COORDINATES

In GIS language, when we say that the coordinates of Delhi is 27° 30' 30" N 77° 25' 45" E, this indicates a particular point on earth which has a latitude of 27° 30' 30" N and longitude of 77° 25' 45" E. What is this latitude and longitude?

Let me first explain the following two concepts which are required to be understood before we go for latitude and longitude.

Equator: This is a circle (great circle) which divides the Earth into two equal hemisphere i.e, Northern & Southern such that the line joining the poles is at right angle to its plane.

Prime Meridian: It is a circle (great circle) which divides the earth into two hemispheres i.e, Eastern & Western passing through London and is taken as reference for longitude 0.

The below images clearly shows the Equator and Prime Meridian.  Latitude: Geodesic Latitude of a point on Earth is the angle made by line drawn perpendicular to the surface through that point on earth on the Equatorial plane. Generally the definition which is taught in schools is: Latitude of a point on Earth is an angle made by line joining this point and the centre of the earth with the Equatorial plane. This definition refers to Geocentric Latitude.

This method will give us two angles i.e, x and (180-x). The smallest of the two angles is taken as the latitude. Remember that the value of latitude cannot exceed 90. If the point falls in northern hemisphere, the latitude is suffixed with N i.e, North else S i.e, South. The above example for Delhi coordinates is in DMS (Degree Minute Second). This Latitude can also be represented in DD (Degree Decimals) in which we can omit N or S prefix. Then how do we come to know whether the point falls in Northern hemisphere of Southern? In this case prefix the latitude with - (negative) sign for Southern hemisphere.

Longitude: Longitude of a point on Earth is the angular distance between the planes formed by connecting the point P bisecting the poles and the Prime Meridian. This method will give us two angles i.e, y and (360-y). The smallest of the two angles is taken as the longitude. Remember that the value of longitude cannot exceed 180. If the point falls east of prime meridian, the longitude is suffixed with E i.e, East else W i.e, West. The longitude may be prefixed with - (negative) sign for points falling west of prime meridian in DD format.

The following diagrams explain the concept of latitude and Longitude.

Definition Consider the Earth as spherical and take a point P on this sphere.  EARTH SHAPE

Let me first explain a few terms which required to understood before proceeding with the Earth Shape.

Geodesy: It is defined as a branch of mathematics which deals with the shape and area of the earth or large portions of it.

Oblate spheroid: It is the shape you get by spinning an ellipse around it is minor axis.

Flattening: It is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Flattening is denoted by f and its definition in terms of the semi-axes of the resulting ellipse or ellipsoid is

flattening f = (a-b)/a

where a and b are the semi-major axis radius and semi-minor axis radius respectively. The shape of our Earth is approximately Sphere. When we say approximately, we mean that it is not a complete sphere. Because of the rotation of earth, the radius of equator is more than that of poles. The radius at equator is taken as 6378.137 Km and on poles, it is measured as 6356.7523 Km. Hence the equator is 42.7694 km wider than Poles in diameter. This makes the shape of earth to bulge on equatorial region making it Oblate spheroid. This results in the flattening value of earth to be (42.7694/12756.274) = 1/298.257.

ELLIPSOID & GEOID

Ellipsoid: A three-dimensional closed geometric shape of which all planar sections are either ellipses or circles. It is a mathematical idealized representation of the physical Earth and is used in all geo-calculations like distance between two points or area of a region.

Geoid: It is a equipotential surface of the Earth's gravity field which best fits, in a least squares sense, global mean sea level. It represents a surface to which the force of gravity is everywhere perpendicular. If one were to remove the tides and currents from the ocean, it would settle onto a smoothly undulating shape (rising where gravity is high, sinking where gravity is low). This irregular shape is called "the geoid," a surface which defines zero elevation.

The gravitational field of the earth is neither not uniform throughout the surface. A flattened ellipsoid is typically used as the idealized earth, but even if the earth were perfectly spherical, the gravitational pull would not be the same everywhere, because of varying density throughout the earth. This is due to magma distributions, mountain ranges, deep sea trenches etc.  Please note that the GPS satellites, orbiting about the center of gravity of the Earth, can only measure heights relative to the ellipsoid. To obtain one's geoidal height, a raw GPS reading must be corrected using Earth Gravity Model (EGM). Click here for more information. This link will calculate the height of Geoid above the Ellipsoid.

