Developing Models to Predict the Number of Fire Hotspots from an Accumulated Fuel Dryness Index by Vegetation Type and Region in Mexico

Article Developing Models to Predict the Number of Fire Hotspots from an Accumulated Fuel Dryness Index by Vegetation Type and Region in Mexico D. J. Vega-Nieva 1, J. Briseño-Reyes 1, M. G. Nava-Miranda 2, E. Calleros-Flores 1, P. M. López-Serrano 2,*, J. J. Corral-Rivas 2ID , E. Montiel-Antuna 1, M. I. Cruz-López 3, M. Cuahutle 3, R. Ressl 3, E. Alvarado-Celestino 4ID , A. González-Cabán5, E. Jiménez 6, J. G. Álvarez-González 7ID , A. D. Ruiz-González 7, R. E. Burgan 8and H. K. Preisler 9 1Facultad de Ciencias Forestales, Universidad Juárez del Estado de Durango, Río Papaloapan y Blvd, Durango S/N Col. Valle del Sur, CP 34120 Durango, Mexico; [email protected] (D.J.V.-N.); [email protected] (J.B.-R.); [email protected] (E.C.-F.); [email protected] (E.M.-A.) 2Instituto de Silvicultura e Industria de la madera, Universidad Juárez del Estado de Durango, Boulevard del Guadiana 501, Ciudad Universitaria, Torre de Investigación, 34120 Durango, Mexico; [email protected] (M.G.N.-M.); [email protected] (J.J.C.-R.) 3Comisión Nacional para el Conocimiento y Uso de la Biodiversidad (CONABIO), Liga Periférico-Insurgentes Sur 4903, Parques del Pedregal, Del. Tlalpan, CP 14010 Ciudad de Mexico, Mexico; [email protected] (M.I.C.-L.); [email protected] (M.C.); rainer[email protected] (R.R.) 4School of Environmental and Forest Sciences. University of Washington, Mailbox 352100, University of Washington, Seattle, WA 98195, USA; [email protected] 5Pacific Southwest Research Station, US Department of Agriculture Forest Service, (retired), 4955 Canyon Crest Drive, Riverside, CA 92507, USA; [email protected] 6Centro de Investigación Forestal–Lourizán, Xunta de Galicia (Spain), Carretera de Marín km 3.5, CP 36153 Pontevedra, Spain; [email protected] 7Departamento de Ingeniería Agroforestal, Universidad de Santiago de Compostela, Escuela Politécnica Superior de Ingeniería, Campus Universitario s/n, 27002 Lugo, Spain; [email protected] (J.G.A.-G.); anadaria.r[email protected] (A.D.R.-G.) 8Rocky Mountain Research Station, USDA Forest Service, (retired), 1505 Khanabad Drive, Missoula, MT 59802, USA; [email protected] 9Pacific Southwest Research Station, USDA Forest Service, 800 Buchanan, St. Albany, CA 94710, USA; [email protected] *Correspondence: [email protected]; Tel.: +52-618-233-6612 Received: 20 February 2018; Accepted: 29 March 2018; Published: 7 April 2018   Abstract: Understanding the linkage between accumulated fuel dryness and temporal fire occurrence risk is key for improving decision-making in forest fire management, especially under growing conditions of vegetation stress associated with climate change. This study addresses the development of models to predict the number of 10-day observed Moderate-Resolution Imaging Spectroradiometer (MODIS) active fire hotspots—expressed as a Fire Hotspot Density index (FHD)—from an Accumulated Fuel Dryness Index (AcFDI), for 17 main vegetation types and regions in Mexico, for the period 2011–2015. The AcFDI was calculated by applying vegetation-specific thresholds for fire occurrence to a satellite-based fuel dryness index (FDI), which was developed after the structure of the Fire Potential Index (FPI). Linear and non-linear models were tested for the prediction of FHD from FDI and AcFDI. Non-linear quantile regression models gave the best results for predicting FHD using AcFDI, together with auto-regression from previously observed hotspot density values. The predictions of 10-day observed FHD values were reasonably good with R 2 values of 0.5 to 0.7 suggesting the potential to be used as an operational tool for predicting the expected number of fire hotspots by vegetation type and region in Mexico. The presented modeling strategy could be replicated for any fire danger index in any region, based on information from MODIS or other remote sensors. Forests 2018,9, 190; doi:10.3390/f9040190 www.mdpi.com/journal/forests Forests 2018,9, 190 2 of 18 Keywords: MODIS; fire hotspots; fire occurrence risk; fire danger systems 1. Introduction The quantification of the influence of varying fuel dryness on temporal fire occurrence risk is critical for improving decision-making in strategic fire management planning (e.g., [ 1 – 3 ]), especially under growing conditions of vegetation stress