Spatial Statistics

Spatial Statistics: GeoSpatial Information Modeling and Thematic Mapping

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  • Brings together GIS and remote sensing technologies, data collection, issues of scale, and statistical modeling and mapping
  • Demonstrates how to integrate all available geoinformation tools
  • Incorporates statistical data analysis methods
  • Provides laboratory exercises for reviewing geospatial information using ArcGIS, ArcView, ArcInfo, and other software


Geospatial information modeling and mapping has become an important tool for the investigation and management of natural resources at the landscape scale. Spatial Statistics: GeoSpatial Information Modeling and Thematic Mapping reviews the types and applications of geospatial information data, such as remote sensing, geographic information systems (GIS), and GPS as well as their integration into landscape-scale geospatial statistical models and maps.

The book explores how to extract information from remotely sensed imagery, GIS, and GPS, and how to combine this with field data—vegetation, soil, and environmental—to produce a spatial model that can be reconstructed and displayed using GIS software. Readers learn the requirements and limitations of each geospatial modeling and mapping tool. Case studies with real-life examples illustrate important applications of the models.

Topics covered in this book include:

  • An overview of the geospatial information sciences and technology and spatial statistics
  • Sampling methods and applications, including probability sampling and nonrandom sampling, and issues to consider in sampling and plot design
  • Fine and coarse scale variability
  • Spatial sampling schemes and spatial pattern
  • Linear and spatial correlation statistics, including Moran’s I, Geary’s C, cross-correlation statistics, and inverse distance weighting
  • Geospatial statistics analysis using stepwise regression, ordinary least squares (OLS), variogram, kriging, spatial auto-regression, binary classification trees, cokriging, and geospatial models for presence and absence data
  • How to use R statistical software to work on statistical analyses and case studies, and to develop a geospatial statistical model

The book includes practical examples and laboratory exercises using ArcInfo, ArcView, ArcGIS, and other popular software for geospatial modeling. It is accessible to readers from various fields, without requiring advanced knowledge of geospatial information sciences or quantitative methods.

Table of Contents

Geospatial Information Technology
Remotely Sensed Data
Instantaneous Field of View (IFOV) at Nadir (Resolution on the Ground)
The SPOT (System Probatori D’Observation de la Terre)
MODIS (Moderate Resolution Imaging Spectroradiometer)
ASTER (Advanced Spaceborne Thermal Emission and Reflection radiometer)
Active Remotely Sensed Data
Derived Remotely Sensed Data
Vegetation Indices
The Tasseled Cap Transformation
Geographic Information Systems (GIS)
Thematic Data Layers
Geospatial Data Conversion
Using ERDAS-IMAGINE Software
Using ARCINFO Software
Select Area of Interest (Study Site)
Topographic Data
Global Positioning System (GPS)
GPS Services
The GPS Satellite System and Fact
GPS Applications

Data Sampling Methods and Applications
Data Representation
Data Collection and Source of Errors
Data Types
Sampling Methods and Applications
Sampling Designs
Simple Random Sampling
Stratified Random Sampling
Systematic Sampling
Nonaligned Systematic Sample
Cluster Sampling
Multiphase (Double) Sampling
Double Sampling and Mapping Accuracy
Pixel Nested Plot (PNP): Case Study
Plot Design
Characteristics of Different Plot Shapes
Plot Size

Spatial Pattern and Correlation Statistics
Spatial Sampling
Errors in Spatial Analysis
Spatial Variability and Method of Prediction
Spatial Pattern
Spatial Point Pattern
Linear Correlation Statistic
Case Study
Statistical Example
Spatial Correlation Statistics
Moran’s I and Geary’s C
Cross-Correlation Statistic
Inverse Distance Weighting (IDW)
Statistical Example

Geospatial Analysis and Modeling–Mapping
Stepwise Regression
Statistical Example
Ordinary Least Squares (OLS)
Variogram and Kriging
Ordinary Kriging
Simple Kriging
Universal Kriging
Developing Variogram Model and Kriging to Predict Plant Diversity at GSENM, Utah
Spatial Autoregressive (SAR)
Statistical Example
Binary Classification Tree (BCTs)
Geospatial Models for Presence and Absence Data
GARP Model
Maxent Model
Logistic Regression
Classification and Regression Tree (CART)
Envelope Model

