P ¼ P ij ¼
P 11
P 12
⋯ P 1m
P 21
P 22
⋯ P 2m
⋯
P m1
⋯
P m2
⋯ ⋯
⋯ P mm
ð3:3Þ
where P stands for probability conversion from state i to state j (Jianping et al. 2005).
The transition probability matrix of the years 1986–1996 and the primary matrix
P (0) were used to derive the forecasted LULC for the year 2006. Similarly, the
forecasted LULC for the year 2036 are derived from the primary matrix. The
simulated LULC map of the Koraiyar basin for the future year 2036 is shown in
Fig. 3.4. The results indicate the percentage of settlement area in the Koraiyar basin
has increased from 45.11% to 104.74% during 1986–2016. For the future year of
2036, an increase of 3.22% is projected. Rapid settlements are observed in the
northern part of the basin area because of major developmental activities such as
residential, commercial, and industrial areas in the basin. The accuracy of the
predicted LULC maps generated by the Markov technique was validated using
observed and predicted LULC maps of the Koraiyar basin.
Fig. 3.4 Simulated future LULC map of year 2036
60
S. Natarajan and N. Radhakrishnan