[GRASS-user] GRASS & earth curvature correction (viewsheds, LOS)

[Markus Metz]

On Thu, May 26, 2011 at 10:50 AM, Hamish <hamish_b at yahoo.com> wrote:
> Hamish wrote:
> [...]
>> > the ideal solution is to have both curvature and refection
>> > corrections implemented as flags in the new & improved
>> > r.viewshed. [...]
>
> Benjamin wrote:
>> That should be really easy to do. All that's needed is to
>> amend the existing correction but taking away 1/7 to
>> account for the adverse effect of refraction.
>
> ok, done for r.viewshed in r46423. Number of visible cells
> reduces slightly when the curvature flag is used, and rebounds
> ever so slightly when the refraction flag is used.
> Please test.
>
>
>> Well, that refraction correction is really a rough
>> simplification of reality. Essentially, it uses the same
>> amount of correction as ArcGIS. There is some justification
>> for this. You can find links to articles here:
>> http://mapaspects.org/content/effects-curvature-earth-refraction-light-air-and-fuzzy-viewsheds-arcgis-92
>
Hm-hm. Citing from the website:
"The problem is that the ratio of change due to air to curvature is
not 1:7 (0.13), as the standard refraction coefficient suggests. It is
0.325.

Last spring I put together an Excel sheet that computes this ratio.
Having the adjustable details (altitude, air pressure, wavelength,
etc.) did show me that the ratio never really changes (given earthly
conditions). What it did show me was that the ratio was always 0.325."

[...]
>
>> But given that most DEMs have an inherent vertical error that
>> is greater than the influence of these effects,
>
> can we quantify that? for example what's STRM 95% confidence
> accuracy?

>From Farr et al. 2007:

Summary of SRTM performance. All quantities represent 90% errors in meters.

	Africa	Australia	Eurasia	Islands	N. America	S. America
Absolute Geolocation Error	11.9	7.2	8.8	9	12.6	9
Absolute Height Error	5.6	6	6.2	8	9	6.2
Relative Height Error	9.8	4.7	8.7	6.2	7	5.5
Long Wavelength Height Error	3.1	6	2.6	3.7	4	4.9

[sorry for the ugly format, it's tab separated]

>
>> I am not sure it's worth spending too much time on (it might
>> be for very long distance visibility -- I just don't know).
>
> it would be good for us to do a rough back of the envelope calc
> to justify that before fully forgetting about it.
>
> I guess for the worst case scenario we could try the views from
> Mt. Everest and/or Olympus Mons and see what difference it makes.

No need to go into mountains, just increase observer elevation offset,
preferably in a moderately flat area to get really far views. Using
correction for earth curvature only, max is a bit more than 100 km
with 3km observation offset. 200km is impossible without leaving
earth's atmosphere.

Markus M