Allometric Equations for Estimating Biomass and Carbon Stocks in the Temperate Forests of North-Western Mexico

Article Allometric Equations for Estimating Biomass and Carbon Stocks in the Temperate Forests of North-Western Mexico Benedicto Vargas-Larreta 1,*, Carlos Antonio López-Sánchez 2ID , JoséJavier Corral-Rivas 2, Jorge Omar López-Martínez 3ID , Cristóbal Gerardo Aguirre-Calderón1and Juan Gabriel Álvarez-González 4ID 1Instituto Tecnológico de El Salto, Mesa del Tecnológico s/n. 34942 El Salto, Durango, Mexico; [email protected] 2 Instituto de Silvicultura e Industria de la Madera, Universidad Juárez del Estado de Durango, Boulevard del Guadiana 501, Ciudad Universitaria, Torre de Investigación, 34120 Durango, Durango, Mexico; [email protected] (C.A.L.-S.); [email protected] (J.J.C.-R.) 3CONACYT-El Colegio de la Frontera Sur. Av. Centenario km 5.5, 77014 Chetumal, Quintana Roo, Mexico; [email protected] 4Departamento de Ingeniería Agroforestal, Universidad de Santiago de Compostela, Escuela Politécnica Superior, 27002 Lugo, Spain; [email protected] *Correspondence: bvar[email protected]; Tel.: +52-675-876-5533 Received: 24 May 2017; Accepted: 27 July 2017; Published: 28 July 2017 Abstract: This paper presents new equations for estimating above-ground biomass (AGB) and biomass components of seventeen forest species in the temperate forests of northwestern Mexico. A data set corresponding to 1336 destructively sampled oak and pine trees was used to fit the models. The generalized method of moments was used to simultaneously fit systems of equations for biomass components and AGB, to ensure additivity. In addition, the carbon content of each tree component was calculated by the dry combustion method, in a TOC analyser. The results of cross-validation indicated that the fitted equations accounted for on average 91%, 82%, 83% and 76% of the observed variance in stem wood and stem bark, branch and foliage biomass, respectively, whereas the total AGB equations explained on average 93% of the total observed variance in AGB. The inclusion of total height (h) or diameter at breast height 2× total height (d 2 h) as a predictor in the d-only based equations systems slightly improved estimates for stem wood, stem bark and total above-ground biomass, and greatly improved the estimates produced by the branch and foliage biomass equations. The predictive power of the proposed equations is higher than that of existing models for the study area. The fitted equations were used to estimate stand level AGB stocks from data on growing stock in 429 permanent sampling plots. Three machine-learning techniques were used to model the estimated stand level AGB and carbon contents; the selected models were used to map the AGB and carbon distributions in the study area, for which mean values of respectively 129.84 Mg ha −1 and 63.80 Mg ha−1were obtained. Keywords: above-ground biomass; GMM; allometry; biomass allocation; machine learning technique 1. Introduction Improved knowledge of carbon stocks and fluxes is needed in order to understand the current state of the carbon cycle and how it might evolve with changing land use and climatic conditions [ 1 ]. This has led to an increased interest in estimating forest biomass for practical forestry purposes and for scientific purposes. Tree biomass is an important component of the carbon pool in forests, and it can be estimated by using biomass expansion factors [ 2 ] or by relating biomass functions to tree-level data Forests 2017,8, 269; doi:10.3390/f8080269 www.mdpi.com/journal/forests Forests 2017,8, 269 2 of 20 obtained in forest inventories [ 3 ]. In both cases, generic biomass functions are used to quantify the carbon in forests [ 4 ] because such functions improve the accuracy of carbon accounting systems and thus allow accurate planning of whole-tree and residual biomass utilization for bioenergy production. Mexico is one of the largest emitters of CO 2 due to deforestation and land degradation, which together account for 4.9 per cent (32 Mt CO 2 e) of the global emissions in the country [ 5 ]. Thus, most states in Mexico are implementing action plans aimed at mitigating the effects of climate change and accessing economic incentives that favour carbon sequestration in