Next Article in Journal
Transcriptome Sequencing and Analysis of Genes Related to Disease Resistance in Pinus thunbergii
Next Article in Special Issue
Individual Tree Aboveground Biomass Estimation Based on UAV Stereo Images in a Eucalyptus Plantation
Previous Article in Journal
Bibliometric Analysis of Forestry Research in Mexico Published by Mexican Journals
Previous Article in Special Issue
Error Analysis on the Five Stand Biomass Growth Estimation Methods for a Sub-Alpine Natural Pine Forest in Yunnan, Southwestern China
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Forests
Volume 14
Issue 3
10.3390/f14030649
forests-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Quercus suber Allometry in the West Mediterranean Basin

by
Catarina Jorge
1,
Margarida Tomé
1,
Ricardo Ruiz-Peinado
2,
Lobna Zribi
3 and
Joana Amaral Paulo
1,*
1
Forest Research Centre, Associated Laboratory TERRA, School of Agriculture, University of Lisbon, Tapada da Ajuda, 1349-017 Lisbon, Portugal
2
Instituto de Ciencias Forestales (ICIFOR-INIA), CSIC, Ctra. A Coruña km 7.5, 28040 Madrid, Spain
3
University of Lorraine, AgroParisTech, INRAE, UMR Silva, 54506 Nancy, France
*
Author to whom correspondence should be addressed.
Forests 2023, 14(3), 649; https://doi.org/10.3390/f14030649
Submission received: 15 February 2023 / Revised: 13 March 2023 / Accepted: 20 March 2023 / Published: 22 March 2023
(This article belongs to the Special Issue Estimating and Modeling Aboveground and Belowground Biomass)
Browse Figures
Versions Notes

Abstract

:
The necessity for accurate biomass estimates is greater than ever for the sustainable management of forest resources, which is an increasingly pressing matter due to climate change. The most used method to estimate biomass for operational purposes is through allometric equations. Typically, each country develops their own models to be applied at the local scale because it is more convenient. But, for Quercus suber, a joint regional model can be more beneficial, since the species is distributed across the Mediterranean and is challenging to account for due to felling limitations and the nature of mature cork biomass itself. We found that these characteristics are reflected in the biomass datasets and compatibility was, perhaps, the largest impediment to such a model. The use of dummy variables to differentiate between countries, as well as compromises in the limits of biomass compartments, allowed us to develop two joint models to estimate aboveground biomass in Portugal, Spain and Tunisia. One model as a function of diameter and another as a function of diameter and total tree height. In addition, we developed a separate model for roots (modelling efficiency of fitting = 0.89), since it was not possible to assure additivity of the whole tree. All coefficients were estimated using Seemingly Unrelated Regressions (SUR) and model fitting assured additivity in the aboveground compartments—leaves and woody biomass (modelling efficiency of fitting = 0.89 and 0.93, respectively). This work proves that it is possible to have a biologically sound and efficient model for the three countries, despite differences in the observed allometric patterns.

1. Introduction

The nature of carbon is temporary. It moves from one ecosystem to the next, changing its form. Excess of carbon residing in the atmosphere has caused severe global changes [1]; however, it is possible to slow the rate of climate change by increasing residence time in terrestrial carbon pools [2]. Forests are a significant part of that carbon pool, as regulators of the carbon global cycle. Furthermore, forests store carbon in their soils and biomass, both above and belowground, and many countries in the European Union have made carbon neutrality commitments [3] using carbon sequestration by forests as a strategy to deal with climate change [4]. So, accurately quantifying carbon biomass in trees, while only part of the solution, is of the utmost importance, either to evaluate stand productivity, the success of forest policies, or to study the processes involved in carbon sequestration [5].
The most accurate method to quantify tree biomass is through tree felling and weighting after drying (destructive sampling), which is always an onerous task. But, even if slightly less accurate, biomass estimates can alternatively be obtained from non-destructive biometric measures using allometric equations e.g., [6,7]. The development of such equations relies on statistical concepts and the existence of suitable datasets obtained from destructive sampling that will ultimately dictate the circumstances in which the models should be applied. A comprehensive review on this subject has been made elsewhere [8], pointing out that models are often developed from small and geographically limited datasets, while discussing the limitations.
An adequate equation to estimate biomass within a given region should ideally be based on a set of trees harvested in stands with different site conditions, so as to encompass the variability of growth patterns observed in trees. The biomass data should preferably be kept without any transformation, in order to avoid biased parameter estimates [9], even if it means that it might be necessary to model the error term variance [10]. It is also important to incorporate the property of biomass additivity, i.e., predicted estimates for the different tree components adding up to the total biomass, to preserve the coefficients biological meaning [11,12]. Furthermore, estimator efficiency is another important aspect to consider, since providing narrower confidence intervals for the equation parameters will ensure better biomass estimates [13]. When attempting to incorporate all these aspects, one of the most commonly used methodologies is an additive system of equations where parameters are estimated with seemingly unrelated regression (SUR) [14,15,16]. Despite these guidelines, the greatest source of error in biomass predictions can be the choice of the model [17], and often times, the performance metrics reported and error procedure methodology can be insufficient [18]. In this regard, well evaluated allometry studies are relevant to understand the adequacy of a model.
Cork oak (Quercus suber L.) is a tree species with economic importance and carbon sink potential in the West Mediterranean basin [19,20,21]. The most commonly used tree variable to model cork oak biomass is diameter at breast height under bark (du); when using two variables, it is customary to add total tree height (h). Portugal has developed a system of equations as a function of du to estimate crown biomass—encompasses leaves and smaller branches—woody and total aboveground biomass [22], but has developed no model for roots. Both Spain and Tunisia have two sets of models: one with du as a regressor, to estimate stem wood, branches of diverging thickness, leaves and belowground biomass; and another set of models that add the h variable to estimate the biomass of aboveground components only [23,24,25]. Several studies have quantified cork oak biomass [26,27,28,29,30,31], but these were focused on individual countries. The use of distinct models and tree compartments in each country is an issue to compare biomass estimates [32], as it makes it difficult to disentangle whether the differences in estimates are due to sampling and data treatment, environmental conditions or allometry. Given these issues, the present work has several objectives to accomplish and questions to investigate:
  • join Quercus suber biomass datasets and compare the different allometries in cork oak growth among three countries—Portugal, Spain and Tunisia;
  • is it feasible to develop a joint model that can consistently estimate biomass in the regions where cork oak is prevalent?
  • is the addition of total tree height significant for biomass prediction?
  • provide two alternative root biomass models and two additive SUR aboveground biomass models—one set as a function of du, to be used when tree height has not been measured, and the other as a function of du and h.

