Tony Oz, you wrote:
This happens when the cold air is above much warmer water, and some sort of miraging appears. In less severe form - the line of sight bends upward hiding low objects on the horizon that are usually visible.
I have two questions here:
- how does this atmospheric condition affect the refraction at higher angles? Say, the angles more than 15°?
- is this line of sight bending equivalent to the additional Dip, HoE change or me being further off from an observed body
For anything higher than a few degrees (like 3-5°), the refraction is basically unchanged. In other words, you can use the usual astronomical refraction tables adjusted by temperature and pressure if necessary. This makes sense if you think about a simple model of the air causing the anomalous dip. Let's suppose it's a layer of air with an unusual temperature distribution 30m (100 feet) thick, which is often reasonable and it may well be thinner. If you're looking out toward the horizon from a deck 8 meters (25 feet) high, you're looking through roughly 5 nautical miles, or 9km or 30,000 feet of that anomalous layer. But if you are looking up, just 5° above the horizon, you pop out of that layer in only about 250m (800 feet). It's a small fraction of the trip to the horizon. And the rest after that is just "normal" decreasing air density with altitude.
I'm not quite sure what you're asking in the second question (but see below --maybe that covers it).
You also wondered if the condition you're describing is equivalent to making the Earth "more round" or "more flat". To a certain extent, you have already answered that in your setup. You have said that object that are usually visible have been hidden from view. That would imply that the optical effect is equivalent to the Earth being a smaller sphere --more round.
It's possible to model directly the effect of simple models of the lapse rate near the ground (the lapse rate is the rate at which temperature falls, or sometimes rises, with altitude above ground). We can easily study linear lapse rate models. Unfortunately these are special cases. They're useful for assessing the potential scale of these effects, and they're useful when, in fact, those conditions exist in the real world. But they're a small fraction of what Nature can throw at us. In simple linear cases, temperature inversions, where the air gets warmer with altitude make the globe effectively flatter and can even lead to the appearance of a bowl-shaped globe (the horizon fades out with distance in this case). Stronger than average decrease in temperature with altitude will make the globe seem smaller, rounder. But if you have multiple layers, or layers where the rate of change is not linear, then all bets are off. Comples layers like these are responsible for the more exotic mirage effects, and there's really no way to to be sure what's happening without an independent, direct measurement of dip.