Modeling Biomass and Nutrients in a Eucalyptus Stand in the Cerrado

: The prediction of biological processes, which involve growth and plant development, is possible via the adjustment of mathematical models. In forest areas, these models assist in management practices, silviculture, harvesting, and soil fertility. Diameter, basal area, and height are predictors of volume and biomass estimates in forest stands. This study utilized di ﬀ erent non-linear models for estimating biomass and nutrient values in the aerial biomass and roots of an unmanaged eucalypt stand in Cerrado dystrophic soil. It was hypothesized that the models would estimate the nutrients of the aboveground biomass and roots after meeting the selection and validation criteria. By statistical analysis of the parameters and subsequent validation, the Schumacher–Hall model was presented to be the best ﬁt for biomass and nutrients. This result conﬁrmed the ability of di ﬀ erent variables, including diameter, basal area, and height, to be predicted. Estimating the nutrient values in the aboveground biomass and roots allowed a better understanding of the quality of the vegetal residues that remained in the soil. For dystrophic soils, which occur in the Cerrado, these estimates become even more relevant. writing—review and editing: M.B.X.V. and F.P.R.; Funding acquisition: M.B.X.V., A.G., and E.P.M.; resources: M.B.X.V., A.G., and E.P.M.; supervision: M.B.X.V., A.G., and E.P.M. All authors the


Introduction
Increasing global demand for wood has resulted in the expansion of tree plantations worldwide, with eucalyptus often the species of choice due to its high productivity. Brazilian plantations have among the highest rates of productivity and the shortest rotations in the world. In 2018, eucalyptus plantations in Brazil had average productivity of 36.0 m 3 ha −1 y −1 [1]. Eucalyptus stands are the main source of wood production and have become Brazil's main producers of sawn wood [2,3] and bioenergy [4]. High productivity has been achieved through extensive research in recent decades, mainly in improvements in genetics and forestry operations. Lately, some concerns have arisen in regard to the sustainability of productivity, which is increasingly shorter, and the high export of nutrients during the harvest [5][6][7].
The maintenance of forest stand production in Brazil has shown importance of maintaining environmental conservation. Some studies have focused on understanding the dynamics of growth Harvest residues provide the return of macronutrients (e.g., P) in eucalypt stands [36]. The incorporate of residues constitute a better way to maintain the nutrient capital in the plantations and to enhance tree growth [37]. Eucalyptus plantations can benefit from nutrient pools inherited from the previous land use over several rotations, and fertilizer applications required in the short-term to maximize stand productivity are likely to be much lower than long-term requirements to balance nutrient budgets [35]. The equatorial climate results in faster amounts of N, P, and K release by harvest residue decomposition than in temperate zones [35].
The objective of this study was to test the application of non-linear models for estimating the biomass and nutrients in a eucalypt stand established in the Cerrado (Brazilian Savanna) oxisol. The hypothesis that the models can estimate the nutrients of the aboveground biomass and roots was tested after the selection and validation criteria were met.

Study Area
The study was conducted at Fazenda Água Limpa (Figure 1), which belongs to the University of Brasília and is located in the Distrito Federal. The eucalypt stand was established in January 2010 (72 months of age), and occupies a total area of 3.29 hectares. The clone I224, Eucalyptus urophylla S. T. Blake × E. grandis Hill ex-Maiden, was planted at 3 × 2 m spacing.
Forests 2020, 11, x FOR PEER REVIEW 3 of 18 to enhance tree growth [37]. Eucalyptus plantations can benefit from nutrient pools inherited from the previous land use over several rotations, and fertilizer applications required in the short-term to maximize stand productivity are likely to be much lower than long-term requirements to balance nutrient budgets [35]. The equatorial climate results in faster amounts of N, P, and K release by harvest residue decomposition than in temperate zones [35]. The objective of this study was to test the application of non-linear models for estimating the biomass and nutrients in a eucalypt stand established in the Cerrado (Brazilian Savanna) oxisol. The hypothesis that the models can estimate the nutrients of the aboveground biomass and roots was tested after the selection and validation criteria were met.

Study Area
The study was conducted at Fazenda Á gua Limpa (Figure 1), which belongs to the University of Brasília and is located in the Distrito Federal. The eucalypt stand was established in January 2010 (72 months of age), and occupies a total area of 3.29 hectares. The clone I224, Eucalyptus urophylla S. T. Blake × E. grandis Hill ex-Maiden, was planted at 3 × 2 m spacing.
The soil was described as Latossolo Vemelho distró fico (oxisol). Prior to planting, grinding and subsoiling at 40 cm depth and fertilization of the planting line were undertaken using 100 g of super simple phosphate and 100 g of NPK -nitrogen, phosphorus and potassium (4-30-16). After 30 days of planting, cover fertilization was added using 100 g of NPK (20-0-20). Liming and supplemental fertilization with micronutrients were not performed.

