Hypsometric Relationship Research Articles

Yield and economic feasibility of Eucalyptus dunnii stands under different management regimes

The aim of this study was to analyze volume yield, number of logs per assortment and economic feasibility of Eucalyptus dunnii stands under different management regimes. The stands are located in Fernandes Pinheiro, Paraná State, Brazil and cover a total area of 2.26 hectares, fragmented into three strata (treatments): A (8 years after coppicing regime), B (9-year old stand after two thinnings), and C (7-year old stand after one thinning). Diameters at breast height (d) of all trees and heights of 110 trees were obtained. The total height of the other trees was estimated by a hypsometric relationship. Tree volume was obtained through a taper function. For the economic analysis comparing the three strata, the periodic equivalent value (PEV) and the internal return rate (IRR) were evaluated considering an interest rate of 8%. The commercial volumetric estimates ranged from 156.61 to 375.53 m³ ha⁻¹. The stratum A yielded more logs, mostly for energy; stratum B yielded larger logs, and stratum C yielded similar number and volume of logs from all assortment classes. For economic analysis, PEV ranged from R$ 196.16 to R$ 1,255.79 ha year⁻¹, and IRR ranged from 12.73% per year (stratum A) to 21.35% per year (stratum C), based on a interest rate of 8%. It was concluded that the management condition of stratum C resulted in higher economic returns, with its product primarily destined for Sawmill 1.

Models for estimating the diameter at breast height as a function of the diameter of the stump Pinus taeda L.

The study addressed the use of models to estimate dendrometric variables in a commercial plantation of Pinus taeda L. Allometric relationships were applied to estimate diameter at breast height (DBH) based on stump diameter (SD), providing a mathematical approach to relate these two variables. Additionally, a "conventional" measurement exclusively of DBH was conducted to compare the values obtained with traditional approach to the results of the proposed modeling. The study also explored hypsometric relationships to estimate tree height as a function of DBH, enabling an efficient and economical assessment of tree characteristics in the forest stand. Furthermore, a forest census was conducted in the area, allowing a comprehensive comparison between the methods used and the actual data from the forest stand, reinforcing the importance of these approaches for effective forest resource management. The results showed that the models were effective in estimating volume, basal area, and the number of trees per hectare, with consistent results compared to the forest census. Therefore, the study concludes that stump inventory methods are effective in estimating dendrometric data in Pinus taeda L. plantations, even after forest cutting events, thereby supporting forestry experts in conducting precise assessments in areas with completed timber harvesting and in making informed decisions. This contributes to the effective and sustainable management of forest resources and the enforcement of laws in cases of environmental or economic damage.

Accuracy of tree height estimation with model extracted from artificial neural network and new linear and nonlinear models

Variable height is commonly used as an input attribute to estimate other variables. Thus, to ensure less susceptibility to errors, it is necessary to obtain the variable height correctly. In addition to DBH, hypsometric relationships are influenced by several factors, such as site, age, genetic variation, and silvicultural practices. The inclusion of these factors in hypsometric models can lead to a gain in the quality of the estimates and in the biological realism. The objective of this study was to propose and evaluate the performance of a model extracted from artificial neural network training and of new models to estimate the total height of eucalyptus trees. The data used in this study originated from temporary forest inventories conducted in eucalyptus stands in Minas Gerais, Brazil. A multilayer perceptron artificial neural network was trained, and a nonlinear equation was extracted from the best-performing network to predict the total heights of trees. New linear and nonlinear hypsometric models were constructed and fit considering variables related to individual trees (DBH) and stands (plot basal area, age and site index). The new hypsometric models proposed in this study showed satisfactory performance and are effective for estimating the total heights of eucalyptus trees, particularly the model extracted from the artificial neural network and the nonlinear model

