Lecture 1 Geospatial Representation and GIS Data Modeling

Review of Introductory GIS Concepts and Components

• The Six Components of GIS: A Geographic Information System (GIS) is defined broadly and includes six core components that work collaboratively for decision-making:

  • People: Individuals who manage the system and develop solutions to real-world problems.

  • Software: The programs used to store, analyze, and display geographic information.

  • Hardware: The physical computer equipment.

  • Data: The geographic information and identifying attributes that are stored in the system.

  • Procedures: The methods and rules used to operate the GIS.

  • Network: An essential component located in the middle that connects all other blocks together to facilitate collaboration.

• Distinction from Other Media: In the context of the broader definition of GIS, physical books are not considered a standard component, although they may be related to the knowledge base surrounding the field.

Tobler's First Law and Spatial Analysis

• Definition: Tobler's First Law of Geography states that "near things are more similar than far things."

• Theoretical Significance: This law is considered a fundamental theory in geography.

• Impact on Spatial Statistics: It highlights a specific problem with geographic data: spatial dependence.

  • Traditional statistics often assume that data points are independent.

  • Spatial data frequently violates the basic assumption of independence because points close to each other tend to share characteristics.

  • Specific spatial statistical technologies must be employed to deal with these spatial relationships and dependencies.

The Nature of GIS Questions and Spatial Data

• Identifying GIS-Specific Questions: GIS is uniquely suited to answer questions that contain a "where" or spatial component.

  • Non-spatial questions examples: "What is the price of ice cream?" (General data), "How old is that tree?" (Single attribute), or "What is the age structure of a population of Sega antelope?" (Statistical distribution).

  • Spatial question example: "Where are the best koala habitats?"

• Comparison with Traditional Databases: Traditional database software, such as Excel or SPSS (Statistical Package for the Social Sciences), typically manages data in table formats. GIS is required when the analysis involves a location component that necessitates spatial analysis software and tools.

Geographical Representation and the Abstraction of Reality

• The Core Problem: The real world is an infinitely complex place. A computer model (GIS) cannot represent all of this complexity and must use abstraction to store data.

• Perspective of Abstraction: There are two fundamental perspectives in GIS regarding how reality is digitally represented:

  1. The Data Model: How the discrete or continuous features are structured.

  2. The Coordinate System: How location is mathematically stored.

• The Abstraction Process: Researchers and data scientists must decide on the level of detail to capture based on resources, time, computational power, and storage capacity. Data storage (data farms) is not unlimited and incurs costs.

• Illustration of Complexity (The Power of 10):

  • Macro Scale: Starting from outer space, moving to the solar system, and then the Earth.

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  • Human Scale: Zooming into a lab or a specific landscape (e.g., $100\,m$ or $10\,m$) where one might track a single leaf.

  • Micro/Nano Scale: Moving into the world of cells and then further to the nanometer level ($100\,nm$, $10\,nm$, $1\,nm$) to see the tiniest structures of the world.

Scales of Measurement and Variable Types

• The Abstract Number System Properties: Real numbers have four specific properties that variables may or may not match:

  1. Identity: Each number has a unique meaning (e.g., $1$ is different from $2$).

  2. Magnitude: Numbers have an inherent order (bigger or smaller).

  3. Interval: The distance between numbers is equal (e.g., the difference between $1$ and $2$ is the same as the difference between $2$ and $3$).

  4. True Zero: The value $0$ means nothing or the absence of the variable.

• The Four Scales of Measurement:

  • Nominal Data: The lowest level. Only possesses the property of identity. Used for categories like Gender (where female might be coded as $1$ and male as $2$, but $2$ is not "greater" than $1$), City names (Brisbane, Melbourne, Perth), or Soil types. You cannot perform mathematical operations on nominal data.

  • Ordinal Data: Possesses identity and magnitude (order). Used for rankings or levels where the distance between levels is not equal. Examples include educational attainment (Bachelor's degree vs. high school) or awards in a competition ($1st$, $2nd$, and $3rd$ place).

  • Interval Data: Possesses identity, magnitude, and equal intervals, but lacks a true zero.

    • Temperature Example: $0$ degrees Celsius or Fahrenheit does not mean there is "no temperature"; it is an arbitrary point.

    • Time Example: $00:00$ in a $24$-hour format is a human-defined starting point.

  • Ratio Data: The highest level, possessing all four properties, including a true zero. Examples include Volume (an empty glass has no volume) or Density.

• Categorization for GIS Software:

  • Categorical Data: Includes Nominal and Ordinal data (discrete).

  • Numerical/Score Data: Includes Interval and Ratio data (continuous). Knowing these types is essential for maintaining the integrity of the database system and ensuring correct operations (e.g., you cannot calculate an average for nominal gender data).

The GIS Data Modeling Process

• Loop of Abstraction:

  1. Real World: Observation of patterns (e.g., higher population density in one area vs. another).

  2. Conceptual Model: Human-oriented brainstorm to identify features (e.g., water bodies, tree cover) and how they connect.