The EGM illustrates the value to be subtracted from the GPS calculated height (height above the ellipsoid) to get the Geoid height which is very close to the Mean Sea Level (MSL) height. You can observe the dark blue colour in South Asia region, which means that the value to be subtracted from GPS height is in negative. It means the height calculated by GPS is less that the actual height and to get the MSL height some 60 - 100 m is to be added to it.

DATUM

A datum is a model of the earth that is used in mapping. The datum consists of a set of reference points that define the shape and size of the ellipsoid and it's orientation in space. Or in other words a datum typically defines the surface (like radius, major axis and minor axis or inverse flattening for the earth and the position of the surface relative to the center of the earth). It is now clear that the shape of the Earth is not an exact ellipsoid and no single smooth ellipsoid will provide a perfect reference surface for the entire Earth. Hence a datum is chosen to give the best possible fit to the true shape of the Earth. The calculation of distance between points and area on earth surface are dependent on Datum.

Let us understand the datum concept practically. We already know that the earth surface is not a perfect sphere or ellipsoid. You can imagine the earth surface as shown below: Now let us define an ellipsoid over this which best approximates to the earth surface. First image below shows the ellipsoid surface in WGS84 datum. You can also see that this datum is not best suited for surface on west side as most of the land surface is above this ellipsoid. This datum will result in error in distance and area calculation. The calculations result will be less in value. Do you know why?

To compensate this mismatch between earth surface and ellipsoid, a new local datum is created by countries falling in the west side by shifting the centre of WGS84 ellipsoid (keeping the same major & minor axis and orientation) as shown below in the second image. Now the earth surface approximates the ellipsoid surface and this datum will be best suited for the west countries.  There are a large number of datums in use. Many of them are optimised for use in one particular part of the world. For example Geodetic 1949 datum has been used in New Zealand, similarly NAD83 (North American Datum 1983) is also a local datum. GPS Systems use WGS-84 (World Geodetic System 1984) datum which is an example of a datum that can be used globally.

Latitude and longitude are frequently used to refer to a specific location on the surface of the Earth. Please note that the value of Latitude and Longitude of a point on Earth will be different if measured in different datum.

PROJECTION

The shape of the Earth is curved, but our digital screen or paper maps etc where we want to see whole world is flat. To see the 3-dimensional earth on 2-dimensional plane, we need to cut/stretch the earth generally from poles to that it fits well on the 2-D plane. This process of flattening out the Earth onto a flat piece of paper or computer screen is a mathematical process called a projection. Examples of projection are LatLong, UTM (Universal Transverse Mercator), polyconic, LCC (Lambert Conformal Conic) etc.

Consider the following two maps in UTM projection and LCC projection. Compare the size of Greenland with African continent. Just remember the area of Africa is approximately 15 times larger than that of Greenland.  UTM projection

LCC projection

From the above images you will find that the size of Greenland in Mercator projection is almost equal to the Africa, which is not a case in LCC projection. During the process of projection from 3D to 2D either one or all of the following will be affected.

(a) Shape

(b) Distance

(c) Area

(d) Direction

Now if you draw two equal length lines on equator and near poles parallel to equator, then the line on equator will cover more distance than that near to poles. Observe the following diagram. Now you can understand the importance of projection. UTM (Universal Transverse Mercator)

The UTM projection system uses 2D Cartesian Coordinates System and instead of degree minute second or degree decimal in Latitude & Longitude, it uses meters. The projection system divides the Earth into sixty zones, each being a six-degree band of longitude.

The UTM system divides the Earth between 80°S and 84°N latitude into 60 zones, each 6° of longitude in width. Zone 1 covers longitude 180° to 174° W; zone numbering increases eastward to zone 60, which covers longitude 174° to 180° E. Each longitude zone is segmented into 20 latitude bands. Each latitude band is 8° high, and is lettered starting from "C" at 80°S, increasing up the English alphabet until "X", omitting the letters "I" and "O" (because of their similarity to the numerals one and zero). The last latitude band, "X", is extended an extra 4°, so it ends at 84°N latitude, thus covering the northernmost land on Earth.  The origin for each UTM zone is the intersection of the equator with the corresponding central meridian. The easting of the central meridian is shifted by 500,000 meters. When being displayed on the southern hemisphere, the northing is shifted by 10,000,000 meters.