forests. Initiatives such as REDD+ (Reducing Emissions from Deforestation and Forest Degradation and enhancement of carbon stocks) are important efforts aimed at combating climate change; however, for effective implementation of such mechanisms, accurate estimation and monitoring of AGB and associated carbon stocks in forests is first required [6]. Several biomass equations and biomass expansion factors have been reported for forest species in Mexico. Acosta-Mireles et al. [ 7 ] generated allometric equations for six species of a mixed hardwood and oak forest in the northern Sierra of Oaxaca. All equations were of the form Y = bX k , where Yis the above-ground biomass (kg), Xis diameter at breast height (cm), and band kare the parameter estimates. Návar [ 8 , 9 ] developed diameter-based allometric biomass equations for nine species of pine and oak in temperate forests in Durango and Chihuahua. Rodríguez-Ortíz et al. [ 10 ] analyzed the effects of thinning on distribution and accumulated above-ground biomass content of Pinus patula in Ixtlán, Oaxaca. Silva-Arredondo and Návar-Cháidez [ 11 ] conducted research in northern Mexico to assess biomass components and biomass expansion factors by using classical allometric equations, and Villegas-Jiménez et al. [ 12 ] estimated above-ground biomass components in 13 Mexican provenances of P. greggii Engelm. in southern Mexico. Other similar studies have been carried out in Mexico by Díaz-Franco et al. [ 13 ], Mendoza-Ponce and Galicia [ 14 ], Búrquez et al. [ 15 ], Aguirre-Salado et al. [ 16 ], and Méndez-González et al. [ 17 ]. Rojas-García et al. [ 18 ] provide a comprehensive database with the above cited and other allometric equations applicable to a large number of tree and shrub species in Mexico. However, biomass equations were only available for nine tree species in the study area [8,9] . Moreover, these equations were developed using tree diameter as the only regressor, and they are not additive, one of the most important properties of biomass equations. Thus, there is still a need for research involving the accurate estimation of forest biomass and carbon stocks in these multi-species forests. Temperate forests occupy 32,330,508 ha in Mexico, i.e., 17 per cent of the total land area. These are the richest ecosystems in Mexico with some 7000 plant species [ 19 ], of which ~150 are species of pines and 170 of oaks together representing more than 50 per cent of all known pine and oak species [ 20 ]. Durango is the most important forestry state in Mexico, with 10.5 million ha of forest cover and a timber production of 1.9 million m 3 per year (32.8% of the national forest production [ 21 ]). Quantification of forest biomass and carbon stocks is important for management of these forests. Furthermore, mapping the spatial pattern of large-scale forest biomass can provide an overall picture of the carbon stocks within a region, which is of great scientific and political importance [ 22 ]. However, as pointed out in studies by Zianis and Mencuccini [ 23 ] and Walker et al. [ 24 ], although forest biomass can be measured directly, the method used (destructive sampling) is expensive and time-consuming and does not yield the continuous spatial distribution of biomass at large scales [ 25 ]. The difficulties associated with the direct estimation of biomass must be solved by quantitative satellite and remote sensing techniques, which represent the most promising methods for estimating biophysical features of forests, along with the development of parametric and nonparametric statistical methods for modelling stand variables [ 26 ]. Together these methods have enabled estimation of biomass at multiple scales with large spatial and temporal coverage [27,28]. The main objective of the present study was to develop species-specific systems of additive equations for predicting total above-ground biomass in the temperate forests of north-western Mexico. In addition, we used the new equations to model the forest biomass and carbon distribution at regional Forests 2017,8, 269 3 of 20 scale by applying remote sensing Landsat-5 TM imagery, terrain parameters and data from permanent research plots. 