2. Materials and Methods

2.1. Dataset Description

A total of 212 trees from Portugal, Spain and Tunisia were gathered into a dataset to fit allometric models. Trees that had already been debarked were considered adult, while trees that were never debarked were considered juvenile. There was a total of 158 juvenile trees (152 from Portugal and 6 from Spain) and a total of 54 adult trees (12 from Portugal, 16 from Tunisia and 26 from Spain). Every country considered different tree compartments in the field procedure to determine biomass, which is described in detail by the respective authors: adult trees in Portugal [33,34], juvenile trees in Portugal [35], trees in Tunisia [24] and trees in Spain [23]. The majority of differences were found in the diameter values to separate branch size along the tree crown architecture. So, in order to make biomass contents compatible, the dataset was homogenized into the three following compartments: leaves, woody biomass—includes stems, branches and virgin cork—and roots. Total aboveground biomass results from the sum of leaves and woody biomass, while belowground biomass is comprised of roots. Mature cork biomass was not considered, as it is periodically extracted. In the case of trees from Spain and Tunisia, it was necessary to estimate the amount of mature cork present in the stem at the moment of felling, since it had not been accounted for in the harvest procedure. This was done in three steps, requiring cork thickness and cork age at felling [36]. When du was not directly measured, it was calculated by deducting the cork thickness. A summary of all available variables for the dataset and basic descriptive statistics is given in Table 1 (full dataset available in the supplementary materials, Table S1).

2.2. Model Fitting

The biomass models were based on the allometric model that has been recognized as appropriate to establish the relationship between two parts of the same organism [37,38]:
B i o m a s s   C o m p a r t m e n t = a × x b ,
where, x is a tree variable (du, in this case); a and b are parameters. The value of the allometric scalar—a—is heavily influenced by the actual values of the tree variables used to build the power law and the respective units, while the allometric exponent—b—is much more stable and captures the growth pattern of a species [9,39].
The model described by Equation (1) will henceforth be referred to as the reduced model. However, the allometric model in its generalized form to two variables, has also been used and will be referred to as the full model:
B i o m a s s   C o m p a r t m e n t = a × x b × y c ,
where, x and y are tree variables (du and h, in this case); a, b and c are parameters.
The biomass models were developed in the following steps:
(1)
fitting individual allometric equations for each biomass compartment using the reduced and full model, without differentiating between countries;
(2)
addition of dummy variables for each country at each individual equation and selection of a model for each biomass compartment, in which all the parameters were significantly different from zero;
(3)
fitting aboveground components in a system of equations, in order to guarantee the additivity between total biomass and the other two biomass components.
The full model fitting procedure was done for both SUR models (reduced and full) and the biomass model for roots did not require step 3, since the additivity property could not be taken into account because root biomass was only available for a small subset of the total trees sampled.
Basic descriptive statistics and scatterplots were produced in the R software [40], while all steps of the model fitting procedure were carried out in SAS software [41] with the MODEL procedure. Steps 1 and 2 used ordinary least squares (OLS) as estimator for all biomass components and step 3 used iterated SUR for the aboveground biomass components only.
The aboveground biomass system has three equations, according to the compartments: leaves, woody biomass and one for the sum of leaves and woody biomass. The starting point to fit the system was to use the best individual model for each compartment selected in step 2. Furthermore, in order to separate the observations by country, two dummy variables were created: SP and TUN. If the tree belonged to Spain, SP = 1 and 0 otherwise. If the tree belonged to Tunisia, TUN = 1 and 0 otherwise. So, if both dummy variables were 0, then the model applied to the trees from Portugal. The general equation with dummy variables is defined as follows:
B i o m a s s   C o m p a r t m e n t = ( a 1 + a 2 × S P + a 3 × T U N ) × d u ( b 1 + b 2 × S P + b 3 × T U N ) × h ( c 1 + c 2 × S P + c 3 × T U N ) ,
where a i , b i and c i are the parameters associated with each dummy variable (i = 1,2 and 3). It is important to note that if SP = 1 or TUN = 1, parameter values are presented taking into account a 1 , b 1 and c 1 , i.e., taking into account similarities between countries through the common parameters. In addition, there were no roots from Portugal, so the baseline of that model was Spain and the only dummy variable is TUN. Parameters were added in a forward stepwise procedure until all were significantly different from zero (α = 0.05), while minimizing the sum of squared errors (SSE).
Reporting metrics of model fit is imperative in order to guarantee model adequacy [42,43,44]. Several performance metrics were used to compare models, namely: SSE, Root Mean Squared Error (RMSE), a measure equivalent to the adjusted coefficient of determination—the modelling efficiency of fitting ( E F f i t ). However, we report only E F f i t , as this is the only comparable measure when different weights are applied to the models. Since the dataset was small and it was not feasible to collect an additional independent dataset, model validation was done using the so called PRESS residuals, that are successively computed for each data point with the parameter estimates obtained with a model fitted without this particular data point (leave-one-out jackknife method) [45]. The following validation statistics were computed: mean of PRESS residuals (mPRESS), mean of absolute PRESS residuals (maPRESS) and predictive modelling efficiency ( E F p r e d . ).
The usual plots to test the regression assumptions of normality and heteroscedasticity of the residuals were evaluated. Weighted regression was applied when heteroscedasticity was not verified and several weight functions were tested, namely the inverse of the response variable, the inverse of the squared fitted values and fitted values, the inverse of the dependent variable and similar variations, following the method described by Parresol [12].

