*2.9. Validation*

In terms of validating the CA-Markov predictions and evaluating the applied models results, validating process map predictions based on actual maps can be achieved. In this study for validating the model, the condition of land cover in 2002 and 2015 was estimated and compared with actual land use maps [56,92]. The precision of simulation or classification image results, pixel-by-pixel, is accessed via the kappa accuracy index.

Kappa index of agreemen<sup>t</sup> provided *Kno, Klocation, KlocationStrata* and *Kstandard* index. This statistic ranges from −1 (significantly worse than random) to 1 (perfect), but it typically lies between 0 and 1. *Kno* (kappa for no ability) showed the proportion between the actual map and the prediction map accurately determine the location, *Klocation* (kappa for location) showed the proportion between the actual map and the prediction map based on input at a location, *Klocationstrata* showed the proportion between the actual map and prediction map based on the number, and *Kstandard* (kappa index) aims to compare the proportion that is observed to be correct with the proportion that is expected due to probability [93]. The formulas for the summary statistics following Equations (10)–(13) [93,94]:

$$K\_{\rm no} = \frac{\left(M \, \left(m\right)N \, \left(n\right)\right)}{\left(P \, \left(p\right) - N \, \left(n\right)\right)}\tag{10}$$

$$K\_{\text{location}} = \frac{\left(M \left(m\right)N \left(m\right)\right)}{\left(P \left(m\right) - N \left(m\right)\right)}\tag{11}$$

$$K\_{\text{locentiustrata}} = \frac{\left(M \, \text{(m)} \, H(m)\right)}{\left(K \, \text{(m)} - H \, \text{(m)}\right)}\tag{12}$$

$$K\_{\text{standard}} = \frac{\left(M \, \text{(m)}N \, \text{(n)}\right)}{\left(P \, \text{(p)} - N \, \text{(n)}\right)}\tag{13}$$

where no information is defined by *N*(*n*), medium stratum level information by *H*(*m*), medium grid cell level information by *M*(*m*), perfect grid cell-level information given imperfect stratum-level information by *K(m)* mean, and perfect grid cell-level information across the landscape by *<sup>P</sup>*(*p*).
