## 1 Introduction  
Over the past few years there has been a tremendous increase in the number of devastating wildland-urban interface (WUI) fires because of climate change, fuel management practices, and increased human development in WUI areas [1, 2]. A couple of recent examples in Asia and North America are the WUI fires that occurred in South Korea in 2019 [3] and those in California in the United States in 2018 [4, 5, 6]. Portugal experienced two major wildfires in 2017, resulting in 117 deaths and 204 injuries, according to reports released by the Portuguese government [7, 8]. Recently, standard wildfire curves that can be used in the protection design of dwellings located in the WUI against wildfires were reported [9]. Firebrands are a dominant mechanism for the spread of fires [10], as they are transported by wind and can ignite secondary fires far away from the fire start point [11]. The formation of firebrands is a part of the fire generation process and an indirect action of wildfire in dwellings. Trees and bushes, being combustible materials in a forest fire, become so warm that they break into small pieces that are carried out by the wind and create spot fires. The firebrand accumulation heats up the contact surface, resulting in the formation of flammable fuel mixtures above the contact surface, and the continuation of heat leads to ignition, which commonly happens in wooden structural components [12, 13]. A better understanding of thermal properties and transportation for firebrands can help to slow down the fire spread in WUI communities. Structures ignite in a WUI fire through three different pathways: direct flame contact, radiation heat transfer, and the transport of firebrands [1], as shown in Figure 1.  
Investigations of past fires [7; 8; 15; 16] have found that firebrands play the main role in structure losses due WUI fires. Firebrands travel from 2 km to 9 km ahead of the fire start point to the dwellings due to the strong action of the wind [7; 16] and remain incandescent for several hours. The safety of dwellings must take into account all of these potential sources of ignition, therefore, the exposure from firebrands (indirect exposure) deserves special attention because the international literature indicates that at least half of ignition is due to them [17]. Firebrand transportation has been studied in recent decades [14; 18; 19; 20; 21; 22; 23], but only recently, several experimental investigations of ignition properties [11], thermal properties, firebrand amount-size exposure [24; 25; 26; 27], and wood structure vulnerability due to firebrands have been addressed [28; 29; 30; 31; 32; 33; 34; 35; 36]. An experimental study is presented that investigates the heat flux from firebrand accumulations to a substrate [37]. The findings show that high-temperature firebrands may not represent the most dangerous condition as these particles do not retain high temperatures for long periods of time. The accumulation is capable of sustaining smouldering compared to fully charred particle accumulations, thus, these may be considered more hazardous to solid combustible structural material [37]. An experimental campaign was conducted, where different types and geometries of firebrands were burned in controlled conditions until they reached the thermal pyrolysis state [38]. The temperature of the firebrands and the transfer temperature to the surfaces were measured using a test setup with metal plates and thermocouples, in order to develop a firebrand accumulation curve to be used in the future design for the protection of dwellings against the indirect action of a wildland fire [38]. Theoretical models and analytical expressions were developed to investigate the interaction of the firebrand with a target fuel bed (contact surface), using the \"hot spot\" theory, which was validated by experiments that consisted in heating the samples in a basket and identifying critical conditions for ignition [39; 40; 41; 42; 43; 44]. [PERSON] et al.