A review and uncertainty analysis of Lake Urmia's hypsometric relationships

Lake Urmia, once the second-largest saline lake worldwide, has almost dried. Several studies have provided bathymetric maps for the lake using different data and techniques but rarely identified the associated uncertainties. This paper provides a comprehensive review of Lake Urmia bathymetric studies and discusses the underlying uncertainties. We developed an updated hybrid bathymetry and hypsometric relationships for Lake Urmia using in-situ and satellite data. The proposed hybrid bathymetry was validated against independent in-situ depth data (with an RMSE < 20 cm) and applied as a baseline for comparison with other available bathymetry models. Results revealed that uncertainties in lake depth measurement, water delineation algorithms from satellite data, spatial interpolation method, and sensor resolution have the highest uncertainty, respectively. Furthermore, the width of the uncertainty bands in the lake level-area relationships is not uniform and peaks at lake levels between 1270 and 1272 m, which are critical for conserving crucial ecosystem services of Lake Urmia, such as island conservation and dust control. Our synthesis indicated that the application of various Lake Urmia bathymetries could lead to about 0.5 and 1 km3differences in the estimated lake volumes for obtaining the ecological and dust control levels, respectively. Our findings provide useful insights for Lake Urmia managers, also applicable for other saline lakes, into considering thedynamic of lake topography and associated uncertainties in lake conservation/restoration programs.

Hybrid Method for Fitting Nonlinear Height–Diameter Functions

Regression analysis is widely applied in many fields of science to estimate important variables. In general, nonlinear regression is a complex optimization problem and presents intrinsic difficulties in estimating reliable parameters. Nonlinear optimization algorithms commonly require a precise initial estimate to return reasonable estimates. In this work, we introduce a new hybrid algorithm based on the association of a genetic algorithm with the Levenberg–Marquardt method (GALM) to adjust biological nonlinear models without knowledge of initial parameter estimates. The proposed hybrid algorithm was applied to 12 nonlinear models widely used in forest sciences and 12 databases under varying conditions considering classic hypsometric relationships to evaluate the robustness of this new approach. The hybrid method involves two stages; the curve approximation process begins with a genetic algorithm with a modified local search approach. The second stage involves the application of the Levenberg–Marquardt algorithm. The final performance of the hybrid method was evaluated using total fitting for all tested models and databases, confirming the reliability of the proposed algorithm in providing stable parameter estimates. The GA was able to predict the initial parameters, which assisted the LM in converging efficiently. The developed GALM method is effective, and its application is recommended for biological nonlinear analyses.

PERFORMANCE OF THE CLONE Eucalyptus urograndis IN A CONVENTIONAL AND SILVOPASTORAL SYSTEM

The objective of this study was to analyze forest productivity, comparing the financial viability of a silvopastoral system versus a conventional forest plantation, both using the clone of the hybrid of Eucalyptus urograndis. For the survey of the volume data, nineteen plots of 40.0 x 15.0 m (600 m²) were installed in conventional planting and fifteen plots of 25.0 x 32.0 m (800 m²) in silvopastoral planting. All tree diameters and heights of each plot were measured. The hypsometric relationship models were obtained using the Stepwise method and the trees were cubed using the Smalian method. The volumes were separated into assortments, according to the sales options for the local market. The financial analysis considered cash flows from the year of implementation until the cutting age (7 years), considering the costs spent for the formation and maintenance of the forest throughout the cycle, discounted at an interest rate of 6.75% per year and the volume sold at market value, considering standing wood, at the end of the cycle. The following were evaluated: net present value, equivalent annual value, internal rate of return, expected value of land and average cost of production. The two production systems were considered economically viable for the suggested 7-year rotation, however the silvopastoral system showed results that demonstrate greater financial viability caused mainly by the lower cost of implementation and maintenance, and to the greater volume of the assortments with greater added value (S1 and S2).