associated with climate change, which can alter the length and severity of the fire seasons (e.g., [4–7]). Based on weather information, several operational fire danger systems have been developed to estimate fuel dryness and associated fire occurrence risk (e.g., [ 8 – 13 ]). Examples of these widely applied weather-based fire danger indices are those from the Canadian Forest Fire Danger Rating System, (CFFDRS) (e.g., [ 14 – 17 ]), or the fire danger indices of the National Fire Danger Rating System, (NFDRS) (e.g., [ 18 – 20 ]). Such indices have demonstrated their usefulness for predicting the temporal fire occurrence probability (e.g., the expected days of fire activity thorough the season; [ 18 , 21 , 22 ]) and also for predicting the temporal evolution in the expected number of fires (e.g., [ 14 , 15 , 23 – 26 ]), which can be used for decision support in strategic fire suppression resource allocation and prioritization (e.g., [ 1 , 27 ]). In addition, some authors have proposed indices that combine both weather and satellite information for predictions of fire occurrence risk [ 28 – 35 ] based on works that have demonstrated the potential of satellite sensors for monitoring vegetation greenness and associated fire danger and risk (e.g., [36–41]). One of the most used operational indices that integrates meteorological and satellite information is the Fire Potential Index (FPI) [ 28 ]. The FPI combines remotely sensed estimates of vegetation greenness—as measured by 10-day Normalized Difference Vegetation Index (NDVI) composites—with daily estimates of dead fuel moisture content [ 42 , 43 ] for mapping fuel dryness conditions and associated fire risk and danger. The FPI fuel dryness index has been operationally used for fire danger monitoring and occurrence risk prediction in the United States of America (USA) [ 28 , 33 – 35 ], Indonesia [ 44 ], and on the European continent (e.g., [ 29 – 31 , 45 ]), including studies of regional application in northern Spain [ 46 – 48 ]. Several of these works have highlighted the need to understand how the same values of a fuel dryness index such as FPI result in different patterns of fire occurrence under different bioclimatic regions and vegetation types. In Mexico, Manzo-Delgado et al. [ 49 , 50 ] demonstrated the potential of the temporal evolution of NDVI-based indices as indicators of fuel drought and associated fire risk for the central region of the country. Some studies have evaluated the role of weather variables such as precipitation or temperature on fire occurrence risk (e.g., [ 51 – 53 ]), mainly at regional or local scales. The work of Pompa-Garcia et al. [ 54 ] explored the association between fire records and the Standardized Precipitation-Evapotranspiration Index (SPEI) drought index, finding that the relationships of drought and fire vary by regions in the country. The FPI system [ 28 ] was tested by Sepulveda et al. [ 55 , 56 ] in the region of Baja California, but its performance has not been tested nationally for fire occurrence prediction. Fire monitoring efforts in Mexico country include the development of an interface for active fire hotspots [ 57 ] near-real time monitoring [ 58 , 59 ]. The monitoring of fire hotspots is used for strategic decision making in fire suppression by considering the number of active fire hotspots as indicators of the level of fire ignitions and potential for forest fire spread in the main regions of the country. Previous analysis of monthly fire MODIS hotspot and NDVI-based fuel greenness dynamics for the main vegetation types in Mexico [ 60 , 61 ] suggested that the relationship between fire hotspots occurrence and fuel dryness varied by month, with similar values of fuel dryness resulting in a higher number of fire hotspots as the fire season advanced. These results suggested that the accumulated dryness from the previous months might have potential for explaining the temporal evolution in fire hotspot occurrence. Forests 2018,9, 190 3 of 18 Based on the above-mentioned results, this study provides further insight into the potential benefit of using an accumulated fuel dryness to explain forest fire occurrence variability. The current study tested an Accumulated Fuel Dryness Index (AcFDI), to predict 10-day (dekad) number of MODIS active fire hotspots, expressed as a Fire Hotspot Density index (FHD). The AcFDI was calculated from the temporal