Determine Transition Matrix

Description

Determines a matrix of transition rates between two time-series maps: a single-step transition matrix for the entire period between the initial and final landscape maps, and a multi-step transition matrix for a given number of time steps into which that period is divided.

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 the initial and final landscape maps. A step can be any unit of time, such as a year or a month, since Dinamica EGO uses it only as an external reference parameter.

Optional Inputs

None.

Outputs

Name	Type	Description
Single Step Matrix	Transition Matrix Type	Transition matrix for the entire period between the initial and final landscape maps.
Multi Step Matrix	Transition Matrix Type	Transition matrix for a single time step, derived by dividing the period between the initial and final landscape maps by Time Steps.

Group

Calibration

Notes

Only the classes present in the categorization of the initial or final map are used when determining the transitions that occurred between the two maps; any other values are ignored.

A cell is ignored in the calculation if its value is null in either the initial or the final map.

To analyze a historical context, Initial Landscape should be the older map of the time series.

Deriving the multi-step matrix from the single-step matrix requires an eigendecomposition of the single-step matrix, which is only possible when that matrix is ergodic, that is, when it has well-defined eigenvalues and eigenvectors. See http://mathworld.wolfram.com/EigenDecompositionTheorem.html for details on this decomposition and on why it is not always possible.

The transition matrix describes a system that changes over discrete time increments, in which the value of any variable in a given period is the sum of fixed percentages of the values of the variables in the previous period. The fractions in each column of the transition matrix sum to one; the diagonal need not be filled in, since it represents the percentage of unchanged cells. The transition rates are passed to the model as a fixed parameter within a given phase; the time step itself can span any amount of time, since Dinamica treats the time unit only as an externally set reference parameter.

Internal Name

DetermineTransitionMatrix

Usage examples

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