Series 3: Computational Spatial Analysis

Series Overview

This series develops the quantitative toolkit for geographic information science, covering map algebra, spatial interpolation, kernel density estimation, spatial autocorrelation, and time series analysis of geographic data. These are the core computational methods underlying modern GIS and spatial data science.

Pedagogical Approach

Algorithms before software. Each method is derived mathematically and implemented from scratch before discussing its application in GIS software. Students understand what ArcGIS or QGIS does internally, not just which buttons to click.

Real rasters, real vectors. All examples use authentic geospatial datasets—DEMs, satellite imagery, census data, GPS tracks. Students work with the data structures and file formats of professional practice.

Learning Objectives

By completing this series, learners will:

Implement map algebra operations on raster datasets (local, focal, zonal, global)
Apply interpolation methods (IDW, kriging, splines) with understanding of their mathematical basis
Estimate spatial densities using kernel methods for point pattern analysis
Detect spatial autocorrelation via Moran’s I and variogram analysis
Perform change detection on multi-temporal imagery
Analyze spatial-temporal data through time series methods
Understand uncertainty propagation in spatial analysis workflows
Select appropriate methods based on data characteristics and analysis goals

Model Sequence

Cluster J: Map Algebra (Models 29-32)

Model 29: Local Operations and Band Math Cell-by-cell operations. NDVI calculation. Boolean masks. Reclassification.

Model 30: Focal Operations and Convolution Neighborhood analysis. Kernel-based filtering. Slope/aspect computation. Edge detection.

Model 31: Zonal Statistics Summary by regions. Categorical analysis. Watershed characterization.

Model 32: Global Operations and Cost-Distance Entire-raster analysis. Distance transforms. Least-cost paths. Connectivity.

Cluster K: Spatial Interpolation (Models 33-36)

Model 33: Inverse Distance Weighting Weighted nearest neighbors. Distance decay functions. Parameter sensitivity.

Model 34: Kriging and Geostatistics Semivariogram modelling. Ordinary kriging. Prediction uncertainty quantification.

Model 35: Spline Interpolation Thin-plate splines. Regularization vs exact interpolation. Smoothness constraints.

Model 36: Interpolation Method Comparison Cross-validation. Error metrics. Method selection criteria.

Cluster L: Point Pattern Analysis (Models 37-40)

Model 37: Kernel Density Estimation Bandwidth selection. Quartic vs Gaussian kernels. Edge effects. Applications to crime mapping.

Model 38: Spatial Autocorrelation - Moran’s I Global vs local indicators. Significance testing. Spatial weights matrices.

Model 39: Hotspot Detection (Getis-Ord Gi*) Local clustering statistics. Z-scores. False discovery rate correction.

Model 40: Point Process Models Homogeneous vs inhomogeneous Poisson. Intensity estimation. Simulation.

Cluster M: Time Series Analysis (Models 41-42)

Model 41: Change Detection in Multi-Temporal Imagery Differencing. Regression. Thresholding. Land cover change quantification.

Model 42: Spatial Time Series Decomposition Trend, seasonality, noise separation. NDVI phenology. Climate decomposition.

Computational Skills Developed

Raster data manipulation (NumPy arrays, GDAL)
Vector geometry operations (Shapely, GeoPandas)
Spatial indexing (R-trees, quadtrees)
Variogram fitting (optimization)
Monte Carlo simulation for uncertainty
Parallel processing for large rasters

Mathematical Progression

Early models: Matrix operations, convolution, weighted averaging

Middle models: Optimization (kriging, splines), probability (spatial statistics)

Late models: Time series methods, hypothesis testing, multiple comparison corrections

Prerequisites

Required: Series 1 (calculus, vectors, optimization basics)

Helpful: Basic linear algebra (matrix multiplication)

Not required: Prior GIS software experience

Entry Points by Background

GIS analysts: Jump directly to this series. Models provide mathematical depth behind familiar tools.

Data scientists: Start Model 33 (interpolation). Spatial methods complement time series/ML background.

Geography students: Complete Series 1 first for mathematical foundation.

Remote sensing focus: Models 29-30 (map algebra) + 41-42 (change detection) most relevant.

Key Insights

Map algebra is array programming. Raster GIS operations are linear algebra on grids.
Interpolation makes assumptions. Every method embeds beliefs about spatial continuity.
Spatial autocorrelation violates independence. Standard statistics fail; spatial methods required.
Bandwidth/distance parameters critical. Small changes dramatically affect results.
Uncertainty compounds. Multi-step workflows accumulate error from each operation.
Edge effects matter. Boundary conditions affect results near dataset limits.
Computational efficiency essential. Large rasters demand algorithmic awareness.

Applications Covered

Agricultural yield mapping (interpolation)
Urban heat island detection (focal operations, hotspots)
Deforestation monitoring (change detection)
Wildlife habitat suitability (map algebra, zonal stats)
Disease clustering (point pattern analysis)
Vegetation phenology (time series)
Watershed delineation (global operations)

Assessment Strategies

Formative:

Implement algorithm on small test dataset
Compare results to ground truth
Vary parameters, observe sensitivity

Summative suggestions:

Complete spatial analysis workflow on novel dataset
Justify method selections with quantitative criteria
Implement custom GIS operation from scratch
Reproduce published analysis, critique methods

Software Integration

While models derive methods from scratch, practical GIS implementation discussed:

Python: GDAL, rasterio, geopandas, pysal
R: sf, stars, gstat, spatstat
QGIS: Processing toolbox equivalents
ArcGIS: Spatial Analyst, Geostatistical Analyst

Extensions and Pathways

For remote sensing: Continue to Series 5 (image classification, spectral analysis)

For environmental modelling: Series 2 + Series 4 (process-based models)

For advanced statistics: Bayesian spatial models, geographically weighted regression (future series)

Estimated Time Investment

Per model: 3-5 hours (derivation + implementation + real data application)

Full series: 45-70 hours

Core GIS sequence (Models 29-32, 33, 37-38): 20-30 hours

Prerequisites: Complete Series 1 before starting. Series 2 helpful but not required.

Next: Series 5 (Remote Sensing) builds on map algebra and change detection methods.