Geospatial Data Models and Coordinate Systems Explained

Posted on Dec 26, 2025 in Mathematics

Geospatial Data Models and Acquisition

The Spaghetti Data Model lacks essential spatial relationships such as connectivity (chaining), adjacency (left/right), or containment (e.g., Polygon X within Polygon Y).

Elements of GIScience: Geospatial Data

Geospatial analysis relies on two primary data types:

  • Vector Data: Represents discrete objects with distinct boundaries.
  • Raster Data: Represents continuous fields where every location has a value.

Data Acquisition Methods

Data acquisition involves obtaining geospatial information through various means. Metadata (data about data) is crucial, especially for public use data.

  • Digitizing new data from existing or historical sources (paper maps, aerial photography, satellite images).
  • Collecting GPS data.
  • Conducting survey data (asking people).
  • Geocoding street addresses (converting XY coordinates to tabular data).

Data Management

Data management transforms raw data into a workable format. This includes:

  • Creating new fields.
  • Adding geometry fields to calculate parameters (e.g., computing population density within a polygon: people per square kilometer).

Data Display and Visualization

Maps are concise, visual tools that display information and can reveal relationships between phenomena and populations. While seemingly simple, maps can be deceptive. Good maps adhere to cartographic principles.

Data Exploration

Data exploration involves visualizing, manipulating, and querying data using maps, tables, and graphs to examine relationships between geographic features. Techniques include:

  • Map-based data classification, aggregation, and comparison.
  • Attribute queries based on attribute tables (exploratory analysis).

Steps of Abstraction: Modeling the Earth

GIScience simplifies the Earth’s complex shape for practical modeling.

Earth Models

  1. Earth: A very irregular, lumpy shape.
  2. Geoid: A smoother mathematical approximation of the Earth, representing the average sea level without winds or tides. It accounts for some surface distortions but ignores topography.
  3. Oblate Spheroid/Ellipsoid: A simpler, nearly spherical model used to represent the Geoid. This model forms the foundation for reference systems defining absolute positioning.

Distortions Ignored in Simplification

The transition to simpler models ignores several factors:

  • Topography (elevation).
  • Gravity differentials (caused by crust thickness variations, creating “sinks” and “floats”).
  • Centrifugal force (Earth is wider at the Equator due to spinning).

Ellipsoid Characteristics

The oblate spheroid/ellipsoid is a good approximation of Earth’s shape, wider at the equator due to centrifugal force. It is defined by its semi-major and semi-minor axes.

Datums and Reference Systems

Datums are reference systems used to fit the spheroid to the Geoid, making calculations easier by assuming a smooth mathematical surface and ignoring localized, unpredictable differences.

  • Global Datums: Use the Earth’s center as the reference point; fit well globally.
  • Local Datums: Use a single point on the Geoid’s surface as the reference point; fit a specific region very well (better for city-scale areas).

Coordinate Reference Systems (CRS)

CRSs take 3D datums (simplified Earth models) and establish absolute positioning on the Earth’s surface. They are coordinate-based systems applicable at any scale.

Geographic Coordinate Systems (GCS)

GCSs identify locations on the curved surface of the Earth using an ellipsoid, a datum, and a prime meridian (the line connecting the North and South Poles).

  • Relative Position: Reference location by what is nearby (e.g., the last house on the left).
  • Absolute Position: A precise set of coordinates pinpointing an exact location.

The reality progression is: Earth $\rightarrow$ Geoid $\rightarrow$ Oblate Spheroid $\rightarrow$ Datums $\rightarrow$ CRS.

Projected Coordinate Systems (PCS)

PCSs create a flat, 2D representation of the Earth, often by dividing it into strips, prioritizing certain characteristics while losing complexity (e.g., Web Mercator).

Module 2: Part 2 – Latitude, Longitude, and Projections

Latitude and Longitude

Degrees of latitude and longitude are defined by their angle from the Earth’s center relative to the equator (latitude) or prime meridian (longitude).

  • Parallels: Run parallel to the equator.
  • Meridians: Not parallels.
  • Latitude Range: -90 to +90 degrees.
  • Longitude Range: -180 to +180 degrees.

One degree of longitude varies in length depending on the latitude.