R Statistical Package
Overview of R Statistics (R)
What Is R?
Strengths of R/S
The R Environment
Working with R on Your COMPUTER
Begin to Use R
Statistical Analysis Examples Using R
Common Statistics
Common Graphics
Common Programming
Create and Examine a Logical Vector
Working on Graphical Display of Data (Data distributions)
Develop a Histogram
Data Comparison between the Data and an Expected Normal Distribution
More Statistical Analysis
Reading New Variable (Enter new data set, WEIGHT)
Plotting Weight and Height
Test of Association
Some Basic Regression Analysis
Case Study
Test for Spatial Autocorrelation Using Moran’s I
Test for Spatial Autocorrelation Using Geary’s C
Test for Spatial Cross-Correlation Using Bi-Moran’s I
Trend Surface Analysis
Test for Spatial Autocorrelation of the Residuals
Test for Moran’s I for Residuals
Using Spatial AR Model without Regression
Using Spatial AR with Regression (Using All Independent Variables as with OLS Model)
Analysis of Residuals
Develop Variogram Model (Modeling Fine Scale Variability)
Plotting Variogram Model

Working with Geospatial Information Data
Exercise 1: Working with Remotely Sensed Data
Exercise 2: Derived Remote Sensing Data and
Digital Elevation Model (DEM)
Deriving Slope and Aspect from DEM Data
Resample GRID
Exercise 3: Geospatial Information Data Extraction
Deriving SLOPE and ASPECT from DEM Data (ELEVATION)
Resample GRID
Select Area of Interest (Study Site)
Data Extraction
Steps for Converting the Geospatial Model to a Thematic Map Product
Working with Vegetation Indices and Tasseled Cap Transformation
Develop Thematic Layer in ARCVIEW or ARCMAP
Map Layout


Author Bio(s)

Dr. Mohammed A. Kalkhan has over 20 years experience in research and teaching at Colorado State University in Fort Collins, Colorado. As a member of the Natural Resource Ecology Laboratory (NREL) there, he has also served as an affiliate faculty in the Department of Forest, Rangeland, and Watershed Stewardship, and as an advisor for the Interdisciplinary Graduate Certificate in Geospatial Science, Graduate Degree Program in Ecology (GDPE), The School of Global Environmental Sustainability (SOGES), and Department of Earth Resources (currently the Department of Geosciences) at Colorado State University (CSU).

Dr. Kalkhan received his BSc in Forestry (1973) and MSc in Forest Mensuration (1980) from the College of Agriculture and Forestry, the University of Mosul, Iraq. He received his PhD in forest biometrics- remote sensing applications from the Department of Forest Sciences at Colorado State University, USA, in 1994. From 1975 to 1982, he was a lecturer in the Department of Forestry, College of Agriculture and Forestry, University of Mosul. In 1994, he joined the Natural Resource Ecology Laboratory.

Dr. Kalkhan’s main interests are in the integration of field data, remote sensing, and GIS with geospatial statistics to understand landscape parameters through the use of a complex model with thematic mapping approaches, including sampling methods and designs, biometrics, determination of uncertainty and mapping accuracy assessment.

Editorial Reviews

"[This book] covers many topics that are poorly treated by others. ... Chapter 2 on sampling is a true gem. It covers all the standard approaches, but in addition has an extensive discussion of multiphase or double sampling which Kalkhan has used extensively in his own research. There is also an extensive discussion of a case study in which a pixel nested plot (PNP) sampling design is used. This is useful material for researchers and course instructors alike. ... This reviewer enjoyed Chapter 4 immensely. It provides a stimulating discussion of geospatial analysis and modeling including the topics of variogram fitting and kriging. These are pitched at just the right level for most applied researchers who want to use these approaches as a tool to solve their spatial analysis problems. A particular treat is the explanation of spatial autoregressive approaches, binary classification trees and the GARP genetic algorithm. These are topics invariably neglected in many of the standard texts."
—Nigel Waters, Geomatica, Vol. 65, No. 4, 2011

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