Data Models, Coordinates, and Geometries

HES 505 Fall 2025: Session 7

Matt Williamson

Today’s Plan

  1. Ways to view the world

  2. What makes data (geo)spatial?

  3. Geometries, support, and spatial messiness

How do you view the world?

…As a Series of Objects?

  • The world is a series of entities located in space.

  • Usually distinguishable, discrete, and bounded

  • Some spaces can hold multiple entities, others are empty

  • Objects are digital representations of entities

…As a Continuous Field

  • The earth is a single entity with properties that vary continuously through space

  • Spatial continuity: Every cell has a value (including “no data” or “not here”)

  • Self-definition: the values define the field

  • Space is tessellated: cells are mutually exclusive

Operationalizing views of space

What is a data model?

  • Data: a collection of discrete values that describe phenomena

  • Your brain stores millions of pieces of data

  • Computers are not your brain

    • Need to organize data systematically
    • Be able to display and access efficiently
    • Need to be able to store and access repeatedly

  • Data models solve this problem

2 Types of Spatial Data Models

  • Raster: grid-cell tessellation of an area. Each raster describes the value of a single phenomenon. More next week…

  • Vector: (many) attributes associated with locations defined by coordinates

The Vector Data Model

  • Vertices (i.e., discrete x-y locations) define the shape of the vector

  • The organization of those vertices define the shape of the vector

  • General types: points, lines, polygons

Image Source: Colin Williams (NEON)

Image Source: QGIS User’s manual

Vectors in Action

  • Useful for locations with discrete, well-defined boundaries

  • Very precise (not necessarily accurate)

Image Source: QGIS User’s manual

The Raster Data Model

  • Raster data represent spatially continuous phenomena (NA is possible)

  • Depict the alignment of data on a regular lattice (often a square)

  • Geometry is implicit; the spatial extent and number of rows and columns define the cell size

Types of Raster Data

  • Regular: constant cell size; axes aligned with Easting and Northing

  • Rotated: constant cell size; axes not aligned with Easting and Northing

  • Sheared: constant cell size; axes not parallel

  • Rectilinear: cell size varies along a dimension

  • Curvilinear: cell size and orientation dependent on the other dimension

Types of Raster Data

  • Continuous: numeric data representing a measurement (e.g., elevation, precipitation)

  • Categorical: integer data representing factors (e.g., land use, land cover)

What makes data (geo)spatial?

Location vs. Place

  • Place: an area having unique physical and human characteristics interconnected with other places

  • Location: the actual position on the earth’s surface

  • Sense of Place: the emotions someone attaches to an area based on experiences

  • Place is location plus meaning

  • nominal: (potentially contested) place names

  • absolute: the physical location on the earth’s surface

Describing Absolute Locations

  • Coordinates: 2 or more measurements that specify location relative to a reference system

  • Cartesian coordinate system

  • origin (O) = the point at which both measurement systems intersect

  • Adaptable to multiple dimensions (e.g. z for altitude)

Cartesian Coordinate System

Describing location: extent

  • How much of the world does the data cover?

  • For rasters, these are the corners of the lattice

  • For vectors, we call this the bounding box

Describing location: resolution

  • Resolution: the accuracy that the location and shape of a map’s features can be depicted

  • Minimum Mapping Unit: The minimum size and dimensions that can be reliably represented at a given map scale.

  • Map scale vs. scale of analysis

Geometries and Support

Geometries

  • Vectors aggregate the locations of a feature into a geometry
  • Most vector operations require simple, valid geometries

Image Source: Colin Williams (NEON)

Valid Geometries

  • A linestring is simple if it does not intersect
  • Valid polygons
  • Are closed (i.e., the last vertex equals the first)
  • Have holes (inner rings) that inside the the exterior boundary
  • Have holes that touch the exterior at no more than one vertex (they don’t extend across a line) - For multipolygons, adjacent polygons touch only at points
  • Do not repeat their own path

Empty Geometries

  • Empty geometries arise when an operation produces NULL outcomes (like looking for the intersection between two non-intersecting polygons)

  • sf allows empty geometries to make sure that information about the data type is retained

  • Similar to a data.frame with no rows or a list with NULL values

  • Most vector operations require simple, valid geometries

Support

Support is the area to which an attribute applies.

For vectors, the attribute-geometry-relationship can be:

  • constant = applies to every point in the geometry (lines and polygons are just lots of points)

  • identity = a value unique to a geometry

  • aggregate = a single value that integrates data across the geometry

Support

Support is the area to which an attribute applies.

For rasters:

  • point = attribute refers to the cell center

  • cell = attribute refers to an area similar to the pixel

Take Homes

  • Data models translate views of space into analytic tools

  • Spatial data requires location

  • We store location in geometries

  • We assign attributes to location based on support