2. Materials and Methods 2.1. Study Area The study was conducted in the uneven-aged and multi-species temperate forest of Durango (22 ◦ 20 0 49 00 to 26 ◦ 46 0 33 00 N; 103 ◦ 46 0 38 00 to 107 ◦ 11 0 36 00 W), which occupies about 23% of the Sierra Madre Occidental ecosystem (Figure 1). The study area is divided in Regional Forest Management Units (in Spanish, Unidades de Manejo Forestal Regional: UMAFORES). The elevation above sea level varies between 363 and 3200 m (average 2264 m). Precipitation ranges from 443 to 1452 mm, with an annual average of 917 mm, whereas the mean annual temperature varies from 8.2 to 26.2 ◦C, with an annual average of 13.3 ◦ C. The predominant forest types are pine and uneven-aged pine-oak, with one or two pine species (usually P. cooperi and P. durangensis) dominating the overstorey and Q. sideroxyla dominating the understorey [29]. Forests2017,8,269 3of20 atregionalscalebyapplyingremotesensingLandsat‐5TMimagery,terrainparametersanddata frompermanentresearchplots. 2.MaterialsandMethods 2.1.StudyArea Thestudywasconductedintheuneven‐agedandmulti‐speciestemperateforestofDurango (22°20′49″to26°46′33″N;103°46′38″to107°11′36″W),whichoccupiesabout23%oftheSierraMadre Occidentalecosystem(Figure1).ThestudyareaisdividedinRegionalForestManagementUnits(in Spanish,UnidadesdeManejoForestalRegional:UMAFORES).Theelevationabovesealevelvaries between363and3200m(average2264m).Precipitationrangesfrom443to1452mm,withanannual averageof917mm,whereasthemeanannualtemperaturevariesfrom8.2to26.2°C,withanannual averageof13.3°C.Thepredominantforesttypesarepineanduneven‐agedpine‐oak,withoneor twopinespecies(usuallyP.cooperiandP.durangensis)dominatingtheoverstoreyandQ.sideroxyla dominatingtheunderstorey[29].  Figure1.Locationofthestudyarea.Trianglesindicatethelocationofthe429permanentsampling plots. 2.2.BiomassData Biomassestimatesforstemwood,stembark,branchesandfoliagewereobtainedfrom1336 destructivelysampledtreesof17species:Pinuscooperi,P.durangensis,P.engelmannii,P.leiophylla,P. herrerae,P.teocote,P.lumholtzii,P.strobiformis,P.oocarpa,P.douglasiana,P.michoacana,Juniperus depeanna,Arbutusbicolor,Quercussideroxyla,Q.rugosa,Q.durifoliaandQ.crassifolia.Asthenumberof specimensofP.michoacanaandP.douglasianawassmall,andasthesespecieshavesimilar morphologicalcharacteristicsandarelocatedinthesameforeststands[30],thedataforthesespecies Figure 1. Location of the study area. Triangles indicate the location of the 429 permanent sampling plots. 2.2. Biomass Data Biomass estimates for stem wood, stem bark, branches and foliage were obtained from 1336 destructively sampled trees of 17 species: Pinus cooperi,P. durangensis,P. engelmannii,P. leiophylla, P. herrerae,P. teocote,P. lumholtzii,P. strobiformis,P. oocarpa,P. douglasiana,P. michoacana,Juniperus depeanna, Arbutus bicolor,Quercus sideroxyla,Q. rugosa,Q. durifolia and Q. crassifolia. As the number of specimens of P. michoacana and P. douglasiana was small, and as these species have similar morphological characteristics and are located in the same forest stands [ 30 ], the data for these species were combined Forests 2017,8, 269 4 of 20 in order to yield sufficient data for model fitting (Table 1). A generic equation was also developed for each biomass component for all pines and all oak trees. For above-ground biomass measurement, the fieldwork included selection, measurement and felling of standing trees, collection of dimensional data, cutting and separating the tree components and weighing fresh components of each biomass component on site. The sample trees were subjectively selected to represent the complete range of diameter at breast height and total tree height; thus, the data were representative of the different growth and structure conditions in the study area. The number of trees sampled varied from a minimum of 30 in the case of P. douglasiana to a maximum of 130 trees of P. durangensis and Q. crassifolia. Diameter at breast height (d) and total height (h) were measured in each sample tree. The number of trees sampled per species depended on the distribution and abundance within the study area. The following biomass components were considered: stem wood, stem bark, branches (including both wood and bark) and foliage (needles/leaves). Stems were divided into smaller sections to facilitate the weighing process. For each felled