Modelling aboveground biomass and fuel load components at stand level in shrub communities in NW Spain
Abstract
Shrub-dominated ecosystems cover large areas globally and play essential roles in ecological processes. Aboveground biomass expressed on an area basis (AGB) is central to many of the ecological processes and services provided by shrublands and is important as the main fuel source for wildfires. Hence, its accurate estimation in shrublands is crucial for ecologists and land managers. This is especially relevant in fire-prone regions such as NW Spain, where shrublands are an important part of the landscape, providing multiple services, but are severely impacted by wildfires. Although biomass models are available for numerous shrub species at the individual plant level, operational models based directly on easily measured shrub stand attributes are scarce. In this study, equations for estimating AGB and loads of different fuel components by size and condition (live and dead) from stand biometric variables were developed for the nine most prevalent shrub communities in NW Spain. Non-linear iterative seemingly unrelated regression was used to fit compatible systems of equations for estimating fuel loads, with shrub stand height and cover and litter depth as predictors for individual shrub communities and all data combined. In general, the goodness-of-fit statistics indicated that the estimates were reasonably accurate for all communities (grouped and ungrouped). The best results were obtained for AGB and total fuel load, including litter, whereas the poorest results were obtained for standing live and dead fine fuel load. Model performance was reduced when height was the only independent variable, although the reduction was small for most fuel categories, except litter load for which the variability was adequately explained by the litter depth. These results illustrate the feasibility of the stand level approach for constructing operational models of shrub fuel load that are accurate for most of fuel components, while also highlighting the ongoing challenges in live and dead fine fuel modelling. The equations developed represent an appreciable advance in shrubland biomass assessment in the region and areas with similar characteristics and may be instrumental in generating fuel maps, fire management improvement and better C storage assessment by vegetation, among other many uses
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Forest Ecology and Management 505 (2022) 119926 Available online 13 December 2021 0378-1127/© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Modelling aboveground biomass and fuel load components at stand level in shrub communities in NW Spain Jos´ e A. Vega a , 1 , St´ efano Arellano-P´ erez b , 1 , Juan Gabriel ´ Alvarez-Gonz´ alez b , Cristina Fern´ andez a , Enrique Jim´ enez a , Jos´ e María Fern´ andez-Alonso a , Daniel J. Vega-Nieva c , Carlos Briones-Herrera c , Cecilia Alonso-Rego b , Teresa Fontúrbel a , Ana Daría Ruiz-Gonz´ alez b , * a Centro de Investigaci´ on Forestal de Louriz´ an, PO Box 127, 36080 Pontevedra, Spain b Unidad de Gesti´ on Ambiental y Forestal Sostenible (UXAFORES), Departamento de Ingeniería Agroforestal, Escuela Polit´ ecnica Superior de Ingeniería, Universidad de Santiago de Compostela, Campus Universitario s/n, 27002 Lugo, Spain c Facultad de Ciencias Forestales, Universidad Ju´ arez del Estado de Durango, Río Papaloapan y Blvd. Durango s/n, Col. Valle del Sur, 34120 Durango, Mexico ARTICLE INFO Keywords: Shrubland biomass Dominant shrub species Compatible equations systems Biometric variables Litter fuel load Fuel fractions load Fuel components Live and dead fine fuel Fuel management ABSTRACT Shrub-dominated ecosystems cover large areas globally and play essential roles in ecological processes. Aboveground biomass expressed on an area basis (AGB) is central to many of the ecological processes and services provided by shrublands and is important as the main fuel source for wildfires. Hence, its accurate estimation in shrublands is crucial for ecologists and land managers. This is especially relevant in fire-prone regions such as NW Spain, where shrublands are an important part of the landscape, providing multiple services, but are severely impacted by wildfires. Although biomass models are available for numerous shrub species at the individual plant level, operational models based directly on easily measured shrub stand attributes are scarce. In this study, equations for estimating AGB and loads of different fuel components by size and condition (live and dead) from stand biometric variables were developed for the nine most prevalent shrub communities in NW Spain. Non-linear iterative seemingly unrelated regression was used to fit compatible systems of equations for estimating fuel loads, with shrub stand height and cover and litter depth as predictors for individual shrub communities and all data combined. In general, the goodness-of-fit statistics indicated that the estimates were reasonably accurate for all communities (grouped and ungrouped). The best results were obtained for AGB and total fuel load, including litter, whereas the poorest results were obtained for standing live and dead fine fuel load. Model performance was reduced when height was the only independent variable, although the reduction was small for most fuel categories, except litter load for which the variability was adequately explained by the litter depth. These results illustrate the feasibility of the stand level approach for constructing operational models of shrub fuel load that are accurate for most of fuel components, while also highlighting the ongoing challenges in live and dead fine fuel modelling. The equations developed represent an appreciable advance in shrubland biomass assessment in the region and areas with similar characteristics and may be instrumental in generating fuel maps, fire management improvement and better C storage assessment by vegetation, among other many uses. 1. Introduction Shrublands cover large areas globally (Di Vittorio et al., 2018) and play essential roles in ecological processes (Lombardo et al., 2020; Lozano et al., 2020; Paz-Kagan et al. 2016; Tubbesing et al., 2021). Shrubs also provide important ecosystem services (Marquart et al., 2020; Paton et al. 2002; Viana et al., 2012). On a global scale there has been an increasing shrubland expansion * Corresponding author. E-mail addresses: [email protected] (J.A. Vega), [email protected] (S. Arellano-P´ erez), [email protected] (J.G. ´ Alvarez-Gonz´ alez), cristina. [email protected] (C. Fern´ andez), [email protected] (E. Jim´ enez), [email protected] (J.M. Fern´ andez-Alonso), [email protected] (D.J. VegaNieva), [email protected] (C. Briones-Herrera), [email protected] (C. Alonso-Rego), [email protected] (T. Fontúrbel), [email protected] (A.D. Ruiz-Gonz´ alez). 1 These authors contributed equally to this work. Contents lists available at ScienceDirect Forest Ecology and Management journal homepage: www.elsevier.com/locate/foreco https://doi.org/10.1016/j.foreco.2021.119926 Received 11 June 2021; Received in revised form 25 October 2021; Accepted 28 November 2021
