Assessment of Standing and Felled Tree Measurements for Volume Estimation

Abstract

Accurate stem-volume estimation supports inventory, valuation and carbon accounting, but Pressler’s single-section formula has never been tested in the highly productive European-beech forests of the Central Rhodope Mountains, Greece. We quantified the bias of Pressler estimates and developed size-specific correction factors. Sixty Fagus sylvatica L. trees felled in 2023–2024 were measured destructively at 1-m intervals. Pressler standing volumes were compared with Smalian-plus-cone reference volumes (hereafter referred to as true volumes) and analysed with generalized additive models. Pressler underestimated true volume (mean bias = −0.088 m³; RMSE = 0.204 m³; MAPE = 21%). Under-estimation increased with diameter. A GAM with DBH and height explained 96.7% of the variance in true volume. We also fit a Random Forest as a complementary check. Multipliers of 1.30 (<25 cm DBH), 1.20 (25–45 cm), 1.30 (45–55 cm) and ≥1.35 (≥55 cm) cut residual error to ≤20% overall and <10% inside the well-sampled 35–45 cm class. A simple DBH-class correction table restores Pressler’s speed while meeting modern accuracy standards for inventory and carbon reporting.

1. Introduction

Accurate estimation of tree volume is fundamental to forest inventory, management and ecological research. Most inventories rely on non-destructive measurements such as diameter at breast height (DBH) and total height. These measurements are combined in volume tables or allometric equations to predict total and merchantable volume [1]. However, the accuracy of standing-tree volume estimates varies with species, form and sampling technique [2]. To validate standing measurements, many researchers have compared them against true volumes derived from felled trees. Early work by [3] used McClure mirror calipers to measure upper-stem diameters and reported that standing-tree volumes agreed within about 2% of volumes computed from felled trees. [4] showed that adding a single upper-stem diameter to a volume table can substantially improve volume predictions for loblolly pine and Douglas-fir. More recently, [5] compared field-based and airborne laser scanning inventories with felled tree measurements in mixed conifer stands and found strong concordance between remote-sensing estimates and true volumes. These examples illustrate that standing-tree measurements can closely approximate felled-tree volumes when appropriate devices and models are used. [6] introduced the Forest Survey Intelligent Dendrometer (FSID), which has achieved a reported accuracy of 96.89% in standing tree volume measurements when compared against conventional methods, i.e., standing-tree single-section (Pressler), form-factor (basal area × form height), and the instrumented workflows used in practice (total station, 3D laser scanner, camera and total station). This device utilizes laser scanning and advanced algorithms to improve measurement precision and has been highlighted in contemporary forestry research. Similarly, technological advancements such as terrestrial LiDAR have been explored to overcome these challenges, providing more detailed data on tree structure [7].

Because single-section methods like Pressler’s rely on one measured point, advances in taper modelling have attracted attention [8]. Taper equations describe the change in diameter along the stem and can predict volumes to any top diameter or log length. [9] fitted integrated taper functions to destructively sampled black-locust trees and found that locally calibrated functions produced more accurate over- and under-bark volume predictions than generic equations. Although that study did not compare standing and felled measurements, it demonstrates the potential of taper models to improve volume estimation. A similar message emerges from the Forest Survey Intelligent Dendrometer (FSID), which uses optical and laser measurements to compute diameters at arbitrary heights in real time and achieved accuracies near 97% on 181 trees [6]. These developments suggest that incorporating taper information or upper-stem diameters can reduce bias in volume estimates.

A limitation of form-factor methods is that they yield only whole-stem volumes. Taper functions, in contrast, model diameter variation along the bole and can be integrated to estimate total or merchantable volume to any top diameter. They provide flexible descriptions of stem form and allow volume ratios and profiles to be predicted for individual trees or stands. In the field, taper is commonly observed with optical dendrometers such as the Spiegel relaskop, which uses calibrated bars to measure diameters aloft. To apply Pressler’s method, the observer backs away from the tree until the DBH spans the relaskop bars, then moves vertically to find the point on the bole where the instrument indicates half of DBH; this height is the Pressler height (H_Pressler). By measuring diameters at successively higher points, the relaskop can also be used to delineate complete taper profiles. Two-thirds of H_Pressler is assumed to approximate the form height, which, when multiplied by basal area at breast height, yields an estimate of total stem volume.

