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Research Article

Modeling of Forests Fuels Load from Dasometric Attributes in Temperate Forests of Northern Mexico

M. Pompa-Garcia, M. Morales-Soto and D.A. Rodriguez-Trejo
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The study of fuels is a factor to define the vulnerability of ecosystems to forest fires. The aim of this study was to model the dead fuel load based on mensuration attributes from forest management inventories. A scatter plot analysis from explanatory trends between the variables considered was performed using the stepwise regression method of SAS. The results showed that the depth of litter, total real stocks and intensities of cut, largely explain the dead fuel load as dependent variable. In addition, to discussing the benefits of statistics of the models studied, it has been concluded that the inventory data management programs are an efficient and inexpensive alternative to estimate forest fuel loads.

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M. Pompa-Garcia, M. Morales-Soto and D.A. Rodriguez-Trejo, 2012. Modeling of Forests Fuels Load from Dasometric Attributes in Temperate Forests of Northern Mexico. Research Journal of Forestry, 6: 66-71.

DOI: 10.17311/rjf.2012.66.71

Received: July 01, 2012; Accepted: August 11, 2012; Published: January 28, 2013


Wildland fires constitute a significant cause of land degradation, yet often they are a natural process (Neri-Perez et al., 2009). For managers, an accurate knowledge of the fuel complex is essential for designing management prescriptions aimed at reducing fire risk (Nuruddin et al., 2006). Fuels are defined according to the physical characteristics of the live and dead biomass that contribute to the spread, intensity and severity of wildland fire (Andrews and Queen, 2001). Dead fuels are all biomass found on the ground; live fuels consist of live grasses, shrubs and trees (Wong and Villers, 2007). Dead fuels in turn are divided according to their weight in light fuels and heavy fuels and are often classified by the amount of time required for them to dry in order to burn (Estrada and Angeles, 2007). They are also classified according to where they are located within a site: ground fuels, surface fuels and aerial fuels (Schwarz, 1999).

The forest fuel is one of the key elements involved in wildfire and is a very important factor in defining the hazard of forest fires (Syaufina and Ainuddin, 2011). The degree of danger depends on the amount and type of combustible material present in corresponding forest areas (Djarwanto and Tachibana, 2010). It is known that the intensity of a fire changes according to fuel material type that is displaced. Therefore, it is essential to design accurate inventories of the fuel loadings in forest. One of the most popular techniques is the planar intersect technique (Brown, 1974). This author mentions that this method can be applied in any type of forest and involves counting intersections of woody pieces with vertical sampling planes. Based on this sample volume is estimated and weight is calculated based on the volume and the application of estimators of specific gravity of the woody materials.

Unfortunately, this technique has as drawback that the data should be taken in situ which require considerable time, effort and money. Indeed, the fuel load is dynamic and for those who have information within a certain time such information will be limited for this purpose. Therefore, the forest land for the quantification of dead fuels is scarce (Brown, 1974).

Currently, there are many procedures to estimate fuel loads in Mexican forests, through remote sensing (Flores-Garnica and Omi, 2003). However, such systems require reliable spatially referenced data, their use has been limited.

A method that facilitates quantification of dead fuels are the allometric relationships, using the stepwise regression; it allows us to obtain an equation to predict the value of the dependent variable if the values of the independent variable are known (Abdelkader et al., 2007; Abdullah et al., 2012). This method is a useful tool, easy and fast to calculate dead fuel material from live fuel material. Also can be developed in all those ecosystems from which there is information of forest inventories necessary for its application.

The aim of this study was to estimate the dead fuel material from the live fuel material by allometric relationships, with a hypothesis that there is correlation between dasometric data and forest fuel load.


Description of the study area: The study area selected is geographically located southwest of the State of Durango, Mexico (Fig. 1). Its geographical coordinates are between 23°07' and 23°39' north latitude and 105°12' and 105°46' west longitude. It has a total area of 240 739 ha, with a topography in a system of plateaus associated with streams and altitude from 500 to 2 800 m.a.s.l. The soils were originated by weathering of igneous rocks. The main land uses are agriculture, livestock and forestry.

Image for - Modeling of Forests Fuels Load from Dasometric Attributes in Temperate Forests of Northern Mexico
Fig. 1: Location of the Ejido Pueblo Nuevo, Durango

Table 1: Models used for estimating fuel load
Image for - Modeling of Forests Fuels Load from Dasometric Attributes in Temperate Forests of Northern Mexico
Where, β1, β2, β3, β4, β5, β6: Regression parameters, H: Litter load (Mg ha-1), P: Slope (%), A: Average height of Pinus (m), R: Average removal (m3), DQ: Quadratic diameter of Quercus (cm), ICP: Intensity of pine cutting (%), ICM: Intensity of average cutting of Pinus (%), T: Total load (mg ha-1), LP: Sum of the light, medium and heavy woody fuels (mg ha-1), ICQ: Intensity of cut of Quercus (%), PES: Load of Heavy woody fuels (mg ha-1), DP: Pine quadratic diameter (cm), OC: Total number of other conifers (No. of individuals), C1, C2, C3: Loads of woody fuel categories with 1, 10 and 100 h of TL (time lag), respectively (Mg ha-1)

Most ecosystems are common property, although there are some lands privately owned. Climates are: C (w2), temperate, sub-humid, summer rains from 5-10.2% a year (A)C(w2), semi-warm, temperate sub-humid, summer rains from 5-10.2% a year, Cb'(w2), temperate, semi-cold, with long cool summers, sub-humid, summer rains from 5-10.2% annually; Aw1, warm, sub-humid, summer rains from 5-10.2% annually; C(w2), temperate, subhumid, summer rains from 5-10.2% annually (Pompa-Garcia, 2012).