3. Results

3.1. The Need for Country Specific Models and for including Total Height

Step 1 of the fitting procedure (Section 2.2) allowed confirmation that the height variable is significant, but most importantly, suggested the need for a dummy variable to differentiate between countries. Step 2 showed the results reported in Table 2, where the need to have country specific models, at least in the aboveground compartments, is clear.
The coefficient a 2 in both of the root biomass models displayed a high p-value at any of the usual significance levels. But it cannot be dropped since it is not an additive term in the model. We opted to keep the estimate fixed because assuming a 2 = 1 was not correct, as it does not fall within the confidence interval for the estimate.
As expected, the coefficients b i are generally always significant and the addition of h always improves model performance. But it is interesting to note that the coefficients b i and c i associated with Spain and Tunisia were not statistically significant for leaves (wl). In addition, coefficient a 2 loses significance when height is added in the woody compartment (ww).

3.2. Two Systems of Equations for Aboveground Biomass

Step 3 of the fitting procedure (simultaneous fitting of the aboveground biomass compartments, Section 2.2) provided the results reported in Table 3, where all parameters remained with the same level of significance as reported in Table 2, or even higher.
As expected, the metric E F f i t improved or was maintained from the individual fits to the simultaneous equation fits. A graphical representation of all final reduced models are shown in Figure 1, where it is possible to see that the compartments with the greatest variability are woody and aboveground biomass. However, their patterns are nearly identical, since most of the biomass can be found in wood at the moment of sampling. Leaves show less variability of observed values but starkly different patterns.

3.3. Evaluating the Models

Regarding model validation (Table 4), the best performance was found to be in the SUR full model for aboveground compartments (wl, ww and wa). Roots also had better predictive ability in the full model.
There were issues with heteroscedasticity for all aboveground compartments. The best method to solve the issues was Parresol’s method to model the error term by taking the logarithm of the squared residuals and the logarithm of the original dependent variable. There were no serious issues with heteroscedasticity for roots. Figure 2 shows all the plots of studentized residual for each compartment.

4. Discussion

4.1. Advantages and Disadvantages of Joining a Dataset from Three Countries

The most obvious limitation to joining separate datasets is the difference in sampling procedures. This is especially true for foliage and roots [8,32], which can have considerable differences due to the practical difficulties associated with the sampling process. Furthermore, there is no standard definition of compartments, so in order to join a dataset the modeler is forced to group compartments to achieve data compatibility. These issues are exacerbated in cork oak trees for two reasons: cork can be extremely heterogeneous and each country accounts for cork biomass with its own guidelines. Another important issue is that cork oak trees are usually protected by legislation which prevents their felling and determines a reduced number of observations. Thus, the gain in joining datasets in the Mediterranean region, for cork oak particularly, could far outweigh the weaknesses.
The advantages of joining datasets are the increase in range of tree characteristics—du and h, in this case—and a higher level of geographical representation. It is common practice to build allometric models based on du alone, since it is highly correlated with biomass growth, while also being relatively easy, accurate and inexpensive to measure. However, this practice assumes a constant d u h , which is not true due to tree competition e.g., [46,47] further deviates from the truth in larger scale models [48]. Several authors support the idea that more complex regional models with a greater availability of data and variables can be useful, especially in regions that are underrepresented [49,50], provided that due diligence in model use and dataset compatibility is exerted.

4.2. Is It Feasible to Develop a Joint Model That Can Consistently Estimate Biomass in the Regions Where Cork Oak Is Prevalent?

