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I need the most precise and highest resolution free digital elevation model for the UK. Would OS terrain 50 or ASTER GDEM be more suitable for view shed analysis?

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Ordnance Survey

As the name suggests, OS Terrain 50 is a product with a 50 metre grid resolution (http://www.ordnancesurvey.co.uk/business-and-government/products/terrain-50.html).

OS Terrain 50 has been compared with GPS points in a range of sample areas to provide a Route Mean Square Error (RMSE) value for the height points in each geographic area; urban and major communication routes, rural and mountain and moorland. OS Terrain 50 grid has been verified to be 4 m RMSE.

Satellite DTM's

ASTER GDEM is about 30metres (http://asterweb.jpl.nasa.gov/gdem.asp).

There's also SRTM, which while it's currently only available at 90 metre accuracy for the UK, will be increasing to 30m (what it is for the USA) within a year (http://www.jpl.nasa.gov/news/news.php?release=2014-321).

For a comparison of the accuracy of these satellite derived products (plus NEXTMap), see this paper: http://www.asprs.org/a/publications/proceedings/sanantonio09/Tighe_2.pdf The accuracy varies considerably depending on the surface, the averages being: SRTM (15.27 m RMSE), and ASTER (18.52 m RMSE) while the published RMSE's are 16m and 20m respectively. Considerably lower than OS Terrain 50.

Resolution vs Accuracy

Because OS Terrain 50 is I believe a scaled-down version of flown data, probably in combination with ground survey data, the accuracy is much better than the space-acquired data. On the other hand you have a reduced resolution.

I leave it as an exercise for someone else to determine whether the increased accuracy of OS Terrain 50 offsets the lower resolution.

In short - I don't believe there's a definitive answer, it depends which you value more. I'd guess accuracy is more important for a viewshed though.

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If you choose ASTER GDEMv2 as your DEM option, you may transform the Geographic Coordinate System (GCS) from WGS-84 (GCS of Earth) to OSGB-36 (GCS of UK). In this case, you might have more accurate DEM data.

See the comparison between ASTER GDEMv2.0, EU-DEMv1.1, and Google Earth: https://github.com/HeZhang1994/digital-elevation-model-tool-tutorial

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