  3. Logical Model: Detailed diagrams (Analyst/Diagram) showing entities, attributes, and relationships.

  4. Physical Model: The actual coding into the GIS as tables, columns, and numbers.

• Operational Principles: GIS models allow geographic features to be digitally represented, stored, and manipulated to address real-world problems. The organizing principle of these models is the geographic location.

Vector Data Model

• Definition: A model that represents discrete objects using points, lines, and polygons.

• Components:

  • Points (Nodes): Represented by an identity number and a single pair of coordinates. Used for features like trees, poles, airports, or cities (depending on scale).

  • Lines: A series of connected points (nodes). Used for streams, streets, or sewage systems.

  • Polygons: A closed area where the first point and the last point are the same coordinates. GIS software enforces this closure in polygon layers. Used for land parcels, countries, or forests.

• Attribute Tables: Every vector feature is associated with a table that stores its ID, location, and non-spatial information (e.g., the address or owner of a land parcel).

Topology and Geometric Relationships

• Definition: Topology refers to geometric characteristics that do not change under transformation (bending or stretching the map). It defines relative relationships rather than absolute coordinates.

• Three Elements of Topology:

  1. Adjacency: Shared boundaries (e.g., Polygon A is to the left of Polygon B).

  2. Containment: Features located inside others (e.g., a specific point P is within a building polygon).

  3. Connectivity: How lines and road segments intersect and connect.

• Importance: Topology is critical for advanced spatial analysis like network analysis (navigation, safe routes to school). It allows software to detect and fix digitizing errors (like "slivers" or gaps between polygons).

• Map Example: A map of a "donut" and a "mark" (distorted shape) can have the same topology if the relative relationship (a hole in the middle) remains constant.

Raster Data Model

• Definition: A simpler model consisting of a grid of cells (or squares) where each cell contains a value representing the attribute of that location.

• Location Recording: Unlike vector data, which records every point, raster data only needs the coordinates of one corner (usually the upper-left cell in ArcGIS Pro) and the cell size. The software calculates the rest.

• Types of Raster Layers:

  1. Base Layer: Aerial photos or satellite imagery showing the actual ground.

  2. Semantic Layer: Categorical data represented by numbers (e.g., Land Use types $1, 2, 3$).

  3. Surface Layer: Continuous data like elevation (DEM), rainfall volume, or wind speed.

• Data Compression (Run-Length Encoding):

  • To save space, the computer can record data by "runs." Instead of recording "$1, 1, 1, 1, 1$" separately, it records that there are five "$1s$."

  • This is effective for categorical data with many identical neighboring cells. A full matrix might take $100\,bytes$, while encoded data might take less than half.

Data Conversion and Comparison

• The Motto: "Raster is Faster, but Vector is Corrector."

  • Raster: Better for computational efficiency and continuous data.

  • Vector: More accurate for recording precise boundaries and objects.

• Conversion Methods (Vector to Raster):

  • Centre of Cell (Centroid): The cell is assigned the value found at the exact center point of the grid square.

  • Maximum Area/Majority: The cell is assigned the value that covers the majority of its area.

• Impact of Cell Size (Resolution): Choosing a different cell size (e.g., $100\,m \times 100\,m$ vs. $50\,m \times 50\,m$) significantly impacts the accuracy and the calculated area of the features.

Georeferencing and Coordinate Systems

• Georeferencing: Identifying where geographic features are on the Earth's surface. Systems include unique coordinates, address systems, place names, and postcodes.

• Geographic Coordinate System (GCS):

  • References unique points on a 3D spherical or ellipsoidal Earth.

  • Measured in Longitude ($-180$ to $+180$ degrees) and Latitude ($-90$ to $+90$ degrees).

  • Prime Meridian: Zero longitude, passing through Greenwich, London.

  • Datum: A mathematical framework (like $WGS\,84$) that represents the Earth's irregular shape (the Geoid).

• Projected Coordinate System (PCS):

  • Transforms the 3D curved Earth into a flat 2D map.

  • Distortion: Projection always causes distortion in distance, shape, area, or direction.

  • Conformal Projections: Preserve angles and shapes (e.g., Mercator, Lambert Conformal Conic). These are good for navigation.

  • Equal Area Projections: Preserve the relative size of regions.

  • Universal Transverse Mercator (UTM): A specific conformal projection system that divides the world into $60$ zones. Each zone has a central meridian.

  • Regional Context: The study area (Brisbane/Saint Lucia) is located in UTM Zone $56$.

Questions & Discussion

• Q: Would mapping urban density be better as continuous or discrete?

  • A: Density is calculated based on an area (like SA1 or LGA). While the underlying census units might be polygons, density is often represented as a continuous surface because it is ratio data that varies across the landscape.

• Q: Under what circumstances would you transform or bend a map?

  • A: Transformation occurs when moving from the 3D Earth to a flat display. While the coordinates change, the topological relationship (adjacency/connectivity) should remain constant. This is also relevant when changing the datum or fixing spatial errors in the data.

• Q: Why do points in some datasets (like road accidents) sometimes appear in the river?

  • A: This is a projection error. If different layers use inconsistent projection systems, the data will not align correctly. In ArcGIS Pro, the first layer added defines the project's projection, but users must ensure all layers are consistent to avoid data being misplaced in "nowhere."