It was not possible to develop a system of equations with additivity for the whole tree, since Portugal had no data on root biomass and in Spain and Tunisia not all trees had been sampled for roots. Therefore, it was necessary to separate between belowground and aboveground biomass.
Belowground biomass models used only data from two countries—Spain and Tunisia—which show that there are significant differences in root allometry (Figure 1 and Table 2). These differences are related to climatic and stand characteristics, as well as soil type and soil water dynamics, since these factors have a great influence in root development [51,52]. However, the best general model for roots is the full model, in which no significant allometric differences were found, but both the fit and predictive modeling efficiencies (Table 2 and Table 4) were better.
Aboveground biomass data allowed a joint model with no distinction between countries, i.e., no dummy variables. However, such a model would not be accurate for any one country. This inadequacy is especially noticeable in the leaves compartment (Figure 1), which was to be expected due to their intrinsic variability [53,54]. But we found that all aboveground biomass estimates for each particular country can be significantly improved by including dummy variables (Equation (3) and Table 2). Furthermore, the full model for woody biomass required dummies for coefficients related to du and h only— b i and c i —which are more related to growth patterns, and thus, indicating that each country has indeed significantly different allometries. On the other hand, the equation for leaf biomass required only dummies for the a i coefficient, which is sensitive to the choice of independent variables and its units [9,39], suggesting that the growth patterns exhibited by tree foliage were masked either by du or by its measurement units.
The growth pattern of tree foliage is influenced by different management practices related to pruning, thinning and stand density and several authors have found that crown variables are tremendously important in describing the leaf allometry of cork oak [6,55,56]. These variables were not available for this study. However, some information on stand density (N, trees/ha) was accessible. Portugal and Tunisia were found to be more similar in the aboveground compartments, despite extremely different stand densities: 4–304 versus 512–560, respectively. The stands in Los Alcornocales Natural Park, Spain, where many biomass samples were collected, have a density in the range 87–334 [57,58]. So it seems that stand density cannot explain all the variability in leaves, at least not straightforwardly. Furthermore, cork oak forests of low density don’t exhibit signs of tree competition and we can expect the management options often applied in these systems, namely pruning, to be the dominant cause of differences [59,60,61,62]. It is also possible that differences in leaf biomass could simply be from a distinct timing in the sampling method itself, since leaf biomass is not static. But a more detailed exploratory analysis of the effect of stand density, crown width and crown length in future studies would be highly enlightening.
Regardless, it is clear that the full SUR model is superior to the individual allometric models, which has been shown by other authors to be true when there is some correlation between the response variables and restrictions on the coefficients are necessary e.g., [11,13]. In addition, and as expected, forcing additivity is a suitable pre-requisite for biomass modelling, since the quality of the SUR model is not worsened by imposing such a restraint (Table 2 and Table 3).

4.3. Is the Addition of Total Tree Height Significant for Biomass Prediction?

The full model with du and h provide better estimates of biomass, in all compartments, than the reduced models (Table 2 and Table 4). But it should be noted that when h was added to the roots reduced model, the coefficients associated with dummy variables were not significant. This indicates that a model with no distinction between countries works well for roots, provided that enough information about tree characteristics, namely du and h, are used. Despite this, we provide the reduced models for every compartment because on its own, du is the best, most common regressor of biomass and h might not be available. Furthermore, h estimation in cork oak could be a bit inaccurate in comparison with other species due to the crown architecture.

5. Conclusions

The biomass estimates for leaves, woody, total aboveground and roots always improve with the addition of height, even though height is not the most adequate variable to estimate leaf biomass. We found that by making reasonable compromises in the level of detail with which biomass compartment limits are set, it is possible to join datasets from three different countries and mitigate the scarcity of cork oak destructive sampling data. Furthermore, each country had significantly different allometries in every biomass compartment, but these differences can be accounted for with dummy variables, thereby allowing a regional model that can harmoniously quantify the carbon stocks of cork oak.

Supplementary Materials

The biomass datasets with which the models were developed are available online at https://www.mdpi.com/article/10.3390/f14030649/s1, Table S1: Dataset_SupMaterials.

Author Contributions

Conceptualization and methodology: C.J., M.T. and J.A.P.; data curation: R.R.-P., L.Z. and J.A.P.; writing—original draft preparation: C.J.; writing—review and editing: M.T., R.R.-P., L.Z. and J.A.P.; supervision: M.T. and J.A.P. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Forest Research Centre, a research unit funded by Fundação para a Ciência e a Tecnologia I.P. (FCT), Portugal (UIDB/00239/2020). Catarina Jorge was funded by Fundação para a Ciência e a Tecnologia I.P. (FCT), under scholarship UI/BD/150757/2020.

Data Availability Statement

The different datasets analyzed in this research were gathered, homogenized and made available in the Supplementary Materials as an excel file.

