#1

#2

#3

#4

#5#6The “Identify” tool links the

Catalog of Federal Domestic Assistance (CFDA) programs to the focus areas, which provide information about potential funding opportunities for the next phase of the project.

Distance to Roads: HIGHOwnership: NON-FEDERALNLCD: NATURALNDVI: HIGH

Essential Attributes and Data

Belief Network

Stories

Focus Areas

Data were collected from each essential attribute to represent the values of each SENRLG agency. Datasets selected for the Albemarle-Pamlico region included Land cover, habitat, longleaf pine, environmental justice and historic places, to name a few.

SENRLG used a belief network to apply probabilistic map algebra to the essential attribute data. Each node of the network represented criteria, which were queried then used to determine areas in the Albemarle-Pamlico region that fit that criteria. These criteria were used to create “stories.”

The SENRLG “stories” described different themes and indicated which areas in the AP met the criteria.

Criteria for Natural Story

Criteria for Drinking Water StoryEnvironmental Justice: YESFirst Order Streams: YESPriority Watersheds: YESSEF: YESPublic Water Supply: YES

Criteria for Biotic Habitat StoryWaterfowl: YESSN Heritage Areas: YESSEF: YESNLCD: NATURAL

Sea Level Rise

40cm

The final focus areas were selected based on criteria for the

SENRLG “stories.” These three regions are located in Onslow and Jones County (1,2), along

the Roanoke River (3,4,5), and in Dare County (6).

Criteria for Tourism StorySEF Recreation: YESNational Register of Historic Places: YES

A Methodological Framework Focused on Integrating GIS and BBN Data for Probabilistic Map Algebra Analysis

J. D. Morgan, M. W. Hutchins, J. Fox, K. L. RogersUNC Asheville’s National Environmental Modeling and Analysis Center (NEMAC)One University Heights Asheville, NC 28804Email: {jdmorgan;mwhutchi;jfox;krogers}@unca.edu

Case Study

Framework

Bayesian Belief Networks (BBNs) provide a graphical (and automated) way to display and interact with probabilities of related event information (Pearl 1988). Integrating spatial data with BBNs, at the resolution of pixels, allows for the opportunity to perform probabilistic map algebra (Taylor 2003; Ames & Anselmo 2008). Belief maps (or probability maps) can be created by transferring the results of probabilistic map algebra back into GIS. The methodological framework presented in this paper proposes a set of structured techniques for utilizing GIS and BBNs to inform spatial decision making and analysis. The methodological framework presented in this paper proposes a set of structured techniques for integrating GIS and BBNs to inform spatial decision making based on belief about causally related datasets. The end result is the ability to produce belief maps based on exploratory analysis of BBNs. Finally, a case study is discussed to put this framework into context.

Bayes’ Theorem can be read that the probability of A (hypothesis) given B (evidence) is equal to the probability of B given A multiplied by the probability of A divided by the probability of B.

Algorithm GENERATE-GEOPIXELS(P)Input. A set P of pixels in the reference raster.Output. A list £ pixel values in row-column order.1. rows ← number of rows in P.2. for r in range[rows]3. cols ← number of columns in P4. for c in range[cols]5. do Append ri cj to £.

Algorithm GENERATE-BBN-NODE(P)Input. A set P of pixels in the reference raster.Output. A list £ classified data values in row-column order.1. rows ← number of rows in P2. for r in range[rows]3. cols ← number of columns in P4. for c in range[cols]5. val ← classified data value at ri cj6. do Append val to £.

Algorithm GENERATE-BELIEF-MAP(£)Input. A list £ of selected pixel values from the BBN.Output. A set P of pixels as a new raster dataset.1. rows ← number of rows in P2. for r in range[rows]3. cols ← number of columns in P4. for c in range[cols]5. if ri cj within £6. then add ri cj to P

Central to the framework presented in this paper is the concept of the geopixel which provides an explicit spatial context to the BBN. The geopixel is simply taxonomy for each raster cell of the prepared datasets. This taxonomy can be created by utilizing a scripting language (e.g. python) with access to the spatial and attribute data (e.g. GDAL). From the output of a raster dataset, P, we can create what we will call in this paper belief maps. These maps are resultant of the probabilistic map algebra approach and BBN exploration.

The cartographic model presented here shows the steps required to prepare both vector and raster datasets for the probabilistic map algebra format.

Prepare Data for input into BBN (GeoPixels)

BBN Exploration Generate Belief Maps

GIS BBN/GISBBN

GeoVisual Exploration

GIS

BBN’s correspond well to MacEachren’s (1995) presentation of geovisualization where the user is not presented with a single passive static view, but rather an active process where map data, imbued within the BBN, goes beyond simple information communication to that of an enabler of knowledge construction.

Case DataBBN

P(E) P(S)

P(T|E,S)

Elevation Temp SeasonHi Cold Winter

Low Mild WinterMedium Mild Spring

Low Hot SummerHi Cold SummerHi Mild Summer

Low Mild WinterMedium Mild Spring

Low Hot SummerHi Cold Summer

P(A|B)=P(B|A) × P(A)/P(B)

The methodological framework presented in this paper builds on previous work considering GIS/BBN integration by Walker et al. (2004). Unique to this paper is a focus on the raster based technique of map algebra, or more specifically probabilistic map-algebra as described in Taylor (2003) and Ames and Anselmo (2008). We identify four broad methodological steps which move us through the probabilistic map algebra framework. Each step proposes techniques, iterative in nature, which are illustrated in the subsequent case study.

Framework

Integrating GIS and BBNs

Exploratory Analysis with BBNs

Geopixels and Belief Maps

Ames, DP & Anselmo, A., 2008. Bayesian Network Integration with GIS, in: Shekhar,S., Xiong, H. (Eds.), Encyclopedia of GIS, Springer, New York, pp. 39-45.

MacEachren, A.M., (1995). How Maps Work: Representation, Visualization and Design. Guilford Press, New York, London, 513 pp.

Pearl, J. (1988). Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, San Mateo.

Taylor, K.J. (2003) Bayesian Belief Networks: A Conceptual Approach to Assessing Risk to Habitat. Utah State University, Logan, Utah, USA.

References

Introduction