tree, stem diameter outside bark was measured at 0.3, 0.6, 1.3 m and thereafter every 2.5 m along the stem to take into account variations in moisture content. The total height of each felled tree was measured with a long fiberglass tape. The green weight of stem and branches was determined by weighing the logs and branches in the field by placing them on a 1000 kg balance (precision 100 g). Whole foliage was totally separated from the trunk and weighed on an analytical balance (precision 1 g). A disc of about 5 cm thick was cut from each log, and representative samples of branches and needles/leaves were weighed in the field (fresh weight) before being transported to the laboratory, where they were oven-dried at 70–85 ◦ C to constant weight (dry weight, measured to the nearest 0.1 g). The time required to reach constant weight was 7–9, 3–4 and 2–3 days for wood discs, branches and foliage, respectively. The biomass of each tree component was calculated on the basis of the ratio of dry biomass to fresh biomass and then summed to produce the total AGB of each tree sampled. The carbon content of each tree component was determined by the dry combustion method, in a TOC analyser (Ol Analytical, College Station, Texas, USA). The number of observations used for tree biomass estimations and the basic description of the tree biomass components data for each species are summarized in Table 1. Table 1. Summary statistics of the felled trees and the main above-ground biomass components used to develop the biomass equations in the study. Tree Species (n)Value Variable Biomass Component d h WwWbWbr WfWt Pinus cooperi (103) Max 52.3 28.0 1586.5 101.0 317.8 28.8 1833.8 Min 5.5 4.2 2.3 0.3 1.5 0.2 4.1 Mean 28.9 17.1 397.5 30.6 97.2 12.5 537.8 SD 10.9 5.0 346.0 23.7 81.4 7.4 444.3 P. durangensis (130) Max 44.5 29.8 1027.5 89.2 312.0 38.4 1319.0 Min 8.7 6.9 8.9 1.3 3.0 0.4 14.4 Mean 25.9 16.6 269.2 37.2 106.6 11.8 424.8 SD 8.5 4.4 210.9 23.4 67.5 8.2 294.5 P. engelmannii (89) Max 51.8 27.8 1825.0 44.3 308.3 30.4 2024.7 Min 6.5 3.8 6.0 0.3 0.5 0.2 6.9 Mean 27.7 15.0 507.5 18.5 107.0 11.8 644.7 SD 9.4 5.4 421.7 11.5 58.9 6.9 479.5 P. leiophylla (84) Max 55.3 29.2 1129.8 89.7 392.0 21.8 1614.6 Min 8.4 5.4 5.7 0.5 1.1 0.4 7.7 Mean 29.6 16.6 329.5 23.2 149.6 7.4 509.7 SD 12.0 5.4 278.6 20.8 111.3 5.7 402.6 Forests 2017,8, 269 5 of 20 Table 1. Cont. Tree Species (n)Value Variable Biomass Component d h WwWbWbr WfWt P. herrerae (97) Max 46.4 31.0 1056.9 72.8 139.4 31.8 1200.4 Min 5.0 5.2 4.0 0.3 0.8 0.4 5.4 Mean 27.8 16.3 354.3 20.3 49.4 13.6 437.6 SD 9.2 4.9 273.0 13.9 34.0 8.6 319.2 P. teocote (81) Max 45.0 24.7 789.3 47.9 161.3 34.8 975.0 Min 10.0 4.5 3.2 0.3 1.1 0.6 5.2 Mean 29.6 15.6 288.9 16.6 50.5 12.2 368.2 SD 9.4 4.0 207.6 12.2 38.3 7.9 261.7 P. lumholtzii (35) Max 42.0 24.9 832.2 37.6 86.9 37.0 981.5 Min 5.0 3.6 2.9 0.2 0.4 0.5 4.0 Mean 22.4 14.7 236.3 10.7 32.0 11.7 290.7 SD 8.6 4.3 209.7 8.5 27.1 10.2 252.7 P. strobiformis (98) Max 49.0 26.6 1240.1 37.6 211.3 40.4 1501.1 Min 5.0 6.3 1.8 0.3 1.5 0.4 4.0 Mean 27.1 16.2 292.9 17.9 73.1 17.2 401.3 SD 9.8 4.8 277.2 9.8 56.2 11.2 354.4 P. oocarpa (37) Max 35.7 18.7 448.9 49.5 173.1 38.0 647.5 Min 7.5 3.2 6.0 0.6 3.0 2.0 11.5 Mean 21.6 12.9 153.4 19.6 53.4 16.8 243.3 SD 6.3 3.6 109.6 12.4 42.0 9.8 167.3 P. douglasiana (30) Max 39.0 25.6 718.4 60.8 124.2 31.2 884.1 Min 8.9 5.6 2.7 0.5 1.1 0.3 4.6 Mean 25.0 17.5 261.9 21.8 40.5 12.4 336.6 SD 7.2 4.4 174.9 15.2 29.5 9.2 224.9 P. michoacana (32) Max 42.1 24.7 866.7 56.2 137.2 39.8 1073.5 Min 12.9 13.5 48.8 4.0 12.9 4.2 69.9 Mean 31.3 20.3 416.6 27.4 64.6 21.4 530.0 SD 8.2 3.0 232.5 13.5 36.6 9.2 285.6 Juniperus deppeana (48) Max 43.7 21.5 357.0 21.8 56.3 27.5 456.3 Min 10.0 4.5 3.7 0.5 1.2 0.8 6.2 Mean 32.9 11.4 183.7 11.4 25.8 13.7 234.7 SD 7.9 3.1 92.7 4.8 15.8 6.9 117.7 Arbutus bicolor (49) Max 44.8 2.5 236.1 9.6 231.1 14.5 375.6 Min 7.9 2.4 3.8 0.2 3.1 0.2 7.2 Mean 22.8 8.9 83.3 3.4 48.5 5.4 140.6 SD 7.8 2.9 53.9 2.4 46.8 3.7 97.6 Quercus sideroxyla (123) Max 57.0 24.8 1018.0 276.3 308.3 29.6 1559.0 Min 11.0 6.3 12.3 3.3 0.4 0.4 16.4 Mean 30.7 14.6 290.9 87.3 75.6 8.5 462.2 SD 9.7 3.7 213.4 90.7 62.2 6.7 331.9 Q. rugosa (61) Max 41.3 20.2 456.1 129.8 132.0 19.4 648.6 Min 9.3 3.3 4.2 1.6 3.2 1.5 14.3 Mean 22.5 11.2 107.2 