High Cadence Monitoring of Reservoir Volume Fluctuations Using PlanetScope Imagery

Satellite images, which are effectively used to monitor changes in water areas, water management and planning, and to determine the measures to be taken against possible natural disasters, provide data with high temporal and spatial resolution. This study represents the monitoring of temporal surface water dynamics and estimating the volume fluctuations by combining the in-situ data with remotely sensed area data for Kemer Dam, containing the Arapapıştı Canyon (Turkey). Also, it demonstrates the production of the underwater topography in the water reservoir areas of absent or difficult to obtain bottom topography by integrating the in-situ water level and the PlanetScope Remote Sensing data in GIS environment. The temporal changes of dynamic volume of the reservoir above the lowest water level were estimated by the Hypsometric Relationship equation, Pyramidal Frustum Model and TIN-based Calculation method and their accuracy were evaluated using in-situ data. The simplicity and ease of application of the Pyramidal Frustum method, as well as its relatively low RMSE and Standard Error Rate of the Regression (SER) values, compared to other methods in this study, increase its usability in such studies. PlanetScope Imagery will make an important contribution to hydrological studies by producing daily images in high-resolution. Mission characteristics of satellite images (e.g. spatial, temporal and spectral resolution and, geometric accuracy), data sparseness, concurrency in parameters, chosen volume calculation method and linearity of hypsometry are important components that affect the performance of the Volume Fluctuation Monitoring studies using satellite images.

Influences of determined and estimated dendrometric variables on the precision of volumetric modelling

The use of independent variables in volumetric modelling is an important step in fitting models to represent tree or stand characteristics. The DBH measured at 1.3 m from the ground level and total tree height (Ht) are the most commonly used independent variables when modelling individual tree volumes. This work aimed to analyze the importance of independent variables in fitting and selecting volumetric equations. A total of 750 trees from an experiment with three Eucalyptus spp. clones planted in five spacings in the semi-arid region of Pernambuco were used. Four statistical procedures were applied to compare the equations: Adjusted Fit Index (AFI), Akaike information criterion (AIC), mean absolute percentage error (MAPE), and a completely random design having the real tree volume as control and the fit equations as treatments. The error measuring heights in the field (EH) was also analyzed. Four heights were evaluated: Ht, height estimated in the field (He) and heights adjusted (Ha) from hypsometric relationships using the DBH [Ha (a)] and D&lt;sub&gt;1.7&lt;/sub&gt; [Ha (b)], which was the diameter most correlated with the volume. The result indicates that all 18 fitted models provided high precision volumetric equations which do not differ at the 5% significance level.

Hypsometric relationship in Tectona grandis L. F. stands using quantile regression

Hypsometric relationship in Tectona grandis L. F. stands using quantile regression

Tracking lake surface elevations with proportional hypsometric relationships, Landsat imagery, and multiple DEMs

AbstractMultidecadal inland surface water dynamics are of increasing interest due to their importance to climate, ecology, and society, yet several key challenges impede long‐term monitoring of inland surface waters globally. This research investigates two novel methods, one addressing subhydroflattened surface estimate uncertainty issues, and a second addressing temporal resolution issues, using 46 water bodies across the western United States. First, low water level estimate uncertainty was reduced using multiple digital elevation models (ALOS, SRTM, and NED) to derive the hypsometric relationship for each lake from the digital elevation model with the lowest hydroflattened water surface. This technique reduced the number of images with subhydroflattened water surfaces by at least 549 over the best individual DEM resulting in higher water surface elevation estimate accuracy. Second, this paper introduces proportional hypsometry which dynamically generates surface area/elevation relationships for every image using clear pixels only by removing contamination from both the image and DEM. Proportional hypsometry was found to be ill‐suited for subhydroflattened water surface levels but produced comparable accuracy to clear images for above hydroflattened water levels. Overall, using the lowest hydroflattened surface along with proportional hypsometry improved temporal resolution enabling analysis of nearly 10,000 additional images while maintaining similar accuracy levels as images with &lt;1% contamination (2.35 m RMSE vs. 2.17 m RMSE). This research increases lower water elevation estimate accuracy and temporal resolution and is scalable enabling regional and global water dynamic analysis.