Conflicts of Interest

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

References

  1. Pörtner, H.-O.; Roberts, D.C.; Tignor, M.; Poloczanska, E.S.; Mintenbeck, K.; Alegría, A.; Craig, M.; Langsdorf, S.; Löschke, S.; Möller, V.; et al. Climate Change 2022: Impacts, Adaptation, and Vulnerability; IPCC: Geneva, Switzerland, 2022. [Google Scholar]
  2. Keenan, T.F.; Williams, C.A. The Terrestrial Carbon Sink. Annu. Rev. Environ. Resour. 2018, 43, 219–243. [Google Scholar] [CrossRef]
  3. Santos, F.D.; Ferreira, P.L.; Pedersen, J.S.T. The Climate Change Challenge: A Review of the Barriers and Solutions to Deliver a Paris Solution. Climate 2022, 10, 75. [Google Scholar] [CrossRef]
  4. Andersen, S.P.; Allen, B.; Domingo, G.C. Biomass in the EU Green Deal: Towards Consensus on the Use of Biomass for EU Bioenergy; Policy Report; Institute for European Environmental Policy (IEEP): Brussels, Belgium, 2021. [Google Scholar]
  5. Brown, S. Measuring Carbon in Forests: Current Status and Future Challenges. Environ. Pollut. 2002, 116, 363–372. [Google Scholar] [CrossRef] [PubMed]
  6. António, N.; Tomé, M.; Tomé, J.; Soares, P.; Fontes, L. Effect of Tree, Stand, and Site Variables on the Allometry of Eucalyptus Globulus Tree Biomass. Can. J. For. Res. 2007, 37, 895–906. [Google Scholar] [CrossRef]
  7. Zianis, D.; Muukkonen, P.; Mäkipää, R.; Mencuccini, M. Biomass and Stem Volume Equations for Tree Species in Europe; Silva Fennica, The Finnish Society of Forest Science: Helsinki, Finland, 2005; Volume 4, ISBN 9514019830. [Google Scholar]
  8. Weiskittel, A.R.; MacFarlane, D.W.; Radtke, P.J.; Affleck, D.L.R.; Temesgen, H.; Woodall, C.W.; Westfall, J.A.; Coulston, J.W. A Call to Improve Methods for Estimating Tree Biomass for Regional and National Assessments. J. For. 2015, 113, 414–424. [Google Scholar] [CrossRef] [Green Version]
  9. Ter-Mikaelian, M.T.; Korzukhin, M.D. Biomass Equations for Sixty-Five North American Tree Species. For. Ecol. Manag. 1997, 97, 1–24. [Google Scholar] [CrossRef] [Green Version]
  10. Trautenmüller, J.W.; Péllico Netto, S.; Balbinot, R.; Watzlawick, L.F.; Dalla Corte, A.P.; Sanquetta, C.R.; Behling, A. Regression Estimators for Aboveground Biomass and Its Constituent Parts of Trees in Native Southern Brazilian Forests. Ecol. Indic. 2021, 130, 108025. [Google Scholar] [CrossRef]
  11. Parresol, B.R. Assessing Tree and Stand Biomass: A Review with Examples and Critical Comparisons. For. Sci. 1999, 4, 573–593. [Google Scholar]
  12. Parresol, B.R. Additivity of Nonlinear Biomass Equations. Can. J. For. Res. 2001, 31, 865–878. [Google Scholar] [CrossRef]
  13. Behling, A.; Netto, S.P.; Sanquetta, C.R.; Corte, A.P.D.; Affleck, D.L.R.; Rodrigues, A.L.; Behling, M. Critical Analyses When Modeling Tree Biomass to Ensure Additivity of Its Components. An. Acad. Bras. Cienc. 2018, 90, 1759–1774. [Google Scholar] [CrossRef] [Green Version]
  14. Carvalho, J.P.; Parresol, B.R. Additivity in Tree Biomass Components of Pyrenean Oak (Quercus pyrenaica Willd.). For. Ecol. Manag. 2003, 179, 269–276. [Google Scholar] [CrossRef]
  15. Poudel, K.P.; Temesgen, H. Methods for Estimating Aboveground Biomass and Its Components for Douglas-Fir and Lodgepole Pine Trees. Can. J. For. Res. 2015, 46, 77–87. [Google Scholar] [CrossRef] [Green Version]
  16. Xie, L.; Li, F.; Zhang, L.; Widagdo, F.R.A.; Dong, L. A Bayesian Approach to Estimating Seemingly Unrelated Regression for Tree Biomass Model Systems. Forests 2020, 11, 1302. [Google Scholar] [CrossRef]
  17. Picard, N.; Boyemba Bosela, F.; Rossi, V. Reducing the Error in Biomass Estimates Strongly Depends on Model Selection. Ann. For. Sci. 2015, 72, 811–823. [Google Scholar] [CrossRef] [Green Version]
  18. Sileshi, G.W. A Critical Review of Forest Biomass Estimation Models, Common Mistakes and Corrective Measures. For. Ecol. Manag. 2014, 329, 237–254. [Google Scholar] [CrossRef]
  19. Oubrahim, H.; Boulmane, M.; R Bakker, M.; Augusto, L.; Mohammed, H. Carbon Storage in Degraded Cork Oak (Quercus suber) Forest on Flat Lowlands in Morocco. Iforest Biogeosci. For. 2016, 9, 125–137. [Google Scholar] [CrossRef] [Green Version]
  20. Palma, J.H.N.; Paulo, J.A.; Tomé, M. Carbon Sequestration of Modern Quercus suber L. Silvoarable Agroforestry Systems in Portugal: A YieldSAFE-Based Estimation. Agrofor. Syst. 2014, 88, 791–801. [Google Scholar] [CrossRef]
  21. Correia, A.C.; Costa e Silva, F.; Correia, A.V.; Hussain, M.Z.; Rodrigues, A.D.; David, J.S.; Pereira, J.S. Carbon Sink Strength of a Mediterranean Cork Oak Understorey: How Do Semi-Deciduous and Evergreen Shrubs Face Summer Drought? J. Veg. Sci. 2014, 25, 411–426. [Google Scholar] [CrossRef]
  22. Paulo, J.A.; Tomé, M. Equações Para Estimação Do Volume e Biomassa de Duas Espécies de Carvalhos: Quercus Suber e Quercus Ilex; Publicações GIMREF RC1/2006; Universidade Técnica de Lisboa—Instituto Superior de Agronomia, Centro de Estudos Florestais: Lisboa, Portugal, 2006. [Google Scholar]
