Land Cover Markov Chain Model

A first-order Markov chain projects future land cover composition from a single observed transition matrix. Adjust the starting class and time horizon below to see how the projected probabilities evolve.

How it works: the transition matrix records how much area moved from each land cover class to every other class between two observed years. Dividing each row by its own total converts that area matrix into a transition probability matrix — the probability that a cell currently in class i ends up in class j after one time step. Repeatedly multiplying a state vector by that matrix projects land cover composition forward, one step (decade, in this dataset) at a time.

Simulation settings

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Projected probability over time

Transition probability matrix

Each row sums to 100%. Row = class at time 1 (the "from" state); column = class at time 2 (the "to" state). Diagonal cells (highlighted) are the probability of staying in the same class.

About the assumptions behind this model

This is a first-order, stationary Markov chain: it assumes (1) the probability of moving to a new class depends only on the current class, not on how the land got there, and (2) the transition probabilities observed between your two source years hold constant for every future step.

Neither assumption is guaranteed to hold in reality. Zoning changes, infrastructure investment, land availability limits (a class can't keep converting to "Developed" forever if it runs out of area), and policy interventions can all change transition rates over time. Treat projections beyond a decade or two past your observed data as illustrative, not predictive.