## 5 Results
The quartile-based classification serves as a complementary tool for spatial interpretation, allowing for the identification of areas with similar environmental conditions that are more or less favorable to water accumulation and runoff. This approach ensures objectivity and reproducibility in the absence of historical flood records, and is grounded in real, observed data. The predictions of the model are used to construct the transition matrix. Figure 10 presents the transition probability matrix derived from the full time series of historical flood risk classifications. The matrix captures the stochastic dynamics of flood risk  
evolution across all available monthly observations. Each cell represents the normalized probability of transitioning from one risk state to another (Low, Moderate, High, Very High) based on observed transitions over time. This matrix is spatially aggregated and reflects the average behavior across the entire study area. The transition matrix is a square matrix in which each element (\(i,j\)) represents the number of transitions observed from state \(i\) to state \(j\) in the model's predictions. The predictions generated with the Markov chain are obtained starting from the initial state (first prediction of the model) and for each subsequent step, the transition matrix is used to determine the probability of transition to the subsequent states. The next state is chosen based on the probability of transition. The transition matrix obtained represents the probabilities of transition between different states of flood risk: low, moderate, high, and very high. Numeric values are displayed within cells for clarity. The values are represented with different colors to identify the level of risk. Analyzing the data reveals that low-risk areas have a 22.2% chance of remaining in their current state. However, they also have a 22.2% probability of transitioning to a moderate-risk state. Additionally, there is a slightly higher probability of 27.8% that these areas will move to a high or very high-risk state. Moderate-risk areas have a 10.7% chance of improving and moving to a low-risk state. They also have a 28.6% probability of remaining in the moderate-risk category. However, the likelihood of worsening and transitioning to a high-risk state is 35.70%, and 24.0% for escalating to a very high-risk state. It is important to note that while the probability of worsening from moderate to high is significant, the reverse transition, from high to moderate, has an even higher likelihood (46.4%). This suggests that high-risk areas are statistically more likely to improve than moderate-risk areas are to deteriorate, highlighting the dynamic and potentially reversible nature of flood risk in certain zones. Figure 10: Transition Matrix. High-risk areas show a 14.3% chance of improving and transitioning to a low-risk state. They have a significant 46.4% probability of moving to a moderate-risk state. The probability of staying in the high-risk category is relatively low, at 17.9%, while there is a notable 22% chance of moving to a very high-risk state. Lastly, areas categorized as very high-risk have a 28.0% chance of improving and transitioning to a low-risk state and a 16.0% chance of moving to a moderate-risk state. The probability of moving to a high-risk state or remaining in the very high-risk category is 32.0% and 24.0%, respectively. For instance, the probability that a moderate-risk area may escalate to a high-risk state (35.7%) indicates the need for prioritized monitoring and preventive measures. Thus, the transition matrix serves not only as a descriptive tool but also as a valuable resource for informed decision-making in proactive risk management. This analysis helps us better understand the transition dynamics between different flood risk states, allowing for more targeted interventions to mitigate risks in the most vulnerable areas.