P. pinea (stone pine) stand (<40 years old) located in the Sierra Morena mountains in southern Spain (coordinates ETRS89 30N: X: 284793-285038; Y: 4218650-4218766) was selected as the study site for full-scale experiments ( Fig. 1 ). P. pinea is one of the most important tree species in the Mediterranean region. It is patchily distributed all around the northern and eastern Mediterranean, from Portugal to Syria as well as along some coastal areas of the Black Sea, from sea level up to 500-600 m in the northern Mediterranean and up to 800-1400 m in the eastern Mediterranean ( Fady et al. , 2004 ). In Spain, P. pinea occupies an area of approximately 480,000 ha in both natural and afforested stands ( Bravo-Oviedo & Montero, 2008 ). For the present study, this species of pine was chosen for an opportunity reason. The area of burning is included in the priority areas of fuel treatment for the reduction of fire hazard planned by the Provincial Forest Fire Service. The selection was based on the annual fuel treatment planning and counted with the support of suppression teams and equipment for a fire escape contingency. In addition, the structure of the young stone pine stands is similar to that of other species of Mediterranean pines, and therefore it is possible to extrapolate the results to other species of pine associated with the model 7 of the Northern Forest Fire Laboratory (NFFL) System ( Anderson, 1982 ). The climate in the selected area is classified as continental Mediterranean (mean annual precipitation, 492.92 mm; mean annual temperature, 15.47 °C; and mean temperature of coldest and hottest months, respectively, 6.62 and 26.31 °C). Altitude ranges from 664 and 716 m, with a mean slope of 34.25 %. The soils are siliceous with acid metasedimentary rocks.

Three rectangular plots (60 m × 30 m) were established in the experimental site. Vegetation in Plots 1 and 2 ( Fig. 1a ) corresponds to the HPM5 surface fuel model ( Rodríguez y Silva & Molina, 2012 ) and is characterized by a combination of litter, grasses and shrubs under canopy. Plot 3 corresponds to model HR, litter under canopy, which is similar to model 9 in the NFFL System.

Litter, duff (humus) and understory fuel (vegetation under canopy) variables (average understory height and cover per species, litter and duff depth and cover) were characterized by continuous measurements made on two perpendicular transects across the plots. The fuel loads were determined by using destructive sampling in adjacent areas (30 quadrats of 0.4 m x 0.4 m for litter and duff and 28 samples of 1 m × 1 m for understory). Litter and understory fuel of thickness less than 6 mm was considered available fuel. The inventories were repeated in the plots after carrying out the experiment to estimate the fuel load consumed during burning.

Canopy and tree variables (diameter at breast height, height, crown base height, crown diameter) were measured in two circular plots (radius 10 m) in each rectangular plot ( Table 1 ). Three representative trees were felled in an adjacent area. The fractions available for burning (branches and needles sorted by diameter size class <6 mm and 6-25 mm) were weighed and dried (100 ºC, 24 h) to enable calculation of the Crown Fuel Load (CFL, kg/m ² ). The load over depth method ( Van Wagner, 1977 ) was used to calculate Canopy Bulk Density (CBD, kg/m ³ ) ( Table 1 ). This inventory was repeated after burning to estimate consumed fuel load by harvesting six trees.

In order to estimate the wind speed correction factor, micrometeorological parameters were measured by three weather stations placed under the canopy (at a height of 1.30 m) for 6 days before the experiment. An additional weather station was sited (at a height of 10 m) in an adjacent area as control (Tables S1, S2, S3 and S4 [suppl]). These automatic weather stations were used to monitor relative humidity, temperature, wind speed and wind direction throughout the experiment.

Samples of fine fuels (dead and live) were collected before the experiment and stored in hermetically sealed plastic bags for subsequent estimation of Fuel Moisture Content (FMC) in the laboratory within 24 hours.

In order to monitor the crown fire Rate of Spread (ROS) and temperatures reached during the experiment, 56 K type thermocouples (1 mm of diameter) were located at four different positions across four transects ( Fig. 1b ): (1) two thermocouples were placed at the Crown Base Height (CBH) level (roughly 2 m) in each tree: one in a windward (and upslope) position and the other one at an angle of 90º from the latter, and (2) two thermocouples were placed in the middle of the length of the crown (at a height of 4 m, in the same positions as before), i.e in the layer with highest canopy bulk density. The flame residence time t _r was estimated in (a) the passive crown fire events as the residence time of flame temperature (above 300 ºC), measured by thermocouples positioned in the same tree (2 and 4 m height), and in (b) the active crown fire events as the residence time of flame temperature (above 300 ºC), measured by thermocouples located in the crown (height 4 m) in two consecutively burned trees.

