Chapter 13

Spatial Analysis

Data is just the raw material. Analysis is the refined product. Learn how to query, overlay, and model the world to answer "What if?"

At a Glance

Prereqs: Ch 01-12 Time: 40 min read + Lab Deliverable: Suitability Model

Learning Outcomes

  • Perform attribute (SQL) and spatial queries.
  • Execute vector overlay operations (Intersect, Union, Clip).
  • Apply Raster Map Algebra for site suitability.
  • Model network accessibility using service areas and routing.
  • Identify spatial analysis pitfalls like MAUP and Ecological Fallacy.

Key Terms

Buffer, Intersect, Union, SQL, Map Algebra, Euclidean Distance, Boolean Logic, Network Analysis, Impedance, MAUP, Ecological Fallacy, Placemaking

The First Law

Tobler's Law of Geography

In 1970, Waldo Tobler coined the single most important rule in spatial analysis. It is the "Gravity" of our field:

"Everything is related to everything else, but near things are more related than distant things."
Why this matters:

If this law wasn't true, we couldn't make maps.
If temperature didn't follow this law, a thermometer reading at the airport would tell you nothing about the temperature at your house 5 miles away. Because spatial autocorrelation exists (near things are similar), we can interpolate surfaces, predict traffic, and model disease spread. It is the foundation of all spatial statistics.

The Analysis Workflow

Analysis usually falls into four categories. Before clicking a tool, identify which category your question belongs to:

🔍 Selection

Finding "Where is it?" (Query)

📏 Measurement

Calculating Distance, Area, & Stats

🥞 Overlay

Stacking layers to find intersections

🕸️ Connectivity

Networks and Surfaces

1. Selection & Query

Attribute Query (SQL): Selecting features based on their data table.
Example: SELECT * FROM Cities WHERE Population > 1,000,000

Spatial Query: Selecting features based on location.
Example: "Select all schools within 1 mile of a hazardous waste site."

Boolean Logic: Queries often use AND, OR, and NOT.
- AND restricts results (must meet both criteria).
- OR expands results (can meet either criteria).

2. Vector Overlay Analysis

Overlay combines the geometry and attributes of two layers. It is the "cookie cutter" of GIS.

Intersect

AND (Common area only)

Union

OR (All areas combined)

Clip

Cookie Cutter (Input cut by Boundary)

Case Study: Do Bars Cause Crime?

A classic application of the Spatial Join is connecting social behaviors to location. A graduate student researcher once asked: "Does the density of alcohol licenses in a neighborhood correlate with the cost of policing that neighborhood?"

The Data Problem

She had two incompatible datasets:

  1. Alcohol Licenses (Points): A spreadsheet from the Texas government with addresses of every bar and liquor store.
  2. Crime Reports (Polygons/Points): Police data summarized by patrol districts.

You cannot simply open these in Excel and comparing them. They share no common ID. They only share Location.

The GIS Solution: Spatial Join

By performing a Point-in-Polygon join, she summed the number of alcohol licenses falling inside each police district.

The Result: A strong linear correlation ($R^2 > 0.7$). She was able to calculate a "Societal Cost" per license. This allowed policymakers to argue that alcohol permit fees should be raised to cover the specific police costs they generate. That is the power of turning where into how much.

3. Raster Map Algebra

Raster analysis often treats layers like math variables. If you have two grids, you can add them, subtract them, or find the average. This is essential for Site Suitability Modeling.

Raster Map Algebra Diagram

Figure 5.4: Basic Map Algebra operations. Notice how 'Add' sums the value of each overlapping cell.

Interactive: Suitability Studio

You are siting a new Eco-Lodge. Adjust the importance (weights) of the three factors below to see which site wins. (Note: Everything must sum to 100%).

Total Weight: 100% (Balanced)

Site A (Mountain Top)
Great View, No Road, Steep.
Site B (Valley Highway)
Bad View, Great Road, Flat.
Site C (Foothills)
Okay View, Okay Road, Moderate.

