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A comet is a highly dynamic object, undergoing a permanent state of change. These changes have to be carefully classified and considered according to their intrinsic temporal and spatial scales. The Rosetta mission has, through its contiguous in-situ and remote sensing coverage of comet 67P/Churyumov-Gerasimenko (hereafter 67P) over the time span of August 2014 to September 2016, monitored the emergence, culmination, and winding down of the gas and dust comae. This provided an unprecedented data set and has spurred a large effort to connect in-situ and remote sensing measurements to the surface. In this review, we address our current understanding of cometary activity and the challenges involved when linking comae data to the surface. We give the current state of research by describing what we know about the physical processes involved from the surface to a few tens of kilometres above it with respect to the gas and dust emission from cometary nuclei. Further, we describe how complex multidimensional cometary gas and dust models have developed from the Halley encounter of 1986 to today. This includes the study of inhomogeneous outgassing and determination of the gas and dust production rates. Additionally, the different approaches used and results obtained to link coma data to the surface will be discussed. We discuss forward and inversion models and we describe the limitations of the respective approaches. The current literature suggests that there does not seem to be a single uniform process behind cometary activity. Rather, activity seems to be the consequence of a variety of erosion processes, including the sublimation of both water ice and more volatile material, but possibly also more exotic processes such as fracture and cliff erosion under thermal and mechanical stress, sub-surface heat storage, and a complex interplay of these processes. Seasons and the nucleus shape are key factors for the distribution and temporal evolution of activity and imply that the heliocentric evolution of activity can be highly individual for every comet, and generalisations can be misleading.
Comets evolve due to sublimation of ices embedded inside porous dust, triggering dust emission (that is, erosion) followed by mass loss, mass redistribution and surface modifications. Surface changes were revealed by the Deep Impact and Stardust NExT missions for comet 9P/Tempel 1 (ref.(1)), and a full inventory of the processes modifying cometary nuclei was provided by Rosetta while it escorted comet 67P/Churyumov-Gerasimenko for approximately two years(2-4). Such observations also showed puzzling water-ice-rich spots that stood out as patches optically brighter and spectrally bluer than the average cometary surfaces(5-9). These are up to tens of metres large and indicate macroscopic compositional dishomogeneities apparently in contrast with the structural homogeneity above centimetre scales of pebble-made nuclei(10). Here we show that the occurrence of blue patches determines the seasonal variability of the nucleus colour(4,11,12) and gives insight into the internal structure of comets. We define a new model that links the centimetre-sized pebbles composing the nucleus(10) and driving cometary activity(13,14) to metre-sized water-ice-enriched blocks embedded in a drier matrix. The emergence of blue patches is due to the matrix erosion driven by CO2-ice sublimation that exposes the water-ice-enriched blocks, which in turn are eroded by water-ice sublimation when exposed to sunlight. Our model explains the observed seasonal evolution of the nucleus and reconciles the available data at micro (sub-centimetre) and macro (metre) scales.