1. Nicholas A. Procopio, Ph.D, GISP
Environmental GIS
Nicholas A. Procopio, Ph.D, GISP

2. Governing Principles The representations we build in GIS are unique;
Our representations of them are necessarily selective of reality and therefore incomplete;
Considers the world as either continuously varying fields or as empty space littered with crisp and well defined objects

3. Governing Principles
We will address three principles related to the nature of spatial variation:
that proximity effects are key to understanding spatial variation, and to joining up incomplete representations of unique places;
that issues of geographic scale and level of detail are key to building appropriate representations of the world;
that different measures of the world co-vary, and understanding the nature of covariation can help us to predict…….

4. and make the best decisions!!!!

5. Spatial Distribution
Some features vary evenly across the landscape (water tables, soils, species communities)
while others exhibit extreme irregularity (species pops).
….and there’s usually a related force.

6. Spatial Distribution
Spatial heterogeneity is the tendency of geographic places and regions to be different from each other.
Measures of spatial and temporal autocorrelation are scale dependent

7. Spatial Autocorrelation
….attempts to measure similarities in location of objects and a particular attribute simultaneously.
If features are similar in location and attribute, then the pattern is said to show positive spatial autocorrelation, and vice versa.
Zero autocorrelation exists when attributes are independent of location

8. Field arrangements of blue and white cells exhibiting
Spatial Distribution
Field arrangements of blue and white cells exhibiting
extreme negative spatial autocorrelation
(B) a dispersed arrangement
(C) spatial independence
(D) spatial clustering
(E) extreme positive spatial autocorrelation
(Source: Goodchild 1986 CATMOG, GeoBooks, Norwich)

9. Spatial Autocorrelation
Usually want to eliminate, or at least greatly minimize autocorrelation in order to maintain independence.
the existence of spatial autocorrelation fundamentally undermines the inferential framework and invalidates the process of generalizing from samples to populations.
But sometimes it is of interest…

10. Groundwater well contamination?????

11. Sample Design
The attempt to represent the complexity of the real world requires us to sample events and occurrences from the universe of all possible elements.
Not always practical!
Must employ some comparable sample design that best represents the desired elements.

12. Sample Design
Classical statistics often emphasizes the importance of randomness in sound sample design.
Remember, the existence of spatial autocorrelation (dependence) undermines statistical theory.

13. Sample Design
Random sampling enables the use of the distribution of samples to predict the likely distribution of the overall population.
Systematic sampling aims to ensure greater evenness of coverage across the sample area.

14. Types of sampling designs include:
simple random
spatially systematic
stratified random
Ensures evenness of coverage
periodic random changes in the sampling grid
Minimum spacing requirements?
Clustered
If population/community is naturally clustered.
sampling along transects or contours

15. Spatial sample designs
simple random sampling
(B) stratified sampling
(C) stratified random sampling;
(D) stratified sampling with random variation in grid spacing
(E) clustered sampling
(F) transect sampling
(G) contour sampling

16. An example of physical terrain in which differential sampling would be advisable in order to construct a representation of elevation
(Source: M. Langford, University of Glamorgan)

17. Distance decay
The effect of distance and the need to make an informed judgment about an appropriate interpolation function and how to weight adjacent observations requires us to model the real world.
i.e. The polluting effect of a chemical spill (the plume) decreases in a predictable fashion with respect to distance from the source.
With these equations (models), the effects of distance are presumed to be regular, continuous, and isotropic (uniform in every direction)

18. Distance decay The attenuating effect of distance
linear distance decay,
(B) negative power distance decay,
(C) negative exponential distance decay.

19. How long until the well is contaminated??

20. Map showing 10-, 20-, and 30-minute travel times to a doctor’s surgery in South London.
(Courtesy Daniel Lewis; travel time data © Transport for London; map data courtesy Open Streetmap

21. The creation of isopleth maps
point attribute values
(B) user-defined classes
(C) interpolation of class boundary between points
(D) addition and labeling of other class boundaries
(E) use of hue to enhance perception of trends
(After Kraak and Ormeling 2003: 134)

27. Bathymetry of a coastal plain pond

28. Choropleth maps a spatially extensive variable, total population
(B) a related but spatially intensive variable, population density
Many cartographers would argue that (A) is misleading and that spatially extensive variables should always be converted to spatially intensive form (as densities, ratios, or proportions) before being displayed as choropleth maps.
(Courtesy Daryl Lloyd)