Forest Ecology and Management 505 (2022) 119926 2 in the last decades affecting a wide variety of biomes with significant ecological effects (Archer et al., 2017; Eldridge et al., 2011; Frost et al., 2018; Van Auken, 2009). Land abandonment, cessation of farming and grazing and climate change have been argued as main driving factors of shrub encroachment (Archer et al., 1995; Fernandes et al., 2014; Naito and Cairns, 2011; Prishchepov et al., 2021). In addition, the conversion of forests to scrubland, due to more frequent wildfires, has been a relevant driver of the above-mentioned expansion in Mediterranean ecosystems (Díaz-Delgado et al. 2002; Fern´ andez-García et al., 2020; Lloret et al., 2003) and it is now considered a widespread phenomenon (Kukavskaya et al., 2016; Coop et al., 2020). AGB assessment is central for determining the structure, function, primary productivity, and ecosystem services provision of shrublands (Archer and Predick, 2014). Regarding fire ecology, AGB is crucial, as fire can only spread when there is enough biomass to burn (Bradstock’s “first fire switch”, 2010), and is critical to the response of fire activity to biomass productivity gradients (Krawchuk and Moritz, 2011), in the socalled “intermediate fire productivity hypothesis” (Pausas and Ribeiro, 2013). In terms of fire management, fuel load (equivalent to AGB) is considered the most important fuel characteristic (Keane, 2013; 2015; Weise and Wright, 2014). In fact, fuel load supplies the energy required for fire ignition and spread, thus modulating fire intensity and severity (Byram, 1959; Fern´ andez-Alonso et al., 2017; Keane, 2015; Parks et al., 2014; Pyne et al., 1996). Furthermore, this information, broken down by fuel stratum, size class (fine, medium and coarse) and condition (live and dead), i.e., the fuel components sensu Keane (2015), is a necessary input in wildland fire behaviour modelling (Larini et al., 1998; Morvan and Dupuy, 2004; Rothermel, 1972) and in derived operational tools (Andrews, 2014; Finney, 1998; 2006). In addition, estimates of greenhouse gas emissions from vegetation fires depend on biomass consumed, also mediated by pre-fire fuel load (Andreae, 2019; van der Werf et al., 2017). For the above reasons, providing ecologists and forest managers with models that accurately estimate shrub fuel loads is imperative (Botequim et al., 2015). This is particularly determinant in fire-prone areas such as the NW Spain, where about 2% of the forest land is burned annually (period 1978–2019) and some two-thirds of which correspond to shrublands (L´ opez-Santalla and L´ opez-Garcia, 2019; Xunta de Galicia, 2020). This type of vegetation, forming part of ancient cultural landscapes in the region (Fagúndez, 2013), has been profoundly affected by dramatic changes in land use occurred particularly in the last decades (Corbelle-Rico and Crecente-Maseda, 2014; Ramil-Rego et al., 2013). In many cases, these changes have led to high fuel accumulation and more severe wildfires in the region (Vega et al., 2021). The expected increase in fire risk in Southern Europe (Dupuy et al., 2020), also affecting NW Spain (Vega et al., 2009), adds further urgency to the need for adequate fuel load assessment in the area. This is further reinforced by the sensitivity of fire activity to climate change in moderately-highly productive ecosystems (Briones-Herrera et al., 2019; Pausas and Ribeiro, 2013), such as in the study region (Del Grosso et al., 2008; S´ anchez Palomares and S´ anchez, 2000). Global change is likely to continue affecting the region in the future, requiring new land use planning and including strategic fuel reduction initiatives (Vega et al., 2021). Therefore, the demand of appropriate models to estimate fuel loading at stand level is likely to increase eventually. Despite shrublands extent and their ecological relevance, estimation of their biomass expressed on an area basis (AGB) has received comparatively less attention than AGB in forest stands (Conti et al., 2019; Poley et al., 2020). While double sampling is the rule for estimating AGB (Bonham, 2013; Catchpole and Wheeler, 1992; Chojnacky and Milton, 2008; Etienne 1989; Shiver and Borders, 1996), two different approaches are used: at the individual plant level and at the stand level. In the first approach, destructive sampling is used to develop allometric equations relating individual species-specific biomass with biometric attributes. These equations are then used in conjunction with density sampling of those species to estimate ABG. Comparatively, most of the shrub biomass modelling effort has been made through this approach (BlancoOyonarte and Navarro-Cerrillo, 2003; Brown, 1976; Conti et al., 2019; De C´ aceres et al., 2019; Hierro et al., 2000; Huff et al., 2017; Paul et al., 2016; Pimont et al., 2018; Yao et al., 2021; Zeng et al, 2010). However, problems associated with its high cost and the impracticability of measuring in dense stands of multi-stemmed plants often make this method unfeasible at large scale. This is the case in the NW Spain communities. In the second approach, allometric fuel load equations are developed at the stand level, using stand attributes directly as predictors (Botequim et al., 2015; Davies et al., 2008; Fernandes and Rego, 1998a; Fonseca et al., 2012; Montero et al., 2020; Pasalodos-Tato et al., 2015; Pearce et al., 2010; Ruiz-Peinado et al., 2013; Viana et al., 2013) Litter layer load estimation is also important due to its critical roles in shrublands (Aerts and Chapin, 1999; Eckstein and Donath, 2005; Facelli and Pickett, 1991; Vega et al., 2005). For fire ecology and fire management, litter load assessment is also relevant, as its combustion contributes substantially to fire emissions (Russell-Smith et al., 2009) while its consumption degree is a determinant factor of soil burn severity (Vega et al., 2013). Nonetheless, relatively few studies have modelled the shrub litter load as a function of its physical attributes (Arellano-P´ erez, 2011; Davies et al., 2008; Fonseca et al., 2012; Kittredge, 1955; Lade, 2010; McCaw, 1997; Montero et al., 2020). The presence in the NW Spain of abundant shrub communities from both the Euro Atlantic and the Mediterranean biogeographic domains, provides a broad range of conditions suitable for fuel loading modelling. Accordingly, the objectives of this study were to construct additive allometric equations from biometric variables, at stand level, and to evaluate their performance for estimating: (i) AGB, i.e. total fuel load of the standing shrub stratum, (ii) litter and shrub total fuel load, and (iii) shrub standing stratum fuel component loads (differentiated by size range and condition –live/dead-) for each one of the most significant shrub communities in NW Spain, for groups of these communities and for all of these together. 2. Material and methods 2.1. Study area, shrub communities considered and inventory plots This study was carried out in Galicia (NW Spain), a region comprised between 41◦40′and 43◦48′N and 6◦44′and 9◦18′W, where shrublands cover about 607,000 ha (some 20% of the total area and 30% of the forest land in the region). Most of the shrublands in Galicia are included in the dry heath communities (Ojeda, 2009), part of the habitat 4030 of the European habitat classification (Council Directive 92/43 CEE), with gorses (Ulex sp.) and heaths (Erica sp.) being the dominant plant genera in terms of area occupied (MARM, 2011b). Most of the Galician shrublands are included in the Calluno-Ulicetea syntaxonomical class (Izco et al., 2006). The gorse-dominated communities cover about 55% of the shrubland area, heath-dominated ones occupy around 22% and broom (Cytisus sp.) fields 11%. The rest of the shrublands is distributed between areas with scarce or no vegetation (55 thousand ha), frequently affected by high fire recurrence, grasslands (8 thousand ha) and rock roses (Cistus sp. and Halimium sp.) with 7,000 ha. The boundary of the Eurosiberian and Mediterranean biogeographic regions traverses Galicia, resulting in a transitional climate with a larger area under oceanic influence, nuanced by the effects of a complex relief (Rodríguez Guiti´ an and RamilRego, 2007). The continentality increases from the coast to inland areas, where summers are dryer, while the maximum temperature increases and the minimum decreases from NW to SE (Retuerto and Carballeira, 1992). The mean annual rainfall is 1200 mm, varying spatially between 500 and 1800 mm, and the mean annual temperature is 13.3 ◦C, ranging seasonally from 8.5 to 19 ◦C (Martínez-Cortizas and P´ erez-Alberti, 1999). These climate conditions favour a high rate of shrub biomass J.A. Vega et al.
