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<div>Option (a) is the desired intent. This is an attempt to translate between GIS pros and Cadastral pros. Many GIS pros back then were not aware of using the Gaussian Sphere to implement the "Sea Level Correction" muchless go above the ellipsoid to the
surface. Minnesota does this on a county-by-county basis; Colombia does city-by-city. This is essentially a scale factor correction for grid to ground distances.</div>
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<div>Sent from Cliff Mugnier's iPhone</div>
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On May 4, 2012, at 5:19, "Mikael Rittri" <<a href="mailto:Mikael.Rittri@carmenta.com">Mikael.Rittri@carmenta.com</a>> wrote:<br>
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<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">Hello,<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">I am trying to understand the ”NAD27 Michigan” datum, EPSG:6268.<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">As represented in EPSG, this is a datum distinct from NAD27,<br>
and uses the ellipsoid “Clarke 1866 <st1:place w:st="on"><st1:state w:st="on">Michigan</st1:state></st1:place>”.
<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">EPSG remarks:
<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">
<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"> “Ellipsoid taken to be 800 ft above the NAD27 reference ellipsoid.”<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">The information source (J. P. Snyder. Map Projections: A Working Manual, p. 56, note 1)<br>
is more precise: <o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"> “The major and minor axes of the ellipsoid are taken at exactly 1.0000382 times those<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"> of the Clarke 1866, for
<st1:state w:st="on"><st1:place w:st="on">Michigan</st1:place></st1:state> only. This incorporates an average elevation throughout<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"> the State of about 800 ft, with limited variation.”<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">Neither EPSG nor Snyder gives any datum shift for NAD 27 Michigan.
<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">However, the Michigan Department of Natural Resources just writes:<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"> Datum: NAD27<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"> Ellipsoid: Modified Clarke, 1866<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">
<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">where the ellipsoid turns out to be the same as “Clarke 1866
<st1:place w:st="on"><st1:state w:st="on">Michigan</st1:state></st1:place>”. <o:p>
</o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">(<a href="http://www.michigan.gov/documents/DNR_Map_Proj_and_MI_Georef_Info_20889_7.pdf"></a><a href="http://www.michigan.gov/documents/DNR_Map_Proj_and_MI_Georef_Info_20889_7.pdf">http://www.michigan.gov/documents/DNR_Map_Proj_and_MI_Georef_Info_20889_7.pdf</a>)<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">So it seems that Michiganders regard the datum NAD27 Michigan to be the same as NAD27:<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">it is not an adjustment or densification or whatever, it just has a different ellipsoid.
<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">But this can be interpreted in two ways:
<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"> a) that long/lat are the same in both datums,<br>
b) or that geocentric Cartesian coordinates X,Y,Z are the same in both datums.<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">If a) is intended, then a correct datum shift for NAD27 Michigan could use the CONUS<br>
grid shift file intended for NAD27.<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">And if b) is intended, then the 3-parameter shift between NAD27 Michigan
<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">and NAD27 would be 0,0,0.<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">These interpretations are not quite equivalent.
<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">I’ve tried out b) in Proj.4, by setting identical towgs84 parameters for both datums.<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">(These are not very accurate, but since they are the same on both sides, they should<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"> cancel each other and give a 0,0,0 shift between NAD 27 Michigan and NAD27.)<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">>cs2cs +proj=longlat +a=6378450.0475 +b=6356826.6215 +towgs84=-9,161,179 +to +proj=longlat +ellps=clrk66 +towgs84=-9,161,179<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">-85 45 0<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">85dW 44d59'59.973"N 243.235<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">So, the point at the ellipsoid surface of NAD27 Michigan is 243.235 m = 798 feet<br>
above the NAD27 ellipsoid, as expected. What surprised me is the latitude<br>
shift of 0.027" = 0.83 meters. Well, I think understand where it comes from: the<br>
line that is perpendicular to the ellipsoid surfaces doesn’t go through the ellipsoid<br>
center(s). But the effect is much larger than I would have thought. <o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">So, does anyone know whether a) or b) or something else is the correct interpretation?<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">Best regards,<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial">Mikael Rittri<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial">Carmenta<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial">Sweden<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial"><a href="http://www.carmenta.com">http://www.carmenta.com</a><o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial"><o:p> </o:p></span></font></p>
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