The fire was initiated with a dip torch. A fire line was established along the border of the experimental area and an upslope fire front was established. Crown fire events were monitored visually by three independent observers and automatically by thermocouples (see above). Passive crown fire events were observed along the fire line, and automatically-collected data were completed with visual observations of flame residence time. All field data were used as inputs to compare with the theoretical predictions from the most common crown fire propagation models.

In previous studies carried out in the Region of Andalusia (southern Spain), validation of crown fire models has relied on wildfires technical reports, cases study of large fires occurred and the experimental fires undertaken in the region. In these studies, comparisons between rates of fire spread observed in the field and their predictions have transmitted a certain degree of uncertainty, as the predictions did not yield similar behaviour parameters to those observed ( Molina, 2015 ). A new approach to crown fire spread was developed on the basis of the models proposed by Rothermel (1991) , Finney (1998) and Cruz et al. (2005) , but with an integration parameter included in order to adapt the simulations to Mediterranean conditions. It was thus necessary to incorporate another two variables (wind speed and canopy cover) to explain real events ( Eq. [1] ). Information about the uncertainty (Ʋ) was important in testing and validating the new model for Mediterranean forest conditions. In this sense, the uncertainty measurement was lower for the new integrated equation ( Ʋ= 43.19) than for approaches used by Rothermel and Finney (Ʋ= 74.70) and by Cruz et al. (Ʋ=58.49) according to some crown fire events (Molina et al. , 2013).

This experiment, conducted in the field facilities of the Lourizán Forest Research Centre (Pontevedra, NW Spain), aimed to obtain direct information on P. pinaster crown ignition caused by the radiation from a high intensity surface fire front, spreading towards a clump of pine trees, simulating conditions in absence of wind-forced convection. A flat terrain and meteorological conditions with very low wind velocity were selected to minimize the effect of air of slope-forced convection on energy transport from the surface fire to tree crown. A plot of length 12 m and width 10 m was installed and surrounded by a fire break. A surface fuel layer made from a mixture of plants of the shrub species Pterospartum tridentatum (L.) Willk. and Erica spp., previously collected in the field and air-dried for several weeks, was constructed and used to carry a surface fire. This added material was weighted and homogenously distributed across the plot to obtain 9.4 kg/m ² (oven-dry basis) of fuel load, with relatively low moisture content to enhance a high combustion rate and the development of a sustained high vertical flame and linear intensity. Twenty measurements of the shrub layer fuel height were systematically made. Eight P . pinaster trees (diameter at breast height from 8.3 to 11.8 cm, total height from 8.2 to 10.5 m, and height to live crown from 1.8 to 4.2 m) were felled in a nearby area and immediately placed in two rows at one end of the plot. The trees were inserted vertically, with the help of a small crane, in previously excavated cylindrical holes, which were filled with water to minimize foliar moisture loss. Eight samples of the added shrub fuel (1 m × 1 m) were collected and classified by size classes (1 h, 10 h and 100 h) and oven-dried in the laboratory for 24 h (100ºC) to determine pre-fire surface fuel load.

Wind direction and speed (2 m, 4 m and 6 m height), relative air humidity and air temperatures during the experiment were measured and recorded every second in a meteorological station installed in the nearby in the upwind position. Immediately before ignition, samples of shrub, trees needles and branches were collected to determine the fuel moisture content after oven-dried for 24 h (80ºC).

The fire was ignited along the edge of the plot opposite the trees rows. Fire behaviour was monitored during the experiment. Eight fine thermocouples were regularly located inside the shrub fuel area to determine fire rate of spread, and four thermocouples were installed in each tree crown at heights of 2 m, 4 m, 6 m and 8 m, on needles fascicles. The thermocouples were inconel-sheathed, type K (chromel-alumel), of 1 mm of diameter, with bared wires of 0.13 mm diameter with an exposed junction. Temperatures were recorded at 1-s intervals during the fire by dataloggers. Images of fire development and flame characteristics were recorded, at ground level, with one infrared thermographic camera and one video camera, and allowed estimate flames length. After flaming, a smouldering phase took place making it inadequate post-fire sampling to calculate fuel consumption during the flaming phase. Hence, linear intensity of the surface fire was calculated following two approaches. First, from the relationship between this parameter and flame length ( Thomas, 1963 ). Second, according to Byram’s equation ( Byram, 1959 ), considering total 1 h material and half 10 h material as consumed fuel load during flame phase. A value of 19,500 kJ/kg was used for the heat content of the fuel complex.

