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In planetary science, surface roughness is regarded to be a measure ofsurface irregularity at small spatial scales, and causes the thermal-infraredbeaming effect (i.e. re-radiation of absorbed sunlight back towards to theSun). Typically, surface roughness exhibits a degeneracy with thermal inertiawhen thermophysical models are fitted to disc-integrated thermal-infraredobservations of asteroids because of this effect. In this work, it isdemonstrated how surface roughness can be constrained for near-Earth asteroid(433) Eros (i.e. the target of NASA's NEAR Shoemaker mission) when using theAdvanced Thermophysical Model with thermal-infrared observations taken duringan "almost pole-on" illumination and viewing geometry. It is found that thesurface roughness of (433) Eros is characterised by an RMS slope of 38 $\pm$8{\deg} at the 0.5-cm spatial scale associated with its thermal-infraredbeaming effect. This is slightly greater than the RMS slope of 25 $\pm$ 5{\deg}implied by the NEAR Shoemaker laser ranging results when extrapolated to thisspatial scale, and indicates that other surface shaping processes mightoperate, in addition to collisions and gravity, at spatial scales under onemetre in order to make asteroid surfaces rougher. For other high obliquityasteroids observed during "pole-on" illumination conditions, thethermal-infrared beaming effect allows surface roughness to be constrained whenthe sub-solar latitude is greater than 60{\deg}, and if the asteroids areobserved at phase angles of less than 40{\deg}. They will likely exhibit NEATMbeaming parameters that are lower than expected for a typical asteroid at allphase angles up to 100{\deg}.

The Surface Roughness of (433) Eros as Measured by Thermal-Infrared Beaming