Data Collection
A forest inventory was documented, with a simple random sampling process in 40 parcels with dimensions of 10 × 10 m, totaling 550 trees. In each plot, the diameter at breast height (DBH) at 1.3 m of each tree was measured using diametric tape. The heights were obtained using the Sunnto clinometer at 15 m for all trees. The soil was described as Latossolo Vemelho distrófico (oxisol). Prior to planting, grinding and subsoiling at 40 cm depth and fertilization of the planting line were undertaken using 100 g of super simple phosphate and 100 g of NPK -nitrogen, phosphorus and potassium (4-30-16). After 30 days of planting, cover fertilization was added using 100 g of NPK (20-0-20). Liming and supplemental fertilization with micronutrients were not performed.

Data Collection
A forest inventory was documented, with a simple random sampling process in 40 parcels with dimensions of 10 × 10 m, totaling 550 trees. In each plot, the diameter at breast height (DBH) at 1.3 m of Forests 2020, 11, 1097 4 of 18 each tree was measured using diametric tape. The heights were obtained using the Sunnto clinometer at 15 m for all trees.
The Smalian method was used to calculate the timber wood volume. This method uses the tree section in n logs, measuring the diameter (di) or circumference (ci) at the ends of each section and the length of the log (h1) [38]. A total of 40 trees with DBH ≥ 5 cm were harvested (Table S1). The trees were chosen in proportion to the number of diameter classes from the forestry inventory. The weights of 40 trees and the different components were measured (e.g., leaves, branches, crown wood, stem wood, and bark) (Tables S2 and S3). According to the regional demand, we determined the commercial high in the forest inventory; up to 8 cm of diameter below this value we consider the crown. We collected branches and leaves (below 8 cm of diameter) from the principal stem. We did not consider the distinction between branches (e.g., fine or thick), and the weight of then was obtained separately from the principal stem.
Samples from all tree components were collected to determine the concentration of the following nutrients: nitrogen (N), phosphorus (P), potassium (K), calcium (Ca), and magnesium (Mg). The K, Ca, and Mg concentrations in the leaves, branches, crown wood, stem wood, bark, and roots were determined by nitro-perchloric digestion and analyzed by inductively coupled plasma. Sulfuric digestion and distillation were used to measure the N concentration using the Kjeldahl method. Phosphorus was determined with the molecular absorption spectrophotometer. All analyses followed the manual described by Silva [39].
The sampled trees were classified as suppressed (between 5 and 11 cm DBH) median (between 11.1 and 17 cm DBH) and dominant (between 17.1 and 23 cm DBH); we choose three trees by each class. We used the data average to estimate the biomass and nutrient roots for all trees in the forest inventory. (Table S4).
The root biomass sampling was done by collecting 10 circular soil cores, with a median diameter of 23 cm for each tree. Within 0.5 m of each stem, four soil cores were collected perpendicular to the planting line and six parallel to the planting line. The choice of 10 soil cores per tree was due to the spatial distribution of the planting arrangement (i.e., 3 × 2 m); if the planting spacing was larger or smaller, we would have to make proportional adjustments to the spacing to carry out representative analyses. The soil cores were stratified into three depth intervals of 0-20, 20-40, and 40-60 cm [6]. The roots were sieved through a mesh of 1 mm and dried with forced air ventilation in a greenhouse (65 ± 5 • C) until a constant weight of dry biomass was obtained.

Volume Estimate, Biomass, and Nutrient Values
After the harvesting and weighing of 40 trees, the modeling of volume and biomass for the stand was undertaken. The adjustment was done with 33 randomly selected trees; the remaining seven trees were used for the validation of the model through t-tests for paired data. Applying the Schumacher-Hall [40] model, two equations were obtained for the volume and biomass predictions for each of the inventoried trees.
Using the equations obtained from the modeling, the estimated volume and biomass, in m 3 and Mg, respectively, for each of the inventoried trees were obtained. From this information, it was possible to obtain the volume and biomass of the stand, in m 3 ha −1 and Mg ha −1 , respectively, and calculate the statistical parameters of the stand (Table 1).
Each inventoried tree was allocated within one of the following classes: dominant, median, and suppressed, as described in the methodology for the collected roots. Using this information and the sum of the nutrient concentrations of the components, whose sample trees were also separated by class, the average concentrations of each nutrient for each inventoried tree was determined.
Multiplying the average class concentration of nutrients by the biomass amount, the value of each nutrient in kg −1 was obtained for each inventoried tree, and the nutrient values in Mg ha −1 were calculated for the 40 parcels. Combining the information of volume, biomass, nutrients, basal area, and average height, the model biomass and nutrients based on the variables DBH, basal area, and height were obtained.

