Fundamentals of Mapping: Coordinates and Projection

Understanding map projections involves understanding how a map is a flat surface that is a representation of the globe. It is necessary to comprehend the principles that govern the understanding of Coordinates and Projections, which include:

Coordinate Systems

Data is engineered in both horizontal and vertical coordinate systems. Horizontal coordinate systems locate data across the Earth’s surface, and vertical coordinate systems locate the depth of data or relative height.

Understanding map projections and about coordinate systems in GIS with the official ArcGIS Pro documentation is what this article is about.

Horizontal Coordinate Systems

There are three types of horizontal coordinate systems: geographic, projected, or local. It is possible to determine the horizontal coordinate system that the data is using by merely checking the property values of the layer.

Geographic Coordinate Systems

Geographic coordinate systems are established on a three-dimensional ellipsoidal or spherical surface, and sites are defined with the use of angular measurements. This is usually in decimal degrees, and measures degrees of longitude (x-coordinates) and degrees of latitude (y-coordinates).

The data location is represented as positive or negative numbers: positive x- and y-values for the north side of the equator and east side of the prime meridian, and negative values for the south side of the equator and west of the prime meridian.

It's distinct from flat map projections, defining locations by angles (degrees, minutes, seconds, or decimal degrees) from the Earth's center, with the WGS84 system being a common example.

Projected Coordinate Systems

Projected coordinate systems are planar systems that use linear measurements for the coordinates instead of angular units. A projected coordinate system comprises a geographic coordinate system and a map projection combination.

A map projection includes the mathematical calculations that transform the geographic coordinate system’s angular geodetic coordinates to the coordinate system of Cartesian coordinates of the planar.

Coordinate systems in GIS

In GIS, coordinate systems offer a structure to define Earth locations, which is primarily split into: -

• Geographic Coordinate Systems (GCS) for angular,

• 3D locations (latitude/longitude on a sphere/ellipsoid like WGS84) and

• The Projected Coordinate Systems (PCS) for flat, 2D maps (with the use of meters/feet, like UTM) are taken from GCS through mathematical projections.

So:

GCS = where things are on the Earth

PCS = how we show them on a flat map

Each of these is suited for different needs, like accurate area/distance analysis or global referencing, with GCS for global, PCS for local precision.

Map coordinate systems guide

Map coordinate systems direct you to different locations, which are primarily divided into: -

l Geographic Coordinate Systems (GCS), using latitude/longitude on a 3D globe (like WGS84 for GPS), and

l The Projected Coordinate Systems (PCS) that represent the world on a 2D plane through the use of X/Y coordinates (as in UTM and Web Mercator) allow easier measurement, but with some distortions.

A GCS specifies location on the Earth's surface in terms of (Seconds, Minutes, Degrees). At the same time, a PCS employs a projection system, such as the Mercator projection, to express these 3D locations as 2D coordinates measurable in linear units, typically meters or feet.

Local Coordinate Systems

The local coordinate system makes use of a false origin (0, 0 or other such values) in an arbitrary site anywhere on Earth. The local coordinate systems are mostly used for large-scale (small area) mapping.

The false origin may or may not be aligned to a known real-world coordinate, but for the goal of data capture, bearings and distances can be measured using the local coordinate system instead of global coordinates. The local coordinate systems are normally expressed in meters or feet.

Vertical Coordinate Systems

Vertical coordinate systems offer a reference for z-coordinates, which are measurements of the height or depth of features. They are always measured in linear units such as meters or feet. A vertical coordinate system would improve the locational precision in editing and analysis, but it is not applied by default to new maps and scenes; you need to precisely choose one.

Vertical coordinate systems are either ellipsoidal or gravity-based. Gravity-based vertical coordinate systems are typically used. They refer to the mean sea level calculation. Ellipsoidal coordinate systems refer to an ellipsoidal surface or a mathematically derived spheroidal surface. As they are calculated on a mathematical model, ellipsoidal coordinate systems are simpler compared to gravity-based vertical coordinate systems. However, they might lack important precision, particularly in large-scale applications.

For instance, when using a large-scale map, it may appear as if the direction of flow of a stream differs based on the application of an ellipsoidal vertical coordinate system. On the other hand, when using an ellipsoidal vertical coordinate system, it is essential to confirm that the horizontal coordinate system is based on a geographic coordinate system.

For example, if in NAD 1983, z-value height is defined, the geographic coordinate system within a projected coordinate system or the geographic coordinate system must also be defined in NAD 1983, rather than WGS 1984.

Vertical coordinate systems in a global scene have to be ellipsoidal, with one exception. Only if they cover a full-world extent can they be gravity-based. EGM96 Geoid and EGM2008 Geoid are two such examples of global gravity-based vertical coordinate systems.