Stocks et al. (2004b) and Taylor et al. (2004) reported that a physically-based model proposed by Nelson & Adkins (1988) yielded better cross-validations than the models developed by Rothermel (1991) and Finney (1998) during the International Crown Fire Modelling Experiment (ICFME) carried out in Canada ( Stocks et al. , 2014a ). This model ( Eq. [2] ) requires the value of residence time of the flame t _r to predict ROS:

Crown fire activity was only observed in Plot 1 and in the lower part of Plot 2 ( Fig. 1 ). Surface fire spread was observed in Plots 1, 2 and 3. The average total surface fuel load consumed was 2.05 kg/m ² ( Table 2 ) and the estimated canopy fuel load consumed was 0.85 kg/m ² ( Table 3 ). Three crown fire events (A, B and C) were monitored in the “Las Traviesas” experiment ( Fig. 1c , Fig. 2 ). Although wind speed was different in event C than in events A and B, the differences in the ROS between “events A and C” and “event B” seem to be due to differences in CBD ( Table 4 ). Wind speed was moderate (5.9 km/h), but a mass fire ( Finney & McAllister, 2016 ) was observed, generating an increase in local wind speed (14 km/h) detected by the meteorological station closest to the crown fire event C ( Table 4 ). The signal recorded by the thermocouples located in the tree crowns ( Fig. 3 ) indicated that ROS ranged between 8 and 21 m/min ( Table 4 ). ROS of event C (21 m/min) differed from that of events A and B (8-10 m/min). Field ROS were compared with the theoretical predictions from the Rothermel-Finney approach, the Cruz et al. approach and the new mathematical integrated approach ( Eq. [1] ).

The most commonly used crown fire models ( Rothermel, 1991 ; Finney, 1998 ; Cruz et al. , 2005 ) underestimated ROS relative to observed values (particularly the Cruz et al. approach) ( Table 4 ). Although the best-fit for event A was yielded by the Rothermel and Finney model, the best-fit for events B and C was achieved with the proposed new integrated model ( Table 4 ).

Shrub fuel load was 5.6 kg/m ² for 1 h material (<0.6 cm of thickness) and 3.8 kg/m ² for 10 h material (between 0.6 and 2.5 cm). Shrub layer bulk density was 7.3 kg/m ³ . FMC immediately before ignition of fuel samples is shown in Table 5 . Air temperature was 20ºC and air humidity was 75%. Mean wind speed during the experimental fire was less than 1 km/h.

Despite low FMC, surface fire ROS was low (2.2 m/min), likely due to low wind velocity and high fuel compactness (more than twice the usual value for similar shrub species; Arellano et al. , 2016 ). Flames reached 7-12 m and were vertical during the fire run. This was likely due to high combustion rate (the heat generated was sufficient to partially melt some 20 mm diameter steel rods placed in the area to indicate the flame height), low wind velocity and fire front indraft, resulting in a high fireline intensity (9,500 kW/m following Thomas (1963) approach, and 5,363 kW/m following Byram (1959) approach). The maximum temperatures reached in the shrub layer ranged from 954 to 1,168 ºC, whereas in the tree crowns maximum temperatures ranged from 82 to 1,224 ºC.

Analysis of the information recorded by thermocouples ( Fig. 4 ) and the images of the infrared thermography camera ( Fig. 5 ) revealed that crowns did not start to ignite (temperatures higher than 300 ºC) until the distance between the fire and trees was less than 2 m. The average of t _r was 22 s (range between 12 s and 31 s). A crown fire simulation using the Crown Fire Initiation and Spread (CFIS) model ( Alexander et al. , 2006 ) using the meteorological and fuel load information of the experimental fire predicted a probability of crown fire initiation of 61%, consistent with that observed in the experiment.

The Mass Loss Calorimeter experiments ( Fig. 6 ) yielded a difference between TFO and TTI values of 44±10 s (average±standard error) as an estimate of t _r (range between 19 s and 71 s). This is consistent with visually observed values for passive crown fire during the “Las Traviesas” experiment (range, 12-30 s, and mean value, 22 s), small-scale experiments (range, 12-31 s, and mean value, 21 s) and is within the range obtained by Taylor et al. (2004) during the ICFME (range 29-37 s, and mean value, 34 s). Madrigal et al. (2013) reported an average t _r value of 30 s obtained during an experimental series of crown fire initiation tests in an outdoor wind tunnel. The prediction yielded by the Nelson & Adkins (1988) model using t _r = 30 s ( Table 6 ) was similar to the rate of spread estimated by Cruz et al. (2005) model and was a poorer estimate than provided by the Rothermel-Finney model ( Table 4 ).

Analysis of time-dependent temperature curve in the crowns during the full-scale experiment ( Fig. 3 ) indicated a t _r of between 12 s and 30 s. The use of average values of t _r = 20 s observed during crown events in the full-scale and small scale experiments ( t _r = 22s) and minimum values during bench-scale experiment ( t _r = 19 s) yielded a better overall estimation of ROS but greatly underestimated the rate of spread ( Table 6 ). The estimates closest to the observed ROS corresponding to t _r = 12 s for event C (considering the sum of consumed surface and crown fuel load as the fuel consumed W in the Nelson and Adkins equation) ( Table 6 ).