Abstract: This is the first part of two papers concerning fire-spotting generated fires. In this part we deal with the impact of macroscale factors, such as the atmospheric stability, and in the second part we deal with mesoscale factors, such as the flame geometry. For this study we adopt an approach where the motion of the front is split into a drifting part and a fluctuating part. The drifting part, that can be provided by choosing an existing operational model, is here based on the level-set method in analogy with WRF-SFIRE model. The fluctuating part, that is the result of a comprehensive statistical description of the physics of the system and includes the random effects, is here physically parametrized to include turbulent hot-air transport and firebrand landing distance. In order to highlight the net effects of the random contributions due to turbulence and firebrand flying, a simplified model without fire-atmosphere coupling is considered. Numerical simulations show that the atmospheric stability is an important factor for wildfire propagation. In particular, unstable conditions boost the number of fire-spotting generated fires at small elapsed times as well as the strength of turbulence leading to rapid merging and the formation of unburned islands surrounded by the fire. Stability conditions have then an effect on the risk and the management associated to fire-spotting generated fires. In fact, with stable conditions (corresponding for example to the night-time) the turbulence is not strong enough to merge the fires and, at large elapsed times, this results into a higher number of independent fires but lower burned area with respect to unstable conditions (corresponding for example to the day-time) when the push of turbulence leads to faster merging resulting into a lower number of independent fires but higher burned area. Finally, with stable conditions less fire fronts need to be managed at short time, but more fire fronts need to be managed than with unstable conditions that however show a higher risk because of the merging of independent fires.
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