Despite advances, discrepancies between standing and felled measurements persist because capturing taper precisely in standing trees is challenging. Single-section methods such as those of Hossfeld, centroid sampling and Pressler have therefore been tested on various species with mixed results [10]. Contemporary tools like terrestrial laser scanning and intelligent dendrometers are improving volume estimates but may be costly or impractical in routine forest inventories. Simple optical methods remain attractive for their speed. In this study we quantify the bias of Pressler’s single-section formula in European beech stands of the Central Rhodope Mountains and develop diameter-class correction factors to align Pressler estimates with true volumes obtained from felled trees. Rigorous comparison and refinement of these methodologies will contribute to enhanced forest management practices, allowing for better predictions of biomass and carbon stocks, critical for ecological assessments and sustainable forestry initiatives [11]. In operational Greek inventories, the single-section Pressler method is still used because it is fast and requires only DBH and one upper-stem observation. Because stem taper in natural forests varies with stand structure and species mixture, and butt swell is occasionally observed in Central Rhodope beech, we evaluate the accuracy of Pressler’s standing-tree volumes against true volumes from felled trees and, if needed, propose simple DBH-class correction factors for practice.

2. Materials and Methods

2.1. Study Area

The study was conducted in the Central Rhodope Mountains of northeastern Greece (Eastern Macedonia and Thrace region). The coordinates of the central point of the study area are 41°16′20.28″N, 24°42′19.92″E, and its elevation is 1,040 m. The study area includes three public forest complexes, Drymos, Kalyva–Margariti, and Oraio and covers an area of 28,400.84 hectares [12,13,14]. Figure 1 shows the locations of the sampled trees within these complexes and the position of the study area within Greece.

The study area constitutes the easternmost part of the Rhodope Mountain Range National Park, which hosts some of the most productive forests in Greece [15]. Recent mensurational work by [16] developed volume equations for F. sylvatica in central-Greek mountains, confirming the high growth potential of beech–fir stands.

The dominant species in the study area include European beech (F. sylvatica L.), Scots pine (Pinus sylvestris L.), silver fir (Abies borisii-regis Mattf.) and oak (Quercus spp.). Among others, there are also silver birch (Betula pendula Roth), Balkan pine (Pinus peuce Griseb.), ash (Fraxinus spp.), hornbeam (Carpinus spp.), hop hornbeam (Ostrya carpinifolia Scop.) and alder (Alnus glutinosa (L.) Gaertn), [12,13,14]. In the northern part of the area, the forest is mainly composed of natural stands of F. sylvatica, P. sylvestris - F. sylvatica, and F. sylvatica - A. borisii-regis stands [17,18].

F. sylvatica occurs from 510 m to 1 803 m above sea level [12,13,14].

2.2. Data Collection

In 2023–2024, a total of 60 European beech (F. sylvatica L.) trees were sampled in the Central Rhodope Mountains (Southeastern Europe) for destructive analysis. Sampling was conducted leveraging an unequal probability design, i.e., trees were selected with varying inclusion probabilities rather than simple random sampling. This approach ensured that a representative range of tree sizes from the harvest area was included in the sample. All standing beech trees in the harvest stands were stratified into three DBH classes ([10,35) cm, [35,55) cm, and [55,70) cm), in broad correspondence with the three diameter classes used in management studies for the area, with thresholds slightly modified to better balance sample sizes and reflect the observed DBH distributions. The total sample size n was determined using the formula of [19]:

$$n={\displaystyle \frac{N\left(\frac{Z^{2}p\left(1-p\right)}{e^2}\right)}{N+\frac{Z^{2}p\left(1-p\right)}{e^2}}}$$

(1)

with parameters N = 3701 (population size), Z = 1.64 (90% confidence level), p = 0.79 (population proportion), and e = 0.09 (acceptable error). This calculation yielded a required sample size of 60. Following proportional allocation across DBH classes, the final sample comprised 42, 17, and 1 trees, respectively.

Before felling, each tree’s DBH was measured at 1.3 m above ground to the nearest 0.5 cm using a diameter caliper, and total height was measured with a Haga hypsometer to the nearest 0.5 m. The hypsometer measurements were taken from a distance of 25–35 m chosen to provide a clear view of the tree top and to minimize parallax. Pressler height H_Pressler was determined using a Spiegel Relaskop by backing away until the DBH filled the instrument bars and then sighting upward to the point where the instrument indicated a diameter equal to half of DBH; this technique provides a direct measure of diameter at height aloft.

After each tree was felled, the total length from ground level to the tip was measured with a tape. Diameters over bark were recorded at the stump (0.3 m above ground) and at successive 1.0 m intervals along the stem starting at 1.3 m. These measurements partitioned the stem into logs for volume calculation.