  23. Ruiz-Peinado, R.; Montero, G.; Del Rio, M. Biomass Models to Estimate Carbon Stocks for Hardwood Tree Species. For. Syst. 2012, 21, 42. [Google Scholar] [CrossRef]
  24. Zribi, L.; Chaar, H.; Khaldi, A.; Hanchi, B.; Mouillot, F.; Gharbi, F. Estimate of Biomass and Carbon Pools in Disturbed and Undisturbed Oak Forests in Tunisia. For. Syst. 2016, 25, e060. [Google Scholar] [CrossRef] [Green Version]
  25. Montero, G.; Ruiz-peinado, R.; Muñoz, M. Producción de Biomasa y Fijación de CO2 Por Los Bosques Españoles; INIA-Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria: Madrid, Spain, 2005; Volume 13, ISBN 84-7498-512-9. [Google Scholar]
  26. Laporta, L.; Domingos, T.; Marta-Pedroso, C. It’s a Keeper: Valuing the Carbon Storage Service of Agroforestry Ecosystems in the Context of CAP Eco-Schemes. Land Use Policy 2021, 109, 105712. [Google Scholar] [CrossRef]
  27. von Essen, M.; do Rosário, I.T.; Santos-Reis, M.; Nicholas, K.A. Valuing and Mapping Cork and Carbon across Land Use Scenarios in a Portuguese Montado Landscape. PLoS ONE 2019, 14, e02121. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  28. Coelho, M.B.; Paulo, J.A.; Palma, J.H.N.; Tomé, M. Contribution of Cork Oak Plantations Installed after 1990 in Portugal to the Kyoto Commitments and to the Landowners Economy. For. Policy Econ. 2012, 17, 59–68. [Google Scholar] [CrossRef]
  29. Cañellas, I.; Sánchez-González, M.; Adame, P.; Moreno-Fernández, D.; Bogino, S.M.; Herrero, C.; Roig, S.; Tomé, M.; Paulo, J.A.; Bravo, F. Carbon Sequestration in Mediterranenan Oak Forests. In Managing Forest Ecosystems: The Challenge of Climate Change; Bravo, F., LeMay, V., Jandl, R., Eds.; Springer: Cham, Switzerland, 2017; pp. 403–427. [Google Scholar]
  30. Demertzi, M.; Sierra-Pérez, J.; Paulo, J.A.; Arroja, L.; Dias, A.C. Environmental Performance of Expanded Cork Slab and Granules through Life Cycle Assessment. J. Clean. Prod. 2017, 145, 294–302. [Google Scholar] [CrossRef]
  31. Demertzi, M.; Paulo, J.A.; Arroja, L.; Dias, A.C. A Carbon Footprint Simulation Model for the Cork Oak Sector. Sci. Total Environ. 2016, 566–567, 499–511. [Google Scholar] [CrossRef]
  32. Neumann, M.; Moreno, A.; Mues, V.; Härkönen, S.; Mura, M.; Bouriaud, O.; Lang, M.; Achten, W.M.J.; Thivolle-Cazat, A.; Bronisz, K.; et al. Comparison of Carbon Estimation Methods for European Forests. For. Ecol. Manag. 2016, 361, 397–420. [Google Scholar] [CrossRef]
  33. Paulo, J.; Tomé, M. Recolha de Dados Para Determinação de Biomassas e Volumes de Sobreiro (Quercus suber). Protocolo Para a Instalação de Parcelas Temporárias e Medição de Árvores Amostra; Publicações FORCHANGE RT3/2008; Universidade Técnica de Lisboa—Instituto Superior de Agronomia, Centro de Estudos Florestais: Lisboa, Portugal, 2008. [Google Scholar]
  34. Paulo, J.A.; Tomé, M.; Uva, J.S. Recolha de Dados de Biomassa de Azinheiras (Quercus Ilex). Protocolo Para a Instalação de Parcelas Temporárias e Medição Das Árvores Amostra.; Publicações GIMREF RT6/2001; Universidade Técnica de Lisboa—Instituto Superior de Agronomia, Centro de Estudos Florestais: Lisboa, Portugal, 2001. [Google Scholar]
  35. Varela, M.C.; Bellarosa, R.; Eriksson, G.; Bariteau, M.; Catalan, G.; Branco, T.; Barros, I.R.; Almeida, H.; Chambel, R.; Sbay, H.; et al. Handbook of the Concerted Action “European Network for the Evaluation of Genetic Resources of Cork Oak for Appropriate Use in Breeding and Gene Conservation Strategies”. Reference—FAIR 1 CT 95-0202; Varela, M.C., Ed.; Estação Florestal Nacional: Lisboa, Portugal, 2000; ISBN 972-95736-7-0. [Google Scholar]
  36. Paulo, J.A.; Tomé, M. Predicting Mature Cork Biomass with t Years of Growth from One Measurement Taken at Any Other Age. For. Ecol. Manag. 2010, 259, 1993–2005. [Google Scholar] [CrossRef]
  37. Attiwill, P.M.; Ovington, J.D. Determination of Forest Biomass. For. Sci. 1968, 14, 13–15. [Google Scholar]
  38. O’Brien, S.T.; Hubbell, S.P.; Spiro, P.; Condit, R.; Foster, R.B. Diameter, Height, Crown, and Age Relationships in Eight Neotropical Tree Species. Ecology 1995, 76, 1926–1939. [Google Scholar] [CrossRef] [Green Version]
  39. Thornley, J.H.M.; Johnson, I.R. Plant and Crop Modelling; Oxford University Press: Oxford, UK, 1990. [Google Scholar]
  40. R Core Team R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2021.
  41. SAS/ETS 13.2 User’s Guide; SAS Institute Inc.: Cary, NC, USA, 2014.
  42. Jara, M.C.; Henry, M.; Réjou-Méchain, M.; Wayson, C.; Zapata-Cuartas, M.; Piotto, D.; Alice Guier, F.; Castañeda Lombis, H.; Castellanos López, E.; Cuenca Lara, R.; et al. Guidelines for Documenting and Reporting Tree Allometric Equations. Ann. For. Sci. 2015, 72, 763–768. [Google Scholar] [CrossRef] [Green Version]
  43. Soares, P.; Tomé, M.; Skovsgaard, J.P.; Vanclay, J.K. Evaluating a Growth Model for Forest Management Using Continuous Forest Inventory Data. For. Ecol. Manage. 1995, 71, 251–265. [Google Scholar] [CrossRef]