Forest Ecology and Management 505 (2022) 119926 3 growth (Montero et al., 2020). Shrublands typically occur on Regosols and Leptosols and to a lesser extent on Cambisols and Umbrisols developed mainly on granitic and schist substrates (Carballas et al., 2016). Nine shrub communities were considered in the present study, each characterized by a dominant species (in terms of coverage in the case of multi-woody species communities). These communities cover about 90% of the shrublands in the region (Izco and García-San Le´ on, 1999; MARM, 2011a, 2011b). These are, except for fern (Pteridium aquilinum L.)-dominated communities, primarily composed of perennial, multistemmed (or highly branched) evergreen woody species (shrubs and sub-bushes), which typically form dense (high number of plants per area) and closed (high coverage) stands ranging in height from medium to moderately high (0.5–3 m). These shrub fuel complexes commonly encompass two strata: the standing shrub and the litter. A few herbaceous plants, including ferns, are occasionally present as understory. Although ferns are non-woody plants and display strong seasonal variations in biomass, P. aquilinum-dominated communities were considered in this study due to these communities forming extensive patches often only temporarily, and occurs after some type of disturbance, accumulating substantial amounts of fine fuel in summer and frequently involved in fires in the region. The shrub communities with similar structural characteristics were considered jointly and identified by a code comprising the initials of the scientific name of the dominant species for which the largest number of plots were inventoried (Table 1). Some communities included more than one dominant species, although with some common structural characteristics allowing them to be combined in a group (e.g., high broom, high heath or low heath). Sites covered with the above-mentioned nine major shrub communities (including bracken fern-dominated community) were selected at random based on the information of the treeless shrub-covered polygons of the Spanish Forest Map 1:25000 (MARM, 2011b). Given the recent and rapid changes in land use in the area (Corbelle-Rico et al., 2012), field reconnaissance was carried out to confirm the persistence of the vegetation composition mapped and site accessibility. Within the corresponding sites the centres of circular shrub inventory plots, in which destructive sampling was conducted, were positioned by randomly selecting an azimuth and a distance within the stand, from a point of access (Marsden-Smedley and Catchpole, 1995; Pereira et al., 1995; Dalgleish et al. 2015; Duff et al., 2017). The number of inventory plots in each shrub community was approximately proportional to the area covered by each in Galicia (MARM, 2011b) and a total of 722 circular plots were inventoried. Some types of community of concern for fire management, such as gum rock rose, which occupies a relatively small area in the region, are over-represented in the sample in order to yield a sufficient sample size to fit the corresponding allometric models. A field survey was conducted to locate fern-covered areas where inventory plots were subjectively established. From the centre of each circular sample plot, a random azimuth for one diameter (20–30 m length, depending on shrub height) was established and another diameter was drawn perpendicular to the first. Four destructive sampling subplots (quadrats) were located at the centre of the four plot radii corresponding to the aforementioned diameters (Fig. 1, middle right). The area of each quadrat ranged from 4 to 36 m 2 , depending on shrub height: for shrubs smaller than 1.0 m in height, 4 m 2 quadrats were destructively sampled; for shrubs taller than 1.0 m, the quadrat size varied from 3 m ×3 m to 6 m ×6 m. 2.2. Biomass sampling We followed the approach of Pearce et al. (2010) for biomass sampling in fairly continuous dense shrub communities, with some modifications, and recommendations by Pitt and Schwab (1988), Carswell et al. (2001) and Payton et al. (2004). Each quadrat was physically delimited by four wooden poles or extendable graduated metallic marker poles (in the higher stands), and a linear transect was laid out, (with a tape), following the perimeter and a diagonal of the quadrat. A strip was carefully cleared around the quadrat to allow correct positioning of markers for subsequent measurements. The vegetation growing inside the quadrat was carefully clipped along the lateral boundaries, taking care to exclude portions of plants growing within the quadrat but hanging outside the boundary. The horizontal lengths of the Table 1 Shrub communities, number of inventoried plots, codes* and dominants and main secondary species. n =number of inventory plots. Shrub community n Code Dominant shrub species Main secondary species Gum rockrose 23 Cl Cistus ladanifer L. Low broom (White Spanish broom) 47 Cm Cytisus multiflorus (L’H´ er.) Sweet Pterospartum tridentatum (L.) Willk., Pteridium aquilinum(L.) Kuhn, Cistus salvifolius L. High broom (Common broom) 44 Cs Cytisus striatus (Hill) Rothm. Ulex minor Roth., Erica umbellata Loefle ex L., Pterospartum tridentatum (L.) Willk., Pteridium aquilinum(L.)Kuhn Cytisus scoparius (L.) Link Pteridium aquilinum (L.) Kuhn, Ulex europaeus L. Genista obstusiramea J. Gay ex Spach. Pterospartum tridentatum (L) Willk. High heath (Spanish heath) 125 Ea Erica australis L. Pterospartum tridentatum (L) Willk., Halimium lasianhtum subsp. alyssoides (Lam.), Erica arborea L., Ulex europaeus L. Erica arborea L. Pteridium aquilinum (L.) Kuhn Erica scoparia L. Ulex europaeus L Pterospartum tridentatum (L.) Willk., Pteridium aquilinum(L.)Kuhn Low heath (Dwarf Spanish heath) 68 Eu Erica umbellata Loefle ex L. Pterospartum tridentatum (L.) Willk., Ulex gallii Planch, Ulex minor Roth., U. Europaeus L., Pteridium aquilinum (L.) Kuhn Erica mackaiana Bab. Erica cinerea L., Calluna vulgaris (L.) Hull, Ulex gallii Planch., Pteridium aquilinum (L.) Kuhn Bracken fern 49 Pa Pteridium aquilinum (L.) Kuhn in Kersten Ulex gallii, Planch., U. minor Roth., Erica cinerea L. Prickled broom 69 Pt Pterospartum tridentatum (L.) Willk. Erica umbellata Loefl. ex L., Halimium lasianhtum subsp.alyssoides (Lam.), E. australis L., Ulex gallii Planch., U. minor Roth., U. europaeus L., Pteridium aquilinum (L.) Kuhn Gorse 191 Ue Ulex europaeus L. Ulex gallii Planch, U. minor Roth., Erica umbellata Loefle ex L, E. cinerea L., Pteridium aquilinum (L.) Kuhn, Low gorse (Western gorse) 106 Ug Ulex gallii Planch. Ulex europaeus L., Erica umbellata Loefle ex L, Daboecia cantabrica (thuds.) K.Koch, Pterospartum tridentatum (L.)Willk., Cistus psilosepalus Sweet, Pteridium aquilinum(L.) Kuhn Ulex minor Roth. *The shrub communities with similar structural characteristics were considered jointly and identified by a code comprising the initials of the scientific name of the dominant species for which the largest number of plots were inventoried. J.A. Vega et al.