accumulation of a remote-sensing-assessed fuel dryness index (FDI)—based on the structure of the FPI index [28]—for the main ecoregions and vegetation types of Mexico. Overall, the considerably wide variety of vegetation domains, meteorological conditions, and fire seasonality patterns existing in Mexico offered a valuable opportunity to explore the relationships of fire occurrence and fuel dryness under a variety of vegetation types, ecoregions, and weather conditions. The specific goals of the current work are (1) to estimate thresholds for fire occurrence for the fuel dryness index (FDI) for each vegetation type and region in Mexico; and (2) to develop models to predict 10-day MODIS Fire Hotspot Density (FHD) for the main vegetation types and regions in Mexico. 2. Materials and Methods 2.1. Study Area The area of study was the whole Mexican territory. Figure 1shows the main vegetation types in the country according to the most recent land use map (INEGI Land Use Map Series V, year 2011, 1:25,000 http://www.inegi.org.mx/geo/contenidos/recnat/usosuelo/) of the National Institute of Geography and Statistics (INEGI in Spanish). Given the well-documented variations in fire regimes seasonality in the country (e.g., [ 62 – 65 ]), five geographical regions were established: Northwest (NW), Northeast (NE), North-Centre (NC), Centre (C), and South (S) (Figure 1). The definition of regions was based on the North American Level 3 Ecoregions Map (EPA, https://www.epa.gov/ecoresearch/ecoregions-north-america), together with previous analysis of the temporal trends and spatial patterns of clustering in fire hotspots in the country [ 54 , 60 , 61 ]. Vegetation types were reclassified into the following categories: temperate forest (FOR), dry tropical forest (DTROPF), seasonally dry tropical forest (SDTROPF), seasonally wet tropical forest (SWTROPF), wet tropical forest (WTROPF), wetlands (WET), desert shrubby vegetation (DSHR), natural pastureland (NPAS), and agricultural croplands (AGR) (Figure 1). Agricultural lands were included in our analysis because of the relevance of agricultural burns, including escaped burns from agriculture and slash-and burn agriculture in the occurrence of forest fires in the country—particularly in the Centre and South regions (e.g., [ 54 , 61 , 66 ]). The desert shrubby vegetation of all regions and natural pastureland of the North-Centre arid region were excluded from our analysis because of the relatively low registered number of hotspots and fire suppression registers in these vegetation types and regions. This resulted in a total of 17 vegetation and region units (Figure 1). 2.2. MODIS Active Fire Hotspots MODIS active fire hotspots for the study period were compiled from the Forest Fire Early Warning System operated by the National Commission for Knowledge and Use of Biodiversity (CONABIO) (http://incendios1.conabio.gob.mx/). Active fires were obtained based on the Contextual Fire Detection Algorithm for MODIS [ 57 ]. The algorithm classifies MODIS pixels as possible active fires by applying minimum thresholds for brightness temperature and considering the context of the surrounding pixels [57,67]. To minimize false detections, active fire hotspot data were filtered by CONABIO following the protocol described by Cruz-Lopez [ 67 ]. This process includes the consideration of specific thresholds for brightness temperature [ 67 ], in order to avoid false detection by sun-light and very high albedo (e.g., [ 68 ]). Several additional masks were also considered in the filtering, such as a NDVI and vegetation mask to remove desert areas without vegetation, or a stable light mask, generated from DMSP satellite images (http://julius.ngdc.noa.gov:8080/production/BIOMASS/night.html), as described in [67]. Forests 2018,9, 190 4 of 18 Figure 1. Map of vegetation types and regions. Source: INEGI Land Use Map Series V (2011), 1:25,000. FOR: temperate forest; DTROPF: dry tropical forest; WTROPF: wet tropical forest; SDTROPF: seasonally dry tropical forest; SWTROPF: seasonally wet tropical forest; WET: wetlands; AGR: agricultural croplands; NPAS: natural pastureland; DSHR: desert shrubby vegetation; POPUL: major population centers; WATER: water bodies; NW, NE, C, NC, S: Northwest, Northeast, Centre, North-Centre, and South regions, respectively. 