Understanding Map Projections

A map projection is the method by which you can display the coordinate system along with your data on a flat surface, like a digital screen or a piece of paper. The map projection’s mathematical calculations are used for converting the coordinate systems that are used on the curved surface of the Earth to the one used on a flat surface.

As there isn't any perfect way for changing a curved surface to a flat surface without some kind of distortion, many map projections exist for satisfying different compromises. For a detailed technical explanation, you can refer to the guide by ESRI on understanding map projections.

Understanding Map Projections can tell you about the preserve area, while others preserve local angles. Some maintain specific directions or distances. The property (area, distance, or shape) location, and the extent you want to preserve must inform your choice of map projection for your projected coordinate system.

ArcGIS has almost 6,000 different coordinate systems, so your system of choice is likely among them. However, if this is not the case, it is also possible for a new projected system of coordinates to be established if more than 100 map projection systems are used..

GIS projection basics

GIS projection basics means understanding map projections and getting to know how the round Earth is shown on a flat map. As the Earth is curved and maps are flat:

• GIS uses math to change the longitude  and latitude into map coordinates

• This step is essential, but never perfect
  

When the Earth is flattened, some things change, such as:

• n direction

• n area

• n Shape or

• n distance

Understanding map projections which are different, can tell you more about them, like how they are selected for reducing these changes based on their purpose:

• Mercator → is good for direction and navigation

• Albers → is good to preserve the area

• UTM → is good for precise local measurements

A Geographic Coordinate System (GCS) uses latitude and longitude measured in degrees, while a Projected Coordinate System (PCS) uses grid coordinates that are measured in meters or feet for mapping.

Map projections explained

Map projection is the essential cartographic technique to transform 3D curved surface of the Earth (a sphere or ellipsoid) onto a 2D flat map, with use of mathematical formulas, for representing longitude and latitude lines (the graticule) on a plane, consequently inducing some distortion in area, shape, distance, or direction, so different projections are selected to minimize specific distortions for different map purposes.

ArcGIS Pro and On-the-Fly Projection

ArcGIS Pro redesigns data on the fly, so any data you add to a map implements the coordinate system definition of the first layer added. As long as the first layer added has its coordinate system defined correctly, all other data with correct coordinate system details reprojects on the fly to the map’s coordinate system.

This approach enables exploring and mapping data, but it should not be used for editing or analysis, as it might lead to imprecision from misaligned data among layers. When data is projected on the fly, it is also slower to draw. If you plan to perform analysis or edit the data, first project it into a systematic coordinate system that is shared by all your layers. This can create a new version of your data.

Foundational Concepts that Support Map Projections

Geodesy for Beginners

Geodesy for beginners is the science of precisely measuring the shape of the Earth, size, space orientation, and gravity field, basically giving our planet a uniform 3D address system for analyzing geological changes,  navigation (like GPS), and mapping.

It uses the advanced tools such as satellites, but starts with the concept that Earth isn't a perfect sphere but an irregular "geoid." Further, it defines coordinate systems (like latitude/longitude) for precise mapping and positioning.

Spatial reference systems

A Spatial Reference System (SRS) or also known as Coordinate Reference System (CRS) is a framework that defines the Earth’s locations by using coordinates (such as latitude/longitude or X, Y), combines a datum (Earth model) and a coordinate system (e.g., Projected or Geographic) to offer precise location data for  GIS, mapping, and applications, and ensure consistency for analysis.

GIS mapping fundamentals

Fundamentals of GIS mapping describe how computer systems are used to work with location-based details. GIS helps turn real-world locations into useful digital maps through the following ways:

• Capture of data that is related to locations on Earth

• Store data in digital form Analyze data to find  relationships and patterns

• Display data as visuals and maps

GIS combines the details of location with descriptive information using:

• Hardware (devices and computers)

• Software (GIS applications)

• Data (spatial and non-spatial information)

• People (analysts and users)

• Methods (workflows and processes)

Key GIS concepts have:

• Vector data (polygons, lines, and points)

• Raster data (images and grids)

• Data layers to organize details

• Spatial analysis to study relationships

• Projections and scales to precisely represent the Earth

With these components working together, the process of mapping real-world attributes from the physical environment into a digital form assists in making better decisions. The ArcGIS Learn site contains details of examples and tutorials for the fundamentals of GIS mapping.

Conclusion

Understanding map projections is integral to precise mapping, decision-making, and spatial analysis in GIS.  By clearly identifying local, projected, and geographic coordinate systems and detecting how map projections and vertical coordinate systems interact, the users can easily ensure spatial precision and minimize distortion.

The concepts of GIS mapping basics, spatial reference systems, and geodesy form a technical and scientific basis for the representation on a flat map of the irregular form of the Earth.

However, when properly applied, the use of these concepts enables a GIS specialist to use an appropriate map projection, ensure the preservation of data integrity, and produce credible and meaningful maps.