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I need to convert a GCS_WGS_1984 data set to NAD_1983_UTM_Zone_14N. What transformation should I use?

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The transformation to use depends on the area of North America that the data resides in. Definitions for the area of use for the Esri transformations (NAD_1983_To_WGS_1984 in your case) can be found in "geographic_transformations.pdf" in your install directory (mine is at C:\Program Files (x86)\ArcGIS\Desktop10.0\Documentation). Here they are for NAD_1983_To_WGS_1984. Note that the transformations are bi-directional:

NAD_1983_To_WGS_1984_1:  1188:  Canada, Central America, Mexico, and United States (Alaska, CONUS)
NAD_1983_To_WGS_1984_2:  1251:  United States - Alaska - Aleutians
NAD_1983_To_WGS_1984_3:  1252:  United States - Hawai'i
NAD_1983_To_WGS_1984_4:  1308:  United States - CORS ITRF94
NAD_1983_To_WGS_1984_5:  1515:  United States - CORS ITRF96
NAD_1983_To_WGS_1984_6:  1696:  Canada - Quebec
NAD_1983_To_WGS_1984_7:  1697:  Canada - Saskatchewan
NAD_1983_To_WGS_1984_8:  1702:  Canada - Alberta
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For ArcGIS 10, see this technical article: support.esri.com/en/knowledgebase/techarticles/detail/21327 –  mkennedy Feb 18 '12 at 1:34

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