Map projections are crucial for representing Earth's curved surface on flat maps. They come in various types, each with unique properties that affect how geographic features are displayed. Understanding these projections helps cartographers choose the best one for their specific mapping needs.

Different projections preserve certain properties like area, shape, distance, or direction. The choice depends on the map's purpose and geographic extent. Cylindrical, conic, and azimuthal projections are common, each suited for different regions and uses. Compromise projections balance overall distortion for general-purpose maps.

Types of map projections

• Map projections are mathematical methods used to represent the curved surface of the Earth on a flat plane, such as a paper map or computer screen
• Different types of map projections have been developed to minimize distortion and preserve certain properties, depending on the purpose and extent of the map

Cylindrical projections

• Cylindrical projections are created by projecting the Earth's surface onto a cylinder that is either tangent to the equator (normal aspect) or a meridian (transverse aspect)
• Meridians and parallels appear as straight lines, forming a rectangular grid (Mercator projection)
• Distortion increases towards the poles, with areas near the poles appearing much larger than they actually are
• Commonly used for world maps and navigation charts

Conic projections

• Conic projections are created by projecting the Earth's surface onto a cone that is tangent to one or two parallels
• Meridians appear as straight lines converging at a point beyond the pole, while parallels are represented as concentric arcs (Albers Equal-Area Conic projection)
• Distortion is minimized along the standard parallels and increases with distance from them
• Often used for maps of mid-latitude regions with a predominantly east-west extent

Azimuthal projections

• Azimuthal projections are created by projecting the Earth's surface onto a plane that is tangent to a point on the globe
• Directions from the center point to any other point on the map are accurate (Stereographic projection)
• Distortion increases with distance from the center point
• Commonly used for polar regions and for maps centered on a specific location

Pseudocylindrical projections

• Pseudocylindrical projections are a compromise between cylindrical and conic projections
• Central meridian and parallels are straight lines, while other meridians are curved (Sinusoidal projection)
• Distortion is reduced compared to cylindrical projections but not eliminated
• Often used for thematic maps and to represent global distributions

Pseudoconic projections

• Pseudoconic projections are a blend of conic and azimuthal projections
• Parallels are concentric circular arcs, and meridians are equally spaced radial lines (Bonne projection)
• Distortion is reduced compared to conic projections, especially for maps of large areas
• Not as commonly used as other projection types but can be suitable for specific purposes

Properties of map projections

• Map projections inherently introduce distortion because it is impossible to perfectly represent the curved surface of the Earth on a flat plane
• Different map projections preserve or compromise certain properties, such as area, shape, distance, or direction

Area vs shape distortion

• Some projections, like the Mercator projection, preserve shape (conformal) but distort area, making landmasses near the poles appear much larger than they actually are
• Other projections, such as the Albers Equal-Area Conic projection, preserve area but distort shape, especially near the edges of the map
• The choice between preserving area or shape depends on the purpose of the map and the importance of each property for the intended use

Conformal vs equal-area projections

• Conformal projections, such as the Mercator and Lambert Conformal Conic projections, preserve local angles and shapes but distort area
• Equal-area projections, like the Albers Equal-Area Conic and the Mollweide projections, maintain the correct proportional size of areas but distort shape
• Conformal projections are often used for navigation and weather mapping, while equal-area projections are preferred for thematic mapping and spatial analysis

Equidistant projections

• Equidistant projections preserve the correct distance from one or two points to all other points on the map
• Examples include the Azimuthal Equidistant projection, which maintains true distances from the center point, and the Equidistant Conic projection, which preserves distances along meridians
• Equidistant projections are useful for showing distances from a specific location or for creating range rings on a map

True direction vs straight lines

• Some projections, like the Gnomonic projection, maintain true direction (great circles) as straight lines but significantly distort shape and area
• Other projections, such as the Mercator projection, represent rhumb lines (lines of constant bearing) as straight lines, which is useful for navigation but results in curved great circles
• The choice between preserving true direction or straight lines depends on the purpose of the map and the importance of each property for the intended use

Compromise projections

• Compromise projections, such as the Robinson and Winkel Tripel projections, aim to minimize overall distortion by balancing the distortion of area, shape, and distance
• These projections do not perfectly preserve any single property but provide a visually appealing representation with acceptable levels of distortion for general-purpose maps
• Compromise projections are often used for world maps in atlases, textbooks, and other educational materials

Choosing appropriate projections

• Selecting the most suitable map projection depends on various factors, including the purpose of the map, the geographic extent, and the properties that need to be preserved

Purpose of the map

• The intended use of the map influences the choice of projection
• For example, navigation maps require projections that preserve direction or maintain straight rhumb lines, while thematic maps often prioritize equal-area projections for accurate representation of spatial patterns

Scale and extent of the map

• The scale and geographic extent of the map affect the level of distortion introduced by different projections
• Large-scale maps (showing a small area in detail) generally have less distortion than small-scale maps (showing a large area)
• The extent of the map, whether it covers a local area, a continent, or the entire world, also influences the choice of projection

Location and shape of the area

• The location and shape of the area being mapped can guide the selection of an appropriate projection
• For areas near the equator, cylindrical projections like the Mercator or Plate Carrée may be suitable
• For mid-latitude regions with a predominantly east-west extent, conic projections such as the Albers Equal-Area Conic or Lambert Conformal Conic are often used
• For polar regions or maps centered on a specific location, azimuthal projections like the Stereographic or Azimuthal Equidistant are commonly employed