Variáveis dendrométricas e produção de Eucalyptus benthamii em diferentes espaçamentos

This study aimed to evaluate the effect of planting spacing on production and dendrometric variables, in experimental planting with improved E. benthamiiseeds, at six years of age. The experimental design adopted was in randomized blocks, with four replications of twenty trees. The treatments were four planting spacing 3 x 2 m, 3 x 3 m, 3 x 4 m and 4 x 4 m. After the field procedures (forest inventory, sampling and cubage of 79 trees), the main dendrometric parameters were obtained in each spacing. The heights were determined by a hypsometric relationship and the volume ofother trees in the stand was estimated by the model of Schumacher and Hall (1933). The dendrometric variables showed a high correlation with the spacing. The wider spacing favored the diameter, height, transversal area and the individual volume, while the smaller vital spaces were responsible for the highest values of basal area and volume per hectare. Production ranged from 238.90 m³ ha-1in the largest spacing to 392.08 m³ ha-1in the smallest spacing. It was concluded that there was an effect of the planting spacing, and that with the trends observed regarding the higher production per hectare in the denser spacing, it is opportune to plan the forest production according to the planting spacing adopted.

The tree height estimated by non-power models on volumetric models provides reliable predictions of wood volume: The Amazon species height modelling issue

Allometries that include height as independent variable usually provide greater accuracy on estimates of volume, biomass or individual carbon than other prediction strategies that rely only diameter at breast height as independent variable. However, when these models are applied in Amazon Forest Inventories, it is common to use estimated heights rather than measured heights to prepare volume, biomass or carbon estimates. This practice is common, but rarely discussed and the effect on predictions and precision is usually overlooked. The aim of this study was to examine hypsometric models and evaluate the effect of estimated height on merchantable volume prediction in Eastern Amazonian forests. The study area was a 3,786 ha Forest Management Unit owned by Jari Florestal S.A., in the Jari Valley Region of the State of Pará, Brazil. The data includes 16,099 trees of 25 species, measured and harvested in 2006. Ten percent of the data were reserved for validation of the hypsometric and volumetric estimates. Five hypsometric models and two modelling techniques (linear regression and mixed-effects model) were examined. The choice of best model was based on graphical analyses of residuals, distribution of residuals, heteroscedasticity of error and presence of outliers as assessed by h-values, DFFITS and Cook's distance. The hypsometric relationship and volumetric estimates using DBH and DBH with estimated height were validated with Graybill's test, Theil's error decomposition, Efficiency, Equivalence test and Tukey's test for species estimates level. Heights estimated using a semi-logarithmic mixed-effects model can improve predictions from volume equations. The results show that exploratory data analysis and validation process helped to provide estimates with greater efficiency and should be adopted in related studies. The prediction of height associated with volumetric models for six different species provided volumetric estimates with an error below 5% for the global average volume. The estimated height by the mixed-effect non-power law model should be included in double input models previously developed for volume prediction.

Spatial organisation and physical characteristics of large peat blocks in an upland fluvial peatland ecosystem

This paper assesses the size, shape and spatial organisation of organic, carbon-rich debris (peat blocks) in an upland fluvial peatland ecosystem. Peat block inventories collected in 2002 and 2012 at an alluvial reach of Trout Beck (North Pennines; United Kingdom) provide independent surveys for investigating the physical characteristics and spatial organisation of the organic debris. Peat blocks deposited along the 450 m reach represent a substantial volume of fluvially derived in-channel sediment and carbon flux at the macroscale (total peat volume 11 m3 (2002) and 17 m3 (2012)). Results show that inferred peat block transport distances depend on their size and shape. Smaller and more spherical equant shaped peat blocks are transported 1.62 and 1.72 times the distance of prolate and elongate shaped peat blocks. Downstream fining relationships provide a first-order approximation of peat block degradation rates. These degradation rates are high (up to 2 mm/m for the a-axis) and indicate considerable fine sediment release during transport. Hypsometric relations show that 73% of peat blocks are distributed within 1 channel width of the thalweg, indicating lateral organisation and a pattern of preferential deposition at the active channel margin. The local effects of obstructions from topography, roughness and slope promote peat block deposition, but given the low density of the blocks and close proximity to the flow the potential for re-entrainment is high.