2.3. Fire Hotspot Density Index (FHD) Calculation For each of the 17 vegetation types and regions considered, Fire Hotspot Density was calculated for each 10-day (dekad) period by dividing the number of MODIS hotspots observed by dekad in each vegetation/region by the surface (km 2 ) of the corresponding vegetation/region considered, scaled to a Fire Hotspot Density index (FHD) as follows (Equation (1)): FHD =Number of hotspots/Surface (km2)×20.000 (1) The scaling factor was chosen as 1/10 of a reference surface of 200.000 km 2 , which is approximately equivalent to the surface of the temperate forests of the Northwest or Centre regions that are the main regions of forest fire occurrence in the country. Therefore, the FHD index directly represents 1/10 of the observed number of hotspots by dekad on a reference surface of 200.000 km2. 2.4. Fuel Dryness Index (FDI) Inputs The inputs for calculating FDI were daily images of the estimated moisture content of 100-h time-lag dead fuels (H 100 ) [ 42 ] and 10-day NDVI composites. The daily H 100 images were calculated in CONABIO following the Cervera-Taboada [ 69 ] calibration of the NFDRS algorithms of dead fuel moisture content [ 42 , 43 ] for Mexico. This is based on temperature and relative humidity from MODIS atmospheric profiles combined with precipitation data from the TRMM satellite [ 58 , 59 , 69 ]. CONABIO calculated the 10-day MODIS NDVI composite images with a spatial resolution of 1×1 km , using the harmonic time series methodology (HANTS) proposed by Roerink et al. (2000), cited by De Badts et al. [ 70 ], as described by Cruz-Lopez [ 67 ]. The study timeframe was from 2011 to 2015, based on the availability of historical H 100 images calculated daily by CONABIO. We computed the average FDI value for 10-day periods for each vegetation type and region in the period of study. Forests 2018,9, 190 5 of 18 2.5. Fuel Dryness Index (FDI) Calculation The FDI was calculated based on the Fire Potential Index (FPI) developed by Burgan et al. [ 28 ], which integrates NDVI information with daily maps of dead fuels moisture content. FDI followed the general index structure proposed by Burgan et al. [28] (Equation (2)): FDI =(1−LR)×(1−MR)×100 (2) where LR is the live ratio obtained from 10-day NDVI images following Equations (3)–(5), and MR is dead fuels moisture ratio obtained following Equation (6). Following Burgan et al. [ 28 ], the index represents the fuel dryness, with values close to 100 when both live and dead fuel moisture values are close to the maximum fuel dryness values, and lowest values when the fuels have higher fuel greenness and higher dead moisture conditions. Whereas some works have suggested a potential improvement by using the Normalized Difference Water Index (NDWI) instead of NDVI for the FPI calculation (e.g., [ 33 ]), we chose to utilize NDVI as in the original model formulation and several related works (e.g., [ 30 , 31 , 34 , 35 ]). The reason for this was the operational availability of 10-day MODIS NDVI compounds from the near-real-time fire monitoring systems of CONABIO [ 58 ]. This availability is advantageous both for the historical period and also for future real-time implementation of the fuel dryness index calculation. The first component of the index—live ratio—was calculated based on relative greenness values following Burgan et al. [28] (Equations (3) and (4)): LR =RG ×LRmax/100 (3) where RG is relative greenness, calculated as: RG =(NDVI0−NDVImin)/(NDVImax −NDVImin)×100 (4) where NDVI 0 is the observed NDVI for each pixel every 10-days, NDVI min and NDVI max are the absolute minimum and maximum NDVI values for each pixel from the period of study, and LR max is the maximum live ratio value for each pixel. In the first FPI formulation [ 37 ], LR max was determined as a function of the live and dead loads, but this original proposal resulted in overestimated FPI values for some areas in the U.S. A second empirical formulation was proposed by Burgan et al. [ 28 ] for the calculation of LR max in the U.S., scaling this index from 35 to 75% based on the NDVI max map. For the FDI index calculation in this work, based on the observed number of hotspots for every LR value in Mexican vegetation types, we scaled LRmax following Equation (5): LRmax =30 +30 ×(NDVImax −125)/(255 −125)(5) where LR max is the live ratio for a given pixel when the vegetation is at maximum greenness, and NDVI max is the historical maximum NDVI observed for a given pixel. The