  44. Vanclay, J.K.; Skovsgaard, J.P. Evaluating Forest Growth Models. Ecol. Modell. 1997, 98, 1–12. [Google Scholar] [CrossRef] [Green Version]
  45. Myers, R.H. Classical and Modern Regression with Applications, 2nd ed.; Duxbury Press: Belmont, CA, USA, 1990. [Google Scholar]
  46. Assmann, E. The Principles of Forest Yield Study; Pergamon Press: Oxford, UK, 1970. [Google Scholar]
  47. Burkhart, H.E.; Tomé, M. Modeling Forest Trees and Stands; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2012; ISBN 978-94-007-1597-4. [Google Scholar] [CrossRef]
  48. Temesgen, H.; Affleck, D.; Poudel, K.; Gray, A.; Sessions, J. A Review of the Challenges and Opportunities in Estimating above Ground Forest Biomass Using Tree-Level Models. Scand. J. For. Res. 2015, 30, 326–335. [Google Scholar] [CrossRef]
  49. Forrester, D.I.; Tachauer, I.H.H.; Annighoefer, P.; Barbeito, I.; Pretzsch, H.; Ruiz-Peinado, R.; Stark, H.; Vacchiano, G.; Zlatanov, T.; Chakraborty, T.; et al. Generalized Biomass and Leaf Area Allometric Equations for European Tree Species Incorporating Stand Structure, Tree Age and Climate. For. Ecol. Manag. 2017, 396, 160–175. [Google Scholar] [CrossRef]
  50. Dutcă, I.; Mather, R.; Ioraș, F. Sampling Trees to Develop Allometric Biomass Models: How Does Tree Selection Affect Model Prediction Accuracy and Precision? Ecol. Indic. 2020, 117, 106553. [Google Scholar] [CrossRef]
  51. David, T.S.; Pinto, C.A.; Nadezhdina, N.; Kurz-Besson, C.; Henriques, M.O.; Quilhó, T.; Cermak, J.; Chaves, M.M.; Pereira, J.S.; David, J.S. Root Functioning, Tree Water Use and Hydraulic Redistribution in Quercus suber Trees: A Modeling Approach Based on Root Sap Flow. For. Ecol. Manag. 2013, 307, 136–146. [Google Scholar] [CrossRef] [Green Version]
  52. David, T.S.; Pinto, C.A.; Nadezhdina, N.; David, J.S. Water and Forests in the Mediterranean Hot Climate Zone: A Review Based on a Hydraulic Interpretation of Tree Functioning. For. Syst. 2016, 25, eR02. [Google Scholar] [CrossRef] [Green Version]
  53. Paulo, J.A.; Tomé, J.; Tomé, M. Ajustamento Simultâneo de Equações de Biomassa de Azinheira. In Proceedings of the Actas do X Congresso da Sociedades Portuguesa de Estadística, Porto, Portugal, 25–28 September 2002. [Google Scholar]
  54. Andivia, E.; Bou, J.; Fernández, M.; Caritat, A.; Alejano, R.; Vilar, L.; Vázquez-Piqué, J. Assessing the Relative Role of Climate on Litterfall in Mediterranean Cork Oak Forests. IForest 2018, 11, 786–793. [Google Scholar] [CrossRef] [Green Version]
  55. Sánchez-González, M.; Cañellas, I.; Montero, G. Generalized Height-Diameter and Crown Diameter Prediction Models for Cork Oak Forests in Spain. Investig. Agrar. Sist. Recur. For. 2007, 16, 76. [Google Scholar] [CrossRef] [Green Version]
  56. Menéndez-Miguélez, M.; Calama, R.; Del Río, M.; Madrigal, G.; López-Senespleda, E.; Pardos, M.; Ruiz-Peinado, R. Species-Specific and Generalized Biomass Models for Estimating Carbon Stocks of Young Reforestations. Biomass Bioenergy 2022, 161, 10645. [Google Scholar] [CrossRef]
  57. Sánchez-González, M.; Calama, R.; Cañellas, I.; Montero, G. Variables Influencing Cork Thickness in Spanish Cork Oak Forests: A Modelling Approach. Ann. For. Sci. 2007, 64, 301–312. [Google Scholar] [CrossRef] [Green Version]
  58. Sánchez-González, M.; Tomé, M.; Montero, G. Modelling Height and Diameter Growth of Dominant Cork Oak Trees in Spain. Ann. For. Sci. 2007, 62, 633–643. [Google Scholar] [CrossRef] [Green Version]
  59. Pasalodos-Tato, M.; Pukkala, T.; Cañellas, I.; Sánchez-González, M. Optimizing the Debarking and Cutting Schedule of Cork Oak Stands. Ann. For. Sci. 2018, 75, 61. [Google Scholar] [CrossRef] [Green Version]
  60. Faias, S.P.; Paulo, J.A.; Tomé, M. Inter-Tree Competition Analysis in Undebarked Cork Oak Plantations as a Support Tool for Management in Portugal. New For. 2020, 51, 489–505. [Google Scholar] [CrossRef]
  61. Palma, J.H.N.; Paulo, J.A.; Faias, S.P.; Garcia-Gonzalo, J.; Borges, J.G.; Tomé, M. Adaptive Management and Debarking Schedule Optimization of Quercus Suber L. Stands under Climate Change: Case Study in Chamusca, Portugal. Reg. Environ. Chang. 2015, 15, 1569–1580. [Google Scholar] [CrossRef]
  62. Campos, P.; Daly-Hassen, H.; Oviedo, J.L.; Ovando, P.; Chebil, A. Accounting for Single and Aggregated Forest Incomes: Application to Public Cork Oak Forests in Jerez (Spain) and Iteimia (Tunisia). Ecol. Econ. 2008, 65, 76–86. [Google Scholar] [CrossRef]
Forests 14 00649 g001 550
Figure 1. Best reduced models with weights for all biomass compartments: leaves, woody and aboveground show the simultaneous equations fit, while roots show the individual equation fit. The green dots represent the models for Portugal, orange triangles represent Spain and purple squares represent Tunisia.
Figure 1. Best reduced models with weights for all biomass compartments: leaves, woody and aboveground show the simultaneous equations fit, while roots show the individual equation fit. The green dots represent the models for Portugal, orange triangles represent Spain and purple squares represent Tunisia.
