In the green belt openness and visual amenity used to be discrete things but it looks like they have merged into one another. For the record, an inspector dealing with an appeal against the refusal of permission for a single dwelling in the green belt in Hertfordshire has set out the relevant court cases (DCS Number 200-008-480).
“The clear conceptual distinction between openness and visual impact, in Timmins V Gedling BC  EWDC 654 (Admin), was found to be incorrect in the Court of Appeal judgement Turner v SSCLG & East Dorset Council  EWCA Civ 466. This judgement confirmed that the openness of the Green Belt has a spatial aspect as well as a visual aspect and assessing openness was found not to be limited to measuring the volume of the existing and proposed structures on the site. Many factors were found to be relevant and could include how built-up the Green Belt was currently and how built-up it would be if the proposed development went ahead.”
“Such an approach on openness of the Green Belt was further confirmed in the Court of Appeal Judgement, Samuel Smith Old Brewery (Tadcaster) & Oxton Farm v North Yorkshire CC & Darrington Quarries Ltd  EWCA Civ 489 which indicated that when a development was likely to have visual effects within the Green Belt, the decision-maker was required to consider how those effects bore on the question of whether the development would preserve the openness of the Green Belt.”
Further information on green belt policy can be found in section 4.251 of DCP Online.