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Journal of Arid Land  2020, Vol. 12 Issue (6): 1046-1055    DOI: 10.1007/s40333-020-0082-x
Research article     
Improving wood volume predictions in dry tropical forest in the semi-arid Brazil
Robson B de LIMA1,*(), Patrícia A B BARRETO-GARCIA2, Alessandro de PAULA2, Jhuly E S PEREIRA3, Flávia F de CARVALHO2, Silvio H M GOMES4
1Department of Forest Engineering, State University of Amapá, Macapá 68900070, Brazil
2Department of Forest Science, State University of Southwest Bahia, Vitória da Conquista 45083900, Brazil
3Universidade Federal de Lavras, Lavras 37200900, Brazil
4Universidade de S?o Paulo, Piracicaba 13418900, Brazil
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The volumetric variability of dry tropical forests in Brazil and the scarcity of studies on the subject show the need for the development of techniques that make it possible to obtain adequate and accurate wood volume estimates. In this study, we analyzed a database of thinning trees from a forest management plan in the Contendas de Sincorá National Forest, southwestern Bahia State, Brazil. The data set included a total of 300 trees with a trunk diameter ranging from 5 to 52 cm. Adjustments, validation and statistical selection of four volumetric models were performed. Due to the difference in height values for the same diameter and the low correlation between both variables, we do not suggest models which only use the diameter at breast height (DBH) variable as a predictor because they accommodate the largest estimation errors. In comparing the best single entry model (Hohenald-Krenn) with the Spurr model (best fit model), it is noted that the exclusion of height as a predictor causes the values of 136.44 and 0.93 for Akaike information criterion (AIC) and adjusted determination coefficient (R2 adj), which are poorer than the second best model (Schumacher-Hall). Regarding the minimum sample size, errors in estimation (root mean square error (RMSE) and bias) of the best model decrease as the sample size increases, especially when a larger number of trees with DBH≥15.0 cm are randomly sampled. Stratified sampling by diameter class produces smaller volume prediction errors than random sampling, especially when considering all trees. In summary, the Spurr and Schumacher-Hall models perform better. These models suggest that the total variance explained in the estimates is not less than 95%, producing reliable forecasts of the total volume with shell. Our estimates indicate that the bias around the average is not greater than 7%. Our results support the decision to use regression methods to build models and estimate their parameters, seeking stratification strategies in diameter classes for the sample trees. Volume estimates with valid confidence intervals can be obtained using the Spurr model for the studied dry forest. Stratified sampling of the data set for model adjustment and selection is necessary, since we find significant results with mean error square root values and bias of up to 70% of the total database.

Key wordsvolume modeling      minimal sample size      Caatinga      Spurr model      forest management     
Received: 07 July 2020      Published: 10 November 2020
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About author: *Robson B de LIMA (E-mail:
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Robson B de LIMA, Patrícia A B BARRETO-GARCIA, Alessandro de PAULA, Jhuly E S PEREIRA, Flávia F de CARVALHO, Silvio H M GOMES. Improving wood volume predictions in dry tropical forest in the semi-arid Brazil. Journal of Arid Land, 2020, 12(6): 1046-1055.

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DBH classes (cm) Class center (cm) Frequency
5.0-13.0 6.50 1.2
13.1-21.0 17.05 96.0
21.1-29.0 25.05 25.0
29.1-37.0 33.05 7.0
37.1-45.0 41.05 4.0
45.1-53.0 49.05 2.0
Table 1 Diametric distribution of tree stems in the dry tropical forest
Model ββ0 (±SE) ββ1 (±SE) ββ2 (±SE) AIC RSE R2 adj RMSE Bias
Husch -8.613 (±0.082) 2.303 (±0.036) - 141.45 0.30 0.93 0.06 0.10
Hohenald-Krenn -9.504 (±0.346) 3.058 (±0.286) -0.151 (±0.057) 136.44 0.30 0.93 0.04 0.09
Spurr -9.914 (±0.089) 1.013 (±0.013) - 58.88 0.27 0.95 0.06 0.07
Schumacher-Hall -9.792 (±0.140) 2.060 (±0.040) 0.909 (±0.092) 59.60 0.27 0.95 0.06 0.07
Table 2 Estimates of parameters and adequacy indices of four volumetric models of individual trees adjusted for the dry tropical forest
Fig. 1 Fitting (a) and validation (b) regression curves (color lines) and 95% CIs (CIs, confidence intervals; grey envelopes) of four models (detailed in Table 1) relating volume and diameter at breast height (DBH) of trees in the dry tropical forest
Fig. 2 Residual distribution of wood volume for the best equation (Spurr) obtained for the trees in the dry tropical forest. (a), fitting; (b), validation.
Sampling strategy RMSE RSE CV (%) Bias Percentile (%)
All trees (stratified) 0.0559 0.2644 65 -0.0710 20
All trees (stratified) 0.0549 0.2632 63 -0.2452 50
All trees (stratified) 0.0541 0.2642 63 -0.0851 70
DBH>15.0 cm (stratified) 0.1120 0.2681 38 0.4497 20
DBH>15.0 cm (stratified) 0.1066 0.2672 36 -0.4606 50
DBH>15.0 cm (stratified) 0.1083 0.2715 37 -0.3180 70
DBH>15.0 cm (random) 0.2400 0.2668 81 9.4526 20
DBH>15.0 cm (random) 0.1373 0.2806 46 3.8118 50
DBH>15.0 cm (random) 0.1345 0.2804 45 3.5025 70
Table 3 Statistical criteria for different tree sampling strategies
Fig. 3 Root mean square error (RMSE; a) and bias (b) of estimated total volume using different percentiles of data size to adjust and validate the best local model
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