Forest Ecology and Management 505 (2022) 119926 4 intercepted crown of the standing shrub species were measured (cm) along the length of the transect, with a graduated tape (Canfield, 1941; Kent and Coker, 1992; Bonham, 2013), to determine the linear cover by the shrubs in terms of the percentage of the transect length intercepted (maximum 100%). Shrub height was determined as the vertical distance (cm) between the surface of leaf litter and the top of the plant canopy and was measured with a graduated tape every 50 cm, on the transect. All vegetation portions of the standing shrub stratum in the vertical projection of the sampling quadrat area were carefully harvested at ground level and placed in bags, which were labelled appropriately and transported to the laboratory. After removal of standing dominant shrub stratum, the understory stratum, if present, was harvested similarly. A wooden frame (1 m ×1 m) was placed at random inside the quadrat area; the litter depth was measured at ten points along the perimeter and diagonal of the frame, and the litter was then collected. The litter was basically formed by dead fine organic material with coarse debris practically absent. This is usual in these shrubs (Fernandes et al., 2000), in which dense branching in the standing shrub stratum often prevents the detached dead material from reaching the ground, leaving it suspended (Plucinski, 2003). Litter is usually shallow and duff (Oe +Oa horizons) is often lacking. The distinction between litter and duff and even between duff and the surface mineral soil is frequently imprecise in these ecosystems (Wall´ en, 1980), as in the forest floor of many forest ecosystems (Crosby and Loomis, 1974; Brown et al., 1982, Federer, 1982; Yanai et al., 2003). However, different organic layers can be recognized in senescent gorse stands (Hely and Forgeard, 1998) and wet E. mackaiana heathlands. Given the subjectivity in distinguishing litter and duff in most cases and the frequent contamination of duff with mineral soil particles during sampling (Kittredge, 1955; Federer, 1982; Yanai et al., 1999, 2003), both layers (when present) were collected together and classified for the sake of simplicity as litter, in this study. This material was bagged and transported to the laboratory. The shrub and litter biometric measurements made on each one of the four sampling quadrats and frames, respectively, of each circular plot were averaged to obtain a value per inventory plot of shrub cover (Cov Shr ); mean shrub height (hShr) and mean litter depth (dLitt). In the laboratory, the material of the standing shrub stratum was physically separated by size-class into fine fuels (diameter <0.6 cm, hereafter G1), medium fuels (0.6 cm ≤diameter <2.5 cm, hereafter G2) and coarse fuels (2.5 cm ≤diameter <7.5 cm, hereafter G3) by using a go-no go gauge (Brown et al., 1982). The material was further subdivided by condition (live and dead), determined by visual inspection. The size categories were selected according to their different surface to volume ratios and, for dead fuels, because they coincide with the size ranges defined by Fosberg et al. (1970), due of the contrasting water absorption and desorption rates (time lags of respectively 1 h, 10 h and 100 h). These three size ranges have also been used to construct custom fuel models for predicting fire behaviour (Burgan and Rothermel, 1984; Finney, 1998; Scott and Burgan, 2005). Once classified, the material was weighted and dried in forced air-drying chambers (105 ◦C for 24 h for fine fuels and 48 h for coarse fuels) for determination of the dry biomass of each fraction. Litter samples were oven-dried for 48 h to 105◦and one oven-dried subsample from each sample was combusted in a muffle furnace at 550 ◦C for 4 h (Federer, 1982) to determine the loss on ignition to correct for mineral soil contamination and ash. The litter load values in this study thus include the organic mass of the floor (Oi +Oe + Oa horizons) per unit area. The fuel load of each fraction was obtained by dividing the respective dry biomass by the respective sampling area. Thus, seven different loads of the respective biomass fractions were computed. Five were related to the standing shrub stratum: W Shr_G1_dead =dead fine shrub load, W Shr_G1_live =live fine shrub load, W Shr_G1 =fine shrub load (dead +live), W Shr_G23 =coarse shrub load and W Shr =total shrub load =W Shr_G1 +W Shr_G23 =AGB at stand level. Fractions G2 and G3 were grouped to avoid loss of data as fraction G3 is infrequent in many of the communities. Given the much higher fuel load in the standing shrub stratum than in the herbaceous understory, the load of the latter (always corresponding to G1) was added to that shrub fraction in all cases. Thus, the term shrub actually encompasses all standing Fig. 1. Geographical location of the 722 inventory plots in Galicia comprising nine shrub communities (left). Coordinate system ETRS89, Zone 29 N (EPGS: 25829). Layout of inventory plot showing transects and location of four destructive sampling subplots (quadrats m, in green) in each inventory plot (middle right). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) J.A. Vega et al.
Forest Ecology and Management 505 (2022) 119926 5 vegetation. In addition, W Litt =litter load and W Shr+Litt =total (shrub and litter) fuel load were also computed. The basic descriptive statistics of shrub and litter strata for the main structural characteristics of each shrub community are shown in Table 2. 2.3. Statistical analysis Equations were developed for estimating the load of each of the seven fractions of the shrub fuel complex for each community. Allometric models (y=b0⋅Xbi i) for estimating fuel loads were tested for all the biomass fractions considering the mean shrub height (hShr) and the transformed shrub cover (Cov Bliss ) as independent variables to be tested. The latter variable was obtained by arcsine-square root transformation of the shrub cover (Cov Shr ) to stabilize the variance and improve normality (Bliss, 1938). Moreover, the mean litter depth (dLitt) was also considered an independent variable for modelling the litter fuel load because in a preliminary analysis it was the most important independent variable, in terms of reduction of root mean square, when modelling litter fuel load for all shrub communities. Allometric equations must fulfil the property of additivity, i.e. the sum of biomass predictions from separate fuel fractions must equal the biomass prediction from the total biomass model (e.g. the sum of dead fine and live fine shrub load estimates must equal fine shrub load estimates or the sum of fine and coarse shrub load estimates must equal total shrub load estimates). Therefore, in a first step, the equation of each fuel fraction of each shrub community was fitted separately, and the complete system of seven equations (one for fraction) was then fitted simultaneously for each shrub community to guarantee additivity. (1) Equation for estimating litter fuel load ( WLitt ) WLitt =a0⋅hShr a1⋅Cova2 Bliss⋅dLitt a3(1) (2) Equation for estimating shrub fuel load ( WShr ) WShr =b0⋅hShr b1⋅Covb2 Bliss (2) Two equations discriminated between fine ( WShr G1) and coarse fuel loads ( WShr G23 ) by disaggregating equation (2): WShr G23 =exp[c0g23 +c1g23 log(hShr)+c2g23 log(CovBliss)] WShr G1=exp[c0g1+c1g1log(hShr)+c2g1log(CovBliss)] WShr G23 WShr = WShr G23 ( WShr G23 + WShr G1)=1 1+( WShr G1/ WShr G23 ) The equation for estimating the coarse fuel loads was then obtained as follows: WShr G23 = WShr 1+exp[c0+c1log(hShr)+c2log(CovBliss)] (3) with c i =c ig1 - c ig23 ; and the equation for estimating the fine fuel load was as follows: WShr G1= WShr − WShr G23 = WShr ⋅exp[c0+c1log(hShr)+c2log(CovBliss)] 1+exp[c0+c1log(hShr)+c2log(CovBliss)] (4) (3) Two equations discriminated between dead fine ( WShr G1dead ) and live fine fuel loads ( WShr G1live) loads by disaggregating equation (4): WShr G1dead =exp[d0g1dead +d1g1dead log(hShr)+d2g1dead log(CovBliss)] WShr G1live =exp[d0g1live +d1g1live log(hShr)+d2g1live log(CovBliss)] WShr G1dead WShr G1= WShr G1dead ( WShr G1dead + WShr G1live )=1 1+( WShr G1live / WShr G1dead ) The equation for estimating the fine dead fuel loads was then obtained: WShr G1dead = WShr G1 1+exp[d0+d1⋅log(hShr)+d2⋅log(CovBliss)] (5) Table 2 Mean values of the standing shrub and litter fuel strata characteristics. Std. dev. =standard