Unfortunately, ABC lets down its audience (as usual) in failing to critically examine the claims made. It took us less than 5 minutes online to find out that about 90% of the OK glacier vanished between 1901 and 1945 well before the onset of late 20th-century global temperature increases. Here's what the publication Glaciers of Iceland has to say about the OK glacier...
"Thoroddsen described the glacier as a regularly-shaped, snow-white mound, like an eggshell, although further down its flanks it was succeeded by scattered patches of snow which gave the mountain the appearance of a spotted leopard. No individual outlet glaciers crept down from the glacier and all its meltwater runoff seeped into the dolerite lava. The ice cap is depicted as being about 38 km2 on Thoroddsen's geological map from 1901, but on the map of the Danish General Staff from 1910, it was only around 15 km2, and only 5 km2 on the map of 1945; the glacial patch had a surface area of just over 3 km2 on an aerial photograph from 1978, just less than 2 km2 on a satellite picture from 2004, and it has been reduced even more since then, the crater at the top of the lava dome now glacier-free."
Here's a graphical indication of when most of the glacier loss occurred in relation to the Global Mean Temperature anomaly. Seems the OK Glacier died quite some time ago!
