{"id":1350,"date":"2016-08-28T23:54:24","date_gmt":"2016-08-28T23:54:24","guid":{"rendered":"http:\/\/blogs.lincoln.ac.nz\/gis\/?p=1350"},"modified":"2023-05-07T00:37:20","modified_gmt":"2023-05-07T00:37:20","slug":"and-standing-up-straight","status":"publish","type":"post","link":"https:\/\/blogs.lincoln.ac.nz\/gis\/and-standing-up-straight\/","title":{"rendered":"…And Standing Up Straight"},"content":{"rendered":"

In this post we cover New Zealand’s new gravity-based vertical datum, NZVD2016.\u00a0 Along the way we’ll get familiar with the weirdly wonderful geoid and WGS84.\u00a0 This post follows on from Keeping Our Heads Above Water,<\/a> hence the title, and has benefited greatly from comments by LINZ’s Geodetic team – thanks!
\n<\/em><\/p>\n

In a previous post we looked at sea level <\/a>and saw that it’s not quite as straightforward as most of us would like to think. \u00a0This time around I’m afraid things are only going to get worse, so buckle up and let’s talk about gravity.\u00a0 The two are related, really, though gravity definitely gets a lot stranger.<\/p>\n

Maybe we should start with the shape of the earth:<\/p>\n

\"6550crop\"<\/a><\/p>\n

From space, the home planet looks nice and spherical.\u00a0 Our globes are nice, perfect spheres, too:<\/p>\n

\"globe\"<\/a><\/p>\n

As you might have already guessed, that’s not quite the reality.\u00a0 Due to gravity and the earth’s spin, it tends to look a bit more like an orange; flattened at the poles and bulging at the equator:<\/p>\n

\"20383186\"<\/a><\/p>\n

We need a model of the earth’s shape to do things like create flat two-dimensional maps, and carry out topographic surveys and anticipate where water will flow.\u00a0 Geodesy, the science (and mathematics) of measuring the shape of the earth (and other planets) has developed a range of models of the earth. \u00a0 Some are roughly spherical, others more like squashed spheres\u00a0– these latter models are called ellipsoids and are better models\u00a0of the earth\u00a0than spheres.<\/p>\n

A Global Ellipsoid: WGS84<\/h5>\n

Let’s talk about one particular ellipsoid that’s become quite important.\u00a0 If you’ve ever used GPS to measure elevation, you’ve already had direct contact with this one (now go and wash your hands!)\u00a0 GPS, the global positioning system, uses a constellation (yes, that’s the proper collective noun) of satellites to determine positions on the surface of the earth.<\/p>\n

\"SPAC_GPS_NAVSTAR_IIA_IIR_IIF_Constellation_lg\"<\/a><\/p>\n

(okay, this image is not to scale.)<\/em>\u00a0 Exactly how it works is the topic for another post, but for now, bear in mind<\/a>\u00a0that it’s actually mapping locations in a three-dimensional space.\u00a0 Built in to every receiver (and satellite) is an ellipsoid model of the shape\u00a0of the earth.\u00a0 When you look at your receiver screen and it displays your latitude and longitude, those are the coordinates on the ellipsoid.\u00a0 And your elevation is how high above or below the ellipsoid surface you are. \u00a0The ellipsoid surface usually doesn’t coincide with the land surface.\u00a0 In New Zealand<\/a>, the differences between the two may be as much as 35 m in Northland, and roughly zero\u00a0near Stewart Island\/Rakiura.\u00a0 Here’s an image of\u00a0my GPS showing\u00a0details about a point on the lawn in front of Ivey Hall:<\/p>\n

\"GPSDisplay\"<\/a><\/p>\n

(Apologies for image quality<\/em>)\u00a0 The\u00a0GPS receiver has calculated my horizontal position as well as an elevation.\u00a0 Note the elevation shown above\u00a0is 20.5 m – that’s my calculated height above the GPS ellipsoid, not mean sea level.\u00a0 If I look on the topo map, my elevation at that same location \u00a0is roughly 10 m but that value is with respect to mean sea level. (Note: if you reset your receiver to a different coordinate system like NZTM<\/a>, it will probably correct your elevations to match closer with reality – geez – that simple comment cries out for a whole ‘nother post…<\/em>)\u00a0 This ellipsoid has a very grand title: the World Geodetic System 1984 (affectionately known as WGS84<\/a>).\u00a0 It’s a geocentric ellipsoid, meaning it shares its centre with the centre of mass of the earth, and has very much become the standard global model of the earth’s shape.<\/p>\n

