Management of eruptions requires a knowledge of lava effusion rates, for which a safe thermal proxy is often used. However, this thermal proxy does not take into account the flow dynamics and is basically time-independent. In order to establish a more robust framework that can link eruption rates and surface thermal signals of lavas measured remotely, we investigate the spreading of a hot, isoviscous, axisymmetric subaerial gravity current injected at constant rate from a point source onto a horizontal substrate. We performed laboratory experiments and found that the surface thermal structure became steady after an initial transient. We develop a theoretical model for a spreading fluid cooled by radiation and convection at its surface that also predicts a steady thermal regime. We show that, despite the model's simplicity relative to lava flows, it yields the correct order of magnitude for the effusion rate required to produce the radiant flux measured on natural lava flows. For typical thermal lava properties and an effusion rate between 0.1 and 10 m3 s−1, the model predicts a steady radiated heat flux ranging from 108 to 1010 W. The assessed effusion rate varies quasi-linearly with the steady heat flux, with much weaker dependence on the flow viscosity. This relationship is valid only after a transient time which scales as the diffusive time, ranging from a few days for small basaltic flows to several years for lava domes. The thermal proxy appears thus less reliable to follow sharp variations of the effusion rate during an eruption.
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