values 125 and 255 are the absolute minimum and maximum NDVI values observed for Mexico, following Burgan et al. [ 28 ]. The second component of the FDI—MR—represents the ratio of dead fuel moisture. In the formulation of Burgan et al. [ 28 ] for the FPI, MR is calculated as a ratio of dead fuels moisture to fuels moisture of extinction based on the NFDRS fuels map for the U.S. Because no fuel extinction moisture map is available for Mexico, we tested the following expression for scaling MR for the FDI (Equation (6)): MR =(H100 −H100min)/(H100max −H100min)(6) where H 100 is the observed value of 100 h dead fuel moisture, and H 100max , H 100min are maximum and minimum observed H100 values for each pixel. Forests 2018,9, 190 6 of 18 2.6. Threshold FDIpValues by Vegetation Type and Region We calculated the accumulated percentage of fire hotspots by FDI for each vegetation type and region for the whole study period. Based on the accumulated percentage of fire hotspots, we calculated the minimum values of FDI above which 85%, 90%, and 95% of the accumulated FHD values occurred (FDIp, with p= 85%, 90%, 95%), similar to the work of Sebastián-López et al. [31]. 2.7. Accumulated Fuel Dryness Index (AcFDI) We tested a simple accumulated fuel dryness index AcFDI, based on the sum of the FDI values above the threshold for fire occurrence (FDI p ) in the previous three months. The index was assumed to be zero at values below the FDIpthreshold (Equation (7)). The index was calculated for each vegetation type and region as follows: If FDIi<FDIp, AcFDIi=0; If FDIi>FDIp, AcFDIi=∑n i=n−9FDIi−FDIp(7) where AcFDI i is the Accumulated Fuel Dryness Index for dekad i, FDI i is the observed Fuel Dryness Index for each dekad i,nis the current dekad, and FDI p is the Fuel Dryness Index threshold for fire occurrence, calculated for each vegetation type and region as the FDI value above which the p percentage of hotpots occurs, with p= 85%, 90% and 95% (Section 2.6). The nine-dekad period for accumulating fuel dryness above the threshold was selected based on previous indices of accumulated fuel dryness derived for tropical countries (e.g., [ 71 ]), together with the observation of the FDI and FHD temporal evolution plots, by observing the average time difference between the start of fuel dryness accumulation above the FDI threshold and the observed starts and peaks of the fire season from FHD observations. 2.8. Models for the Prediction of Fire Hotspot Density (FHD) We tested linear and non-linear models for the prediction of FHD i from FDI i or AcFDI i . Because the most robust results were obtained from non-linear models, here we report only results for these non-linear models. However, results for all linear models tested are available upon request from the corresponding author. The non-linear models tested were (Equations (8) and (9)): FHDi=a×FHDib(8) FHDi=a×AcFDIib(9) where FHD i is Fire Hotspot Density index for dekad i(Equation (1)), FDI i is Fuel Dryness Index for dekad i(Equation (2)), AcFDI i is Accumulated Fuel Dryness Index for dekad i(Equation (7)), and a and bare model coefficients to be estimated. In addition, we also tested the following non-linear model, including an autoregressive term to account for the effect of the fires that occurred in the previous dekad FHD i−1 on the predicted FHD i values at dekad i, as follows (Equation (10)): FHDi=a×AcFDIib+c×FHDi−1(10) The ccoefficient for the autocorrelation of FHD was estimated as the calculated correlation coefficient between FHDiand FHDi−1values for each vegetation type and region. The models were fitted using non-linear least-squares regression (NLS) and non-linear quantile regression (NLQ) [ 72 ], using the packages nls and nlrq, respectively, of the software R [ 73 ]. For the quantile regression, we tested as candidate percentile values ranging 5 percentile units from 55 to 95%. These candidate models were evaluated by using the coefficient of determination for nonlinear regression (R 2 ) as a statistical criterion (see [ 74 ], pp. 419 and 424), together with root mean square error (RMSE) and model Bias. R 2 is defined as the square correlation coefficient between the measured Forests 2018,9, 190 7 of 18 and estimated values ( ryiˆyi ) and the root mean square error (RMSE), which can be defined as follows (Equations (11)–(13)): R2=r2yiˆ yi(11) RMSE =s∑(yi−ˆ yi)2 n−p(12) Bias =∑(yi−ˆ yi)/n(13) where yi and ˆ yi are the observed and estimated values of the dependent variable, respectively, nis the total number of observations used to fit the model, and pis the number of model parameters. Because the models will be used for fire risk strategic decision making, conservative predictions would be preferred. Therefore, in addition to highest R 2 and lowest RMSE values, we established as a criteria for selecting as best models those where the bias ranged from − 5 to − 15, therefore providing conservative overestimations for most of the observed values, as preferred for cautious risk decision making. 