Models like WGS84 are quite useful but they can’t accurately represent the rough, convoluted topography that we’ve built our lives upon – they’re not designed to represent topography but do give us a simple model of the earth that makes some computations easier.<\/p>\n

Gravity and Mean Sea Level<\/h5>\n

All well and good, but let’s get back to mean sea level and something more meaningful.\u00a0 Tide level measurements are relatively easy to make.\u00a0 Average them out over a long enough period and you can estimate mean sea level (pay no attention to the elephant in the room – we know it’s changing<\/em>). \u00a0We’ve already seen that mean sea level is different in different places: the\u00a0driver behind this\u00a0is gravity.\u00a0 And gravity varies as the mass beneath our feet varies.\u00a0 Happily, it is measurable, \u00a0No, not by dropping apples are various places and measuring their acceleration<\/del> (my sources at LINZ tell me this is actually pretty close to how\u00a0it’s really done), with\u00a0gravimeter<\/a>s.\u00a0 Increasingly, gravity measurements are remotely sensed\u00a0by instruments in satellites and airplanes, so it’s become much easier to measure and map gravity around the globe. \u00a0Here’s a map of how gravity varies in our neighbourhood:<\/p>\n

\"geo_bouguer-gravity-map-nz\"<\/a>
http:\/\/www.linz.govt.nz\/data\/geodetic-system\/datums-projections-and-heights\/vertical-datums\/gravity-and-geoid<\/figcaption><\/figure>\n

If you’re familiar with New Zealand bathymetry, some of this map should look a bit familiar.\u00a0 The Kermadec Trench trends northeast from the east coast of the North Island and coincides with the Pacific plate subducting beneath the Australian plate.\u00a0 To the southwest, another subduction zone can be seen, the Puysegur Trench – notice these are areas of higher gravity (reds) right next to areas of lower gravity (blues).\u00a0 The line of irregular red dots to the north east are the remains of a migrating hot spot (well, really it’s the plate that’s been migrating), the same type that would have created the Hawaiian Islands.\u00a0 They are areas of denser volcanic magma and so have higher gravity.<\/p>\n

A Gravity Model: the Geoid<\/h5>\n

We must now talk about another three-dimensional surface: the geoid. \u00a0Using gravimeters to map out the local gravitational field, we could create a surface where every point has the same arbitrary value of gravitational potential (which is closely related to gravity, although not quite the same) –<\/span> t<\/span><\/span>his is called an equipotential surface.\u00a0 Since gravity determines where sea level is, if we picked our arbitrary value of gravitational potential such that it matched sea level, we then have a (very) special surface – the geoid.\u00a0 At sea, the geoid essentially matches what sea level would be without the effect of tides and winds and currents. \u00a0The geoid continues under the land surface and if you start reading up on this you’ll come across notions of canals being cut through the land and filling up with sea water – the level the water would settle at would be the geoid surface (try getting a resources consent for that<\/em>!).\u00a0 Because this is a surface of gravity, objects dropped from above the geoid\u00a0fall towards the surface at a right angle, the plumb line, and spirit levels would be horizontal to it.\u00a0 Here’s the thing – rather than being essentially flat, it undulates, varying from place to place depending on local mass.\u00a0 The geoid surface is quite irregular but relatively smooth, a bit like our orange peel.\u00a0 Where land surface elevations may range from +8,848 meters above sea level (there’s that pesky phrase again<\/em>) at Mt Everest to -427 m below sea level at the Dead Sea, vertical distances\u00a0between high and low points on the geoid may only differ\u00a0by about 200 m.\u00a0 Here’s an image of how the height of the geoid varies globally:<\/p>\n

\"EGM08_Geoid_thumb\"<\/a>
http:\/\/earth-info.nga.mil\/GandG\/wgs84\/gravitymod\/egm2008\/egm08_wgs84.html<\/a><\/figcaption><\/figure>\n

What does zero mean here?\u00a0 (Good question!<\/em>)\u00a0 On this figure, zero is where the geoid and WGS84 meet.\u00a0 Positive values are above WGS84, negative values are below. (Note that if you travelled from Papua New Guinea to Sri Lanka, you would never notice the difference.) \u00a0<\/em>Below is an animated image of the geoid that shows the variations in its shape:<\/p>\n