# Survey

## Geographical coordinate system¶

A *geographic coordinate system (GCS)* * takes a three-dimensional spherical surface for a basis to define locations on the Earth. To compare, datum is not a geographic coordinate system. The datum is a part of a GCS.

The GCS is composed of:

- an angular unit of measurement,
- a prime meridian,
- and a datum (based on a
*spheroid*).

To define the location on the ground, a point is determined by its longitude and latitude. As the angles, longitude and latitude are measured from the Earth's center to a point on the Earth's surface. These measurements are acquired in degrees.

The spherical system consists of parallels and meridians.

Parallels are the horizontal lines of the East–West direction. They are placed within equal latitude. Meridians are vertical lines of the North–South direction. They are placed within equal longitude. Parallels and meridians encompass the globe and form a graticule, the gridded net on the globe.The equator is a parallel which defines zero latitude, and is located in the midway between the poles.

The prime meridian is a meridian which defines zero longitude. Most of the geographic coordinate systems take the Greenwich meridian as the prime one. But in some other GCS, the prime meridian is said to pass through Bern, Bogota, and Paris. The intersection of the equator and the prime meridian is called the origin of the graticule (0,0). Thus, the globe is divided into four quadrants that are based on compass azimuths. North is above the equator. South is below the equator. West is to the left of meridian. East is to the right of meridian.

The measurements of latitude and longitude are made in degrees, minutes and seconds. Latitude is stated in relation to the equator, and the longitude - in relation to the meridian. Subsequently, latitude takes the range of up to -90° at the South Pole, and up to +90° at the North Pole. Longitude values are measured relative to the prime meridian. And the longitude takes the range of up to -180° towards West, and up to +180° towards East.

Note that degrees of latitude and longitude don't have a standard length. Therefore, the measurements cannot be done accurately.

## Projected coordinate system¶

A projected coordinate system is a two-dimensional representative system of geographical coordinates. The coordinates are defined on a flat surface, therefore, it has constant lengths and angles. A geographic coordinate system serves as a basis for the projected coordinate system.

In a projected coordinate system, the coordinates are stated using X and Y values on a grid, starting from the center of the grid. The position is specified by the horizontal (X axis) and vertical (Y axis) specifications of the location. At the original point of the grid, i.e. the center, the values of X and Y are both equal to 0.

Opposite to the geographical coordinate system, the horizontal and vertical lines are equally spaced across the grid within the projected coordinate system. The positive values of X axis are above the central X axis, and the negative values of X axis are below it. The positive values of Y axis are to the right of the Y axis, and the negative values are to the left of it. Hence, the four quadrants make possible combinations of positive and negative values.

## Vertical coordinate system¶

A vertical coordinate system is a coordinate system defining height/depth of the surface. The measurements are done in linear measurement system, be it metric or imperial. In terms of axis, the vertical coordinate system is represented by Z-axis.

There are two types of vertical coordinate system measurements: measured according to either mean sea level or mean low water level.

The mean sea level is considered as a zero level for measuring height. Additionally, the mean low water level is used to measure depths. Therefore, both of the measurements of the height and the measurements of the depths are expressed in positive values but the direction of measurement differs. That is:

- The point above the mean sea level will have a positive value, and the point below the mean sea level will have a negative value.
- The point above the mean low water will have a negative value, and the point below the mean low water will have a positive value.

## The geoid, ellipsoid, spheroid and datum¶

*Geoid* is an equipotential Earth's water level surface which is a relative representation of still ocean surface supposed the atmosphere and Earth's rotation were excluded. The surface of geoid is perpendicular to the direction of gravity towards Earth's center. The shape of geoid is unstable due to the Earth's gravity force.

*Spheroid* is a 3-dimensional revolving ellipsoid with two equal semi-diameters. The ellipsoid is made of a minor and a major (principal) axes. Due to the combination of the gravity and rotation, the planet Earth is slightly flattened at its rotation axis. Such shape is called the oblate spheroid.

The contemporary World Geodetic System employs a spheroid with the radius of 6,378.137 km at the equator, and 6,356.752 km at the poles. The semimajor (half of the major) axis is a radius from the center to the equator, and the semiminor (half of the minor) axis is a radius from the center to the pole. It is noteworthy to add, that measurements of the semiminor and semimajor axes of the spheroids are the distinctive features for different types of spheroids. For example, WGS84 and GRS80 have slightly different values of the semiminor and semimajor axes. Thus, the datum is build in relation to the chosen spheroid.

Specific geographic areas use different spheroids, selecting the one that reflects the surface of the geoid for a particular area. Consequently, even for the same geographical object, the coordinate values differ depending on the selected spheroid and datum.

## Georeferencing¶

Georeferencing is a process of aligning geographical data to a selected map coordinate system. In other words, an expression of the coordinates of a raster image in terms of projected and vertical coordinate systems, i.e. referring to the object in the values of X, Y and Z axes.

In aerial imagery, the raster images, sets of points, lines, polygons or even 3D structures can be bound to the geographical coordinate values. Images are encoded using the GIS file formats, or accompanied by the coordinate data in the world file.

Usually, the aerial imagery datasets acquired with the UAVs, have a spatial reference information embedded in the raster files, or accompanied by a separate file containing coordinates values.

In comparison to georeferencing, geotagging is bounding the imagery to a geographic identification metadata, i.e. the geographic location. Most often, the position of the photographer is associated with the geographical location while taking the photo. But for the photogrammeric purposes, the RTK (Real Time Kinematic) devices are used to acquire precision data for the professional geotagging. Hence, the object displayed in the image can be bound to highly precise coordinates. For information on how to use GCP's for georeferencing in Pixpro software, see Ground Control Point Workflow page.

## Supported map projections¶

Supported map projections are the coordinate reference systems used worldwide to define the geographic datum. The coordinate reference systems and coordinate transformations can be global, regional, national or local. National reference systems are recommended to use in order to reflect the country's surface specifics best. The local systems provide additional data of the local post zip codes and the data alike.

The spatial references are listed on the website http://spatialreference.org/ref/epsg/. This is one of the most complex lists providing the references to various coordinate reference systems used worldwide.

The most recent information on the coordinate reference systems and their transformations can be found on the official website of the International Association of Oil and Gas Producers. The EPSG Geodetic Parameter Dataset is a structured dataset of Coordinate Reference Systems and Coordinate Transformations http://www.epsg-registry.org/.

As mentioned in previous sections, there are used different coordinate reference systems all over the world, and to read the geographic datum correctly, the coordinate transformations must be used. The website links above provide a possibility to transform the geographic datum from one reference system to the other in order to avoid reading errors and get as correct reading as possible.