deviation, n =number of plots, hShr =shrub height, Cov Shr =shrub cover, dLitt =litter depth, W Shr+Litt =shrub and litter fuel load, W Shr =total shrub fuel load, W Litt =litter fuel load, W Shr_G23 =coarse shrub fuel load, W Shr_G1 =fine shrub fuel load, W Shr_G1_dead =dead fine shrub fuel load, W Shr_G1_live =live fine shrub fuel load. See definitions in the text. Variable Statistic Cl Cm Cs Ea Eu Pa Pt Ue Ug n 23 47 44 125 68 49 69 191 106 hShr mean 120.04 114.49 241.70 110.40 51.75 105.24 90.54 115.09 74.99 (cm) std. dev. 38.33 52.91 157.43 76.30 19.09 31.63 52.13 60.08 27.77 Cov Shr mean 69.26 85.09 84.59 89.77 92.18 83.49 83.76 84.62 93.38 (%) std. dev. 14.90 16.29 17.26 17.38 14.46 13.43 17.47 22.74 14.40 dLitt mean 1.13 2.26 2.83 2.06 2.36 2.87 1.49 4.02 3.09 (cm) std. dev. 0.44 1.32 1.66 2.05 1.70 1.16 0.79 2.94 1.80 W Shr+Litt mean 1.45 3.05 6.19 3.31 2.96 1.81 3.01 4.73 3.98 (kg m −2 ) std. dev. 0.43 1.46 4.00 2.49 1.48 0.68 1.58 2.28 1.52 W Shr mean 1.11 2.37 5.37 2.47 1.97 1.05 2.49 3.36 2.84 (kg m −2 ) std. dev. 0.34 1.06 3.60 1.84 0.88 0.52 1.30 1.45 0.89 W Litt mean 0.34 0.69 0.81 0.84 0.99 0.75 0.51 1.37 1.14 (kg m −2 ) std. dev. 0.14 0.46 0.55 0.71 0.68 0.29 0.34 1.04 0.79 W Shr_G23 mean 0.29 0.84 3.54 0.99 0.26 0.17 0.63 1.26 0.56 (kg m −2 ) std. dev. 0.18 0.78 3.18 1.23 0.26 0.14 0.69 1.06 0.54 W Shr_G1 mean 0.82 1.52 1.83 1.48 1.71 0.88 1.86 2.10 2.28 (kg m −2 ) std. dev. 0.20 0.34 0.61 0.77 0.71 0.40 0.74 0.68 0.65 W Shr_G1_dead mean 0.07 0.49 0.48 0.40 0.56 0.43 0.70 0.82 0.77 (kg m −2 ) std. dev. 0.04 0.36 0.25 0.28 0.33 0.32 0.29 0.37 0.39 W Shr_G1_live mean 0.74 1.04 1.36 1.07 1.15 0.45 1.16 1.28 1.51 (kg m −2 ) std. dev. 0.20 0.28 0.46 0.53 0.44 0.24 0.56 0.43 0.41 Cl =Cistus ladanifer, Cm =Cytisus multiflorus, Cs =Cytisus striatus, Ea =Erica australis, Eu =Erica umbellata, Pa =Pteridium aquilinum, Pt =Pterospartum tridentatum, Ue =Ulex europaeus and Ug =Ulex gallii J.A. Vega et al.
Forest Ecology and Management 505 (2022) 119926 6 with d i =d ig1_live - d ig1_dead ; and the following equation was fitted to estimate the live fine fuel load: WShr G1live = WShr G1− WShr G1dead = = WShr G1⋅exp[d0+d1log(hShr)+d2log(CovBliss)] 1+exp[d0+d1log(hShr)+d2log(CovBliss)] (6) (4) Finally the equation for estimating the total shrub and litter fuel load ( WShr+Litt ) was obtained by aggregating equations (1) and (2): WShr+Litt =a0⋅hShr a1⋅Cova2 Bliss⋅dLitt a3+b0⋅hShr b1⋅Covb2 Bliss (7) Due to the special biology of P. aquilinum and its wide structural and physiological variability throughout the year, the fine fuel load was not disaggregated in this shrub community. The allometric equations for fern should be applied for upstanding plants only. In addition to the systems fitted for the 9 shrub communities, other systems with the same structure (Eqs. (1)–(7)) were fitted to the pooled data of all the shrub communities, excluding the fern-dominated community, and for three different groups of shrub communities with similar structural characteristics or frequent association: i) brooms (Cm +Cs = Cytisus multiflorus and Cytisus striatus), ii) gorses (Ue +Ug =Ulex europaeus and U. gallii) and iii) low heath and prickled broom (Eu +Pt = Erica umbellata and Pterospartum tridentatum). The first two groups are included in the classification of shrub communities used in the Spanish Forest Map SFM25 (MARM, 2011b) within the shrub formations 230 and 240, respectively, based on their similar physiognomic features. The group of low heath and prickled broom includes dominant species of different genus (Eu and Pt), which usually form part of the Pterosparto lasianthi-Ericetum cinereae phytosociological association (Rivas-Martínez et al., 2002), within the Ericenion umbellatae suballiance (Rivas-Martínez, 1979) and frequently dominated by P. tridentatum and E. umbellata (Fernandes and Rego, 1998a). The Ea community was not included in this third group because of its very different fuel structural characteristics (shrub height, bulk density and fuel load), regardless of the existing Pterosparto lasianthi-Ericetum aragonensis phytosociological association (Rivas-Martínez et al., 2002), included in the Ericenion aragonensis suballiance (Rivas-Martínez, 1979) and frequently dominated by E. australis in the area. Moreover, to explore the predictive potential of hShr and to provide more operational tools to assess shrub AGB and fuel load, simplifying where appropriate the collection of biometric data at stand level or to use with remote sensing data, the system of seven equations was refitted to each of the nine communities and each of the four groups of communities with hShr as the only independent variable. To evaluate the presence of multicollinearity among variables in the equations fitted, the condition number was used. According to Myers (1990) condition numbers higher than 1000 √indicate problems associated with multicollinearity. The presence of heteroscedasticity was analysed by the White test (White, 1980) and by visual inspection of studentized residuals plotted against fitted values. When heteroscedasticity was detected, each observation was weighted by the inverse of its estimated variance ( σ 2 i), assuming that this variance can be modelled as a power function of the independent variables (Cailliez, 1980), i.e. σ 2 i= (Xi)k. The value of the exponential term k was optimized to provide the most homogeneous studentized residual plot by using the method proposed by Harvey (1976). The systems were fitted using the nonlinear seemingly unrelated regression (NLSUR) method, which considers the cross-equation correlations, using the cross-equation error covariance matrix obtained by ordinary least squares to initiate the iterative procedure. The weighting factor for heteroscedasticity, when necessary, was programmed in the MODEL procedure of SAS/ETS® (SAS Institute Inc., 2004). Two goodness-of fit statistics were used to check the accuracy of estimates: model efficiency (ME) (Vanclay and Skovsgaard, 1997) and root mean square error (RMSE). Table 3 Parameter estimates and approximate standard errors obtained by simultaneously fitting the system of seven equations (Eqs. (1)–(7)) for each shrub community. W Litt =litter fuel load, W Shr =total shrub fuel load, W Shr_G23 =coarse shrub fuel load, W Shr_G1 =fine shrub fuel load, W Shr_G1_dead =dead fine shrub fuel load, W Shr_G1_live =live fine shrub fuel load. Variable Parameter Statistic Cl Cm Cs Ea Eu Pa Pt Ue Ug W Litt a 0 Estimate 0.2988 0.0799 0.2180 0.5413 0.3866 0.3685 0.0675 0.4165 0.4012 Approx. Std. error 0.0112 0.0169 0.0373 0.0125 0.0495 0.0119 0.0116 0.0166 0.0160 a 1 Estimate – 0.2955 – – – – 0.3421 – – Approx. Std. error – 0.0530 – – – – 0.0385 – – a 2 Estimate – – – – 0.8291 – – – – Approx. Std. error – – – – 0.2584 – – – – a 3 Estimate 0.9966 0.9031 1.2047 0.7310 0.8060 0.7172 1.0652 0.8912 0.9521 Approx. Std. error 0.0897 0.0522 0.1188 0.0153 0.0515 0.0285 0.0425 0.0190 0.0263 W Shr b 0 Estimate 0.0176 0.0818 0.0372 0.0294 0.0343 0.0010 0.0834 0.1111 0.1639 Approx. Std. error 0.0074 0.0223 0.0125 0.0031 0.0130 0.0005 0.0103 0.0132 0.0338 b 1 Estimate 0.8670 0.7009 0.9019 0.9054 1.0245 1.4630 0.7230 0.7087 0.6292 Approx. Std. error 0.0853 0.0571 0.0580 0.0235 0.0914 0.0964 0.0289 0.0240 0.0486 b 2 Estimate 0.3568 0.3352 – 0.5545 – 0.3705 0.7533 0.2868 0.4081 Approx. Std. error 0.1356 0.1075 – 0.0798 – 0.1162 0.0820 0.0484 0.1077 W Shr_G23 W Shr_G1 c 0 Estimate 6.7665 6.9849 7.7831 8.7639 7.8354 5.0526 8.6549 6.1173 11.4396 Approx. Std. error 1.5595 0.9589 0.9210 0.5986 1.4702 1.3247 0.7898 0.3740 1.1045 c 1 Estimate −1.1772 −1.3238 −1.4833 −1.6587 −1.4537 −0.7193 −1.5952 −1.1590 −2.2453 Approx. Std. error 0.3104 0.1882 0.1548 0.1127 0.3437 0.2704 0.1566 0.0738 0.2362 c 2 Estimate – – – – – – – – – Approx. Std. error – – – – – – – – – W Shr_G1_dead W Shr_G1_live d 0 Estimate – – 3.1796 2.4096 3.6971 – 0.8831 1.6570 2.2733 Approx. Std. error – – 0.5518 0.3062 0.6179 – 0.0453 0.3165 0.5907 d 1 Estimate – – −0.4028 −0.3032 −0.7410 – −0.0708 −0.2582 −0.3746 Approx. Std. error – – 0.0993 0.0610 0.1488 – 0.0097 0.0657 0.1348 d 2 Estimate – – – – – – – – – Approx. Std. error – – – – – – – – – Cl =Cistus ladanifer, Cm =Cytisus multiflorus, Cs =Cytisus striatus, Ea =Erica australis, Eu =Erica umbellata, Pa =Pteridium aquilinum, Pt =Pterospartum tridentatum, Ue =Ulex europaeus and Ug =Ulex gallii. J.A. Vega et al.
