By georeferenced information we mean that the collected data is referred to a physical location on the earth's surface through coordinates relative to a geographic reference system. Georeferencing or geocoding can be defined as the set of techniques that allow identifying the position of such information within a reference system. We can distinguish two types of georeferencing: direct georeferencing consists in the detection, through appropriate instrumentation, of the position of the object of interest. Indirect georeferencing aims to identify the position of an object based on the relationship between this and other positions already identified in the reference system.
The use of georeferenced data has become increasingly intense and common in recent times. This is especially thanks to devices that use this technique to position information on the territory for tourist or economic purposes. This tool often provides the key to extend the available information well beyond what was planned at the time of data collection. It, in fact, allows adding to the original dataset enormous amounts of information from different sources made homogeneous and communicated using spatial location as the key. Nowadays, information on infrastructure is easily available on web portals, for example of municipalities or regions or ISTAT. This allows associating socio-demographic census information to each territorial location.
Georeferencing positions each observation on the earth's surface. As seen, this operation requires reference systems or datums. A datum is a reference system that allows defining in mathematical terms the position of points on earth, thus allowing the georeferencing of places or objects. This tool is always defined by a mathematical model created to approximate more or less precisely the earth's surface. #### Geoid The geoid is a solid whose shape is not describable in geometric terms through an explicit mathematical formula. It can instead be defined in physical terms as the equipotential surface of the earth's gravitational field, that is, that surface that joins all points with equal gravitational force. The trend of the geoid surface is affected by masses and therefore reacts to the presence or absence of mass (mountains or depressions). The geoid in the context of geolocation on the earth's surface is not very manageable as it would be necessary to know at each point the direction of the gravitational force which in turn also depends on the materials constituting the territory. #### Ellipsoid
The most used model to define reference systems is that of the ellipsoid, in particular an oblate spheroid, that is, an ellipsoid obtained by rotation of an ellipse around its minor axis, assuming the typical flattened shape at the poles typical of our planet. The equation that defines this ellipsoid in canonical form depends on two parameters \(a\) and \(c\) where \(a\) is the length of the major semi-axis called "equatorial" and \(c\) is the length of the minor semi-axis, called polar. \[ \frac{x^2+y^2}{a^2} + \frac{z^2}{c^2}=1 \space \space \space t.c. \space \space a>c \] The ellipsoid is defined by particular parameters such as the length of the equatorial and polar axis or by dimensionless parameters such as: The eccentricity defined as: \[ e = \sqrt{\frac{a^2 – c^2}{a^2}} \] The flattening defined as: \[ f = \frac{a-c}{a}\] Since the earth is not a perfect ellipsoid, ellipsoidal models are not unique. The two most important ellipsoid models are that of Bessel (\(a=6377397.155m\) and \(e^2=0.006674372\)) and that of Hayford (\(a=6378388m\) and \(e^2=0.00672267\)). In this model, each point P on the ellipsoid can be expressed through a pair of geographic coordinates, called latitude (which constitutes the angle formed by the vector joining the center of the ellipsoid with the plane passing through the origin and orthogonal to the earth's rotation axis, that is, in the model the equatorial plane) and longitude (the angle formed between the plane exiting from the rotation axis and passing through the center and another plane passing through the origin and orthogonal to the equatorial plane assumed as reference. These degrees are represented in sexagesimal degrees and latitude can assume values from 0° to 90° while longitude assumes values between 0° and 180°. For example: Milan has a latitude of 45.4636707 and a longitude of 9.1881263. Obviously, the complete identification of the location of a point also requires knowledge of its altitude.
The cartographic representation system consists in the transformation, through appropriate mathematical operations called cartographic projections, of angular geographic coordinates (long, lat) into plane or cartographic coordinates (x,y), expressed in units of length. These relationships are called representation equations. In other terms, the representation of the ellipsoid on the plane is defined by two functions (x = X(long, lat) and y = Y(long, lat)) that establish the one-to-one correspondence between the position of a point P on the ellipsoid and the corresponding position of point P' on the representation and therefore allow conversion from a numerical point of view. These functions are implicitly determined in a complex way and are constructed to guarantee appropriate properties to the projection reported below.
A geographic information system (GIS) is an integrated system of data and software programs that allows the acquisition, recording, analysis, visualization and restitution of information derived from georeferenced data. GIS technology is composed of a series of software tools capable of associating to each geographic element one or more alphanumeric descriptions that define the geographic position of the object. The GIS is in fact a form of Database Management System capable of managing geographic data. The main fields of use of GIS are urban planning, cartography, marketing, sales and environmental impact assessments. From an informational point of view, the GIS manages information through a relational database in which spatial and non-spatial information is stored in tables that can be interconnected through appropriate key fields. The non-spatial information of each element is stored in a data table and uniquely identified by an identification field (ID). The real world can be represented in a geographic information system through two main types of data: vector data (consisting of simple elements such as points, lines and polygons, encoded and stored based on their coordinates.) and raster data (allowing to represent the real world through a matrix of cells, generally square-shaped, called pixels [point elements are represented by a single cell, linear elements are represented by a series of adjacent cells]). GIS allow the processing and analysis of geographic data, in vector and raster format, exploiting their natural complementarity and provide the possibility to switch from one format to another and vice versa. Among the various formats with which spatial data can be entered into a GIS, the most used is the shapefile, developed by ESRI to increase interchangeability between systems implemented by the company and other GIS. Today it has become a standard and is used by a wide variety of GIS systems. Connected to the shape file you can find many other files that allow having more information about the territory: each record of the .shp file represents a spatial entity through a list of vertices; each row of the .dbf corresponds to an object encoded in the .shp file.; The .prj file reports information on the reference system and map projection.