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Jake
Osiris (Active Member)
Joined: 14 Jun 2005
Posts: 18
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 Posted: Mon Feb 13, 2006 1:54 pm Post subject: Profiles with planetary cuvature |
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Trent,
I'm interested in drawing some profiles over large areas that also show planetary curvature. Is there a good projection that you would suggest that could be used for this purpose?
Jake
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thare
GIS Support Team
Joined: 22 Mar 2004
Posts: 657
Location: USGS Astrogeology Research Program, Flagstaff, AZ
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| Posted: Tue Feb 14, 2006 10:06 am Post subject: |
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I have seen some applications with this built-in (i.e. Global Mapper). But I would watch out because the radius used in the curvature calculation is most likely set to Earth. So for any application, even if you set a Mars datum, it still may have WGS84 (Earth reference) hard-wired. The method below is a semi-manual method to get the job done.
How to create a profile with Mars curvature w/o refraction
Notes:
-This method can also help with more accurate planetary viewsheds and line-of-sight analysis (i.e what can the rover see from here).
-Mars Radius: 3396190.0 m
-This only uses a sphere not an ellipse.
-No refraction taken into account (not sure what it would be for Mars anyway).
-Your DEM should be in an equidistant or localized projection to minimize distance errors. So Azimuthal Equidistant with Central Meridian and Latitude of origin close to the center of your area. Or for a profile you may want to try Two-Point Equidistant with the start and end of the profile set as the input parameters. If the area is fairly small then any projection that tries to minimize the local errors should work.
This can be done in most GIS apps. The example here is in ArcMap.
-reproject your piece of MOLA or other topography to a more equidistance projection (see Notes above).
-create a single point for your profile in the current projection. If the point is decimal degrees, right click data, export data -> and toggle to use projection of dataframe before exporting. Add new projected single point layer back in.
-under spatial analyst options, set extent to area of interest (i.e. clipped out MOLA DEM), and set cellsize to input DEM
-under spatial analyst, convert, features to raster, use point layer, any field. You should get a new raster with a single pixel but the extent of the area of interest as set in the last step.
-In Arctoolbox, Spatial Analyst Tools folder, Distance, double click the Euclidean Distance tool. Use the new raster (with the single pixel) and run. You will end up with a circle pattern from the original point.
-Now to apply Mars’ curvature. Again we are not going to take into account atmospheric refraction. ( http://mintaka.sdsu.edu/GF/explain/atmos_refr/dip.html )
So in the Spatial Analyst, raster calculator type:
Sqr([EucDist_Raster]) / (3396190 * 2)
This will create another raster that "falls off" showing Mars’ curvature.
-Now back in raster calculator, type:
[original_dem] - [fall_off_raster]
right click on new raster and "Make Permanent".
-Tip: to prove this is good take it into 3D Analyst, kind-of a mini ArcGlobe or Google Earth effect (see attachment).
-Now you can use your favorite profiler (i.e. EZ Profiler) to create you profile or/and export your table. Tip: when not using the EZprofiler add-in, turn it off or you may have problems with data frames without raster.
A little painful but gets the job done. To see attachment you have to login.
Trent
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thare
GIS Support Team
Joined: 22 Mar 2004
Posts: 657
Location: USGS Astrogeology Research Program, Flagstaff, AZ
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| Posted: Wed Feb 15, 2006 10:09 am Post subject: |
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I realized yesterday, when talking to a colleague about this that the Y axis showing the Z values means nothing because the fall amount was subtracted. Not sure how to best display this but one idea is to add a few Y axis curvature lines to show the original Z value (more below).
And to create this fall-off profile it is easier to just calculate it in Excel or other spreadsheet. You still should have a good projection that minimizes distance errors. So create a normal profile using MOLA (i.e. profile extractor) and export table to spreadsheet. Now just apply the same equation to apply the curvature amount to a new Z column using the profile’s distance column and the DEM’s Z column:
ZCurvature = OrigZ - DIST^2 / (3396190 * 2)
For the Y axis curvature or “fall off” values create a few new column and set to:
newCol at 0 = DIST ^2/(3396190*2) * -1
newCol at 2000 = (DIST^2/(3396190*2)*-1 + 2000)
newCol at -2000 = (DIST^2/(3396190*2)*-1 - 2000)
newCol at -4000 = (DIST^2/(3396190*2)*-1 - 4000)
Of course these would have to be set so they are appropriate for your data. I’m not 100% happy with the method but I guess it sort of works.
One last way is to plot the original profile along side of the fall off profile so people understand what is going on.
Trent
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