40.6 51.1 19.2 218.0 SD 8.1 3.7 95.8 31.4 33.4 13.0 166.2 Q. durifolia (131) Max 45.5 22.1 930.9 118.4 421.9 63.9 1526.3 Min 7.0 5.4 6.4 1.3 2.1 0.3 10.2 Mean 27.2 12.4 344.4 32.5 125.6 25.1 527.6 SD 8.8 3.5 226.6 26.9 109.6 18.3 371.7 Q. crassifolia (108) Max 43.1 18.8 533.9 88.3 274.6 35.5 865.0 Min 8.5 6.0 14.3 1.3 11.0 1.0 33.4 Mean 25.5 11.2 218.5 25.6 93.3 14.2 351.5 SD 7.7 2.6 134.7 18.7 62.0 8.2 212.5 where n= number of trees, d= diameter at breast height (cm), h= total height (m), W w = stem wood biomass (kg tree −1 ), W b = stem bark biomass (kg tree −1 ), W br = wood plus bark biomass of branches (kg tree −1 ), W f = foliage (leaves/needles) biomass (kg tree−1), Wt= total above-ground biomass (Ww+Wb+Wbr +Wf) (kg tree−1). Forests 2017,8, 269 6 of 20 2.3. Procedures for Developing the Species-Specific Biomass Equations 2.3.1. Basic Models We used three basic model forms as starting points for model selection (Equations (1)–(3)). w=αdβ+εi(1) w=αdβhγ+εi(2) w=αd2h+εi(3) where α , β , and γ are the equation parameters, wcan be total tree AGB or any of the tree biomass components considered in the study, and εiis the model error. In a first step the models were linearized by using natural logarithms, and the stepwise variable selection approach was used to select the best set of independent variables for each biomass component equation. The significance level for entering and maintaining variables in the model was restricted to 0.001 [ 2 ]. In a second step, a species-specific system of equations with cross-equation constraints on the structural parameters and cross-equation error correlation was then defined for additive prediction of tree component and above-ground biomass [31,32]. The species-specific biomass equation system is formulated as follows: Wi=αiXβij j+εi(4) Wt= n ∑ i=1 Wi+εt(5) where W i represents the tree biomass for the i-th component, W t is the total tree AGB (i.e., the sum of all the tree biomass components), X j are tree variables (j=d,h,d 2 h), αi , βij are parameters to be estimated in the fitting process, and εi,εtare inter-correlated error terms [32]. 2.3.2. Simultaneous Fitting of Tree Biomass Components and Total AGB Total tree AGB was formulated as the sum of the equations for each tree component, and the system of equations was fitted using the Generalized Method of Moments (GMM) in the PROC MODEL procedure of SAS/ETS ® [ 33 ]. This method produces efficient parameter estimates under potentially heteroscedastic conditions, without specifying the nature of the heteroscedasticity [ 34 ], and it thus avoids estimating the heteroscedastic error variance. Bi et al. [ 32 ] and Castedo et al. [ 2 ] state that the GMM procedure of SAS overcomes the above-mentioned problem of the linear combination of the error terms of the tree biomass component equations by computing a generalized inverse of the variance covariance matrix (by setting part of the matrix for whole-tree biomass to zero) and that estimation of parameters by simultaneously fitting the biomass component equations guarantees that AGB will be the sum of the tree component estimates. 2.3.3. Comparison of Equations Statistical and graphical analyses were used to compare the performance of the equations. Moreover, a 10-fold cross-validation approach was used to evaluate the predictive performance of the models. The root mean square error (RMSE) and the coefficient of determination (R 2 ), calculated by Equations (6) and (7), were estimated using the residuals from the 10 fold cross-validation. RMSE = v u u t∑n i=1Yij −ˆ Yij2 n−p(6) R2=1− ∑n i=1Yij −ˆ Yij2 ∑n i=1Yij −Yij2(7) Forests 2017,8, 269 7 of 20 where Y ij and ˆ Yij are the j-th observed and predicted values of biomass for component i, Yij is the mean of nobserved values for the same component, and pis the number of parameters in the model. 