What is the importance of 500,000 m & 10,000,000 m shift in easting and northing (in southern hemisphere) respectively?

The main reason is to make the values of easting & northing in UTM to be always positive. This can be positive when we start the origin at such point such that even if we go backward/forward or up/down in any UTM zone, we are never going below zero. Taking approximately 6400 Km as the earth radius (since we can choose any datum), we can calculate the distance from equator to 80° S (since shift of origin will towards south) and 3° shift along the equator (since easting distance will be maximum on Equator)

( 6,400,000 x 2π ) x ( 80° / 360° ) = 8,936,085 (for Northing)
( 6,400,000 x 2π ) x ( 3° / 360° ) = 335,103 (for Easting)

The above calculations give us a clear indication that why we have chosen a shift 500,000 m & 10,000,000 m shift in easting and northing (in southern hemisphere) respectively.

RASTERS

In Spatial taxonomy, the rasters consist of a matrix of cells or pixels organized in grid type structure where each cell represents a value like a colour. Or in simple words, raster data are image files in formats like tif (tagged image format), ecw (Enhanced Compression Wavelet), png (portable network graphics), jpg (joint photographic expert group) etc. There are more than 140 such formats. See GDAL rasters page for more info.

Rasters files can be georeferenced (generally tif, ecw, img) or non-georeferenced (generally jpg, png etc). When we say a raster is geo-referenced, it means that the data carries informations like coordinates, coordinate system, origin, overviews etc. How to see these informations in a raster? See GDAL tools page. Let us define some terms associated with rasters:

Resolution: This can be classified into four categories:

(a) Spatial Resolution: It is defined as the distance covered on ground by each pixel of the raster data. The smaller the distance covered the higher is the resolution. For example WorldView-4 Satellite provides raster image of spatial resolution 31cm. It means each pixel will cover 31 cm of the ground.

You can download Bluemarble raster files of entire globe in 250m spatial resolution from here.

(b) Radiometric Resolution: The radiometric resolution of raster data describes the max number of values each pixels can represent. Basically it refers to the number of divisions of bit depth. For example 256 (0-255) for 8-bit, 65,536 (0-65535) for 16-bit in data collected by a sensor.

(c) Spectral Resolution: The spectral resolution may be defined as the ability of a sensor to define fine wavelength intervals or the ability of a sensor to resolve the energy received in a spectral bandwidth to characterize different constituents of earth surface. The finer the spectral resolution, the narrower the wavelength range for a particular channel or band. For example IRS LISS-III uses 4 bands: 0.52-0.59 (green), 0.62-0.68 (red), 0.77-0.86 (near IR) and 1.55-1.70 (mid-IR).

(d) Temporal Resolution: Temporal resolution is defined as the amount of time needed to revisit and acquire data for the exact same location. Depending upon the orbital characteristics of the sensor platform as well as sensor characteristics, it is usually expressed in days.

8bit Data: 8 bit can also be written as 28, which is equal to 256. If a raster data is of 8-bit, it means each of its pixel can have values ranging from 0 to 255. Similarly in case of 16-bit raster data, the range will be from 0 to 65535. Raster data can be signed or unsigned. The above examples are for unsigned data where the pixel values can have only positive number. In case of signed raster data, the pixel can take negative values and 8-bit signed raster will have values ranging from -128 to 127.

Multispectral: A multispectral raster data are those which have more than one band. For example if the sensor can image the ground in red, green and blue bands, it will produce a colour raster data. These bands can be in invisible regions like near infra red, ultra violet etc.

Panchromatic: Panchromatic raster data are those which are created by sensors which are sensitive to all the bands of the visible spectrum. The result is a single band image. DEM: It stands for Digital Elevation Model. Every pixel of this type of raster data represents a height values. These height values are the altitude of geographic feature above mean sea level. If this height includes the ground features like buildings etc, then they are called as DSM (Digital Surface Model) and have high resolution. Generally DEM/DSM data are required for generating 3D model of earth.