2.3. Volume Calculations

We estimated standing whole-stem volume using Pressler’s formula [4]. Let G (m²) denote the basal area at breast height (computed as

$$\mathrm{G}=\mathsf{\pi }{\left({\displaystyle \frac{\mathrm{DBH}}{200}}\right)}^2$$

(2)

for DBH in cm) and let H_Pressler (m) denote the height where the stem diameter equals half of DBH. Form height (FH) is defined as two-thirds of H_Pressler. Pressler volume V_Pressler is then ${\mathrm{V}}_{\mathrm{Pressler}}=\mathrm{G}\times \mathrm{FH}$ [20], where V_Pressler is expressed in m³.

The true volume (the felled-tree volume obtained from contiguous 1-m Smalian sections plus a conical tip, over bark) was computed by summing the volumes of consecutive logs measured after felling. For two consecutive measurement points with diameters d_i and d_(i+1) separated by length L_i (1 m), we approximated the section volume V_i using Smalian’s formula:

$${\mathrm{V}}_{\mathrm{i}}={\displaystyle \frac{\mathsf{\pi }\times \mathrm{L}}{2}}\left({\left({\displaystyle \frac{{\mathrm{d}}_{\mathrm{i}}}{200}}\right)}^2+{\left({\displaystyle \frac{{\mathrm{d}}_{(\mathrm{i}+1)}}{200}}\right)}^2\right)$$

(3)

The tip was treated as a cone with volume

$${\mathrm{V}}_{\mathrm{tip}}=\mathsf{\pi }\times {\displaystyle \frac{{\mathrm{d}}_{\mathrm{tip}}^2}{12}}{\mathrm{H}}_{\mathrm{tip}}$$

(4)

where d_tip is the last measured diameter and H_tip is the remaining length. Summing the sections and tip yields true volume V_true.

We summarised the distribution of DBH, total height (H), Pressler height (H_Pressler), form height (FH), standing volume (V_Pressler) and true volume (V_true) using the mean, standard deviation (SD), minimum and maximum values.

Table 1. Summary statistics (mean, standard deviation (SD), minimum (Min) and maximum (Max)) for diameter at breast height (DBH), total height (H), Pressler height (H_Pressler), form height (FH), standing volume estimated with Pressler’s method (V_Pressler) and true volume (V_true) for the 60 destructively sampled European beech trees.

Variable	Mean	SD	Min	Max
DBH (cm)	29.73	13.47	11.00	79.00
H (m)	17.69	5.83	8.30	30.30
HPressler (m)	7.33	3.33	2.10	15.47
FH	4.88	2.22	1.40	10.31
VPressler (m3)	0.52	0.75	0.01	4.84
Vtrue (m3)	0.61	0.78	0.03	4.48

lists these summary statistics and provides context for the variation in tree size and volume in our sample. Such descriptive statistics respond to reviewer requests for transparency in sample characterisation and form the basis for evaluating estimation bias.

2.4. Statistical Analysis

2.4.1. Visual Exploratory Analysis and Statistical Errors

Data visualization was performed using scatter plots and Bland–Altman plots to assess agreement between measured and estimated volumes [21]. Statistical analyses involved calculating RMSE, bias, and MAPE as metrics of accuracy and precision [22]:

$$\mathrm{Bias}={\displaystyle \frac{{\displaystyle \sum \left({\mathrm{V}}_{\mathrm{Pressler}}-{\mathrm{V}}_{\mathrm{true}}\right)}}{60}}$$

(5)

$$\mathrm{Root} \mathrm{Mean} \mathrm{Square} \mathrm{Error} \left(\mathrm{RMSE}\right)=\sqrt{{\displaystyle \frac{{\displaystyle \sum {\left({\mathrm{V}}_{\mathrm{Pressler}}-{\mathrm{V}}_{\mathrm{true}}\right)}^2}}{60}}}$$

(6)

$$\mathrm{Mean} \mathrm{Absolute} \mathrm{Percentage} \mathrm{Error} \left(\mathrm{MAPE}\right)={\displaystyle \frac{100}{60}}{\displaystyle \sum \left|\frac{{\mathrm{V}}_{\mathrm{Pressler}}-{\mathrm{V}}_{\mathrm{true}}}{{\mathrm{V}}_{\mathrm{true}}}\right|}$$

(7)