2.4. Applying the Proposed Above-Ground Biomass Equations A data set from a network of 429 permanent research sampling plots (Sitios Permanentes de Investigación Forestal y de Suelos: SPIFyS), distributed across the Sierra Madre Occidental in Durango was used to relate stand biomass and carbon stocks to variables obtained from remote sensors. The plots were installed between 2007 and 2011 using the protocol developed by [ 35 ]. The data from these permanent sample plots are used to monitor the growth and yield of the main types of forest in Durango. The plots are 50 × 50 m in size and they were distributed by systematic sampling, with a variable grid ranging from 3 to 5 km, depending on the size of the forest properties. The sampling plots are intended to be re-measured at five-year intervals. Among other variables, tag number, species code, breast height diameter (measured in cm at 1.3 m above ground level), total tree height (m), height to the live crown (m), azimuth ( ◦ ) and radius (m) from the centre of the plot to all trees equal or larger than 7.5 cm in diameter were recorded. The total AGB in each stand was calculated by applying the new tree-level biomass equations (to each tree), converted into carbon content by using the carbon proportion estimated for each component and expressed per unit area (ha). The species or group species-specific AGB models reported by Rojas-García et al. [ 18 ] were used to estimate total AGB for the tree species present in the permanent plots and for which no biomass equations were developed in this study. The spectral data were derived from Landsat TM5 (Thematic Mapper) satellite images obtained during the same period that the SPIFyS were established (2007 to 2011) and are freely available from the National Landsat Archive Processing System (NLAPS). The Landsat 4-5 Thematic Mapper product, level 1 of surface reflectance (radiometrically and atmospherically corrected) was processed using the Standard Landsat Product Generation System (LPGS) via the Landsat Ecosystem Disturbance Adaptive Processing System (LEDAPS) algorithm (both available at [ 36 ]), which uses a 6S radiative transfer model to correct for atmospheric effects on a given date [ 37 ]. Landsat TM5 bands 1, 2, 3, 4, 5 and 7 were used. Band 6, which is designed for thermal mapping and determining soil moisture, was not considered because of its lower (120 m) spatial resolution [ 38 ]. Some common Vegetation Indexes (VI) and other derived parameters were computed from the atmospherically corrected image bands: the Normalized Difference Vegetation Index (NDVI); the Soil Adjusted Vegetation Index (SAVI) and its modification (MSAVI); the Enhanced Vegetation Index (EVI); the Normalized Burn Ratio using bands 4 and 7 (NBR1); the difference Normalized Burn Ratio 2 (NBR2) using bands 5 and 7; and the Normalized Difference Moisture Index (NDMI). These indices have been widely used as comprehensive indicators of the interaction between land cover and solar radiation in the visible and near-infrared regions of the electromagnetic spectrum [26,39–41]. The direct relationship between terrain variables and forest species composition, tree height growth and other stand variables enables these forest variables to be modelled [ 42 , 43 ]. First- and second-order terrain parameters were computed from a Digital Elevation Model (DEM) of the study area with a spatial resolution of 15 m [ 44 ]. Prior to these calculations, a low pass filter with a 5 × 5 moving window was applied to the original DEM in order to reduce the banding effects present in the original file. The first-order terrain parameters selected were elevation, slope, aspect, transformed aspect, profile curvature, plan curvature and curvature, while the second-order terrain parameters were terrain shape index and wetness index. These parameters are potentially related to key features for forest stand development, such as overall climate characteristics, insolation, evapotranspiration, run-off, infiltration, wind exposure and site productivity [42,45]. The sample plots were geolocated in order to extract the average pixel value with an associated buffer of 25 m for each potential predictor. The pixel data were extracted using R statistical software [ 46 ] and the “raster” package. Finally, a database was constructed with the mean biomass values for each Forests 2017,8, 269 8 of 20 plot; the corrected bands of the Landsat-5 TM sensor (6 bands: 1, 2, 3, 4, 5 and 7), the vegetation indexes (7 indexes) and the terrain variables derived from the DEM (9 variables). 