3. Results 3.1. Observed Fuel Dryness Index for Vegetation Types and Regions As expected, the observed temporal evolution of FDI varied by vegetation type and region. The observed FDI temporal trends for temperate forests of four regions (Figure 2top plot) and for four tropical forests in the South region (Figure 2bottom plot) for the five years of study are shown in Figure 2. Figure 2. Observed Fuel Dryness Index (FDI) for temperate forest of the Northwest (NW), Northeast (NE), Centre (C), and South (S) regions and for dry and wet tropical forests and wetlands of the South (S) region. FDI: Fuel dryness Index; FOR: temperate forest; DTROPF: dry topical forest; WTROPF: wet topical forest; WET: wetlands. Dotted lines of the corresponding color represent the FDI 95 threshold values for each vegetation type (Table 1). Table 1. FDIpthreshold values for p= 95%, 90%, 80%. Veg_Reg FDI95 FDI90 FDI85 FOR_NW 59 66 70 FOR_NE 52 55 59 FOR_C 47 53 57 Forests 2018,9, 190 8 of 18 Table 1. Cont. Veg_Reg FDI95 FDI90 FDI85 FOR_S 38 42 45 FOR_NC 59 66 70 DTROPF_C 46 53 57 DTROPF_S 48 52 54 DTROPF_NE 46 51 53 DTROPF_NW 59 65 68 SWTROPF_S 46 50 53 SDTROPF_S 48 51 53 WTROPF_S 41 45 47 WET_S 43 46 48 AGR_C 44 51 55 AGR_NW 57 64 68 AGR_NE 52 54 58 AGR_S 42 47 50 NPAS_C 50 56 60 p: percentage of hotspots that occurred above the FDI p value; Veg_Reg: vegetation type and region; FOR: temperate forest; DTROPF: dry tropical forest; WTROPF: wet tropical forest; SDTROPF: seasonally dry tropical forest; SWTROPF: seasonally wet tropical forest; WET: wetlands; AGR: agricultural cropland; NPAS: natural pastureland; NW, NE, C, NC, S: Northwest, Northeast, Centre, North-Centre, and South regions, respectively. Results show that more arid regions had higher FDI values, with the highest values found for temperate forest of the Northwest that reached maximum values of close to 90 in the years 2011, 2012, and 2013, and up to 80 for the wetter years 2014 and 2015. In the case of temperate forest of the Centre and Northeast regions, the maximum values of approximately 80–85 were reached in the dry years 2011 and 2013 (Figure 2). The lowest FDI values for the temperate forest were observed for the South region, which receives the highest precipitations in the country (>2000 mm). In this more humid region, the highest observed FDI values were approximately 70 in the dry years 2011 and 2013, reaching maximum values of 60 to 65 in the remaining years (Figure 2). As expected, higher FDI values were found for the dry tropical forest compared to the wet tropical forest in the south region, the latter reaching maximum values from around 60 to approximately 50 in the wet year 2014. The dates at which FDI started rising and decreasing also varied by vegetation type, region, and year (Figure 2). 3.2. Threshold FDIpValues by Vegetation Type and Region Based on the accumulated percentage of hotspot distributions, we calculated the threshold FDI p values above which accumulated percentages values pof 85%, 90%, and 95% of the fire hotspots occurred for each vegetation type. The FDI p values for each vegetation type are shown in Table 1. Drier regions such as temperate and tropical forest of the Northwest had higher threshold values for fire occurrence (e.g., FDI 95 of approximately 60), compared to lower thresholds observed in the wetter vegetation types and regions such as temperate and wet tropical forests of the south, with FDI 95 values of approximately 40. The Centre and Northeast regions showed intermediate threshold values, with FDI95 values in the range of 45–50. Thresholds for FDI 95 are shown together with temporal evolution plots of FDI i in Figure 2for some vegetation types. These plots allow visualization of the trends of fuel dryness accumulation above the threshold for the AcFDI