General Height-Diameter Equation Depending on the Stand Variables, for Eucalyptus benthamii

Abstract The aim of this study was to develop a general applicability equation to represent the hypsometric relationship of Eucalyptus benthamii Maiden et Cambage stands in Irani, Santa Catarina. The data came from a continuous forest inventory, with a simple random sampling design and the Bitterlich method. The functions to represent the hypsometric relationship were adjusted with their parameters linear function of stands variables, based on the Gauss-Newton algorithm. The models were evaluated according to the criteria of adjustment and precision, accuracy and validation. In general, the Harrison model, adjusted with the coefficient “c” linear function of age, dominant diameter and basal area, presented the best statistical performance to represent the hypsometric relationship of Eucalyptus benthamii.

Geomorphometric relief classification with the k-median method in the Silesian Upland, southern Poland

The aim of this study is geomorphometric relief classification of a temperate latitude upland area in Central Europe. The Silesian Upland represents diversified structural relief which contains a fan-shaped configuration of long thresholds and wide erosion depressions. A 20 m × 20 m digital elevation model (DEM) provided input data for the analysis. The k-median method was applied to examine morphometric variables of the relief. The aim of these activities was to identify clusters with objects of similar mathematical characteristics. These clusters were the basis of landform classification. Smaller numbers of clusters 4 transparently show hypsometric relationships. Key elements of the morphology of the area were clearly visible. The division into 6 clusters gives the best results—a detailed but clear image of the morphological diversity by distinguishing characteristic landform elements. The results for 8 clusters show significant background noise and are ambiguous, which makes them difficult to identify. Our research has confirmed that the k-median method is a useful tool for landform classifications. We determined optimal parameters of this method (filtering window size, DEM resolution, number of clusters, aspect influence).

Stratification in the adjustment of hypsometric relationship models in forest fragment

The objective of this study was to find a hypsometric relationship model capable of estimating the height of trees in unequal forest fragment, testing the efficiency of stratification by species, ecological group and diametric class. In the unequal forest fragment (2.2 ha) belonging to the Federal Rural University of Rio de Janeiro, Seropédica / RJ, a census was carried out, botanical identification of trees with a diameter ≥ 5 cm, being this variable measured, as well as their respective height total. The data were stratified into ecological group, species and diametric class, and then ten traditional models of hypsometric relation were adjusted for the general database and for each stratum. The significance of the models was evaluated by the F test and the t test, with 95% probability. Trends of the estimates were verified with graphical analysis of the residues, being also observed the coefficient of determination (R2 aj.) and standard error of the estimate in percentage (Syx%). By means of the regression parameters, the Graybill models identity test was subsidized. The Trorey model was chosen and it was observed that the stratification by species and ecological group made the adjustment more efficient. Stratification in diametric class showed no gain.

Hypsometric models for a clonal plantation of Tectona grandis Linn F. subjected to selective thinning

At a moment when the importance of planted forests in the Amazon region is increasing, hypsometric models become highly relevant tools as they allow monitoring of and planning for tree plantations in a way that is practical and economic for the producer. Thus, the objective of the current study was to select and adjust a model of hypsometric relationships for a clonal plantation of Tectona grandis Linn F., submitted to selective&#x0D; thinning, located in Capitão Poço municipality, Pará state, Brazil. Data were collected from permanent plots in five-year-old stands using the fixed area method and systematic process. The best adjusted model was selected with an adjusted determination coefficient (R²aj.%), residual standard deviation of the percentage estimate (Syx%), recalculated residual standard error (Syxr%), diagnosis of distribution of residuals as a percentage and&#x0D; the Percent Average Deviation (PAD%). Hyperbolic models 2 and 3 had the highest determination coefficients (83.42 and 83.40%) and lowest PAD (-0.006 and -0.154%). The polynomial (1) and hyperbolic models (2 and 3) showed the smallest errors in related to the estimates. Model 2 (hyperbolic) was found to generate the&#x0D; best estimate of total T. grandis clonal plantation height. Use of this hypsometric model will allow a significant&#x0D; reduction of costs and time in forest inventory studies.

