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Update:

A good example of my confusion: on the Wikipedia page for "digital terrain model" one can find the following statement about a satellite in the "See Also" section:

TanDEM-X: generation of a world-wide, consistent, timely, high-precision Digital Elevation Model

Can I take this statement and swap the word precision for the word resolution? Would you agree that it means the same after doing so?

Original Question:

A question about Precision vs Accuracy has already been asked and answered, but I believe my question is different.

In the context of files that store elevation models, a TIFF for example, what is the difference between Precision and Resolution in the elevation detail? Are they the same thing?

Normally, when I think of low resolution elevation models I think of terrain that ends up looking blocky:

enter image description here

and high resolution corresponding to terrain that will look smooth and have more detail.

Then, when I think of losing precision I think of floating point values that get clamped to some value that is close enough to one the system can represent.

Can these terms (precision/resolution) be used interchangeably when talking about the "detail" in an elevation model? Is it erroneous to say that the terrain in the image above has lost precision from its original representation?

This post almost looked like what I was looking for, but I believe not - because it speaks of the terms in the context of a different domain - the instrument measurements domain. (Correct me if I am wrong here)

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What do you mean by the "original representation" of your DEM? –  whuber Aug 19 '13 at 14:34
    
Yes, I suppose I left that somewhat vague. What I meant was whoever created that image may have not started out with a model that was blocky - but instead a model with much more detail - something that would appear more like earths actual terrain. –  dtmland Aug 19 '13 at 15:25
    
One way to assess that image is to think of it as a particularly poor interpolation of the data. Those data could be absolutely correct insofar as they represented (say) the elevations at the middles of the cells, and thereby could claim to have infinite precision. That helps make it clear that what you are reacting to is a graphical representation of the elevations at points where you do not have any data. There's always going to be some uncertainty at such unsampled locations: that's the sense in which resolution is indirectly related to precision. –  whuber Aug 19 '13 at 17:02
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3 Answers

up vote 7 down vote accepted

I think I can answer it for you.

If you look at the precision vs. accuracy image on the link you provided, precision refers to the repeatability of the observation. For example, if I measure the distance from one point to another and it is always vaying only by a very small amount, then I am making measurements at a high precision.

But, basically, resolution and precision are not the same. You can have a high-resolution image or elevation model that is not precise, just like you can have a high-precision elevation model that is not high resolution.

TanDEM-X in particular is aiming to be a 12 m resolution global DEM with a precision of 2 m in relative and 10 m in absolute (from Wikipedia). This implies that this elevation will be high-precision, low(ish)-accuracy and high-resolution (for a global DEM).

EDIT: just a note, the type of data used to represent the data, i.e., int, float, has nothing to do with precision. You should not kid yourself that holding lots of numbers after the decimal point means that an observation is precise!

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+1 It's worth noting, though, that data type is related to precision. For instance, because each integer represents a unit range of values, it automatically includes at least +-0.5 imprecision. That much is negligible when the measurements inherently are much less precise, but it is not negligible for high-precision measurements (such as 2 m relative precision). –  whuber Aug 19 '13 at 14:33
    
I like the direction here - what is an example of a high-precision elevation model that is not high resolution? –  dtmland Aug 19 '13 at 15:30
    
Hi dtmland, the TanDEM-X is high-precision and low resolution! 12 m resolution and 2 m precision is pretty good! A detail survey, carried out by a surveyor and theodolite is an example of another high-precision survey that isn't really high resolution, since the coverage is relatively low. While a laser scan of the area would be high resolution but low precision. (Everything's relative, of course!) –  alexgleith Aug 20 '13 at 0:47
    
Whuber, I think that I disagree. The datatype must be able to contain the precision of a dataset, but shouldn't be used as a measure of the actual precision of the dataset. So, sure, a double precision float has 15 significant figures, but if you're using that to store a value that has a precision of 2 m then you might as well use an int. The datatype has no relevance, no correlation to the precision of the observation. –  alexgleith Aug 20 '13 at 0:50
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Resolution in raster/grid context is the "cellssize", or the width/height in a certain unit (meter, feet etc) of each cell/pixel in the grid.

I have seen the term precision used in two ways with grids:

  1. Most of the time, the same as you referred to, the accuracy of the measurement
  2. Datatype being used for cell/band values, e.g float, double, integers
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As far as number one is concerned, this would refer to the idea of the terrain model being a measurement of its real world counterpart? –  dtmland Aug 17 '13 at 15:01
    
And with this answer in mind - as I mention at the end - is it erroneous to say that the terrain (in the image from my post) has lost precision from its original representation? –  dtmland Aug 17 '13 at 15:04
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A DTM is an approximation from which it is possible to infer meaning about the world. Publishers of height data tend to give measurements of how closely a model fits the real world. But that does not tell you how well it will infer meaning for a particular question.

For example, if you want to calculate gradient for a very flat area of land a sparse model will be sufficient. The same model will be much less useful in terrain with very close canyons and steep cliff edges.

It is possible to use sparse data to model the world and correctly infer meaning if the data is right for that particular purpose. It is also possible to yield bad results from accurate and precise data.

Low resolution data can give accurate predictions about a specific phenomena if it is suitable for that particular use.

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So are you saying precision and resolution are different in this context? –  dtmland Aug 19 '13 at 2:39
    
Its difficult to not get bogged down in semantics. You can say that higher resolution is better than low resolution, and quantify that using precision and accuracy. But most of the time analysis is performed to answer a particular question and you want to get the right answer. Is the data precise enough for your analysis? This is certainly linked to resolution but it is more complicated than just resolution. –  Matthew Snape Aug 19 '13 at 13:15
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