination of two or three polar satellites results in uncertainties of 0.08 Wm^-2 or 0.02 Wm^-2, respectively. In conclusion, at least two satellites that complement each other are necessary in order to ensure global coverage and achieve sampling uncertainty well below the current estimate of the energy imbalance.