I have a geosciences question that I can’t come up with the answer (no it isn’t homework-those days are long behind me. ).
I want to identify a natural process or object that can be part of a picture such that the object can be a natural length (size) scale. Think of it this way: I have a camera on my satellite/drone/airplane that takes a picture of the earth’s surface. I know the distance from my camera to the surface. I don’t want to use the camera specifications (the usual method for doing this problem). I want to take a picture of something that has a known size. I am not picky about what I photograph, but the more realistic the better. So far neither I nor the several PhDs in geosciences I have asked has come up with much.
Deep water waves would work if you could take several pictures and get the wave speed. You could get lucky and catch a coconut falling to the ground-you know the acceleration and the time so you can find the distance. Even those two ideas require multiple pictures. Can anyone think of some natural process/object suitable for being in a photograph that has an inherent length scale?
If we can come up with something, it will make a great trivia question!
What about man-made landmarks or objects? Buildings, cars, roads, etc. Or are you looking for something common, made by nature, and always has the same intrisic size?
Animals might work. Most animal species don’t have all that much size variation, and you could do even better if you can see a whole herd of them and take an average size.
Some areas have roads placed on a pretty regular grid – much of the land in the Midwest was divided up in a relatively precise way, and resultingly there are large areas with a very regular one mile grid of roads. Southeast Michigan in particular.
On a similar sort of tack, roads themselves will have a pretty regular width, particularly the interstates that have pretty rigorous standardizations for the width of lanes and shoulders.
Any lake with two points that have a known distance.
Many things are identifiable in aerial photos. Pick any two that you can find the distance between. Get them in two different directions so you can tell if the picture was taken while more or less level and it will improve the accuracy of your scaling. The points should be at the same elevation. That is why bodies of water are usually pretty good. The edges are usually at the same elevation.
I don’t know if any of these are quite what the OP is looking for, but I’ll throw out a few ideas:
How about a post in the ocean. Take pictures of it at high and low tide on the same day. Can the distance between those two points be calculated by knowing the position of the sun and moon? (Harbors can exaggerate the effects of tides, as the tidal surge flows into the mouth of the harbor and then has nowhere to go. The post would have to be in a place where the water was free to flow around it and measure just the surge. There may be no such place.)
Is there any sort of refraction that would make the shock wave from a lightning strike visible in a photograph? Two pictures at a known interval would tell you how far the shockwave had travelled.
Are there any natural angles, like a ship’s wake or the spectrum from a prism, that could be used to define a distance in a photograph?
How about other wavelengths, like an infra-red picture of a metal bar with one end near a heat source. Could the temperature gradiant along its surface be used to calculate a length?
my goal is to find something that I can use as a scale without knowing the size of a given object in advance. Buildings or roads would qualify if there is a natural rule (not a manmade convention) that sets the size. In other words, buildings are out.
I don’t think it applies to a photograph of the earth. Though the curvature of the horizon has been proposed. Kind of the extreme edge of what I have in mind though.
some of those are good possibilities. But my physics degree is too old to remember the details. I like the wake idea the best. I will ask some people who should know.
One of the current fads in geoscience is fractals. Sort of predictible in a way. (I presented a paper at a workshop a year ago debunking some of this, but there it is.) The fractal theology of course is scale invariance. So, so far as there are fractal processes in geoscale features, you would intrinsically be unable to determine scale.
There are without doubt fractal processes at work. But usefully they have minimum and maximum scale sizes. These are not hard edged numbers, and vary somewhat, but should provide some guidance.
For instance look at a river delta. You get branching rivulets, that beget smaller rivulets. But there is a size below which the branching ceases. This is determined by a mix of grain size and fluid mechanics. But in general, observation should allow you to look at a delta and look for the feature scale below which sub-branches cease.
The idea may extend elsewhere. The physics of many things prevents them exisitng at scales bigger or smaller than given limits. So rather than look for a specific item, look for the lack of something beyond a given scale.
If natural objects are OK, trees show a little more variation, but they’re a lot easier to find.
But if the OP allows man-made features, a lane of highway is pretty standard width, within 20% or so, I’d guess. Maybe more so if you can find multi-lane highways, so you’re not trying to figure out where the shoulder begins. If you’re looking at a U.S. state, and know which one, the length of new lane stripes will be consistent and can be looked up (I don’t know if they’re identical across states; I’m fairly sure they have not always been). I imagine other countries have standards, too, for striping.
Width of railroad tracks will be even more standardized within a country/region and accurate to within an inch or less.
But I can’t think of any purely geological features with an inherent scale other than ocean waves, at least at the macro level (soil particles do have inherent size on average, as different rocks tend to weather to different sizes, but that’s on a microscopic scale).
In theory, at least, couldn’t you use the shadows from two tall objectives that are fairly far apart. If you measure the angles of the two shadows - you should be able to calculate the distance between the objects creating the shadows. Although you’d have to know the distance to the sun. Precision would probably be a challenge - but it should work in theory.
I wonder about meandering rivers and if there is a way to predict the size of the meanders.
The talk of fractals reminded me of that because I once had a map at a scale of about 1:1,500,000 and I could see the South Saskatchewan river meandering on about 4 levels of scale.
By the way, you do realize that the scale of an aerial photograph is different at every point and that no reliable measurements can be made don’t you?
Thanks!
not sure I understand your last point. Of course the scale of an aerial (or satellite) photograph is different at every point but it is a predictable change. Given the details of the camera and a knowledge of the location of the camera and the direction it is looking, the scale of every pixel can be calculated. In my OP I am saying I don’t want to use those calculations-or more exactly I want to identify a ground feature that I can use as an independent check. That is what happens when satellite and aerial photos are warped. A raw satellite image of the earth is actually often a pretty disappointing photograph. Once it is properly processed, then you get some amazing images. I know in the work we do, satellite oceanography (admittedly a pretty extreme example), 99% of the light received by the camera is considered noise. We filter all but one percent out to get the images we are interested in. The geometrical warping is also a major step. Being able to do this kind of warping is one reason why satellite imaging devices are so expensive. First you design a very high precision mechanical device, laboratory grade or better, then you shake it really hard (during launch), then you leave it in a vacuum where the temperature changes by 300 degrees every couple of hours, don’t allow any maintenance whatever, and you need to maintain pointing accuracy to a couple of microns. Oh, it has to perform reliably for 5 years or more.
sometimes it IS rocket science!
To be clear, you do know the surface gravity, atmospheric composition and thickness, size of the planet, etc.?
I think you might be able to use convection cells over a partially-frozen lake, if you can find some way to see them. I say over a partially-frozen lake, because those would be temperature-dependent, and the lake being partially frozen tells you its temperature.
The scale varies with the distance from the centre of the photo and with the elevation of the land at each point. The effect of elevation, of course, depends on the distance from the photo centre. Also, the pitch and yaw of the plane has to be taken into account. Maybe you’re already aware of all this but if not, here’s a 101. That’ll give you an idea of the issues involved if you don’t already know.
).