## 1 Introduction
Machine learning (ML) algorithms such as Random Forest (RF), Support Vector Machines (SVMs), and deep neural networks have demonstrated strong capabilities in processing large-scale, heterogeneous environmental datasets, including meteorological time series, topographic features, land use classifications, and hydrological indicators. These models are particularly effective in capturing complex, nonlinear interactions among variables, enabling the classification of flood-prone areas and the forecasting of extreme events with enhanced accuracy. For instance, RF is widely adopted for its robustness, interpretability, and suitability for spatial risk mapping, while deep learning architectures such as Long Short-Term Memory (LSTM) networks and Convolutional Neural Networks (CNNs) are increasingly employed to model temporal dependencies and spatial patterns in flood dynamics. These AI-driven approaches are reshaping predictive modeling in environmental sciences by offering scalable, data-driven solutions that complement or surpass traditional hydrological models [14; 15; 16; 17; 18]. Additionally, the integration of sequential models, such as Long Short-Term Memory (LSTM) [19], has enhanced temporal event prediction by capturing long-term dependencies in historical data. However, these models require significant computational resources and a complex training phase. In this context, flood risk forecasting is crucial in spatial planning and civil protection. However, the current state of traditional forecasting models that rely on hydrological or statistical approaches is not without its limitations. These models often struggle with accuracy and adaptability to complex and dynamic scenarios, highlighting the need for a new approach. This study proposes an innovative approach that could potentially revolutionize flood risk forecasting. It integrates machine learning algorithms, specifically Random Forest, with Markov chains. It utilizes high-resolution data derived from LIDAR, lithological maps, land use, and precipitation to improve the accuracy of flood risk assessments and support informed decision-making in land management. The main contributions of this work include the following:  
* Developing a hybrid RF-Markov predictive model for the dynamic simulation of flood risk. * The use of LIDAR data to generate high-resolution digital terrain models. * A quantitative comparison with LSTM models to validate the effectiveness of the proposed method. * Creating flood susceptibility maps to aid urban planning and mitigation strategies. The recent literature has explored employing deep learning techniques and probabilistic models for flood prediction. However, the effective integration of spatial accuracy and temporal modeling is often lacking. Our approach bridges this gap by combining the robustness of tree-based models with the capability of Markov chains to model the temporal evolution of risk. Our challenge is the difficulty of accurately predicting flood-prone areas in complex urban environments. Our model addresses this issue by integrating geospatial and temporal data into a predictive framework that is interpretable, efficient, and adaptable to various territorial contexts.