2.4.2. Residual Analysis with Generalized Additive Model (GAM)

Because size effects are non-linear, we used a Generalized Additive Model (GAM) to model true volumes and diagnose size-dependent bias in Pressler estimates. GAMs were fitted in R (mgcv) with penalized cubic regression splines (P-splines) [23]; smoothness was selected by REML. For the true-volume model we used s(DBH) and s(H) with basis dimensions kDBH = 6 and kH = 6. For the bias analysis, residuals were defined as V_Pressler−V_true (positive values indicate over-estimation by Pressler; negative values indicate under-estimation) and were modelled with a GAM using s(V_Pressler) with kV_Pressler = 7. We verified adequacy via the k-index and standard residual diagnostics (gam.check). Foundational treatments of GAMs can be found in [24]. For a broad, accessible overview see [25]. This flexible framework does not impose a strict parametric form; instead, smooth functions are estimated from the data, allowing non-linear relationships to be captured without oversimplification [26,27]. Practical modeling guidance is provided in [28]. Early ecological applications include [29].

2.4.3. Machine Learning Analysis

A Random Forest regressor was employed to predict the felled stem volumes of trees using diameter at breast height (DBH) and total tree height as input features. This machine learning technique, introduced by [30], is particularly well-suited for handling complex interactions and non-linear relationships in ecological data due to its ensemble learning approach. By constructing a multitude of decision trees during training and outputting the mode of their predictions, Random Forests effectively reduce overfitting and improve predictive accuracy.

To ensure robustness and generalizability of the model performance, Random Forest used ntrees = 1000, mtry = 1 (given two predictors), min_node_size = 5 (regression default) (software: ranger in R), with out-of-bag (OOB) RMSE and R² reported; uncertainty was summarised with a 1000-iteration bootstrap. This resampling method provides a non-parametric means to estimate the distribution of the metric without the assumption of normality, offering confidence in the model’s stability across different data subsets [31].

Feature importance analysis was conducted on the Random Forest model to assess the relative influence of DBH and height on volume predictions. This analysis revealed which predictors contributed most significantly to the model’s accuracy, guiding data interpretation and ensuring transparency in ecological modeling [32]. Understanding feature importance is critical in ecological studies for hypothesis generation and decision-making about which variables are most essential in influencing the response variable [33].

Random Forests have demonstrated significant utility in ecological and forestry research, offering a robust alternative to traditional parametric models due to their ability to capture intricate data patterns [34,35]. By leveraging this advanced modeling technique, the study aims to enhance the accuracy and reliability of tree volume predictions, thereby supporting more informed forest management practices and ecological assessments.

3. Results

3.1. Visual Exploratory Analysis and Statistical Errors

Most observations fall above the 1:1 line, confirming that Pressler’s formula consistently produces lower volumes than those obtained from full-stem measurements (Figure 2). The discrepancy widens as tree size increases:

• Small stems, with volume < 1.5 m³, cluster tightly along the 1:1 line, with an average bias of −0.056 m³.
• Medium stems, with [1.5,1.8) m³ diverge substantially, showing under-estimations of −0.741 m³ on average.
• Large stems are sparse in this sample, but for the six trees whose actual volume exceeded 1.8 m³, the average bias was −0.259 m³.

This pattern illustrates the size-dependent bias and motivates the DBH-class correction factors proposed for operational use.

The Bland–Altman plot (Figure 3) confirms a systematic negative bias. The overall mean difference between Pressler-estimated and felled-tree volume is 0.563 m³, with 95% bootstrap CI from 0.393 to 0.776 m³. Residuals trend downward as the mean of the two measurements increases, indicating that under-estimation grows with stem size, as follows:

• Large stems: For the six trees whose actual volume exceeded 1.8 m³—equivalent to a Bland–Altman mean volume above 1.5 m³—the average error was −0.259 m³.
• Smaller stems: For the 53 trees with actual volume < 1.5 m³ (mean volume below 1.5 m³), the mean error was only −0.056 m³.
• One intermediate tree, with actual volume [1.5,1.8) m³, fell between these groups and followed the downward trend.

The single tree with V_true > 4 m³ had DBH = 79 cm and H = 30.3 m.

Thus, while Pressler’s formula is reasonably accurate, its bias becomes operationally significant, reinforcing the need for size-specific correction factors.

