LULC scenarios were modeled using Cellular Automata (CA) and Markov chain analysis in IDRISI TerrSet software from Clark Labs. In a first stage, a transition probability matrix for the period 1986 – 2001 was calculated using Markov chains with the LULC map of 1986 as the first land cover image and the map of 2001 as the later land cover image. The transition areas and the conditional probabilities created in the step previous were used in a Cellular Automata analysis to predict the LULC in 2017. This prediction was used for model validation. A second transition probability matrix was calculated using the LULC maps of 2001 and 2017 and used to predict LULC in 2033. Finally, a transition matrix for the whole period (1986 – 2017) was calculated and used to predict the LULC in 2050. These transition probabilities matrices have the information about the probability that each land cover category will change to every other category (Eastman 2016; Wang et al. 2016). During the Markov chain model setting stage, the number of time periods to forward projection was set accordingly the number of time periods between the first and the second image for each period analyzed. In the Cellular Automata/Markov Change prediction setting, the later land cover image used in the Markov Chain analysis was used as the starting point for change simulation, a standard 5*5 contiguity filter was applied meanwhile the number of Cellular Automata iterations it depended on the number of time periods for forward projection specified in the Markov chain analysis (Takada et al. 2010; Wang et al. 2018).
To quantify the predictive power of the model, we compared the result simulation (2017) with the reference map (2017) using Kappa variations (Pontius 2000): Kappa standard (Kstandard), Kappa for no information (Kno), and Kappa for location (Klocation). For all of the Kappa statistics, 0% indicates that the level of agreement is equal to the agreement due to chance and 100% indicates perfect agreement. In comparing the map of reality to the alternative map, Kno indicates the overall agreement. Klocation indicates the extent to which the two maps agree in terms of location of each category (Eastman 2016). The model was accepted to make future projections only if the Kappa value was greater than 80% (Araya and Cabral 2010).