Probabilistic Forecasting of Urban Sprawl

A probabilistic geospatial modelling framework for forecasting urban sprawl dynamics from Earth observation data using Bayesian spatio-temporal machine learning.

Overview

Rapid urbanisation across Sub-Saharan Africa is frequently characterised by fragmented, low-density expansion that outpaces infrastructure provision and extends into peri-urban regions. While satellite-based Earth observation datasets have enabled detailed retrospective analyses of urban growth, relatively few approaches provide spatially explicit forecasts with quantified uncertainty suitable for municipal planning.

This project develops a probabilistic framework for forecasting urban sprawl processes. Using Yaoundé, Cameroon as a case study, historical urban expansion is reconstructed from multi-decadal Landsat imagery before forecasting future development patterns through 2035 using a Spatio-Temporal Sparse Variational Gaussian Process (ST-SVGP).

Unlike conventional deterministic forecasting approaches, this framework produces calibrated probabilistic predictions, enabling uncertainty-aware urban planning and supporting more informed land-use decision making.

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Objectives

• Reconstruct historical urban expansion (1990–2020) from Landsat imagery.
• Quantify urban sprawl using spatial indicators.
• Forecast future urban sprawl to 2035 using Bayesian spatio-temporal modelling.
• Quantify predictive uncertainty associated with future urban expansion.
• Develop a transferable framework for urban sprawl forecasting using Earth observation data.

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Methodology

1. Historical Urban Mapping

Annual Landsat imagery is processed to reconstruct built-up land dynamics between 1990 and 2020.

Outputs include:

• Annual built-up extent
• Urban expansion maps
• Historical growth trajectories

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2. Urban Sprawl Metrics

Spatial analysis is used to derive quantitative indicators describing different forms of urban expansion, including:

• Leapfrog development
• Spatial dispersion
• Fragmentation
• Urban density characteristics

These metrics form the response variables used for forecasting future sprawl behaviour.

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3. Probabilistic Forecasting

Future urban expansion is predicted using a

Spatio-Temporal Sparse Variational Gaussian Process (ST-SVGP)

which provides:

• Bayesian probabilistic predictions
• Predictive uncertainty estimates
• Scalability to long Earth observation time series
• Spatially explicit forecasts through 2035

Unlike deterministic neural networks or regression models, the ST-SVGP captures uncertainty associated with future land-use transitions, making predictions more suitable for evidence-based urban planning.

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Workflow

Landsat Time Series (1990–2020)
            │
            ▼
 Historical Built-up Mapping
            │
            ▼
 Urban Sprawl Metrics
            │
            ▼
Feature Engineering
            │
            ▼
      ST-SVGP Model
            │
            ▼
 Probabilistic Urban Forecasts
            │
            ▼
 Uncertainty Analysis

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Repository Structure

.
├── data/
│   ├── raw/
│   └── processed/
│
├── notebooks/
│
├── src/
│   ├── preprocessing/
│   ├── feature_engineering/
│   ├── models/
│   │   ├── st_svgp/
│   │   └── evaluation/
│   ├── analysis/
│   └── visualization/
│
├── outputs/
│   ├── forecasts/
│   ├── uncertainty/
│   ├── figures/
│   └── maps/
│
├── README.md
└── pyproject.toml

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Data Sources

Earth Observation

• Landsat annual imagery (1990–2020)

Spatial Predictors

Potential predictors include:

• Distance to roads
• Distance to urban centres
• Existing built-up areas
• Accessibility
• Topography
• Population density
• Additional environmental variables

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Model

Primary Forecasting Model

Spatio-Temporal Sparse Variational Gaussian Process (ST-SVGP)

Advantages:

• Bayesian inference
• Scalable Gaussian Processes
• Probabilistic forecasting
• Spatial and temporal modelling
• Predictive uncertainty estimation

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Outputs

The framework generates:

• Historical urban expansion maps
• Urban sprawl indicator layers
• Probabilistic urban forecasts (2035)
• Predictive uncertainty maps
• Forecast evaluation metrics

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Study Area

Yaoundé, Cameroon

Yaoundé provides a representative example of a rapidly expanding Sub-Saharan African city experiencing dispersed urbanisation.

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Applications

This framework is designed to support:

• Municipal land-use planning
• Urban growth management
• Infrastructure planning
• Sustainable urban development
• Earth observation research
• Spatio-temporal forecasting research

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Key Features

• Multi-decadal Earth observation analysis
• Bayesian spatio-temporal forecasting
• Spatially explicit uncertainty quantification
• Scalable Gaussian Process modelling
• Transferable workflow for rapidly urbanising regions

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Citation

If you use this repository in academic work, please cite the associated publication once available.

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License

Specify an appropriate open-source license (e.g., MIT, BSD-3-Clause, or GPL-3.0) before distribution.