Spatial Theory: Von Thünen's Isolated State

Before GIS existed, economists were already thinking spatially. Johann Heinrich von Thünen (1783–1850) was a German landowner who developed one of the first formal models of spatial economics—explaining how distance from a market affects land use.

Von Thünen's Isolated State model showing concentric rings of land use around a central market, with modification along a river transportation corridor

Von Thünen's model: Concentric rings modified by a navigable river

The "Isolated State" Assumptions

Von Thünen imagined a perfectly isolated city-state with:

  • A single central market town
  • Uniform flat terrain (an isotropic plain)
  • Equal soil fertility everywhere
  • No roads—only horse-drawn carts radiating outward
  • Farmers who maximize profit (economic rationality)

The Concentric Ring Pattern

Under these conditions, land use arranges itself in concentric rings based on transportation cost:

  1. Ring 1 (Closest): Intensive farming—dairy, vegetables, fruits. These are perishable and heavy, so transport cost is critical.
  2. Ring 2: Forestry—wood for fuel and building is bulky and expensive to move.
  3. Ring 3: Grain crops—less perishable, can travel farther economically.
  4. Ring 4 (Farthest): Ranching/livestock—animals walk themselves to market!

🚢 The Transportation Modification

Von Thünen recognized that his idealized rings would be distorted by transportation infrastructure. A navigable river or road extending from the city would:

  • Lower transport costs along its corridor
  • Stretch the rings outward like pulling taffy—intensive uses extend farther from the city along the river
  • Create a "wedge" or "finger" of inner-ring land uses penetrating into outer zones

Modern Implication: This is why you see vegetable farms and dairies along highways and rail lines far from cities, while remote areas without good transportation remain as pasture or forest—exactly as Von Thünen predicted 200 years ago!

🗺️ Why This Matters for GIS:

Von Thünen's model is the intellectual ancestor of cost-distance analysis and accessibility modeling in GIS. When you calculate "travel time to the nearest hospital" or model urban sprawl, you're applying the same logic: distance (or travel cost) from a central point determines spatial patterns. Modern GIS simply replaces his uniform plain with real terrain, real roads, and real friction surfaces.

4. Neighborhoods & Proximity

Buffering

Creating a zone of a specific distance around a feature. Useful for regulatory zones (e.g., "No drilling within 500ft of a house").

  • Constant Buffer: Same width everywhere.
  • Variable Distance: Width based on an attribute (e.g., wider buffer for larger rivers).
  • Multi-ring Buffer: Concentric rings showing levels of influence.

Interpolation

Predicting values between known points. We use this to turn weather station points into a continuous temperature map (Isolines).

Areal Interpolation: Estimating data for one set of areas (e.g., zip codes) from another set (e.g., census tracts). This is critical when data boundaries don't align.

5. Network Analysis: The Science of Connectivity

While Euclidean Distance measures "as the crow flies," Network Analysis measures distance along a structured path—like a road, pipeline, or blood vessel. It is the study of how things move through a system.

Network Components

  • Edges: The paths (roads, pipes).
  • Nodes: The intersections or end points.
  • Impedance: The "cost" of travel (time, distance, fuel).
  • Turns: Rules about where you can go (e.g., no left turn).

Common Applications

  • Best Route: Finding the fastest way from A to B.
  • Service Area: What areas can be reached within 10 minutes?
  • Closest Facility: Which ambulance is nearest to this accident?

Interactive: Mobility Explorer

Click anywhere on the map below to generate a 15-minute walk-shed (Service Area) based on the local street network. Notice how the shape isn't a perfect circle—it follows the "grain" of the infrastructure.

Click on the map to calculate accessibility.

Spatial Solutions: The "Pixie" Mobile Pharmacy

How do you deliver healthcare when there is no hospital? A student team designed "Pixie," an automated medication dispenser for Mars, but found a critical use case on Earth: Rural Accessibility.

The Space Problem

On a 3-year Mars mission, drugs degrade due to radiation. You need an automated, AI-driven inventory system to synthesize or dispense doses without a pharmacist.

