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I've been given some NetCDF data in a Mercator projection with a centre longitude of 173.9581, centre latitude of -41.0870 and rotation of 40 degrees. I have tried to create a new CRS based on Mercator41 (a NZ equivalent) and rotate it using the PROJ option in QGIS 3.16.11 but I get an error saying CRS matches the world Mercator EPSG. I have then tried using WKT script, and found reference to affine transformations, but the answers I have found here use a corner reference not a central pole. How would I rotate it by 40 deg? And is the lat long of natural origin where I set the central coordinates?

PROJCRS["WGS 84 / Mercator 41",
    BASEGEOGCRS["WGS 84",
        ENSEMBLE["World Geodetic System 1984 ensemble",
            MEMBER["World Geodetic System 1984 (Transit)"],
            MEMBER["World Geodetic System 1984 (G730)"],
            MEMBER["World Geodetic System 1984 (G873)"],
            MEMBER["World Geodetic System 1984 (G1150)"],
            MEMBER["World Geodetic System 1984 (G1674)"],
            MEMBER["World Geodetic System 1984 (G1762)"],
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]],
            ENSEMBLEACCURACY[2.0]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4326]],
    CONVERSION["Mercator 41",
        METHOD["Mercator (variant A)",
            ID["EPSG",9804]],
        PARAMETER["Latitude of natural origin",-41.0870,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",173.9581,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["easting (X)",east,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["northing (Y)",north,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Topographic mapping (medium and small scale)."],
        AREA["Southwestern Pacific Ocean and Southern Ocean areas surrounding New Zealand."],
        BBOX[-60,155,-25,-170]],

1 Answer 1

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I suggest to use a hotine oblique mercator

WKT
PROJCRS["WGS 84 / NZ Oblique Mercator",
BASEGEOGCRS["WGS 84",
    DATUM["World Geodetic System 1984",
        ELLIPSOID["WGS 84",6378137,298.257223563,
            LENGTHUNIT["metre",1]],
        ID["EPSG",6326]],
    PRIMEM["Greenwich",0,
        ANGLEUNIT["degree",0.0174532925199433],
        ID["EPSG",8901]]],
CONVERSION["NZ Oblique Mercator",
    METHOD["Hotine Oblique Mercator (variant B)",
        ID["EPSG",9815]],
    PARAMETER["Latitude of projection centre",-41.087,
        ANGLEUNIT["degree",0.0174532925199433],
        ID["EPSG",8811]],
    PARAMETER["Longitude of projection centre",173.9581,
        ANGLEUNIT["degree",0.0174532925199433],
        ID["EPSG",8812]],
    PARAMETER["Azimuth of initial line",40,
        ANGLEUNIT["degree",0.0174532925199433],
        ID["EPSG",8813]],
    PARAMETER["Angle from Rectified to Skew Grid",40,
        ANGLEUNIT["degree",0.0174532925199433],
        ID["EPSG",8814]],
    PARAMETER["Scale factor on initial line",1,
        SCALEUNIT["unity",1],
        ID["EPSG",8815]],
    PARAMETER["Easting at projection centre",0,
        LENGTHUNIT["metre",1],
        ID["EPSG",8816]],
    PARAMETER["Northing at projection centre",0,
        LENGTHUNIT["metre",1],
        ID["EPSG",8817]]],
CS[Cartesian,2],
    AXIS["(E)",east,
        ORDER[1],
        LENGTHUNIT["metre",1,
            ID["EPSG",9001]]],
    AXIS["(N)",north,
        ORDER[2],
        LENGTHUNIT["metre",1,
            ID["EPSG",9001]]]]
3
  • Proj4 string works for me as well in QGIS…
    – Hans Erren
    May 9, 2022 at 5:10
  • What would the corresponding Proj4 code be to try?
    – Seagus
    May 9, 2022 at 20:33
  • +proj=omerc +lonc=173.9581 +lat_0=-41.0870 +alpha=40 +datum=WGS84 +units=m +no_defs
    – Hans Erren
    May 10, 2022 at 18:26

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