How long is an arc second?


 


 Guth, P. (2024). How long is one arc second?. Zenodo. https://doi.org/10.5281/zenodo.13963457 ]

One arc second DEMs are still the best available digital topography for much of the world, and are appropriate for many analyses even when higher resolution DEMs are available.  SRTM was the first of these DEMs, but should now be replaced with the Copernicus DEM (Bielski and others, 2024; Guth and others, 2024).

Many operations with DEMs, such as computation of slope, aspect, or hillshades, requires the data spacing, and an arc second DEM has different spacings in the x and y directions.  At point software required reinterpolating to a UTM or similar projection, but it is an easy operation to correctly compute the two spacings (Guth and Geoffroy, 2021).

There are several ways to compute the two spacings:

·         Require the user to specify a single value, which might be the average of the two spacings.

·         Use a spherical earth approximation, which has relatively simple equations.

·         Use an ellipsoidal earth, and compute the spacings at a single point or average location.

·         Use an ellipsoidal earth, and compute the spacing for every row in the DEM.

The data sets presented here as CVV files provide look up tables, computed using the WGS84 ellipsoid and the Vicenty equations (Vicenty, 1975).  There are tables with values every degree, quarter degree, tenth of a degree, and hundredth of a degree of latitude.  The values do not depend on longitude, and are the same in both hemispheres.  Software that does not have access to geodetic formulas can use the look up tables, which have three columns: the latitude, the length in meters of an arc second in the x (longitude) direction, and the length in meters of an arc second in the y (latitude( direction).  The lengths are computed to the tenth of a millimeter, which is excessive, but might be useful for multiplying to get the length of longer distances like a minute or degree.

Computations done with MICRODEM (https://microdem.org/; https://github.com/prof-pguth/git_microdem).

References

Bielski, C.; López-Vázquez, C.; Grohmann, C.H.; Guth. P.L.; Hawker, L.; Gesch, D.; Trevisani, S.; Herrera-Cruz, V.; Riazanoff, S.; Corseaux, A.; Reuter, H.; Strobl, P., 2024. Novel approach for ranking DEMs: Copernicus DEM improves one arc second open global topography. IEEE Transactions on Geoscience & Remote Sensing.  vol. 62, pp. 1-22, 2024, Art no. 4503922, https://doi.org/10.1109/TGRS.2024.3368015

Guth, P. L., & Geoffroy, T. M. (2021). LiDAR point cloud and ICESat-2 evaluation of 1 second global digital elevation models: Copernicus wins. Transactions in GIS, 25, 2245– 2261. https://doi.org/10.1111/tgis.12825

Guth, P.L.; Trevisani, S.; Grohmann, C.H.; Lindsay, J.; Gesch, D.; Hawker, L.; Bielski, C. Ranking of 10 Global One-Arc-Second DEMs Reveals Limitations in Terrain Morphology Representation. Remote Sens. 2024, 16, 3273. https://doi.org/10.3390/rs16173273 

 

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