You can download 90 meter SRTM (Shuttle Radar Topography Mission) data free of cost. 30 meter STRM and ASTER GDEM data is available free on EarthExplorer site (one time registration required). You can also download High Resolution DEM (ALOS PALSAR DEM 12.5 m) from Alaska Satellite Facility (one time registration required in vertex development application).

In the adjacent DEM image, the altitude of white pixels are more than those of black. The DEM file is always single band panchromatic product.

Overview: This is also known as pyramid layer. If a raster data having 9000 x 9000 pixels is viewed on a digital screen having size of 1000 x 1000 pixel then every 9x9 pixels of the raster is averaged out to 1x1 pixels. This process takes time because of which geospatial viewer takes time to render the data if zoom in/out. Raster data can have this pyramid layers pre-built internally or externally using geospatial applications like Quantum GIS or GDAL tool gdaladdo.

Below is an example of Original image preview with 8 pyramid layers. Notice the changing resolution which changes like 1024x512, 512x256, 256x128, 128x64, 64x32, 32x16, 16x8 etc.

## Pyramid Layers Preview         World File: The Worldfile acts as a source of georeferencing for the raster file. It has the same extension followed by 'w' as the associated raster file (or .wld extension). For example a.pngw is the world file for a.png raster file. Even extension formed by removing the middle alphabet is also supported like a.pgw world file for previous raster file. The world file consists of 6 lines each with significance as mentioned in the below example. In GIS we expect second and third line to be 0 as shown below:

• 0.01411597633136094
• 0
• 0
• -0.01411597633136094
• 51.96475029585798211
• 34.72150295857988311

Line 1: degrees/pixel along longitude
Line 4: degrees/pixel along latitude, it carries negative value as the latitude decreases as we move down from top left pixel
Line 5: Longitude of the center of the upper left pixel
Line 6: Latitude of the center of the upper left pixel

VECTORS

Vectors are a coordinate-based data model that represents geographic features such as points, lines and polygons. Each point feature is represented as a single coordinate pair of latitude & longitude, while line as ordered lists of vertices and polygon as ordered lists of vertices where first pair and last pair is same. Attributes may be associated with each vector feature. Vectors are useful for storing data that has discrete boundaries, such as country borders, land parcels, and streets.

There are more than 80 vector data types available. Most common are Esri shapfiles, KML (Keyhole Markup Language), GML (Geography Markup Language), geojson etc.See GDAL vectors page for more info.

The most common form of vector is a shapefile. A single shapefile consists of at least the following first three files:

• abc.shp : It contains the geometry (points lines, polygons etc).
• abc.shx : It contains an index to the geometry file i.e, abc.shp.
• abc.dbf : It contains the feature attributes.
• abc.prj : It contains the projection information of the geometry.

You can open abc.dbf file MS Excel and view the attributes. abc.prj file is optional. You can provide the projection information to shapefiles in the GIS application you load it to.

A shapefile can be of three types depending on what it represents i.e, points, lines or polygons. No shapefile file can have a combination these geometries. Oracle spatial database can save both rasters as well as vectors. Vectors in oracle spatial are represented by sdo_geometry. For example sdo_geometry(2001, 8307, sdo_point_type(92.2565, 33.6578, null), null, null) is equivalent to a point (2001) having latitude (33.6578), longitude (92.2565) in Geolatlong projection and WGS-84 datum (8307). For more information go to Spatial Databases.

 QUICK LINKS Coordinates Earth Shape Ellipsoid & Geoid Datum Projection UTM Rasters Vectors GDAL GDAL Setup GDAL Rasters GDAL Vectors GDAL Tools WMS MS4W Spatial DB Oracle Spatial SDO_GEOMETRY Geo-Crawler Web Clients OL3+ Closest Distance Map Openlayers v2.x Openlayers+Cesiumjs ThreeJS Terrain Viewer Bluemarble (250m tiff) JS Tools Geographiclib JS2Shapefile CSV2Shape