NavList:

Bruce, you wrote:
"I've been told that surveyors were supposed to take critical precise measurements in the middle of the day when refraction was less significant."

It was believed to be less significant at mid-day, but was that lore or reality? Probably some of both. Certainly on clear days in winter months, temperature inversions and the associated increase in terrestrial refraction are common in early morning hours. These are the same conditions that lead to morning fog. Radiative cooling over-night creates a layer of air close to the ground that is much cooler than air just fifty to a hundred feet higher up. That inversion of the normal temperature profile creates greater refraction per mile (a larger value of that "k" --minutes of arc of rotation per nautical mile). The air layer close to the ground is considerably denser than normal --like a layer of cold syrup lying next to the surface. As the Sun climbs and convection sets in, the normal temperature profile in the atmosphere usually returns by mid-morning. BUT these same conditions can occur at any time of day and indeed they can last all day long. You definitely do not want to make observations like this in winter in the first few hours after sunrise, but you can find an unusual temperature profile at any time of day and any time of year.

And just to reiterate, most of the discussions of the variations in temperature profiles here have focused on the simplest models where there is a linear change in air temperature with altitude. We could define three ranges of cases:
1) "Normal" refraction and dip. This is the result of the usual linear lapse rate of about 5°C per km in place and yields approximately a sixth of a minute of arc rotation in light rays per nautical miles. Its effect on surface-skimming light phenomena including dip is equivalent to the standard non-refracted, purely geometric problem of light phenomena but with the Earth's radius increased by about one-fifth (R0, the true radius, replaced by R0/(1-1/6)).
2) "Linearly variable" refraction and dip. This is the result of linear change in air temperature with altitude but NOT the normal rate. The temperature may fall with height as rapidly as 10°C per km or it may in fact rise with height and as a result the rotation of light rays with distance, while still constant, may be nearly zero or it may approach or even exceed one minute of arc per nautical mile (if it exceeds 1, no horizon is visible). Linearly variable refraction can still be fully accounted for by solving the purely geometric, non-refracted problems of light phenomena but now replacing the radius of the Earth with some value R0/(1-k) where k can be derived from physical analysis in model cases but usually has to be left to observations.
3) "Abnormal" refraction and dip. Here we abandon the simple model case where air temperature changes linearly, at a constant rate, with altitude above the ground. There may be a complex layering of air with different temperatures and therefore complex refraction phenomena. This can lead to light rays curving downward until they curve sharply upward upon reaching some low-lying layer that is heated near the ground. These complex layers are responsible for mirages and other large changes in refraction and can lead to observed dip that is significantly greater than tabulated. Mirage-like phenomena including "floating islands" are evidence of "abnormal" refraction.

In the practical world, we need to know how "normal" is normal refraction. How often can a single table satisfy our needs? How "normal" is normal twenty miles offshore? Or in the Gulf Stream? It would also be useful to know if we can get any handle on cases where "linearly variable" refraction can be predicted or even properly accounted for. At least it would be nice to know what counts as "not rare" (like the photos I posted a while back). That's probably the best we can hope for. And finally we need to be prepared for cases of "abnormal" refraction. They exist. Certain inshore locations are prone to abnormal refraction and certain conditions at sea, for example in the Arctic, promote abnormal refraction.

You commented:
"Maybe temperature and pressure gradients over land were less severe. Agree?"

Well, in comparison to gradients over the sea? Then no. Temperature profile variations are definitely more severe over land than over ocean though they do exist at sea, especially near major ocean currents and the cold and warm eddies they spawn. As above, the same conditions that promote surface fog also lead to unusual refraction conditions.

You wrote:
"Furthermore the issue of temperature and pressure gradients cannot be thought about without considering wind. The turbulence and mixing created by the wind alters the equations. When you consider the boundary layer, particularly at low elevations mixing becomes an issue."

Yes, that's right. Turbulent, convective mixing, which may or may not be accompanied by noticeable wind, restores the normal temperature profile. It's not so much wind as vertical mixing --usually that also implies at least some horizontal wind. This is EXACTLY the origin of the "normal" temperature profile of the troposphere. Indeed the name troposphere itself is derived from the observation that this is the region where the atmosphere is continually mixed by turbulent convection. The troposphere is the turbulent sphere. As air rises, it expands. And expanding air cools at a fairly dependable rate based on its composition. Therefore the air gets cooler with altitude in a dependable fashion. The rate of change in air temperature is what's known as the "lapse rate". The range of lapse rates generally falls between the dry adiabatic rate (zero water vapor) which is nearly 10°C per km of altitude and the wet adiabatic rate (near 100% water vapor) which is around 5°C per km but varies with the temperature. To put those numbers in perspective, that's only 0.3 degrees Fahrenheit for a 100 foot change in altitude --barely measurable. If there is convective mixing, which there certainly is when there's significant wind, then you can count on a relatively reliable temperature profile for the atmosphere. A calm hazy day or a calm morning after patchy early morning fog should make you worry about refraction. I must emphasize though that the two photos I posted with significantly different "k" rates visible were both taken in the late afternoon just one day apart on pleasant days with no noticeable difference in the weather. We get "hints" that refraction may be variable, but they're only that.

You added:
"Even though a boat or a beach can be a local heat source/sink, the observer's eyes are high enough "to feel the wind in your face"."

You may be commenting on Paul's suggestion that a vessel might be a 'heat island'. This really has no relevance to this discussion, and actually it's a fairly wacky suggestion on his part. Dip is not affected by the atmospheric conditions right near the observer unless they are so radical that the air is visibly "boiling". Remember that the temperature profile in question here is the change in temperature along the miles-long line of sight from the observer to the horizon. The normal rotation of a light ray is about one-sixth of a minute of arc per nautical mile. If that rate is doubled, it still takes miles of travel through the air before we see any measurable difference. A highly localized variation in the temperature profile, like around a "hot" vessel at sea will have very little effect overall on these phenomena.

You wrote:
"I would not set up in a parking lot overlooking a cold ocean, or a blazing hot sandy beach."

Right. But what is the eastern end of Long Island Sound? The very reason we see unusual horizon conditions there is that you ARE looking over a cold ocean (with deep mixing near the Race where nearly all of the water of Long Island Sound blasts through that narrow deep channel twice a day in the relatively resonant tidal cycle of that nearly enclosed body of water) from locations which are on land and driven by daily heating cycles.

You also wrote:
"Getting representative data is tough."

Well, that right there, is the whole problem. What would constitute "representative data"? We are interested in conditions at sea because that's where celestial navigation is (or was) mostly done. But then again, as we've heard many times, who cares if you're off by a mile or three when you're out in the middle of the ocean? On the other hand, if you're twelve hours from landfall, a few miles might well matter to you. Of course, if we're in sight of land, then this becomes mostly an academic question. We have little cause to worry so much about dip and celestial sights in piloting waters. Personally, I think it's important to understand the possible ranges of these phenomena and to have some sense of when they can become more important. Yes, you can see variations of dip under "normal" at sea conditions of several tenths of a minute of arc, but any exotic conditions could yield significantly greater variations. What do we really mean by "normal" dip? And if not normal, what would be "representative" dip variations?

-FER

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