1. Types of Spatial Analysis
We will consider six categories of spatial analyses:
Queries
Measurements
Transformations
Descriptive summaries
Optimization
Hypothesis testing

2. 4. Descriptive summaries

3. Point Pattern Analysis
There are many ways to quantify the dispersion of points in region.
Clustered
Regular
Random

4. Landscape Pattern Analysis
There is a whole field devoted to quantifying the pattern of landcover polygons in a landscape: Landscape Ecology.

5. Landscape Ecology
According to the International Association for Landscape Ecology:
Landscape Ecology is the study of spatial variation in landscapes at a variety of scales. It includes the biophysical and societal causes and consequences of landscape heterogeneity.
Landscape Ecology is concerned with such questions as:
How have humans changed the landscape?
How has landcover composition changed?
How has landcover pattern changed?
How fragmented has the landscape become?
Are large tracts of forest left? And in what spatial pattern?
Are there connecting corridors of natural areas between large patches?
What are the consequences of (primarily human-induced) changes in the landscape?
How have changes in landcover composition and pattern affected biodiversity?
How have changes in landcover composition and pattern affected populations, society and the economy?

6. Landcover Pattern Metrics
Landcover pattern metrics describe the pattern of landcover in a landscape.
Landcover fragmentation
Average patch size
Distance between patches of the same landcover
Patch shape
Long and thin vs. round or square
Jagged edges vs. clean edges

7. Core Natural Areas: Gauja National Park, Latvia

8. Preservation of Nature
Largest forest patch – follows Gauja River
Park’s goal is to increase the protection of core areas.

9. Nature & Biodiversity
In Latvia, the Black Stork (Ciconia nigre) and Lesser Spotted Eagle (Aquila pomarina) require large forest tracts and generally nest at least 250 meters from the forest edge.
Core forested area is defined here as forest that is greater than 250 meters from its patch edge.
After the early post-independence forest cutting took place (by 1994), marked increases in core areas of forest indicated that Park’s policies, designed to protect biodiversity and core nature areas, were successful.

10. Development in GNP
9 yr. period
5 yr. period
3 yr. period
Exponential development occurring in market economy after privatization.

11. Latvian Cultural Landscape
An icon of national pride
Latvia’s cultural landscape is “characterized not by rural villages, but by a dispersed rural settlement pattern of family farmsteads made up of small clusters of distinct buildings… surrounded by a matrix of small, well-maintained forest patches, agricultural fields and meadows, with churches and pubs interspersed throughout the landscape” (Bunkše, 2000).

12. Latvian Cultural Landscape
Land restitution led to a resurgence of the Latvian cultural landscape, with a matrix of small patches of forest, agricultural fields and meadows by the late 1990’s.
The current lack of economic sustainability of family farming in Latvia has led to plot consolidation for corporate agriculture and corporate tree farming.

13. Deforestation in the Amazon
1975
To the left are three images of part of the state of Rondonia in the Brazilian Amazon basin, collected in 1975, 1986, and 1992
Note the increasing fragmentation of the natural habitat as a result of settlement (forest canopy appears deep red, locations of development appear cyan blue)
Such fragmentation can adversely affect the success of wildlife populations
Fragmentation statistics (a subset of pattern metrics) quantify the amount and pattern of fragmentation in a landscape.
1986
1992

14. 5. Optimization
Spatial analysis can be used to solve many problems of design, such as “where is the best place to build a new x”
The decision of where to build a new facility is often approached by minimizing travel time from a certain catchment or service area,
e.g. In an area where the nearest hospital is an unacceptably long drive away, we may want to locate a hospital there.
but where should we put it to best serve the residents in the area and minimize overall travel time for the area?
We can do this using Euclidean distance.
Better to use travel time.

15. Location-Allocation Problems
This class of problems in known as location-allocation problems, and solving them usually involves choosing locations for services, and allocating demand to them to achieve specified goals
Those goals might include:
minimizing total distance traveled
minimizing the largest distance traveled by any customer
maximizing profits
minimizing a combination of travel distance and facility operating cost

16. Routing Problems
Another type of optimization problems is known as routing problems:
Suppose we have a set of locations we need to visit, and we want to find the optimum route to travel to minimize travel time.
The ‘traveling salesman problem’ is just this sort of problem:
Find the shortest tour from an origin, through a set of destinations, that returns back to the origin.

17. Routing service technicians for Schindler Elevator: Every day this company’s service crews must visit a different set of locations in Los Angeles.
GIS is used to partition the day’s workload among the crews and trucks (color coding) and to optimize the route to minimize time and cost.

18. Optimum Paths
Another sort of optimization problem is encountered when we have a known origin and destination, and we need to find the best route between the two, given data that describes the ‘cost’ of taking various paths
The goal is to find the best path across a continuous cost surface
The goal is to minimize total cost
The cost may combine construction, environmental impact, land acquisition, and operating costs
This is used to locate highways, power lines, pipelines
It requires a raster representation
(Finding the optimal route between two locations on a vector road network is a related sort of problem)

19. Least-Cost Path Example
The figure to the left shows the solution of a least-cost path problem:
The white line represents the optimum solution, or path of least total cost, across a friction surface represented as a raster layer
The area is dominated by a mountain range, and cost in this example is determined by elevation and slope
The best route uses a narrow pass through the range. The blue line results from solving the same problem using a coarser raster

20. 6. Hypothesis Testing
Hypothesis testing is a recognized branch of statistics.
We collect data and test relationships between variables, such as:
Respiratory disease and distance from polluting factories.
Distance from power lines and brain cancer incidence.
Do more wildlife survive when greater than a mile from regular human activity?
Do the restaurants of a chain located in higher income areas bring in more revenue?
What combination of soil type, climatic conditions, and fertilizer use generally produce the highest crop yield?