Coordinate Conversion

Conversion between DMS (Degrees, Minutes, Seconds) and DD (Decimal Degrees):

1 degree = 60 minutes; 1 minute = 60 seconds (1 degree = 3600 seconds).

Decimal Degrees = Degrees + (Minutes/60) + (Seconds/3600). Use negative values for West or South.

Map Projections (3D to 2D)

Features are projected onto different “flattenable surfaces.” Most projections use a mathematical formula.

Projection Methods

These methods describe how the surface touches the globe:

  • Planar Projections: Touch the surface at a single point; simplest but often most distorted.
  • Conical Projections: Touch the Earth along one or two continuous lines (like placing a cone over a sphere).
  • Cylindrical Projections: Touch along a specific line or two but are open at the top and bottom.

Tangent: Projection touches the surface at one point or line. Secant: Projection touches along two lines.

Projection Properties

Projections can preserve one property at the expense of others:

  • Preserve Shape (Conformal Projection): Local angles and shapes are maintained, but area/size is distorted (e.g., areas near the poles appear larger).
  • Preserve Area (Equal Area Projection): Area is maintained, but shapes may become pinched. Good for calculating population density.
  • Preserve Distance (Equidistant Projection): Proximity of features to a central point reflects reality, but other properties are distorted.
  • Preserve Direction (True Direction Projections): Maintains accurate direction from a central point.

Compromise Projections: Balance different types of distortion.

Azimuthal Equidistant Projection

This projection accurately preserves all distances and directions from a central point, making it useful for flight route planning.

Assessing Distortion: Tissot’s Indicatrix

Tissot’s Indicatrix is a mathematical tool visualizing distortions caused by map projections. It analyzes how shape, area, distance, and direction are affected. When a globe is projected, distortions of circles reflect projection errors, increasing away from the standard point or line.

Universal Transverse Mercator (UTM)

UTM divides the Earth into 6-degree wide strips (80°N to 80°S). It is a special type of conformal projection, minimizing distortion within zones, making it suitable for small areas.

Projection Selection

The choice of projection depends on the investigation’s purpose:

  • Navigational Maps: Mercator (conformal).
  • Thematic Maps (densities/distributions): Equal Area projections.

Gerardus Mercator

Flemish geographer who created the eponymous cylindrical map projection in 1569. It preserves landmass shapes (conformal) and places North up. His maps were crucial for navigation during the Age of Discovery but also served colonial expansion.

Map Scale

The relationship between map distance and real-world distance (e.g., 1 cm on map = 1 km on Earth). Represented graphically, verbally, or as a representative fraction (RF).

  • Small Scale (e.g., 1:10,000,000): Shows large areas with less detail; requires generalization (simplifying details for readability).
  • Large Scale (e.g., 1:1,000): Shows smaller areas with high detail.

Module 3: Data Representation

Data Definition

Data consists of facts and statistics collected for reference or analysis, conveying quantity, quality, or meaning.

Vector vs. Raster Data

Discrete Objects (Vectors)

Objects with distinct boundaries, countable, and exactly measurable.

  • Example: A lightning strike (singular event at a specific place).
  • Vectors:
    • Points: X,Y coordinate pair; zero-dimensional (no length, width, or area).
    • Lines: A set of connected points (vertices); one-dimensional (only length).
    • Polygons: Three or more connected vertices forming an enclosed shape; two-dimensional (have length and width, thus area).
  • Vector Topology: A data structure indicating connections between nodes and entities.

Continuous Fields (Rasters)

Fields with no distinct boundaries; every location has a value and are infinitely divisible.

  • Example: Strike frequency (everywhere has a value, even if it is 0).
  • Arbitrary: Something chosen without a fixed rule, based on human decision rather than absolute truth (e.g., defining a coastline boundary at a small scale).
  • Rasters: A rectangular grid of equally sized cells. Multiple attributes require multiple bands (e.g., Red, Green, Blue for color photos).

Raster Properties

  • Resolution (Cell Size): The smallest resolvable feature.
  • Extent (Domain): Determined by the number of rows/columns and cell size (e.g., 5×5 cells at 1m size covers 25 m²). More cells mean more detail.

Mixed Cell Problem

When a cell contains multiple phenomena, resolution must be assigned using methods like:

  • Winner Take All.
  • Cell Center (what is at the center).
  • Containment (if the value of interest is present).