Methodology: The variables utilized in this study were forest litter (mg ha-1) light, medium and heavy woody fuels (mg ha-1), slope (percent), average height of Pinus (m), average removal (m3), oak-pine quadratic diameter (cm), intensities of pine-oak cuts (%), pine and hardwoods, real stocks of each species (number of individuals); total Mean Annual Increment (MAI) and productivity level of the stands all obtained from the forest management inventory of the Ejido Pueblo Nuevo Durango. In order to visually identify correlations between variables, a scatter plot analysis was performed of dead fuel material versus live fuel material variables. Having been identified the explanatory variables with greatest dependence, they were processed by the stepwise method of linear regression using SAS program to fit the linear relationships between dead fuel with live fuel. The models used for estimating the dead load of the fuel were as follows (Table 1).

The criterion for evaluating the goodness of fit of the models was based on numerical analysis involving the comparison of three statistics frequently used in forest modeling (Pompa-Garcia et al., 2012): (1) the bias (E) which evaluates the deviation of the model with respect to the observed values; the Root Mean Square Error (RMSE) which examines the accuracy of the estimates; the fitted coefficient of determination R2adj which represents the part of the variance explained by the model, taking into account the number of parameters in it. Their expressions are:


Image for - Modeling of Forests Fuels Load from Dasometric Attributes in Temperate Forests of Northern Mexico

Root mean square error:

Image for - Modeling of Forests Fuels Load from Dasometric Attributes in Temperate Forests of Northern Mexico

Fitted coefficient of determination:

Image for - Modeling of Forests Fuels Load from Dasometric Attributes in Temperate Forests of Northern Mexico

where, y1, Image for - Modeling of Forests Fuels Load from Dasometric Attributes in Temperate Forests of Northern Mexico and Image for - Modeling of Forests Fuels Load from Dasometric Attributes in Temperate Forests of Northern Mexico are the value observed, estimated and mean of the dependent variable; n is the total number of observations used to fit the model; p is the number of parameter of the model.


According to the fit statistics obtained by the stepwise method of linear regression, the independent variables that explain mainly the influence of dead fuel load are: intensity of cutting of pine and oak, the total real stock of pine, oak and other hardwoods and depth of litter (Table 2).

In Table 2, the results shows standard errors close to zero and reliable R2. Thus, indicates that there is great percentage of the variation in the response variable can that be explained by the explanatory variable. It is important to note that although some models (2, 3, 4, 5, 6, 7 and 8) measured lower number of parameters, their results are equally reliable to models with a higher number. As shown in models 1 and 2 that although they differ in number of estimated parameters the variable calculated is the same and its results are similar.

In model 1, quantity of litter, there are near-zero standard errors and fit statistics show an R2 of 0.761 indicating that there is good correlation between litter and the dependent variables. In model 2 total fuel load, in the same way it throws us standard errors close to zero, with an R2 of 0.683. The results show that both models yield statistically reliable data even when they differ in the number of estimated parameters.

Table 2: Models estimated of dead fuels from live fuels
Image for - Modeling of Forests Fuels Load from Dasometric Attributes in Temperate Forests of Northern Mexico
RMSE: Root mean square error

On the other hand, the models show that the main factors of the concentration of forest fuels are a function of the waste generated during the treatments of cuts and by the total actual stock, as outlined by Renteria et al. (2005).

According to the results obtained, the variables intensity of cut, total real stocks and litter depth can be reliably used in calculating fuel load, despite its classification is difficult in terms of dimensions (light, medium and heavy) and where they are located (ground, surface and aerial). However, can make an estimate of the fuel load used in different strategies for distributing fuel models. Flores-Garnica and Omi (2003) consider changes in the distribution of fuel loads, required to identify the areas most prone to occurrence of forest fires, thus to direct strategies for prevention, control and combat of these forest fires as set out by Estrada and Angeles (2007), who mention that the values obtained in any evaluation of forest fuels can serve as a basis for mapping of forest fire risk by combining other parameters. Also by this method is not necessary to conduct an inventory of forest fuels that requires time, effort and funding. The fuel data can be updated while updating the forest inventory (Heshmatol Vaezin et al., 2008).


The dead fuel load can be calculated from live fuels by statistically supported techniques of correlation from mensuration data. In this study the variables that best explained the models were: intensity of cut, total real stocks and litter depth. It was determined that this method of correlation is a fast, viable and efficient tool as the dependent variables are taken from existing inventory data. It also can be a tool in the modeling of fire danger, regimes and management strategies of forest fires.


This work was conducted in the frame of Academic mobility supported by the UJED. We would like to thank the support given by the technical head of the Ejido Pueblo Nuevo who supported the provision of data used in this study. Also we recognize the support of Science and Technology Council in Durango State (COCYTED) and Carlos A. Muñoz R.


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