# Interpolation of contours (from one “main-contour-shapefile”)

I calculated, that the best and smalest possible äquidistance (equidistant) for my map is 30m. After I generlized my DHM, I extracted contours of a intervall of 30m and smoothed them. Now I have my "main-contours".

But I also want contours with 10m äquidistance (equidistant), and I need to interpolate it from my main-contours (because my DHM is not accurate enough to extract 10m-contours directly).

EDIT: The 10m-contours are just for optical reasons (counting) and dont have to be accurate. The accuracy of the 30 m-contours is fine enough!

Is that possible with Grass, Saga or Qgis?

Thanks! Martin

EDIT: The 30m-contours are accurate, (vertical error less then 15m), the 10m-contours have errors so I dont want them! :)

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In a previous conversation I think you mentioned that you are using ASTER DEMs. I've only ever been able to make horrible contours from these. This will sound strange, but perhaps you might have better luck with SRTM DEMs (V4.1), even at this scale. Project the DEM, clip out just the part you need and then make the contours. A vertical interval of 15 metres seems to work quite well. Then generalise the resulting contours, if required. Just a thought.. – nhopton May 14 '12 at 14:45
It is possible that the "errors" you've pointed out are closer to reality than lines that simply run equidistant between the 30m contour. We can't know either way without a more accurate, more detailed DHM. – user3461 May 14 '12 at 14:56
This question is predicated on a false assumption: namely, that one cannot "accurately" compute contours with elevation differences smaller than the vertical accuracy of the DEM. The mistake lies in confusing accuracy (which measures agreement with a reference or "real" value) with either precision or relative accuracy. If contours are "erratic," that is due either to poor precision (and the cure lies in smoothing the data) or to a bad contour-extraction algorithm (which is fixed by using different software). – whuber May 14 '12 at 16:15
@nhopton: Im using the GDEM2, it is more accurate then the SRTM 4.1 in my area (I tested with 90 reference-points). The RMSE of ASTER GDEM2 is nearly the same like SRTM with the difference, that in my area (most altitudes are between 3000 and 3700m) the SRTM has too much errors. In fact I can extract 30m contours with nearly the same error of SRTM but with higher resolution and without voids. The higher resolution is needed, because of the very small and steep valleys in my area. – MAP May 14 '12 at 17:08
MAP, you definitely can interpolate contours from contours: the best approach is to create a DEM from the contours and then contour that! Since you mention having a DEM to begin with, all that would be accomplished by this circuitous interpolation of contours approach would be to degrade the accuracy of the output and perform many more steps than are needed. These considerations suggest that you ought to rethink the process and critically examine your assumptions that the original DEM is inadequate for creating the intermediate contours. – whuber May 14 '12 at 17:40

If your DHM isn't accurate enough to support 10m contours, then the 30m contours that were created from the DHM also are not accurate enough to support 10m contours.

You would essentially be drawing equidistant isolines 1/3 and 2/3 between each of the "main" (30m) contours, resulting in a bad interpolation of 10m. This is for two reasons: the main contours don't always represent 30m on the surface, and 10m and 20m won't always be equidistant between the 30m contours.

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I'm assuming a DHM is similar to a DEM, DTM, or DSM; a model of elevations (with or without natural and man-made features is not relevant to this question) on a surface. – user3461 May 14 '12 at 12:32
The smalest usefull/possible contour intervall I can extract from my DHM is 30,2m. Everything below is too inaccurate, and everything above means loosing available information. So I want to extract the best intervall (for my DHM 30m) and interpolate all countours I need, also that ones with a bigger intervall like 50m. The final map will have 50m-counting-contours, and 10m intermediate contours. – MAP May 14 '12 at 12:40
+1 You can only be as accurate as your lowest resolution data-layer. – Roy May 14 '12 at 12:48
But they dont have to be more accurate then 30m. – MAP May 14 '12 at 13:42
As I have suggested in comments to the question, the preceding comments confuse accuracy and precision. Resolution is a matter of precision, not accuracy: low-resolution layers can be more accurate than higher-resolution ones. (Compare, say, a 5m orthophoto from a satellite to a 0.1 uncorrected photo from an airplane.) The contour interval (10m or 30m) actually has little to do with either accuracy or precision. A DEM can have, say, a stated vertical accuracy of 100m and still produce excellent 10m contours: they won't be any more or less "accurate" than 30m or even 100m contours are. – whuber May 14 '12 at 17:43

Not a technical answer but a procedural one: Should you be doing this? Because if your DHM isn't accurate enough to produce 10m contours then any contours that you're interpolating at this point won't necessarily reflect the landscape they're supposed to depict.

Example:

``````---------- 0m  ----------
*
*
---------- 30m ----------
``````

When you interpolate, the 10m lines will appear where the stars are above, however the reality may be as shown below (SE code makes this really hard to depict):

``````---------- 0m  ----------
--- 10m ---
--- 20m ---
*
*
---------- 30m ----------
``````

i.e., a steep incline from 0 to 20, then a gentle slope from 20-30.

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The 10m-Contours cant reflect the real landscape, that is true, but on a map with a scale of 1:40k that fact doasnt realy matter. The 30m ones are accurate enougth, the contours between them are for "optical" reasons, to count them, and to make steep slopes more visible. They dont carry any adequate informations, not for that kind of map (very steep mountains). So, is there a way to interpolate? – MAP May 14 '12 at 12:54
Perhaps consider a hillshade map to make the steep slopes more visible, and show only the 30m contours. That way you you will not imply accuracy >30m and can still illustrate steeper slopes. – user3461 May 14 '12 at 14:59