2.5. Machine Learning Techniques (MLTs) We compared the performance of three machine learning techniques for estimating the ABG and carbon at stand level: (i) the non-parametric Support Vector Machine (SVM) for Regression technique; (ii) Regression by Discretization based on Random Forest (RD-RF); and (iii) parametric multiple linear regression (MLR). SVMs have proven useful in remote sensing of forest environments [ 47 , 48 ]. The Shevade et al. [ 49 ] modification of the Sequential Minimal Optimization (SMO) with a polynomial kernel and a trade-off parameter value of 1 was used in this study for SVM ensemble. On the other hand, RD-RF employed a classifier (random forest, in this case) on a copy of the data in which the response variable is discretized with equal width. The predicted value is the expected value of the mean class value for each discretized interval (based on the predicted probabilities for each interval). In this study, we used the random forest classification algorithm [ 50 ]. The success of this technique is based on the use of numerous trees developed with different independent variables that are randomly selected from the complete original set of variables. The number of bins for discretization was fixed at 10 and the number of trees fitted was established at 100. Finally, MLR—the technique most commonly used in this kind of study [51]—was used to select the best set of independent variables for the model. The equation was initially built on all descriptors, and descriptors with the smallest standardized regression coefficients were then removed step-wise from the model until no improvement was observed in the estimate of the average prediction error given by the Akaike information criterion [ 52 ]. WEKA open source software [53] was used to implement all three techniques used. Several approaches can be used to test the accuracy of supervised learning algorithms. We used the common method of k-fold cross validation. In this process, the data set is divided into ksubsets. In each application, one of the ksubsets is used as the test set and the other k-1 subsets form the training set. Error statistics are calculated across all ktrials. This provides a good indication of how well the classifier will perform on unseen data. We used k= 10 and computed several standard performance metrics to calculate the goodness-of-fit statistics for each technique. We compared the performance of the MLTs by using the root mean square error (RMSE), the coefficient of determination (R 2 ) and a paired t-test (corrected) based on Student’s t-criterion. Finally, we used the selected MLT to generate above-ground biomass and carbon maps for the study area. 3. Results 3.1. Tree-Level Biomass Equations Table 2depicts the parameter estimates and goodness-of-fit statistics of cross-validation of the equations systems fitted for each species and groups of species. All the parameter estimates were significant at α = 0.05. Stem wood biomass and AGB estimates were the most accurate, as indicated by the R 2 and RMSE values, whereas foliage and branch biomass estimates were the least accurate. The values of the goodness-statistics calculated using the residuals of cross-validation indicated that the selected equations performed well. The results of the coefficient of determination indicated that the fitted models explained between 57% and 98% of the observed biomass variance per component for all species, with mean values of 91%, 82%, 83% and 76% of the observed variance in stem wood and stem bark, branch and foliage biomass, respectively, whereas the total AGB equations explained on average 93% of the total observed variance in AGB. Nevertheless, as mentioned above, the explained variation was lower than 70% for three of the components: branch biomass in P. engelmannii (59%) and P. leiophylla (63%); foliage biomass in P. herrerae (60%), Q. crassifolia (64%) and Juniperus depeanna (67%); and stem bark biomass in Juniperus depeanna (57%). Forests 2017,8, 269 9 of 20 Table 2. Estimated parameters and goodness of fit statistics for the biomass equations for temperate forest species in Durango state, Mexico. Tree Biomass Component Equation Cross-Validation Tree Biomass Component Equation Cross-Validation R2RMSE R2RMSE Pinus cooperi P. douglasiana and P. michoacana Ww=0.031126d2.09355h0.768845 0.97 41.22 Ww=0.11997d2.34448 0.89 68.85 Wb=0.011361d1.676006h0.74627 0.81 10.43 Wb=0.03126d1.978201 0.77 6.94 Wbr =0.007965d1.599044h1.347388 0.89 27.06 Wbr =0.014982d2.40887 0.90 11.25 Wf=0.049925d1.122846h0.600293 0.74 3.79 Wf=0.01168d2.148631 0.83 4.24 Wt=ΣWi0.94 87.21 Wt=ΣWi0.91 76.01 P. durangensis Juniperus depeanna Ww=0.01204d1.76074h1.45047 0.96 39.77 Ww=0.01289d2h0.91 28.98 Wb=0.01706d1.37067h1.10922 0.87 8.44 Wb=0.000772d2h0.57 3.15 Wbr =0.14589d1.64608h0.41109 0.71 36.74 Wbr =0.00204d2h0.81 5.87 Wf=0.00301d1.50863h1.15013 0.83 3.38 Wf=0.00098d2h0.67 3.92 Wt=ΣWi0.96 56.05 Wt=ΣWi0.90 37.00 P. engelmannii Arbutus bicolor Ww=0.09798d1.67370h1.02867 0.91 127.64 Ww=0.06438d1.66448h0.86489 0.93 15.11 Wb=0.037974d1.11488h0.88389 0.98 1.64 Wb=0.00328d1.51833h0.95083 0.87 0.85 Wbr =1.39092d1.25795h0.05199 0.59 37.66 Wbr =0.02125d1.81216h0.8198 0.95 6.99 Wf=0.069316d1.24804h0.34853 0.70 3.77 Wf=0.00698d1.50325h0.84794 0.79 1.72 Wt=ΣWi0.92 140.91 Wt=ΣWi0.95 22.81 P. leiophylla Quercus sideroxyla Ww=0.015582d2h0.94 68.35 Ww=0.033462d1.739234h1.111268 0.90 65.75 Wb=0.001074d2h0.89 6.92 Wb=0.03022d1.66927h0.80238 0.79 27.87 Wbr =0.007269d2h0.63 67.38 Wbr =0.005154d1.92033h1.06618 0.80 27.31 Wf=0.000343d2h0.81 2.53 Wf=0.00092d1.57684h1.34236 0.74 3.45 Wt=ΣWi0.92 110.21 Wt=ΣWi0.92 96.83 P. herrerae Q. rugosa Ww=0.06741d2.520356 0.82 114.23 Ww=0.01988d2.28684h0.52175 0.90 29.42 Wb=0.02468d1.98837 0.72 7.37 Wb=0.05621d2.0764 0.77 15.14 Wbr =0.05085d2.03574 0.72 18.01 Wbr =0.11276d1.52164h0.53343 0.86 12.56 Wf=0.05437d1.64335 0.60 5.41 Wf=0.0377d1.42193h0.70675 0.84 5.21 Wt=ΣWi0.85 124.12 Wt=ΣWi0.94 41.8 P. teocote Q. durifolia Ww=0.04428d1.8953h0.84674 0.92 58.5 Ww=0.1254d1.7402h0.8114 0.94 55.64 Wb=0.00341d1.96215h0.66178 0.93 9.34 Wb=0.00235d2.30073h0.68619 0.87 9.53 Wbr =0.0051d1.78757h1.12341 0.93 3.02 Wbr =0.00355d2.66464h0.56009 0.89 35.50 Wf=0.03041d1.78361 0.73 16.67 Wf=0.0073d2.05034h0.48685 0.86 6.87 Wt=ΣWi0.95 76.11 Wt=ΣWi0.95 80.97 P. lumholtzii Q. crassifolia Ww=0.078527d2.5043 0.91 65.02 Ww=0.02542d2h0.83 56.45 Wb=0.022809d1.93859 0.76 16.98 Wb=0.00305d2h0.81 8.12 Wbr =0.03461d2.1666 0.83 4.21 Wbr =0.01113d2h0.82 25.96 Wf=0.011642d2.16799 0.82 4.14 Wf=0.00165d2h0.64 4.92 Wt=ΣWi0.90 83.32 Wt=ΣWi0.91 64.58 P. strobiformis All pine species Ww=0.00716d2.02253h1.30938 0.90 88.01 Ww=0.0291d1.74165h1.16614 0.92 72.12 Wb=0.03088d1.10021h1.09925 0.88 6.34 Wb=0.02029d1.33299h0.92887 0.63 11.65 Wbr =0.01613d1.90578h0.70112 0.93 15.24 Wbr =0.02508d1.83773h0.54626 0.61 31.05 Wf=0.03886d1.53515h0.31776 0.72 5.55 Wf=0.05227d1.28231h0.43275 0.52 5.98 Wt=ΣWi0.93 93.02 Wt=ΣWi0.93 83.04 P. oocarpa All oak species Ww=0.01753d1.8261h1.28397 0.93 27.12 Ww=0.11618d1.77395h0.68708 0.78 94.25 Wb=0.02898d2.08978 0.87 4.44 Wb=0.00827d2.54589 0.65 27.68 Wbr =0.00948d2.7493 0.87 15.32 Wbr =0.0502d1.97638h0.34229 0.57 53.64 Wf=0.04163d1.93601 0.83 3.96 Wf=0.08234d1.59396 0.29 11.95 Wt=ΣWi0.94 39.66 Wt=ΣWi0.82 134.12 n= number of trees, d= diameter at breast height (cm), h= total height (m), W w = stem wood biomass (kg tree −1 ), W b = stem bark biomass (kg tree −1 ), W br = wood plus bark biomass of branches (kg tree −1 ), W f = foliage (leaves/needles) biomass (kg tree −1 ), W t = total above-ground biomass (W w +W b +W br +W f ) (kg tree −1 ), RMSE, root mean square error. Forests 2017,8, 269 16 of 20 because the spectral data are available free of charge. However, the use of new and more accurate biomass equations, such as the systems of equations fitted in this study, combined with high resolution remote sensing data (e.g., Sentinel satellites) to develop predictive machine learning models will enable more realistic and accurate prediction of biomass and carbon stocks at regional level by model-based inference. Acknowledgments: This study was financially supported by the Mexican National Council for Science and Technology (CONACyT) and by the State of Durango Government (Project FOMIXDGO-2011-C01-165681). The authors are grateful to the three anonymous reviewers and the academic editor for the constructive and insightful comments. Author Contributions: B.V.-L. conceived the research design, conducted the field data collection, analysis, and wrote the manuscript. C.A.L.-S. conducted the analysis of satellite data. 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