The Earth Application

"Medical Deserts": Many rural regions are hours from a CVS or hospital. A "Mobile Pixie" van could use Network Analysis to route itself to isolated communities, dispensing prescriptions like an ice cream truck for health.

GIS connection: This is a classic Location-Allocation problem. Where do you place these mobile units to minimize travel time for the maximum number of people?

Geographic Inquiry: The "Food Mile" Paradox

We often assume "Organic" and "Local" are synonyms for "Sustainable." But geography teaches us to measure, not assume. Using Network Analysis, students in Texas tracked the origin of produce to test this hypothesis.

The Experiment

They calculated the network distance (road miles) for apples, eggs, and milk at three types of stores:

  • Farmer's Markets
    ("Local")
  • Grocery Chains
    (H-E-B)
  • Natural Stores
    (Whole Foods)

The Findings:

Ironically, the "Natural" stores often had the highest food miles. Why? To stock 100% organic produce year-round, they had to source from global networks. Conventional stores stuck to regional distribution hubs.

The Gentrification Signal: By mapping the catchment areas (where customers come from), they found that conventional stores had small, local catchments. The downtown Farmer's Market, however, pulled customers from the entire city. In urban studies, the arrival of a Farmer's Market is now considered a Leading Indicator of Gentrification—signaling a demographic shift often before property values even spike.

6. Challenges in Spatial Analysis

Spatial analysis is powerful, but it's prone to unique errors that non-spatial statistics often miss. As an analyst, you must watch out for these two traps:

MAUP

Modifiable Areal Unit Problem.

The results of shared data (like density) change depending on how you draw the boundaries. If you analyze by Zip Code vs. Census Tract, you might get opposite conclusions. This is the mathematical basis for Gerrymandering.

Ecological Fallacy

The trap of aggregation.

Assuming that what is true for a large group (an entire county) must be true for every individual in that county. For example, a "wealthy" neighborhood still contains people living in poverty. GIS often hides individual variation inside polygon averages.

Deep Dive: The Gerrymandering Trap

MAUP states that results change depending on how you draw the boundaries.

Imagine a state that is 60% Blue voters and 40% Red voters.

  • Scenario A: Divide it into 5 vertical strips? Blue wins all 5.
  • Scenario B: Divide it into specific shapes? Red could win 3 of 5.

The underlying people (the data) never changed. Only the aggregation units changed.

"Is there a solution?"

NO.

It is an inherent property of aggregating spatial data. You can only declare your boundaries and defend your choice.

🛑 Critical GIS: The "Black Box" of Weights

In the Suitability Studio above, you saw how changing weights changes the "best" site. In the real world, these weights are often decided by politicians or developers, not just data. If you weight "Property Value" higher than "Community Impact," your map will suggest gentrification. Algorithms are opinions embedded in code.

Regional Decisions

Placemaking in the Hybrid Era

As remote and hybrid work become permanent, geographers are re-evaluating the "Workplace." Using the IPAT Equation (Impact = Population × Affluence × Technology), we can model the environmental impact of shifting from a central office to a distributed network.

The GIS Challenge:

Imagine you are a consultant for a large tech firm. They want to move from one central tower in Dallas to three smaller "neighborhood hubs."

Option A: Single Central Tower

  • High total commute volume.
  • Longest average distance per employee.
  • Intense environmental footprint at one node.

Option B: Distributed Neighborhood Hubs

  • Commutes shifted to walking/biking (The 15-Minute City).
  • Reduced total VMT (Vehicle Miles Traveled).
  • Requires Network Analysis to find the optimal hubs based on employee home locations.

Refining "Placemaking"

Placemaking isn't just about buildings; it's about meaningful connections. GIS helps identify where hubs should be to maximize social collision and minimize travel friction. This is the future of sustainable workplace design.

Chapter 13 Checkpoint

1. Which vector operation results in a layer containing ONLY the shared area between two inputs?

2. In a weighted suitability model, if "Slope" is weighted at 60%, what does that imply?

← Chapter 12: LiDAR Next: Chapter 14: Raster Analysis →

BoK Alignment

Topics in the UCGIS GIS&T Body of Knowledge that support this chapter.