Determine Transition Matrix

Description

This functor determines a matrix of transition rates between two time-series maps.

Inputs

Name	Type	Description
Initial Landscape	Categorical Map Type	Initial map of land use and cover classes.
Final Landscape	Categorical Map Type	Final map of land use and cover classes.
Time Steps	Positive Integer Value Type	Number of time steps between initial and final landscape maps. Step can be any time unit, such as year, month, etc.

Output

Name	Type	Description
Single Step Matrix	Transition Matrix Type	Transition matrix for the entire period.
Single Step Matrix	Transition Matrix Type	Transition matrix for the time step specified by the number of units that the time period is divided.

Group

Calibration

Notes

To analyze a historical context, the initial map should be considered the older map of the time series.

Multi-step transition matrix only applies to an ergodic matrix, i.e. a matrix that possesses eigenvalues and vectors.

The transition matrix describes a system that changes over discrete time increments, in which the value of any variable in a given time period is the sum of fixed percentages of the value of the variables in the previous time period. The sum of fractions along the column of the transition matrix is equal to one. The diagonal Line of the transition matrix needs not to be filled in since it models the percentage of unchangeable cells. The transition rates are passed on to the model as a fixed parameter within a given phase. For Dinamica, time step can comprise any span of time, since the time unit is only a reference parameter externally set.

, j = 1, 2 ... n

An estimation of is given below, where n is the number of states

...

The transition matrix is calculated for a time period. Dinamica can also be run in multiple time steps. It is necessary for this purpose to derive the multiple time step transition matrix, as this is equivalent to the number of time steps in which the time period is divided.

H and V are Eigen values and Eigen vector matrices.

Internal Name

DetermineTransitionMatrix

Usage examples

See practical examples of this functor in Lesson 18: Building a land-use and land-cover change simulation model