Modeling of Biomass and Nutrients
From the information obtained on the biomass and the respective value of each nutrient in Mg ha −1 , the sum of each portion for every variable was obtained. These were subjected to Pearson's correlation analysis, in which DBH, basal area, and total tree height were defined as the predictor variables, and biomass and nutrients were the dependent variables (Table 2). Based on the correlation values between the predictive and independent variables, the variables that composed the models were chosen. Basal area and total height were used for biomass adjustment; DBH and total height for N; and basal area for P, K, Ca, and Mg. A total of 40 plots were used to model the biomass and nutrients, of which 30 were used for the adjustment and the other 10 for the validation.
The non-linear regression models (Table 3) used were Richards [41], Weibull [42], and Schumacher-Hall [40]. The first model was originally proposed for inserting biological factors in the growth estimates of Cucumis melo L., a variety of melon [41]. The second model was used to estimate the population growth of protozoa, the size of a bean grain, and the strength capacity of Indian cotton fiber [42]. The double entry model proposed by Schumacher and Hall [40] was proposed to estimate the volume of wood based on the correlation between diameter and height. The different parameters chosen (e.g., basal area, height, and diameter at breast height) to compose the models changed according to the correlation between predictor and dependent variables ( Table 2). Table 3. Non-linear models and their equations used to estimate the biomass and nutrients in the eucalypt stand.

Results
The N, P, K, Ca, and Mg percentages measured in each of components of the 40 trees showed that the leaves had the highest percentages of N, P, and K, whereas the Ca and Mg percentages were higher in the bark than in the other components ( Table 4). The percentage of each nutrient in different compartments was calculated by the sample nutrient concentrations in the compartment. The relationship between weight and concentration was estimated to be the total weight of each 40 trees. The non-linear models tested estimated the dependent variables. The statistical parameters used to choose the best models, such as the correlation of the coefficient and estimated standard error, presented similar values for biomass (Table 5), N (Table 6), P (Table 7), K (Table 8), Ca (Table 9), and Mg (Table 10).
The visual presentation of the ratio of the observed and estimated data, i.e., the plot of the residuals in percentage as a function of the observed data and the frequency of the distribution of the error classes, contributed to the choice of the best adjustment. Thus, the Schumacher-Hall model was considered the best model for all the estimated variables, presenting a distribution frequency concentrated in the lowest error classes (Figures 2-7).   * Regression coefficients; ** standard deviation *** estimated standard error; **** standard error of estimate (in percentage); ***** correlation coefficient.              * Regression coefficients; ** standard deviation *** estimated standard error; **** standard error of estimate (in percentage); ***** correlation coefficient. The standard error in percentage resulting from the adjustments presented the lowest value for biomass estimation (Table 5), and N was the nutrient with the largest error ( Table 6). The visual interpretation of the residues as a percentage function of the observed data showed that the adjusted values for nutrients were slightly overestimated (Figures 2-7). This pattern, in which N, P, K, Ca, and Mg were overestimated was also verified using the negative percentage of the aggregate difference between the observed and estimated values. Nevertheless, the observed and estimated values for biomass and nutrients did not present statistical differences from the t-tests for the paired data that were used to validate the Schumacher-Hall model (Table 11).

Discussion
In general, non-linear models provide good outcomes for biomass estimations in eucalypt stands [43][44][45]. Using diameter measurements, Wernsdörfer et al. [46] modeled nutrients in a Fagus sylvatica settlement. However, for nutrients, estimates have been made indirectly, applying a logarithmic model to estimate the volume and establishing a relationship with the concentration of nutrients [47]. The product of the average concentration of nutrients and biomass can also be used to quantify the nutrients [48].
Using methodological distinctions in biomass and nutrient estimates, the statistical and visual parameters resulting from the adjustments were adequate for choosing the best model. The ratio

