EPSG:5711 — AHD height

VERTCRS[
    "AHD height",
    VDATUM["Australian Height Datum",ID["EPSG",5111]],
    CS[vertical,1,ID["EPSG",6499]],
    AXIS["Gravity-related height (H)",up],
    LENGTHUNIT["metre",1,ID["EPSG",9001]],
    GEOIDMODEL["GDA94 to AHD height (49)",ID["EPSG",5656]],
    GEOIDMODEL["GDA2020 to AHD height (1)",ID["EPSG",8451]],
    ID["EPSG",5711]
]

+vunits=m +no_defs +type=crs

proj4.defs("EPSG:5711", "+vunits=m +no_defs +type=crs");

{
  "type": "CoordinateReferenceSystem",
  "code": 5711,
  "name": "AHD height",
  "kind": "vertical",
  "area": "Australia Christmas and Cocos - onshore",
  "unit": "metre",
  "bbox": [
    -43.7,
    96.76,
    -9.86,
    153.69
  ],
  "proj4": "+vunits=m +no_defs +type=crs"
}

INSERT INTO spatial_ref_sys (srid, auth_name, auth_srid, proj4text, srtext)
VALUES (5711, 'EPSG', 5711, '+vunits=m +no_defs +type=crs', 'VERT_CS["AHD height",VERT_DATUM["Australian Height Datum",2005,AUTHORITY["EPSG","5111"]],UNIT["metre",1,AUTHORITY["EPSG","9001"]],AXIS["Gravity-related height",UP],AUTHORITY["EPSG","5711"]]');

PROJECTION
  "+vunits=m"
  "+no_defs"
  "+type=crs"
END

5711=VERT_CS["AHD height",VERT_DATUM["Australian Height Datum",2005,AUTHORITY["EPSG","5111"]],UNIT["metre",1,AUTHORITY["EPSG","9001"]],AXIS["Gravity-related height",UP],AUTHORITY["EPSG","5711"]]