The long and short of it is that there is no current means to calculate and adjust for it in real time because air density is very variable and fluid. The biggest cause of refraction is changes in air density between you and the target AND even the angle of the light reflected from the target.
This is a know issue in surveying though and surveying incorporates a standard value to account for refraction when surveying long distances. The value is: 1/7 of the earths curvature error. The curvature error at 5 miles is about 14 ft.
I used the above numbers to calculate that the refraction error is about 2.75" at 1000 yards (as would be used in surveying). This is about 1/4 MOA. So, you could derive that light refraction in the atmosphere can account for an average of about 1/4 MOA Point of Impact error at any given time of day, temp, or pressure. It could also be way less or way more. But I would not be surprised at all to see a POI of 1/4 to 1/2 MOA at 1000 yards between morning and evening shoots. Then there is that cloud that rolls over right during you shot group and cools the air between you and the target....
I would also say that the possible 1/4 MOA change could also be present at 100 yards. Just depends on the air between you and the target. Litz actually discusses this phenomenon at about the 10 minute mark in the AB live question answer session they did a few days ago. He basically says there is no current method to accurately account for it in a ballistics solution. He also mentions that the error is usually more the closer to the ground the target is. I have read this is to be true due to the temp changes that can occur because of a cold pocket of air moving over a warm area of ground. It causes a warm to cold to warm air spot between you and the target. Makes sense right? Litz also says that the error almost doesn't exist in cross canyon shots where the air temp is more likely to be stable between shooter and target. Makes sense right?
Anyway here are a few links that discuss some of this stuff in varying degrees of detail. First one is a good Youtube video that explains the issue in surveying and how it is dealt with (refraction is discussed at about 2:18 in the vid.)
Second has the Litz comments at about 10 minutes in.
Rest are links to previous discussions on the forum.
Hope it helps.
https://www.longrangehunting.com/threads/light-and-its-effects-on-poi.36794/
https://www.longrangehunting.com/threads/how-does-sunlight-affect-your-poi.63167/