LUC :  Reference Manual
    Release Level 1.0
    Release Date 2008 11
    Revision Level 1.0

Scenario editor, modifying rules

The a priori transition probabilities from the basic transition matrix can be modified by a set of RULES one set for each possible transition, that can modify the a priori probabilities using a set of operators that use spatial and temporal aggregate and neighborhood properties to modify the transition probabilities.

A special case of the spatial constraints or driving forces are of course global properties of the area considered.

Other rules can be based on any attribute or property a given spatial unit has such as soil, geology and terrain features, climatic variables, infrastructure, and population, available in auxiliary matrices parallel to the initial lanuse matrix.

Rules

RULES are expressed as first order production rules:

     IF condition
        AND/OR condition
     THEN
        probability(n,m) CHANGE-OPERATOR VALUE 
where
    condition: a function return value of the type: TRUE/FALSE for the functions FRACTION (spatial neighborhood), FREQUENCY (temporal neighborhood), and LAST (history of state).

    CHANGE-OPERATORs are:

      REL-INCREASE, REL-DECREASE, ABS-INCREASE, ABS-DECREASE, ABSOLUTE (set);

    Please note:

    REL-* functions modify the current probability in RELATIVE terms:

    • REL-DECREASE 500 makes 100 out of 200);
    ABS-* function are additive: the amount specified will be added to or substructed from the original probability:
    • ABS-INCREASE 100 makes 500 out of 400 (REL-INCREASE 250 would have the same effect in this case);
    • ABSOLUTE just sets the value to its argument: ABSOLUTE 300 makes 300 out of anything.

    Probability is the a priori transition probability from class n to class m;

    VALUE: degree of change, e.g., 500o/oo, or -100o/oo
    Please note: all probabilities are expressed as INTEGER values in 1/10 of a percent (promille).

Operators and functions

the following functions are used:
  1. FRACTION (N,i) is the local fraction of LUC N in a neighborhood of size i (i= 1, 2, 3, 4,..) where the number describes a radius in terms of cells around the current cell: i.e., 1 refers to a total area of 3x3=9 cells, 2 is 5x5, 3 is 7,7 i.e., 2*r+1; FRACTION (N,0) is the global fraction.
  2. FREQUENCY (N,i) is the temporal equivalent, i.e., frequency of class N over i previous time steps. FREQUENCY (N,1) = 1 would imply that the cell was of class N in the previous time step.
  3. LAST(i) returns the LUC value of a cell i steps back.

    Please note: for consistency, BOTH FRACTIOn, FREQUENCY and all probabilities are expressed in promille, i.e., in the intervall from 0-1000 or 1/10 of a percent.

Rule examples

IF FRACTION(1.1,1) > 500 THEN P(1.1) RE-INCREASE 500
IF more than half the immediate neighbours of a cell are city (1.1), then the probability of transition to city increases by 50%; please note that the same principle of contagion can be expressed differently as well:
IF FRACTION(1.1,1) < 100 THEN P(1.1) REL-DECREASE 950
with somewhat different behaviour.
IF FRACTION(1.1,2) > 950 THEN P(1.1) REL-DECREASE 900
IF more than 95% of the neighbours in a 5x5 area around a cell (all but 2 ?) are already city, decrease the probability of transition of the last cells into city.


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