Forest Ecology and Management 505 (2022) 119926 7 ME =1−∑n i=1(Yi− Yi)2 ∑n i=1(Yi−Y)2(8) RMSE = ∑ n i=1(Yi− Yi)2 n−1 √ √ √ √ √(9) Table 4 Goodness-of fit statistics and weights used to correct heteroscedasticity for fuel load estimates in each fuel fraction and shrub community. W Shr+Litt =shrub and litter load, W Shr =AGB =total shrub load, W Litt =litter load, W Shr_G23 =coarse shrub load, W Shr_G1 =fine shrub load, W Shr_G1_dead =dead fine shrub load and W Shr_G1_live =live fine shrub load. Equation Statistic Cl Cm Cs Ea Eu Pa Pt Ue Ug W Shr+Litt RMSE (kg m −2 ) 0.1449 0.5102 1.9637 0.7381 0.5560 0.2109 0.5227 0.7331 0.6872 ME 0.8921 0.8806 0.7642 0.9131 0.8601 0.9044 0.8924 0.8969 0.7980 Bias (kg m −2 ) 0.0042 −0.0296 0.0238 0.0282 0.0003 −0.0140 0.0108 −0.0486 −0.0182 weight – – – (hShr⋅CovBliss)−1.32 – – (hShr⋅CovBliss)−0.95 – – W Shr RMSE (kg m −2 ) 0.1412 0.4788 1.8950 0.6691 0.4961 0.1803 0.4992 0.5909 0.5019 ME 0.8327 0.8001 0.7286 0.8693 0.6870 0.8801 0.8552 0.8345 0.6879 Bias (kg m −2 ) 0.0049 −0.0252 0.0226 0.0076 0.0052 −0.0036 −0.0032 −0.0145 0.0062 weight – – – (hShr⋅CovBliss)−1.32 – – (hShr⋅CovBliss)−0.95 – – W Litt RMSE (kg m −2 ) 0.0437 0.1044 0.2142 0.2054 0.2417 0.1338 0.1254 0.4049 0.3829 ME 0.9045 0.9298 0.8019 0.9153 0.8617 0.7066 0.8683 0.8458 0.7679 Bias (kg m −2 ) −0.0007 −0.0052 0.0137 0.0215 −0.0053 −0.0108 0.0104 −0.0352 −0.0244 weight – (hShr⋅dLitt)−1.05 – – – (dLitt)−1.01 (dLitt)−1.05 (dLitt)−0.65 (dLitt)−1.05 W Shr_G23 RMSE (kg m −2 ) 0.1068 0.3968 1.7408 0.4552 0.1735 0.0792 0.2625 0.4616 0.3240 ME 0.6553 0.7463 0.7006 0.8632 0.5467 0.7019 0.8584 0.8117 0.6314 Bias (kg m −2 ) 0.0072 −0.0250 0.0229 0.0032 0.0047 0.0010 0.0096 −0.0036 0.0062 W Shr_G1 RMSE (kg m −2 ) 0.0988 0.1920 0.4056 0.3901 0.4479 0.1503 0.4104 0.4798 0.4873 ME 0.7612 0.6936 0.5705 0.7425 0.6055 0.8610 0.6958 0.5033 0.4342 Bias (kg m −2 ) −0.0023 −0.0002 0.0018 −0.0024 0.0005 0.0007 −0.0013 −0.0108 −0.0031 W Shr_G1_dead RMSE (kg m −2 ) – – 0.1237 0.1504 0.1957 – 0.2120 0.2914 0.3256 ME – – 0.7601 0.7102 0.6594 – 0.4605 0.3948 0.3060 Bias (kg m −2 ) – – −0.0012 −0.0010 0.0008 – 0.0017 −0.0059 −0.0018 W Shr_G1_live RMSE (kg m −2 ) – – 0.3943 0.3200 0.3391 – 0.3728 0.3443 0.3566 ME – – 0.2704 0.6421 0.4170 – 0.5596 0.3543 0.2626 Bias (kg m −2 ) – – 0.0030 −0.0014 −0.0003 – −0.0030 −0.0049 −0.0014 Cl =Cistus ladanifer, Cm =Cytisus multiflorus, Cs =Cytisus striatus, Ea =Erica australis, Eu =Erica umbellata, Pa =Pteridium aquilinum, Pt =Pterospartum tridentatum, Ue =Ulex europaeus and Ug =Ulex gallii Table 5 Parameter estimates and approximate standard errors obtained by simultaneously fitting the system of seven equations (Eqs. (1)–(7)) for each fuel fraction and group of shrub communities. W Litt =litter fuel load, W Shr =total shrub fuel load, W Shr_G23 =coarse shrub fuel load, W Shr_G1 =fine shrub fuel load, W Shr_G1_dead =dead fine shrub fuel load, W Shr_G1_live =live fine shrub fuel load. Variable Par. Statistic Cm +Cs Eu +Pt Ue +Ug All-Pa W Litt a 0 Estimate 0.2299 0.4099 0.3921 0.4140 Approx. Std. error 0.0073 0.0123 0.0125 0.0092 a 1 Estimate – – – – Approx. Std. error – – – – a 2 Estimate – – – – Approx. Std. error – – – – a 3 Estimate 1.2295 0.9335 0.9445 0.8752 Approx. Std. error 0.0257 0.0215 0.0186 0.0172 W Shr b 0 Estimate 0.0379 0.0913 0.1276 0.0582 Approx. Std. error 0.0048 0.0133 0.0072 0.0021 b 1 Estimate 0.8966 0.7155 0.6688 0.7962 Approx. Std. error 0.0236 0.0314 0.0118 0.0080 b 2 Estimate – 0.6275 0.4775 0.5536 Approx. Std. error – 0.1049 0.0301 0.0256 W Shr_G23 W Shr_G1 c 0 Estimate 6.7573 7.9918 7.3568 8.2607 Approx. Std. error 0.2976 0.4989 0.3194 0.1998 c 1 Estimate −1.3047 −1.4643 −1.3979 −1.5653 Approx. Std. error 0.0529 0.1015 0.0642 0.0380 c 2 Estimate – – – – Approx. Std. error – – – – W Shr_G1_dead W Shr_G1_live d 0 Estimate – 1.3662 2.2010 1.5991 Approx. Std. error – 0.3006 0.2733 0.1806 d 1 Estimate – −0.1755 −0.3662 −0.1990 Approx. Std. error – 0.0674 0.0585 0.0376 d 2 Estimate – – – – Approx. Std. error – – – – Brooms (Cm +Cs =Cytisus multiflorus and Cytisus striatus), low heather and prickled broom (Eu +Pt =Erica umbellata and Pterospartum tridentatum), gorses (Ue +Ug = Ulex europaeus and U. gallii) and the pooled data for all shrub communities excluding the fern-dominated community (All-Pa). J.A. Vega et al.