index (Equation (7)). Once the FDI goes down to values below the threshold, fires are predicted to cease, according to the first condition of Equation (7). Therefore, these plots also allow visual interpretation of the predicted ends of the fire season each year based on FDI. FDI values in forests of the Northwest and Northeast generally started to decrease and reached values below the threshold one month later (June–July) than forests of Centre and South regions (May–June). The date of the FDI decrease also varied between years, possibly reflecting the differences in the occurrence of rain events between years and regions. Forests 2018,9, 190 9 of 18 3.3. Predicting Fire Hotspot Density (FHD) from AcFDI by Vegetation Type and Region Non-linear models based on fuel dryness showed higher goodness of fit statistics compared to linear models. The R 2 values for non-linear models using AcFDI and FDI (Equations (8) and (9), respectively) are shown in Table S1. For all vegetation types and regions, higher or similar predictive capacity for estimation of FHD was obtained using AcFDI compared to FDI (Table S1). The highest improvements for FHD using AcFDI instead of FDI were observed for temperate and tropical forests of Centre and temperate forests of the Northwest (NW), where R 2 values increased from 0.19, 0.21, and 0.35 to 0.51, 0.50, and 0.74, respectively (Table S1). Smaller gains or marginal increases were obtained for tropical forests of the South (S) and Northeast (NE) regions. The best models for predicting fire FHD by vegetation type and region and the corresponding goodness of fit coefficients are summarized in Table 2. The best fitted models were obtained with AcFDI, calculated with FDI p threshold values of p= 95% (FDI 95 ) from Table 1, using a non-linear expression, including autoregressive terms (Equation (10)), for all vegetation types. The chosen percentile for the best fit percentile regression models ranged from 65 to 90, with most vegetation types having a best fit for percentile values of 70 to 80. As defined in the criteria for model selection, the bias of the selected models in Table 1ranged from − 5 to − 15, which was chosen to represent a conservative overestimation for cautions risk decision making. The R 2 values of the best fit models ranged from approximately 0.5 to 0.7 (Table 2), with the highest R 2 values for temperate forests of the Northwest and Centre regions and for dry tropical forest of the Centre region. The lowest values for several tropical forests of the South and Northeast regions, and for the temperate forest of the arid North-Centre region. RMSE values ranged from approximately 20 to 80, with most vegetation types having RMSE values in the range 30–60, as shown in Table 2. Table 2. Coefficients and goodness of fit statistics of the best models for predicting fire hotspot density. Veg_Reg Perc Coefficients Goodness of Fit a b c R2RMSE Bias FOR_NW 80 13.7 3.14 0.76 0.707 43.4 −10.6 FOR_NE 90 22.8 2.20 0.80 0.619 39.6 −8.6 FOR_C 80 11.5 1.98 0.83 0.703 41.6 −9.5 FOR_S 70 1.8 4.70 0.72 0.575 57.4 −5.9 FOR_NC 95 5.6 3.49 0.61 0.463 21.4 −6.9 DTROPF_C 80 9.6 1.98 0.84 0.725 40.3 −12.9 DTROPF_NW 85 41.9 0.88 0.70 0.523 29.1 −11.1 DTROPF_NE 90 35.7 0.95 0.59 0.461 21.7 −5.1 DTROPF_S 80 78.6 0.59 0.75 0.601 60.3 −13.5 WTROPF_S 80 38.6 1.95 0.74 0.587 31.9 −8.2 SWTROPF_S 65 100.8 1.35 0.70 0.625 62.1 −7.92 SDTROPF_S 75 129.4 0.77 0.71 0.496 81.4 −7.5 WET_S 70 16.9 2.49 0.67 0.511 48.1 −8.69 AGR_C 90 9.9 1.83 0.80 0.712 32.6 −14.4 AGR_NW 90 24.4 0.82 0.61 0.457 23.5 −10.8 AGR_NE 90 25.8 0.61 0.78 0.615 18.9 −9.2 AGR_S 65 20.2 1.59 0.83 0.708 42.2 −8.7 NPAS_C 80 11.1 1.29 0.84 0.727 24.1 −7.7 Veg_Reg: vegetation type and region; Perc: percentile selected for the best fitted percentile non-linear regression model; a,b, and care model coefficients for Equation (10), using the threshold values FDI 95 for calculation of AcFDI; R 2 : coefficient of determination; RMSE: root mean square error (FHD units: Equation (1)); Bias: model bias (FHD units: Equation (1)); FOR: temperate forest; DTROPF: dry tropical forest; WTROPF: wet tropical forest; SDTROPF: seasonally dry tropical forest; SWTROPF: seasonally wet tropical forest; WET: wetlands; AGR: agriculture; NPAS: natural pastureland; NW, NE, C, NC, S: Northwest, Northeast, Centre, North-Centre, and South regions. 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