Regarding the key error metrics for the dataset, the bias (mean bias; Equation(5)) = −0.088 m³ with 95% bootstrap CI from −0.137 to −0.045 m³ indicate that Pressler’s formula consistently under-estimates stem volume. The RMSE = 0.204 m³ (Equation(6)) with 95% bootstrap CI from 0.128 to 0.270 m³ shows a deviation of 0.2 m³ that is considerable; for the smallest stems it exceeds the whole true volume. The MAPE = 21.22% (Equation(7)) with 95% bootstrap CI from 18.1% to 24.5% shows that, on average, Pressler’s estimates differ from felled-tree volumes by more than 20%. Together these statistics confirm a substantial under-estimation of tree volume.

3.2. Residual Analysis with Generalized Additive Model (GAM)

A GAM fitted to true volume with s(DBH) and s(H) (penalized cubic regression splines; REML) accounted for virtually all systematic variation in felled-tree volume. The partial effect for DBH increased steeply at small to intermediate diameters and then tapered, whereas that for the height was near-linear and weaker. Confidence bands around both partials were narrow across the observed range, indicating stable fits. The model’s pseudo-R² was 0.967, showing that the smooth terms captured the non-linear dependence of volume on tree size and height. The dominance of DBH is consistent with the quadratic growth of basal area, while height adds a modest refinement.

For bias-focused analyses, residuals were defined as V_Pressler−V_true, so that positive values indicate over-estimation by Pressler and negative values indicate under-estimation. A second GAM modelled residuals as a smooth function of V_Pressler (penalized cubic regression spline; REML). The smooth departed from zero with increasing V_Pressler, indicating increasingly negative residuals (stronger under-estimation) at larger Pressler volumes. Thus, the size-dependent bias is continuous rather than confined to arbitrary classes (Figure 4).

Standard diagnostics for the volume GAM (residuals vs. fitted values) formed a compact, symmetric cloud centered near zero with no systematic trend; however, the spread increased slightly at higher volumes, consistent with mild heteroscedasticity. The effect is modest and does not change the direction or magnitude of the bias pattern identified above. Standard diagnostics (k-index, gam.check) indicated adequate basis dimensions and well-behaved residuals.

3.3. Machine Learning Analysis

A Random-Forest (RF) regressor was re-trained on the updated data set using DBH and total height as predictors. The model attained an R² = 0.971, confirming that the ensemble captures almost all of the non-linear variation in felled-tree volume.

Feature-importance scores (Figure 5) show a strongly unbalanced contribution, accounting for 80.50% of predictor importance for DBH, while height contributes 19.50%. DBH therefore drives more than two-thirds of the model’s decisions, echoing the allometric principle that stem volume is governed chiefly by basal area, while height fine-tunes the estimate.

Regarding operational implications, precise DBH measurement proves paramount—errors in diameter propagate almost linearly into volume error, whereas moderate height mis-reads have a smaller impact. Height remains useful for distinguishing trees of identical DBH, but it plays a clearly secondary role.

4. Discussion

Using a 60-tree data set, Pressler’s standing estimates were −0.088 m³ lower on average than the Smalian-derived felled volumes (bias = −0.088 m³; RMSE = 0.204 m³; MAPE 22.12%). For the 53 sampled trees with actual volume <1.5 m³ and DBH range [11,50] cm, mean bias was -0.056 m³ and MAPE 21.22%. For the 1 sampled tree with actual volume [1.5,1.8) m³ and DBH 49 cm, mean bias was −0.741 m³ and MAPE 45.47%, while for the 6 trees with actual volume ≥1.8 m³ and DBH range [48,79] cm, mean bias was −0.259 m³ and MAPE 18.04%.

Pressler’s formula underestimates volume, because of:

• Form-height mismatch. Beech on humid montane sites shows butt swell and strong upper-stem taper; a single diameter at 0.5 × DBH height cannot represent that taper [36,37].
• Under-measured height. Haga readings were 1–3 m short in tall stems; because Pressler computes volume as basal area × form height, any height error is amplified.
• No butt-log correction. The formula ignores extra cubic volume in flared butt sections.

A penalised-spline GAM absorbed nearly all systematic curvature (adjusted R² = 0.967). The DBH spline is strongly curved—as expected when volume scales with DBH²—while height adds a weak linear tweak. Because our goal is bias calibration rather than full allometric inference, we restricted GAM smooths to low effective degrees of freedom and verified diagnostics. This parsimony makes the approach appropriate for n = 60 in a single-species, single-region context.

A Random-Forest achieved R² = 0.971; feature-importance scores assign 80.50% of predictive weight to DBH and 19.50% to height, echoing the GAM findings and long-held allometric theory.

Dividing felled volume by Pressler volume and grouping by DBH yields stable DBH correction factors (

Table 2. Suggested correction factors per DBH class.

