EPSG:4440 — NZVD2009 height

VERTCRS[
    "NZVD2009 height",
    VDATUM["New Zealand Vertical Datum 2009",ID["EPSG",1039]],
    CS[vertical,1,ID["EPSG",6499]],
    AXIS["Gravity-related height (H)",up],
    LENGTHUNIT["metre",1,ID["EPSG",9001]],
    GEOIDMODEL["NZGD2000 to NZVD2009 height (2)",ID["EPSG",9325]],
    ID["EPSG",4440]
]

+vunits=m +no_defs +type=crs

proj4.defs("EPSG:4440", "+vunits=m +no_defs +type=crs");

{
  "type": "CoordinateReferenceSystem",
  "code": 4440,
  "name": "NZVD2009 height",
  "kind": "vertical",
  "area": "New Zealand",
  "unit": "metre",
  "bbox": [
    -55.95,
    160.6,
    -25.88,
    -171.2
  ],
  "proj4": "+vunits=m +no_defs +type=crs"
}

INSERT INTO spatial_ref_sys (srid, auth_name, auth_srid, proj4text, srtext)
VALUES (4440, 'EPSG', 4440, '+vunits=m +no_defs +type=crs', 'VERT_CS["NZVD2009 height",VERT_DATUM["New Zealand Vertical Datum 2009",2005,AUTHORITY["EPSG","1039"]],UNIT["metre",1,AUTHORITY["EPSG","9001"]],AXIS["Gravity-related height",UP],AUTHORITY["EPSG","4440"]]');

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

4440=VERT_CS["NZVD2009 height",VERT_DATUM["New Zealand Vertical Datum 2009",2005,AUTHORITY["EPSG","1039"]],UNIT["metre",1,AUTHORITY["EPSG","9001"]],AXIS["Gravity-related height",UP],AUTHORITY["EPSG","4440"]]