Discussion
In general, non-linear models provide good outcomes for biomass estimations in eucalypt stands [43][44][45]. Using diameter measurements, Wernsdörfer et al. [46] modeled nutrients in a Fagus sylvatica settlement. However, for nutrients, estimates have been made indirectly, applying a logarithmic model to estimate the volume and establishing a relationship with the concentration of nutrients [47]. The product of the average concentration of nutrients and biomass can also be used to quantify the nutrients [48].
Using methodological distinctions in biomass and nutrient estimates, the statistical and visual parameters resulting from the adjustments were adequate for choosing the best model. The ratio between the residues and observed variables [49], the aggregate difference [23], and the dispersion of the observed value for the estimated value [50] all proved the efficacy of all models tested in the present study.
The interpretation of these parameters was essential for choosing the Schumacher-Hall model as the best for biomass and nutrient estimations. This is a double-entry model and is well-established in forestry management for volume [22,25,51] and biomass estimates [19,52]. Although the Richards and Weibull models include biological interpretations, population dynamics, and growth over time [53][54][55], Campos and Leite [56] highlighted the Schumacher-Hall model results in less biased estimates.
In large-scale crops, N is the most important element, and its application represents the highest soil fertilization costs. Nitrogen is strictly linked to the increase in productivity of annual and perennial crops; however, this macronutrient does not have high assimilation by eucalypt seedlings under nursery conditions [57]. The increment of N fertilization in established planting cannot increase the density of the wood, as was observed by Assis et al. [24] in a hybrid stand of E. grandis × E. urophylla in Minas Gerais state, Brazil. Thus, post-harvest organic residues are the alternative to increase the levels of organic matter and nutrients in the soil.
The conventional harvest operation in eucalypt stand leads to macronutrient exports of between 66% and 76%, and micronutrient exports of between 58% and 89% of the amount in the aboveground biomass [58]. The rate of nutrient exportation is very high, reaching 33.6 ha −1 year −1 of N, 1.15 of P, 13.8 of K, 15.5 of Ca, and 5.8 kg of Mg [58]. Different systems harvest (e.g., stemwood, stemwood without debarking, and full-tree) shows an increase of nutrient exported levels with harvest intensification [59].
The permanence time of organic eucalypt residue is long, and can take five years [60]. Lignin, cellulose, waxes, and tannins, such as leaves, branches, and petioles, still remain, reducing the rate of decomposition [61][62][63]. Roots are the only component that present faster decomposition than the aboveground components [64]. Leaves, bark, and branches are the main residues that remain in eucalypt stand soil. In the present study, these components had higher concentrations of N and Ca than did the other components. A higher concentration of N in the leaves was observed by Gatto et al. [6] in oxisol and Verão et al. [28] in Argissolos (Ultisols) in an E. grandis × E. urophylla stand in the western center. This pattern was also verified by Vieira et al. [65] in an E. urophylla × E. globulus stand in Argissolos (Ultisols) in the south. The highest concentration of Ca that was verified in the bark may be related to its low mobility in plant tissues, resulting in structuring the pectic chains present in the cell wall [66]. Leaves and branches had the highest percentages of nutrients, which has been verified in newer tree structures [29] and is related to mobility and metabolic activity.
Even when nutrients presented good statistical parameters, the percentage of the standard error of the adjustments was higher than that of the biomass. This may be associated with the mobility and distribution of nutrients along the stem [67]. Téo et al. [68] showed that mathematical models, traditionally used for volume estimates in forest areas, did not present a satisfactory performance for estimating the micronutrient content in individuals of Mimosa scabrella. The authors attributed this result to the site conditions and age of the sampled individuals.
For N, the inherent complexity of its cycle, which according to Wink et al. [69] is influenced by several factors, such as losses in aboveground biomass and translocation of N to the soil through the root system [70], was justified by the highest percentage of estimated standard error compared with the other nutrients. The difficulty in determining N remains even after the litterfall. Plant residue quality, microbial activity, and the Ca/N ratio are variables that may influence the adjustment of N [71,72].
Nevertheless, there are models designed for forest ecosystems that can simulate biogeochemical dynamics in response to environmental changes in forest ecosystems [73,74]. The non-linear forest ecosystem model ForSAFE has correctly reproduced the chemical aspects of soil water, aboveground biomass, and N and P concentrations in coniferous forests [74]. The concentrations and distribution of Al, Ca, Cl, K, Mg, and Mn in distinct fractions of the aboveground biomass in pine forests were estimated using a compartment model [75]. Thus, the studied elements in the present study followed the same pathways inside the tree, allowing an understanding of the cycling of nutrients in forest ecosystems that suffered radioactive accidents.

Conclusions
Non-linear models were tested to estimate the biomass and nutrients using DBH, basal area, and height variables, and were effective in the studi eucalypt stand. Thus, these models could predict the nutrient values in the aboveground biomass, and so the hypothesis raised was corroborated.
All tested models presented good adjustments; however, the Schumacher-Hall model was the best for estimating the N, P, K, Ca, and Mg concentrations of the aboveground biomass and roots. Analyzing both the visual plots and statistical parameters of the adjustments was important.
By predicting biomass and nutrients, the nutrient values of the eucalypt stand could be estimated. For secondary crop rotation, the coefficients obtained via the model adjustments could determine the input of nutrients and carbon in the soil system after harvesting. Considering the dystrophic character of Cerrado soils, this knowledge is very important for the management of these areas.
Supplementary Materials: The following are available online at http://www.mdpi.com/1999-4907/11/10/1097/s1, Table S1: Parameters obtained from the forest inventory of 40 plots in eucalypt stand, Table S2: Compartment's weight of the felled trees in eucalypt stand, Table S3: Nutrient estimating from trees components and according 40 plots in eucalypt stand, Table S4: Mean of roots data and nutrients according 9 diameter categories in eucalypt stand.