Forests 14 00649 g001
Forests 14 00649 g002 550
Figure 2. Fitted values versus studentized residuals of the best models for all biomass compartments: the fitted values for leaves, woody and aboveground are from the full SUR model and the residuals are weighted; the fitted values for roots are from the individual full model and the residuals are not weighted.
Figure 2. Fitted values versus studentized residuals of the best models for all biomass compartments: the fitted values for leaves, woody and aboveground are from the full SUR model and the residuals are weighted; the fitted values for roots are from the individual full model and the residuals are not weighted.
Forests 14 00649 g002
Table
Table 1. A summary of the available tree variables.
Table 1. A summary of the available tree variables.
Variable 1nMin.MedianMeanMax.sd
du (cm)2122.455.9513.4979.4414.68
h (m)2121.522.444.7515.803.93
wl (kg)2120.101.254.9551.288.52
ww (kg)2120.646.51178.863032.49412.02
wa (kg)2120.997.67183.813078.68418.79
wr (kg)267.42116.67132.10454.0688.89
1 du: diameter at breast height under bark, h: total height, wl: leaf biomass, ww: woody biomass, wa: aboveground biomass and wr: root biomass.
Table
Table 2. Coefficients and performance metrics for the weighted models described by Equation (3).
Table 2. Coefficients and performance metrics for the weighted models described by Equation (3).
Model DescriptionCoefficientsPerformance
a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 E F f i t
Reduced modelwl0.09 ***0.02 ***0.06 ***1.58 *** 0.86
ww0.08 ***0.24 * 2.60 ***2.13 ***2.49 *** 0.87
wa0.15 *** 2.42 ***2.23 ***2.31 *** 0.88
wr 1 0.26 2 1.76 ***1.86 *** 0.87
Full modelwl0.10 ***0.02 ***0.05 ***1.21 *** 1.80 *** 0.89
ww0.10 *** 2.07 ***1.48 **1.84 ***0.75 ***1.41 * 0.92
wa0.14 *** 1.97 ***1.81 ***1.75 ***0.74 *** 0.89
wr 1 0.16 2 1.43 *** 0.76 *** 0.89
All coefficients a i , b i and c i , were marked with symbols according to the following: *** indicates p < 0.001, ** p < 0.01 and * p < 0.05. Empty cells indicate that the parameter was not significantly different from zero at the usual α levels. Greyed out cells indicate that the parameter is not part of the model fitting. wl: leaf biomass, ww: woody biomass, wa: aboveground biomass, wr: root biomass. E F f i t : modelling efficiency of fitting, calculated with non-weighted residuals. 1 Both models for roots do not have weights. 2 The coefficient estimate was fixed.
Table
Table 3. Coefficients and performance metrics for the SUR weighted systems of equations.
Table 3. Coefficients and performance metrics for the SUR weighted systems of equations.
Model DescriptionCoefficientsPerformance
a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 E F f i t
Reduced modelwl0.09 ***0.02 ***0.06 ***1.60 *** 0.86
ww0.08 ***0.26 ** 2.59 ***2.09 ***2.48 *** 0.89
wawl + ww0.89
Full modelwl0.11 ***0.03 ***0.05 ***1.13 *** 0.65 *** 0.89
ww0.10 *** 2.07 ***1.40 ***1.84 ***0.75 ***1.54 ** 0.93
wawl + ww0.93
All coefficients a i , b i and c i , were marked with symbols according to the following: *** indicates p < 0.001 and ** p < 0.01. Empty values indicate that the parameter was not significantly different from zero at the usual α levels. Greyed out cells indicate that the parameter is not part of the model fitting. wl: leaf biomass, ww: woody biomass, wa: aboveground biomass. E F f i t : modelling efficiency of fitting, calculated with non-weighted residuals.
Table
Table 4. Cross-validation metrics for all models.
Table 4. Cross-validation metrics for all models.
Model DescriptionCross-Validation Metrics
mPRESSmaPRESS E F p r e d .
INDIVIDUAL EQUATIONSReduced modelwl−0.00320.140.84
ww−0.00050.060.85
wa−0.02860.360.86
wr3.1725.500.59
Full modelwl−0.00130.080.87
ww0.00020.040.90
wa0.00020.050.88
wr1.4824.280.84
SURReduced modelwl0.00290.140.86
ww0.00200.040.89
wa0.00530.080.89
Full modelwl−0.00600.080.89
ww−0.00020.040.93
wa−0.00070.050.93
wl: leaf biomass, ww: woody biomass, wa: aboveground biomass, wr: root biomass. mPRESS: mean of PRESS residuals, maPRESS: mean of absolute PRESS residuals and E F p r e d . : predictive modelling efficiency.
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Jorge, C.; Tomé, M.; Ruiz-Peinado, R.; Zribi, L.; Paulo, J.A. Quercus suber Allometry in the West Mediterranean Basin. Forests 2023, 14, 649. https://doi.org/10.3390/f14030649

AMA Style

Jorge C, Tomé M, Ruiz-Peinado R, Zribi L, Paulo JA. Quercus suber Allometry in the West Mediterranean Basin. Forests. 2023; 14(3):649. https://doi.org/10.3390/f14030649

Chicago/Turabian Style

Jorge, Catarina, Margarida Tomé, Ricardo Ruiz-Peinado, Lobna Zribi, and Joana Amaral Paulo. 2023. "Quercus suber Allometry in the West Mediterranean Basin" Forests 14, no. 3: 649. https://doi.org/10.3390/f14030649

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop