Cellular Automata & Land Change

Spatially explicit simulation of land use/land cover change using CA-Markov, SLEUTH, and transition probability models

Overview

Cellular Automata (CA) are discrete dynamic systems where cells in a grid update their states based on transition rules and the states of neighboring cells. When combined with Markov chain transition probabilities, CA models (CA-Markov) simulate future land use/land cover (LULC) scenarios. The SLEUTH model (Slope, Land use, Exclusion, Urban, Transportation, Hillshade) specifically models urban growth. These models are critical for understanding coastal urbanization, mangrove loss, agricultural expansion, and land degradation — all directly affecting coastal ecosystems and water quality.

Key Concepts

Markov Chain Transition

A Markov chain models LULC transitions as a stochastic process. The transition probability matrix P(t) gives the probability of changing from class i to class j over time interval t. The Chapman-Kolmogorov equation allows multi-step projection.

S(t+1) = S(t) × P
P(2t) = P(t) × P(t)

CA Neighborhood Rules

CA models add spatial context: a cell's transition depends on its neighbors (Moore/von Neumann neighborhood). This captures spatial contiguity of land change — urban areas expand from existing urban edges, not randomly.

SLEUTH Urban Growth

SLEUTH uses Monte Carlo simulation with 5 growth rules (spontaneous, new spreading, edge, road-influenced, slope). Calibration uses historical LULC maps to tune coefficients. It models urban sprawl and infilling.

Change Detection Input

Multi-temporal satellite imagery (Landsat, Sentinel-2) provides the LULC classification maps that serve as inputs. Change detection identifies which pixels changed class between time periods. Accuracy assessment validates classifications.

Validation Methods

Kappa statistic, figure of merit (FoM), and quantity/allocation disagreement assess model accuracy. Pontius et al. (2008) framework distinguishes errors of quantity (wrong totals) from errors of allocation (wrong locations).

Coastal Applications

CA-Markov projects mangrove deforestation rates, coastal urbanization impacts on water quality, shrimp farm expansion, and land subsidence scenarios. Results inform coastal zone management planning.

Interactive Visualizations

Land Use Change Over Time — Stacked Area Chart

Transition Probability Matrix Heatmap

Simulated CA Grid — Urban Growth (Animated Concept)

Key References

  1. Clarke, K.C., Hoppen, S. & Gaydos, L. (1997). A self-modifying cellular automaton model of historical urbanization. Environment and Planning B, 24(2), 247–261.
  2. Pontius Jr., R.G. et al. (2008). Comparing the input, output, and validation maps for several models of land change. Annals of Regional Science, 42, 11–37.
  3. Eastman, J.R. (2012). IDRISI Selva: Guide to GIS and Image Processing. Clark University.
  4. Ahmed, A. et al. (2018). Where is the coast? Monitoring coastal land dynamics in Bangladesh. Ocean and Coastal Management, 151, 10–24.
  5. Mas, J.F. et al. (2014). Inductive pattern-based land use/cover change models. Landscape Ecology, 29, 1–13.