Forest Ecology and Management 505 (2022) 119926 8 where Y i , Yi and Y are the observed, predicted and mean values of the dependent variable and n is the number of observations used to fit the equation. 3. Results 3.1. Fuel load equations for shrub community with no restrictions on independent variables The values of the parameter estimates and the asymptotic standard errors of the system of seven equations fitted to each of the nine shrub communities are shown in Table 3. As previously commented, equations for estimating W Shr_G1_dead and W Shr_G1_live for Pa were not fitted. Moreover, for Cl and Cm it was not possible to disaggregate the estimates of these two fractions (W Shr_G1_dead and W Shr_G1_live ) due to problems associated with convergence of the complete system. The goodness-of-fit statistics of the equations and the weighting factors used to prevent heteroscedasticity are shown in Table 4. The results of the White test indicated moderate problems of heteroscedasticity only for three fractions in some shrub communities: total shrub and litter fuel load (W Shr+Litt ), total shrub load (W Shr =AGB) and especially litter load (W Litt ). The values of the condition number did not indicate problems of multicollinearity for any fuel fraction of any shrub community. According to the partial values of ME, the mean shrub height (hShr) was the most important independent variable for all the shrub-layer fuel fractions of the nine communities studied and was the only significant variable for W Shr_G1_dead and W Shr_G1_live equations for all the communities where these fractions were disaggregated. The litter depth (dLitt) was the most important independent variable for estimating the fuel load of the litter layer (W Litt ), in terms of partial values of ME and, except for Cm and Pt, for which hShr was also included in the equation, and Eu, for which Cov Bliss was also significant, dLitt was the only significant variable (p < 0.05) for estimating this fraction. The values and signs of all the parameters were biologically consistent, and graphical inspection of the studentized residuals showed random patterns of residuals around zero with homogeneous variance and no discernible trends. Plots of observed versus predicted values of AGB (W Shr ) and W Litt are shown in Figure SM1 in Supplementary Material. Overall, the best results were obtained for Ea and Pt communities and the poorest results for Ug and Cs communities. The best goodness-of-fit statistics were obtained for the equations fitted to estimate W Shr+Litt and W Litt , with ME values ranging from 0.7642 to 0.9131 for the first fuel load and from 0.7066 to 0.9298 for the second. The equations used to estimate AGB (W Shr ) explained between 68.70 and 88.01% of the observed variance; the percentage of observed variance explained by the equations used to estimate W Shr_G1 and W Shr_G23 ranged from 43.42 to 86.10% for the fine fuel fraction and from 54.67 to 85.84% for the coarse fuel fraction. Finally, the worst results, in terms of goodness-of-fit statistics, were obtained for the equations used to disaggregate the fine fraction, especially for W Shr_G1_live , with ME values ranging from 0.2626 for Ug to 0.6421 for Ea. 3.2. Fuel load equations for groups of communities and pooled data with no restrictions on independent variables As previously commented, some communities were combined and four groups were considered: (i) brooms (Cm +Cs), (ii) gorses (Ue +Ug), (iii) low heath and prickled broom (Eu +Pt) and iv) pooled data for all shrub communities excluding the fern-dominated community (All-Pa). The values of the parameter estimate and the asymptotic standard errors of the system of seven equations fitted to each of these four groups are shown in Table 5 and the goodness-of-fit statistics and the weighting factors used to prevent heteroscedasticity are shown in Table 6. The results obtained were similar to those corresponding to the nine shrub communities, i.e. moderate heteroscedasticity was only observed for W Shr+Litt , W Shr and W Litt ; no multicollinearity was detected for any equation; taking into account the partial values of ME, hShr was the most important independent variable for all the shrub fuel fractions of the four groups and was the only significant variable for W Shr_G1_dead and Table 6 Goodness-of fit statistics and weights used to correct heteroscedasticity in fuel load estimates for each fuel fraction and group of shrub communities. W Shr+Litt =shrub and litter load, W Shr =AGB =total shrub load, W Litt =litter fuel load, W Shr_G23 =coarse shrub load, W Shr_G1 =fine shrub load, W Shr_G1_dead =dead fine shrub load and W Shr_G1_live =live fine shrub load. Equation Statistic Cm +Cs Eu +Pt Ue +Ug All-Pa W Shr+Litt RMSE (kg m −2 ) 1.4225 0.5729 0.7308 0.9877 ME 0.8226 0.8609 0.8759 0.8290 Bias (kg m −2 ) −0.0009 0.0184 0.0026 0.0159 weight (hShr)−1.21 – (hShr⋅CovBliss)−0.35 (hShr⋅CovBliss)−0.96 W Shr RMSE (kg m −2 ) 1.3844 0.5092 0.5824 0.8924 ME 0.7915 0.8033 0.8009 0.7562 Bias (kg m −2 ) 0.0060 0.0109 0.0437 0.0146 weight (hShr)−1.21 – (hShr⋅CovBliss)−0.35 (hShr⋅CovBliss)−0.96 W Litt RMSE (kg m −2 ) 0.1825 0.2355 0.3994 0.3283 ME 0.8288 0.8363 0.8267 0.8401 Bias (kg m −2 ) −0.0171 0.0078 −0.0420 0.0537 weight (dLitt)−2.12 (dLitt)−0.96 (dLitt)−0.85 (dLitt)−0.98 W Shr_G23 RMSE (kg m −2 ) 1.2231 0.2268 0.4356 0.6085 ME 0.7963 0.8345 0.7991 0.8126 Bias (kg m −2 ) 0.0128 0.0140 0.0140 0.0129 W Shr_G1 RMSE (kg m −2 ) 0.3310 0.4367 0.5073 0.5604 ME 0.5928 0.6425 0.4336 0.4451 Bias (kg m −2 ) −0.0024 −0.0031 0.0297 0.0093 W Shr_G1_dead RMSE (kg m −2 ) – 0.2137 0.3053 0.3182 ME – 0.5517 0.3565 0.3248 Bias (kg m −2 ) – 0.0016 0.0098 0.0073 W Shr_G1_live RMSE (kg m −2 ) – 0.3628 0.3705 0.3948 ME – 0.4838 0.2845 0.3345 Bias (kg m −2 ) – −0.0046 0.0199 0.0089 Brooms (Cm +Cs =Cytisus multiflorus and Cytisus striatus), low heather and prickled broom (Eu +Pt =Erica umbellata and Pterospartum tridentatum), gorses (Ue +Ug = Ulex europaeus and U. gallii) and the pooled data for all shrub communities excluding the fern-dominated community (All-Pa). J.A. Vega et al.
