## 1 Introduction  
The EU figure of 770,710 hectares burned in 2022 is the highest since records began in 2006. Spain leads the ranking with 299,436 hectares devastated by fire, more than triple the ten-year average, according to data provided by the European Forest Fire Information System (EFFIS) consulted at the end of September (see Figure 1 and [1]). In just one province, Zamora, more than 60,000 hectares have been burned in two of the largest fires thus far in Spain. in this area so far. Their rate has nonetheless increased in the U.S. Pacific Northwest and Western Canada. The above data provided only a very partial view of the problem of forest fires. Africa, where fires are widely used to clear grasslands and savanna, accounts for around seventy percent of the area burned globally. Many of the fires in South America involve the Amazon rainforest. The latest fire season in the Amazon region (August-September) has registered the highest number of fires in the last decade, although it is not clear whether this upward trend will continue. The bushfire season in Australia recorded the most-serious fires. For an overall view of the global wildfire situation, we recommend [3] and its references. Although some wildfires occur naturally and help keep forest ecosystems healthy, an astonishing percentage are caused by human-related activities. Wildfires not only destroy lives, wildlife habitats, forests, and property, they also accelerate climate change. Understanding and predicting the behavior of a system as complex as a wildfire is an undeniably useful tool for reducing its negative effects. Mathematical modeling and numerical simulation play a fundamental role, and they can ultimately assist in decision-making in prevention, fire-fighting, and further analysis. Improved remote sensing information technologies, advanced computational capabilities, and the development of communication technology have exponentially increased the efficiency and applicability of wildfire modeling. The quasi-empirical models combined with the software developed for extending the utility of these models to the landscape level has resulted in comprehensive and accurate tools for predicting wildfire spread, such as FlamMap-FARSITE [4; 5] and Prometheus [6]. The rapid increase in computing power and advances in technology allow more complex models to become a real option, so research is focusing on physical-based models coupled with the atmosphere [7], for example HIGRAD/FIRETEC [8] or WFDS [9]. These models are computationally expensive, but there are also other more affordable atmosphere-wildfire models combining empirical or simplified quasi-physical fire models with atmospheric ones, such as WRF-SFIRE [10] or MesoNH-ForeFire [11]. The advances made in remote sensing information technologies (i.e., satellites, aircraft, and drones) have provided more and better data for feeding wildfire simulation models. A new type of model, referred to as data-driven or data-assimilation [12], is a result of these technologies. Their objective is to reduce the uncertainties in both model fidelity and input data by using real-time observations of wildfire dynamics. Artificial intelligence can also exploit the current ability to obtain increasingly more reliable data on wildfires for predicting their behavior [13]. Nevertheless, the use of wildfire spread modeling and the tools developed accordingly have been relatively limited in practice due to the high  
Figure 1: Burned hectares in the most-affected European countries (more than 10,000 ha) during 2022. Data from EFFIS on 28 September 2022.  
level of uncertainty in both the models and the available data for their initialization and parametrization. Reducing the level of uncertainty continues to be one of the unresolved challenges of wildfire modeling. The model described in this paper, PhyFire, is framed within the physical-based models. It is a single-phase simplified two-dimensional model based on the fundamental physics of combustion and fire spread.