Dear all,
Could you please advice? Thank you very much in advance.
I am working on calculating the combined factor in the projected transformation. Thanks to this forum that I got the equations to do so. However, I am a bit confused about when I should report the combined factor.
Let's have an example: an elevation point is UTM zone 18, horizontally and vertically referenced in ITRF2008 and I would like to reference it in WGS84, geographic. Should I report the combined factor for the input point, given that I could calculate the orthometric height NAVD88 and the combined factor is: scale_factor * elevation_factor
where:
elevation_factor = GRS80.majorAxis / (GRS80.majorAxis + NAVD88_height)?
Another example: same input, output is WGS84 UTM. Am I right to say that there's no combined factor for this transformation? Or should I calculate the combined factor (=scale_factor * elevation_factor) where:
elevation_factor = WGS84.majorAxis / (WGS84.majorAxis + WGS84_height + EGM2008_height)?
(I made up this equation based on the formula on GRS80. Is there such an equation on WGS84 by the way?).
Thank you very much once again.
Have a great evening/day!
Amy.Le
The main reason for reporting CSF is so that surface distance can be placed on the utm map in your example. The simple equation for that is utm distance/surface distance. There are utm conversion programs on line for determining geographic coordinates. If the surface distance is unknown it can be computed if the geographic coordinates and surface height are known. You may want to refer to NGS toolkit as well.
To simply perform a conversion from UTM to geographic position there is no real need to compute the combine factor. In the case you expressed you can easily use the NGS toolkit utility UTMS - http://www.ngs.noaa.gov/TOOLS/utm.shtml . Select the option for NAD 83 as this will use the GRS80 ellipsoid which is all but identical to the WGS 84 ellipsoid. Also note that you are making the modest assumption that the ITRF2008 value is equivalent to the current realization of WGS 84 referenced as WGS 84 (G1674). If you want to compute the combined factor correctly you don't want to use the orthometric height (NAVD 88), which by the way there is no direct way to get an NAVD 88 height from an ITRF referenced position. The equation you provided is in error:
elevation_factor = GRS80.majorAxis / (GRS80.majorAxis + NAVD88_height
it should be:
elevation_factor = Radius of Curvature in Azimuth (Ra) / Ra + h (ellipsoid height)
Where Ra = SqrRt of (Radius of Curvature perpendicular to the meridian * Radius of Curvature in the meridian)
See reference page 14 of USC&GS Special Publication 195 -- http://docs.lib.noaa.gov/rescue/cgs_specpubs/QB275U35no1951935.pdf
The equations are the same regardless of which reference ellipsoid is used.