LUC dynamic land use change model: An Introduction
Land use is a major driving force for water demand,
which in turn may be a constraint on land use change options.
LUC calculates dynamic development (annual time step) of land use
over decades, and estimates regional water use as a function of
land use. This estimate is intended as a rough check on the much more detailed
WaterWare water budget, but with a longterm perspective and change over decades.
The model has two main purposes:
 Testing hypotheses about land use change, patterns and the effect of regulations
 Estimating regional water budgets and related indicators as a consistency check
for WaterWare.
LUC is a dynamic land use change model based on
 A set of well defined land use classes (CORINE)
and transitional classes for longterm (construction) projects;
 A matrix of a priori transition probabilities;
 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.
 Properties of spatial units other than the land use itself can be used to model
the evolution of related variables describing the area, such as regional product,
income and revenues, employment, resource consumption (in particular water and energy),
waste generation, and effects on population growth and migration,
Land use classes
LUC uses the basic set of CORINE land use classes, extended by transitional classes for land use
that can not be reached in one time step (usually, a year);
examples would be urban or industrial that can not be reached in a single step
from, for example, pasture.
The basic land use classes used in LUC are:
CORINE level 2 or level 3 classification.
However, and in principle, ANY set of land use classes can be modeled, provided there
is the corresponding set of transition probabilities, RULES.
Data requirements
The model requires:
 A geographical domain definition and background map (the results are
generated, inter alia, as a color coded LU overlay of that map).
 A land use classification in the CORINE classes with the highest possible
resolution (1 ha, 1 km) as polygons or a raster.
 Optionally, more than one land use classification with several years
interval to derive an initial estimate for the transition probabilities.
 Any other information (narrative) than can be used to derive transition probabilities or
adjustment rules, see below.
Input data formats
LUC uses its own binary data format for the initial land use map and data set;
the attributes (land use classes) of both polygons or rasters
are supposed to be derived from the CORINE classification, obtaining integer values by simply deleting
the dots ".", i.e., class 3.2 becomes the integer number 32.
Land use data (initial conditions) can be imported from various formats:
Vector formats:
 Arc/Info export format
 ESRI Shape file
 MapInfo Data Interchange Format
 GRASS
Raster formats:
 Arc/Info export format
 ERDAS rev. 7 and 8
 GRASS
 BIL and BIP
In principle, we can also process GIF and TIF formats; however if three digit codes are used
this is somewhat more complex. If you have no other option, please contact
info@ess.co.at for detailed instructions for
data preparation.
Model concepts
Transition probabilities
Transition probabilities are expressed as a complete matrix of land use classes, where
the rows of the matrix sum to 1.0, and the diagonal cells represent the probability that a class
remains what it was (i.e., does not change).
Rules
RULES are expressed as first order production rules:
IF condition
AND/OR condition
THEN
probability(n,m) CHANGEOPERATOR 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).
CHANGEOPERATORs are:
RELINCREASE, RELDECREASE, ABSINCREASE, ABSDECREASE, ABSOLUTE (set);
Please note:
REL* functions modify the current probability in RELATIVE terms:

RELDECREASE 500 makes 100 out of 200);
ABS* function are additive:
the amount specified will be added to or subtracted from the original probability:
 ABSINCREASE 100 makes 500 out of 400 (RELINCREASE 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:
 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.
 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.
 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 interval from 01000 or 1/10 of a percent.
Rule examples
IF FRACTION(1.1,1) > 500 THEN P(1.1) REINCREASE 500
IF more than half the immediate neighbors 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) RELDECREASE 950
with somewhat different behaviour.
IF FRACTION(1.1,2) > 950 THEN P(1.1) RELDECREASE 900
IF more than 95% of the neighbors in a 5x5 area around a cell
(all but 2 ?) are already city, decrease the probability of
transition of the last cells into city.
Driving Forces
The model is basically driven by the internal transition probabilities;
This can be extended by a set of possible EXTERNAL DRIVING FORCES
that represent factors such as:
 demographic development;
 regional development policies;
 world market effects (energy prices, emission constraints such as Kyoto targets,
tourism demand or demand for specific regional products).
Lookahead and iterative adjustments
Each cycle is executed in a twostep procedure:
a NAIVE run, that uses the values of the last state for all
rules and adjustments;
on the basis of the NAIVE run, all FUNCTION values are recalculated
for a second round of adjustments;
after the NAIVE forecast run, ex post transition probabilities are
estimated (the number of cells should be reasonably large to make that feasible);
if a priori and ex post probabilities or frequencies differ
more than some THRESHOLD, a percentage CHANGE is tried.
Depending on performance, this can be done iteratively,
but under adaptive control:
The predictorcorrector method should be controlled
by either:
 a MAXLOOP number of iterative trials;
 or MAXDEV maximum admissible (average) normalized deviation
of a priori and ex post matrices.
Implementation and user interface
The model is implemented as a webbased client server system:
A scenario selector to select available cases, consisting
of two parts:
 the region (initially, start time initial conditions, and time horizon (50 years) are
fixed;
 the development scenario (transition probabilities and rules
 possibly also initial conditions and time frame.
The make the model behave more smoothly,
the transition probabilities estimated are corrected by a sigmoid
constraint that modifies the probabilities
according to a logistic model between 0 and MAX global percentage
of the target land use class after any specific adjusting rules have been applied.
This behaves like a global implicit META RULE. For test purposes,
it can bet ON or OFF in the basic model configuration LOGISTIC=ON/OFF
Thus, the maximum global fraction any given land use class can reach is MAX
(which, however can be set to 100% !) and the transition probabilities
are adjusted based on the predicted and uncorrected fraction of class N
after a given time step.
Output and Reports
Model results include:
 A MAP for each time step, indicating land use by color coding;
this should again use the various matrix viewing options shared
with other dynamic spatially distributed models:
one map at a time, a simple viewer, the Java animation applet;
 a land use PIE CHART for each time step
 a TABULAR summary with absolute and relative LUC;
 a TRANSITION MATRIX of actual transition cases/frequencies;
 a TIME SERIES graph of select sets of LUCs;
 Global evaluation provides an annual summary, over the entire region, of:
 water use (Mm3/ha)
 energy use (MWhrs/ha)
 waste water generation (Mm3/ha)
 solid waste generation (tons);
The output is added to the transition tabels with the
annual land use fractions.