Forest Ecology and Management 505 (2022) 119926 9 W Shr_G1_live equations for all the groups for which these fractions were disaggregated, whereas dLitt was the only significant independent variable for estimating W Litt for all the groups. As found for the nine communities, the values and signs of all the parameters were biologically consistent and a homogeneous variance distribution of studentized residuals without visual trends was observed for all the equations. Plots of observed versus predicted values of W Shr and W Litt are shown in Figure SM2 in Supplementary material. The Eu +Pt group yielded the best overall results from the four groups analysed. Nonetheless, for all four groups very accurate estimates were obtained for all the fractions (ME ranging from 0.7562 to 0.8759), except for fine fuels and its disaggregated fractions (W Shr_G1, W Shr_G1_dead and W Shr_G1_live ), with percentages of observed variance explained ranging from 28.45 to 64.25%. Table 7 shows the percentage increase in RMSE, i.e., reduction in accuracy, resulting from using the equations fitted for each of the four groups relative to the equations fitted for each community independently. The reduction in the accuracy of estimates is particularly remarkable in the All-Pa group and in the W Litt equations for Cm +Cs and Eu +Pt groups. 3.3. Fuel load equations for each community with hShr as the only independent variable The system of seven equations was refitted to each of the nine communities and each of the four groups of communities with hShr as the only independent variable used to estimate shrub fuel loading at stand level. The goal was to explore the predictive potential of hShr and to provide additional operational tools for assessing shrub AGB and fuel load by simplifying, where appropriate, the collection of biometric data at stand level or by using remote sensing data. The parameter estimates and their associated asymptotic standard errors and the goodness-of-fit statistics are shown in Appendix 1 (Tables A1 and A2 for the nine communities and in Tables A3 and A4 for the four groups considered, respectively). All comments about the structure and distribution of the residuals of the previously fitted systems of equations are also valid for the systems refitted using only hShr as the independent variable. Regarding the nine communities, overall, the most accurate estimates were obtained for Ea (ME ranging from 0.5860 for W Shr_G1_live to 0.8875 for W Shr+Litt ) and the worst results were obtained for Ug (ME ranging from 0.1604 for W Litt to 0.6430 for W Shr ). As expected, the litter layer (W Litt ) was the fraction for which the accuracy of estimates, in terms of percentage increase in RMSE, was relatively more affected than estimates based on equations also including shrub cover or litter depth, with increases in RMSE (%) ranging from 53.07% for Ea to 147.14% for Cl (Table 8). For all the communities except Cs, the equation W Shr+Litt was also greatly affected, with increases in RMSE ranging from 13.68% for Ea to 63.29% for Ug (Table 8). 3.4. Fuel load equations for groups of communities and pooled data with hShr as the only independent variable For the four groups of communities, overall, the most accurate estimates were obtained for Cm +Cs (ME ranging from 0.5900 for W Shr_G1 to 0.8155 for W Shr+Litt ) and the poorest results were obtained for All-Pa (ME ranging from 0.2346 for W Litt to 0.8133 for W Shr_G23 ). Comparison of the RMSE values of the systems fitted using hShr as the Table 7 Increase in RMSE (%) produced by using the equations fitted for each fuel fraction load of four groups of communities relative to the equations fitted for each community independently, in both cases without restriction on independent variables. W Shr+Litt =shrub and litter, W Shr =AGB =total shrub, W Litt = litter, W Shr_G23 =coarse shrub, W Shr_G1 =fine shrub, W Shr_G1_dead =dead fine shrub and W Shr_G1_live =live fine shrub. ≈indicates values <2%. Increase in RMSE (%) Cm +Cs Eu +Pt Ue +Ug All-Pa W Shr+Litt ≈6.59 2.08 22.51 W Shr 2.26 2.70 4.02 24.16 W Litt 9.92 24.45 ≈9.85 W Shr_G23 ≈2.16 4.42 7.94 W Shr_G1 6.04 2.07 5.32 31.84 W Shr_G1_dead – 5.10 ≈36.10 W Shr_G1_live – 2.15 6.42 20.27 Brooms (Cm +Cs =Cytisus multiflorus and Cytisus striatus), low heather and prickled broom (Eu +Pt =Erica umbellata and Pterospartum tridentatum), gorses (Ue +Ug =Ulex europaeus and U. gallii) and the pooled data for all shrub communities excluding the fern-dominated community (All-Pa). Table 8 Increase in RMSE (%) produced by using the equations fitted for each fuel fraction load and community with hShr as the only independent variable, relative to the equations fitted with no restrictions on independent variables. W Shr+Litt =shrub and litter, W Shr =AGB =total shrub, W Litt =litter, W Shr_G23 =coarse shrub, W Shr_G1 = fine shrub, W Shr_G1_dead =dead fine shrub and W Shr_G1_live =live fine shrub. ≈indicates values <2%. Increase in RMSE (%) Cl Cm Cs Ea Eu Pa Pt Ue Ug W Shr+Litt 32.78 19.76 ≈13.91 48.90 33.48 35.60 55.18 61.03 W Shr 10.91 9.52 ≈3.29 ≈8.26 8.65 8.56 6.50 W Litt 147.14 111.21 78.43 53.07 99.13 61.96 102.55 100.00 89.45 W Shr_G23 3.28 5.85 ≈ ≈ ≈ ≈ 3.50 ≈2.84 W Shr_G1 13.56 10.36 ≈4.31 ≈12.51 11.57 9.15 7.00 W Shr_G1_dead ≈1.80 ≈4.60 2.70 W Shr_G1_live ≈7.91 ≈6.51 5.36 Cl =Cistus ladanifer, Cm =Cytisus multiflorus, Cs =Cytisus striatus, Ea =Erica australis, Eu =Erica umbellata, Pa =Pteridium aquilinum, Pt =Pterospartum tridentatum, Ue =Ulex europaeus and Ug =Ulex gallii. Table 9 Increase in RMSE (%) produced by using the equations fitted for each fuel fraction load of the four groups of communities with hShr as the only independent variable, relative to the equations fitted for the four groups of communities with no restrictions on independent variables. W Shr+Litt =shrub and litter, W Shr = AGB =total shrub, W Litt =litter, W Shr_G23 =coarse shrub, W Shr_G1 =fine shrub, W Shr_G1_dead =dead fine shrub and W Shr_G1_live =live fine shrub. ≈indicates values <2%. Equation Cm +Cs Eu +Pt Ue +Ug All-Pa W Shr+Litt 2.28 75.79 56.84 42.09 W Shr ≈12.59 7.59 5.76 W Litt 90.68 138.94 95.42 126.17 W Shr_G23 ≈4.67 ≈ ≈ W Shr_G1 ≈11.40 11.93 9.35 W Shr_G1_dead – 3.79 4.72 5.03 W Shr_G1_live – 9.37 9.39 7.09 Brooms (Cm +Cs =Cytisus multiflorus and Cytisus striatus), low heather and prickled broom (Eu +Pt =Erica umbellata and Pterospartum tridentatum), gorses (Ue +Ug =Ulex europaeus and U. gallii) and the pooled data for all shrub communities excluding the fern-dominated community (All-Pa). J.A. Vega et al.
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