16 Table 2.3 Non-Spatial Data
Data Type Date Production
Source of Data Population Data
1991 - 2008 BPS
1
Village potential statistics Potensi Desa
1991 and 2000 BPS
1
1 Central Statistics Agency Badan Pusat Statistik
Several software were used to process the necessary data consist of Microsoft Office, GIS and Remote Sensing application software. The following application
software can be seen in Table 2.4.
Table 2.4 List of Software Application No
Software Type
Function 1.
Arc GIS desktop 10 GIS Application
Processing, Analyzing,
Viewing and Manipulating Spatial Data.
2. Er-Mapper 7.1
Remote Sensing Application
Processing, Extracting
Analyzing Satellite Imagery Data.
3. Microsoft Excel
2007 Spreadsheet
Application Statistic
Tabular data
analyzing.
2.3.2. Priority of Landcover Conversion using Markov Change Detection.
Markov Chain change detection is one application of change detection that can be used to predict future changes based on the rates of past change, based on
probability that a given piece of land will change from one mutually exclusive state to another.
Markov chain models have several assumptions Parzen, 1962; Haan, 1977; Wang, 1986; Stewart, 1994. One basic assumption is to regard land use and land
cover change as a stochastic process, and different categories are the states of a chain. A chain is defined as a stochastic process having the property that the value
17 of the process at time t, X
t
, depends only on its value at time t-1, X
t-1
,and not on the sequence of values X
t-2
, X
t-3
,...,X that the process passed through in arriving at
X
t-1
.It can be expressed as:
1 1
1 1
| ,
,........., |
t j
t i
t j
t i
P X a
X a X
a X
a P X
a X
a
1.1
Moreover, it is convenient to regard the change process as one which is discrete in time t = 0,1,2,.... The
1
|
t j
t i
P X a
X a
, known as the one-step transitional probability, gives the probability that the process makes the transition
from state a
i
to state a
j
in one time period. When steps are needed to implement this transition, the
1
|
t j
t i
P X a
X a
is then called the step transition
probability,
ij
P
. If the
ij
P
is independent of times and dependent only upon states a
i
, a
j
and , then the Markov chain is said to be homogeneous. The
treatment of Markov chains in this study will be limited to first order homogeneous Markov chains. In this event:
1
|
t j
t i
ij
P X a
X a
P
1.2
Where P
ij
can be estimated from observed data by tabulating the number of times the observed data went from state i to j, n
ij
, and by summing the number of times that state a
i
occurred, n
i
, then
ij ij
i
n P
n
1.3 As the Markov chain advances in time, the probability of being in state j
after a sufficiently large number of steps becomes independent of the initial state of the chain. When this situation occurs, the chain is said to have reached a steady
state. Then the limit probability, P
j
, is used to determine the value of
ij
P
:
lim
n ij
j n
P P
1.4 where:
18 1, 2,......,
1
n j
i ij
i j
P PP
j m state
P P
In this research, markov chain change detection used to get landcover type priorities conversion to urban build up area based on matrix probabilities. The
calculation process can be explained in Figure 2.2.
Markov Chain change detection in year t and t+1 Transition Area Transitional Probability Matrix
Trend Prediction Conversion Priority of Landcover type into Built up Area
Image Classification Result from Satellite
Imagery in1991, 1997, 2000 and 2007
Figure 2.2 Priority of Conversion using Markov Change Detection In the first step image classification processed using visual interpretation
methods was done. The result from this processed can be divided into seven class type of landcover, there are ; built-up area, forest, paddy field, plantation,
agricultural, shrub and water body. Second step is to create a transition matrix of pixels in each class for two
times. This is the same as the cross tabulation matrix, which can be used for accuracy assessment. From this step, trend prediction will be calculated using
matrix probabilities. Landcover priorities scenarios can be derived from transitional probabilities of landcover type in year t that changed into built-up area
in year t+1. Afterwards, the value of probabilities has been ranked from higher to lower probabilities. This step was done to get decision of landcover type
priorities.
19
2.3.3. Calculation of Driving Forces