ARTIFICIAL NEURAL NETWORKS FOR MODELING HYPSOMETRIC RELATIONSHIPS OF Pinus caribaea Morelet var. caribaea Barr. &amp; Golf.

The present study was carried out to compare the performances of regression models and Artificial Neural Networks (ANNs) in hypsometric relationships modeling and to analyze the influence of ANN type and sample size on ANN performance. The database was consisted by 65 circular plots of 500 m² in which Diameter at Breast Height - DBH (cm) and Total Height - Ht (m) of 2538 trees were measured in plantations of Pinus caribaea var. caribaea in Macurije forest company, Cuba. The study was carried out in three stages: i) Fit of traditional hypsometric models and sigmoidal growth models; ii) ANNs training and comparison of the selected ANN with the regression model selected; iii) Analysis of sample size and ANN type influences on the estimates precision by means of a completely random experimental design with 5x2 factorial arrangement, with the factors sample size (N) and ANN type (R). The results indicated that the best equation to estimate trees heights was that of Gompertz. The ANNs MLP 1-4-1 and MLP 8-4-1 were superior to the selected equation (Gompertz). Multi-Layer Perceptron ANNs generated more accurate estimates and their performances were less influenced by the sample size.

Tree height prediction in Brazilian Khaya ivorensis stands

Tree height measurement is one of the most difficult activities in forest inventory data gathering, although it is a fundamental variable to support forest management, since it is an input for modelling growth and yield. To overcome this obstacle and ensure that the heights of trees are estimated accurately, hypsometric relationships are used. Therefore, the objective of this study was to compare different fitting strategies (i.e. nonlinear least squares and mixed-effects) to predict tree height in African mahogany Brazilian plantations using well know local (using only tree height and diameter) and generalized (using height, diameter and plot level variables) models. Data were gathered on 149 permanent plots sampled in different Brazilian regions and ages, totaling 4,201 height-diameter pairs. Different models were evaluated and the best method to estimate the height-diameter relationship was based on statistical and graphical criteria. A local model using mixed-effects with correction of heteroscedasticity was efficient and superior to other models evaluated. However, when using an independent data base, the generalized model fitted by nonlinear least squares generates adequate results that are scaled to the plots’ productivity, since the inclusion of dominant height into the model helps to predict height locally.

MODELAGEM NÃO LINEAR DA RELAÇÃO HIPSOMÉTRICA E DO CRESCIMENTO DAS ÁRVORES DOMINANTES E CODOMINANTES DE &lt;i&gt;Eucalyptus&lt;/i&gt; sp.

Este trabalho teve por objetivo avaliar modelos lineares e não lineares clássicos e generalizados com adição de covariáveis, para modelagem da relação hipsométrica e do crescimento em altura das árvores dominantes e codominantes de clones de eucalipto. Foram ajustados dois modelos lineares e dois não lineares para estimativa da relação hipsométrica e quatro modelos não lineares para classificação de sítio. Com relação à hipsometria, para o modelo que propiciou as melhores estatísticas, utilizou-se a técnica de inclusão de covariáveis para o ajuste, visando obter melhor precisão das estimativas. A seleção e a qualidade de ajuste dos modelos se deram com base no erro padrão percentual “Syx (%)”, critério de informação de Akaike (AIC), critério de informação Bayesiano (BIC) e no teste de razão da máxima verossimilhança (TRMV), além da análise gráfica dos resíduos. Para a manipulação, ajuste e processamento dos dados foi utilizado o software R. De acordo com as análises estatísticas dos modelos, para a relação hipsométrica, o logístico com quatro parâmetros mostrou-se superior em relação aos outros modelos ajustados. O modelo logístico com adição de covariáveis obteve uma melhor precisão em comparação ao modelo logístico clássico. Para a estimativa do crescimento em altura das árvores dominantes e codominantes, o modelo logístico com três parâmetros obteve as melhores estatísticas de precisão, sendo, então, utilizado para a construção das curvas de índice de sítio.