DBH Class (cm)	Trees	$\mathbf{Mean} \frac{{\mathbf{V}}_{\mathbf{true}}}{{\mathbf{V}}_{\mathbf{Pressler}}}$	SD	Suggested Field Factor	Residual MAPE after Factor
<25	26	1.32	0.01	1.30	19.50%
[25,35)	16	1.21	0.25	1.20	16.57%
[35,45)	10	1.21	0.16	1.20	9.71%
[45,55)	7	1.28	0.32	1.30	20.27%
≥ 55*	1	0.93	-	≥1.35 (provisional)	-

^* Single observation; until more ≥ 55 cm stems are destructively sampled, apply at least 1.35.

):

• For the two well-populated mid-classes [25,35) and [35,45) cm, the multiplier is stable around 1.20, cutting the residual MAPE to < 10% in the [35,45) cm DBH class.
• Small stems (<25 cm) require a slightly higher factor (~1.30) but still retain ~20% error because tiny denominators amplify percentage noise.
• Large stems [45,55) average a multiplier of 1.28; rounding to 1.30 retains simplicity while reducing under-estimation to ~20%.
• The single ≥ 55 cm tree is not representative; field crews should apply ≥ 1.35 (in line with the [45,55) cm trend) until more data are available.

These factors reflect the bias structure; using them in the field preserves the speed of Pressler’s one-instrument method while keeping residual volume error within ±20% and below ±10% in the [35,45) cm DBH class.

Operational implications of this research can be described as follows:

• Inventory & valuation: In mature beech stands where many stems fall in the [45,55) cm DBH class, using raw Pressler volumes would undervalue merchantable yield by ≈ 20% (mean multiplier ≈ 1.28). Applying the class-specific factor 1.30 corrects this bias and protects stumpage pricing and allowable-cut calculations from systematic shortfalls.
• Carbon accounting: A negative bias concentrated in the larger-diameter classes propagates to landscape-scale biomass and carbon estimates, just as [38] reported for upper-stem errors in Norway spruce. Employing the DBH multipliers (1.20 for [25,45) cm; 1.30 for [45,55) cm; ≥1.35 provisionally for ≥ 55 cm) removes most of that downward drift.
• Routine cruising: In pole or sapling stands (<25 cm DBH) the raw Pressler method remains serviceable; the < 25 cm factor (1.30) lowers the residual MAPE to ≈ 19%, acceptable for reconnaissance surveys. For the mid-class [35,45) cm the 1.20 factor brings the error below 10%, matching cruising tolerances of FSC/PEFC [39,40]. Because DBH explains ~80% of Random-Forest predictive power, careful diameter tape or caliper work is more valuable than ultra-precise hypsometry once stems exceed sapling size.

Limitations of this research are noted regarding the only one tree exceeding 55 cm DBH; destructive sampling of additional big stems is needed for a firm ≥ 55 cm multiplier. Also, we should have in mind that calibration is site-specific (Central Rhodope beech). Applying these factors elsewhere will require a small local benchmark sample, as [41] advised. Our findings support the caution of [36] that single-section taper methods must be locally tuned. The DBH-stratified multipliers offered here retrofit Pressler’s 19th-century convenience to 21st-century accuracy, showing how destructive benchmarking, bias quantification, and class-wise correction can rehabilitate classical mensuration tools for modern management.

5. Conclusions

This study shows that Pressler’s single-point volume formula, while fast and inexpensive, produces a clear size-dependent under-estimation in European beech stands of the Central Rhodope Mountains. Class-wise correction factors of 1.30 for DBH < 25 cm, 1.20 for DBH [25,45) cm, 1.30 for DBH [45,55) cm and ≥ 1.35 for DBH ≥ 55 cm, keep residual volume error within ± 20% for every class and under ± 10% in the critical [35,45) cm DBH class, all while preserving the one-instrument speed of Pressler’s method. Applying these factors brings Pressler’s quick field estimate in line with modern accuracy requirements. The approach—destructive check, bias quantification, class-wise correction—preserves Pressler’s one-instrument efficiency while eliminating its systematic bias.

In sum, traditional mensuration tools can be modernized with modest, field-ready adjustments. By integrating Pressler’s simplicity with empirical, size-specific multipliers, practitioners obtain reliable, scalable, and context-sensitive volume estimates across heterogeneous F. sylvatica landscapes—demonstrating that 19th-century methods still have a place in 21st-century forest management when properly tuned.