Minimizing distortion

• The choice of projection should aim to minimize the distortion of properties that are most important for the map's purpose
• For example, if preserving area is crucial for a thematic map, an equal-area projection like the Mollweide or Goode Homolosine should be considered
• If maintaining shape is essential for a map used for visual recognition, a conformal projection like the Mercator or Lambert Conformal Conic may be appropriate

Common projection choices

• Some projections are widely used for specific purposes or regions
• The Mercator projection is commonly used for web mapping applications and navigation charts
• The Robinson and Winkel Tripel projections are often employed for world maps in educational and general-purpose contexts
• The Universal Transverse Mercator (UTM) projection is widely used for large-scale mapping, surveying, and GIS applications

Distortion patterns

• Understanding the distortion patterns associated with different map projections is essential for interpreting the information presented on the map and assessing its suitability for a given purpose

Tissot's indicatrix

• Tissot's indicatrix is a tool used to visualize the distortion patterns of a map projection
• It consists of a series of circles of equal size placed at regular intervals on the globe, which are then projected onto the map
• The resulting ellipses on the map indicate the direction, magnitude, and spatial variation of distortion in area, shape, and scale

Distortion along meridians and parallels

• Map projections often have distinct distortion patterns along meridians (lines of longitude) and parallels (lines of latitude)
• In cylindrical projections like the Mercator, meridians and parallels appear as straight lines, with distortion increasing towards the poles
• In conic projections, such as the Albers Equal-Area Conic, meridians converge at a point, and parallels are represented as concentric arcs, with distortion increasing away from the standard parallels

Distortion at different latitudes

• The magnitude and direction of distortion often vary with latitude, depending on the projection
• In the Mercator projection, distortion is minimal near the equator but increases significantly towards the poles, resulting in the exaggeration of areas at high latitudes
• In the Lambert Conformal Conic projection, distortion is minimized along the standard parallels but increases with distance from these parallels

Visualizing distortion with flex projector

• Flex Projector is an interactive online tool that allows users to explore and compare the distortion patterns of various map projections
• Users can manipulate the parameters of a projection, such as the standard parallels or the central meridian, to observe how distortion changes across the map
• Flex Projector provides a visual representation of distortion using Tissot's indicatrices and overlays, helping users understand the trade-offs associated with different projections

Coordinate systems and datums

• Coordinate systems and datums are essential components of map projections, as they provide the framework for defining the positions of features on the Earth's surface and on the map

Geographic coordinate systems

• Geographic coordinate systems use latitude and longitude to define the position of a point on the Earth's surface
• Latitude represents the angular distance north or south of the equator, while longitude represents the angular distance east or west of the Prime Meridian
• Geographic coordinates are often expressed in degrees, minutes, and seconds (DMS) or decimal degrees (DD)

Projected coordinate systems

• Projected coordinate systems are based on a map projection and use linear units (e.g., meters or feet) to define the position of a point on a flat map
• Examples of projected coordinate systems include Universal Transverse Mercator (UTM) and State Plane Coordinate System (SPCS)
• Projected coordinates are typically expressed as easting (x) and northing (y) values

Importance of datum selection

• A datum is a reference surface used to define the positions of features on the Earth's surface
• The choice of datum is critical because it affects the coordinates of features and the alignment of map layers
• Common datums include World Geodetic System 1984 (WGS84), used for GPS and global mapping, and North American Datum 1983 (NAD83), used for mapping in North America

Coordinate transformations

• Coordinate transformations are necessary when working with data from different coordinate systems or datums
• Transformations involve converting coordinates from one system to another, ensuring the proper alignment of map layers and the accurate representation of features
• GIS software packages often provide tools for performing coordinate transformations, such as the Project tool in ArcGIS or the Reproject tool in QGIS

Applying map projections

• Map projections are applied in various contexts, including GIS software, web mapping applications, and data management

In GIS software

• GIS software packages, such as ArcGIS and QGIS, provide tools for applying and managing map projections
• Users can define the projection of a map layer, reproject data from one coordinate system to another, and create custom projections
• GIS software also allows users to visualize the distortion patterns of different projections using tools like the Data Frame Properties in ArcGIS or the Project Properties in QGIS

In web mapping applications

• Web mapping applications, such as Google Maps and OpenStreetMap, use map projections to display geographic data in a web browser
• The Web Mercator projection (EPSG:3857) is commonly used for web mapping due to its compatibility with tile caching and its ability to maintain the shape of features
• Web mapping APIs, such as Leaflet and OpenLayers, provide options for defining the projection of a map and reprojecting data on-the-fly

Reprojecting data

• Reprojecting data involves transforming the coordinates of a dataset from one projection to another
• This process is necessary when combining data from different sources or when working with data in a projection that is not suitable for the intended purpose
• GIS software and programming libraries, such as GDAL and Proj.4, offer tools for reprojecting vector and raster data

Defining custom projections

• In some cases, users may need to define custom projections to meet specific requirements or to work with unconventional coordinate systems
• GIS software and programming libraries allow users to create custom projections by specifying the projection parameters, such as the central meridian, standard parallels, and false easting/northing
• Custom projections can be saved and shared using well-known text (WKT) strings or projection files (e.g., .prj files)

Handling projection issues

• Working with map projections can sometimes lead to issues, such as misaligned data, incorrect measurements, or distorted maps
• Common projection issues include using the wrong projection for the intended purpose, mixing data from different coordinate systems without proper transformation, and failing to define the projection of a dataset
• To avoid projection issues, users should carefully consider the purpose and extent of the map, choose an appropriate projection, and ensure that all data is properly projected and transformed