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

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

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…….

and make the best decisions!!!!

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

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

Spatial Autocorrelation ….attempts to measure similarities in location of objects and a particular attribute simultaneously. ….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. 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 Zero autocorrelation exists when attributes are independent of location

Field arrangements of blue and white cells exhibiting (A)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) Spatial Distribution

Usually want to eliminate, or at least greatly minimize autocorrelation in order to maintain independence. 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.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… But sometimes it is of interest… Spatial Autocorrelation

Groundwater well contamination?????

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. 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!Not always practical! Must employ some comparable sample design that best represents the desired elements. Must employ some comparable sample design that best represents the desired elements.

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

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

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

Spatial sample designs (A)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

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)

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.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) With these equations (models), the effects of distance are presumed to be regular, continuous, and isotropic (uniform in every direction)

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

How long until the well is contaminated??

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

(A)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) The creation of isopleth maps

Bathymetry of a coastal plain pond

Choropleth maps (A)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)