Simple Height and Volume Equations for on-the-Fly Estimation of Productivity in Hybrid Poplar (Populus × euroamericana) Plantations in the Duero Basin (Northwestern Spain) ^†

Abstract

Hybrid poplar plantations are becoming increasingly important as a source of income for farmers in the Duero Basin (northwestern Spain), as rural depopulations and aging prevent farmers from planting other labor-intensive crops. However, forest owners, usually elderly and without formal forestry backgrounds, lack simple tools to estimate the size and volume of their plantations by themselves. Therefore, farmers are usually forced to rely on the estimates made by the timber companies that are buying their trees. With the objective of providing a simple but empowering tool for these forest owners, simple equations based only on the diameter to estimate individual tree height and volume were developed for the region. To do so, growth in height, diameter, and volume were measured for 10 years (2009–2019) in 404 trees planted in three poplar plantations in Leon province (northern Spain). An average growth per tree of 1.66 cm year⁻¹ in diameter, 1.52 m year⁻¹ in height, and 0.03 m³ year⁻¹ in volume was estimated, which translated into annual volume growth of 13.02 m³ ha⁻¹ year⁻¹. However, annual volume growth was different among plots due to their fertility, with two plots reaching maximum growth around 13 years of tree age and another at 15 years, encompassing the typical productivity range in plantations in this region. Such data allowed developing simple lineal, polynomic, and power equations to estimate height and volume explaining 76% to 97% of the observed variability. Such equations can be easily implemented in any cellphone with a calculator, allowing forest owners to accurately estimate their timber existences by using only a regular measuring tape to measure tree diameter.

1. Introduction

Poplar plantations, typically considered as short-term silviculture, are usually established in former agricultural lands or in fertile forestlands with little or non-degradation [1]. Such short-term plantations cover 7% of planted areas, but provide 50% of wood volume used in the industry.

In Spain, and particularly in the Duero and Ebro river basins, poplar plantations are under expansion, due to its rapid growth and timber quality [2]. In 2016, poplar stands in Spain accounted for 145,000 ha, being one-third natural stands and two-thirds plantations. Such plantations have been traditionally used for pulp, plywood or veneers. Socially, such plantations have an important function, as they provide additional income from low-productive croplands to farmers or urban owners not willing to work their farmlands. In addition, the current aging process in the rural countryside, particularly among farmers, makes poplar plantations increasingly popular as a production system that only requires a few labor days in a typical ~15-year rotation.

However, due to the lack of formal training in forestry, most owners do not know how much volume their plantations have, and when selling the timber to sawmills, they have to accept the price that are offered. Such lack of negotiation power reduces forests´ owners profits and creates an unbalanced market in which timber companies and sawmills impose their economic objectives over the plantation owners. A simple way to empower forest owners (mostly senior) is by providing simple, easy-to-use tools to assess standing timber volume on-the-fly. Simple volume equations, which can be implemented in a cellphone (ubiquitous nowadays even in rural areas), are suitable for the proposed end if they use, as inputs, a single, easy to measure variable, such as tree diameter, which can be estimated with a simple measuring tape.

Therefore, the objective of this research was to develop such simple volume equations for poplar plantations in northwestern Spain, one of the European regions with the highest production of poplar timber, but at the same time, one of the regions with the highest level of rural abandonment and an rural aging population.

2. Material and Methods

2.1. Trees and Management

Three research plots, located in the town of Villarejo de Órbigo (León province, northwest Spain) were used for this research. Placed in former agricultural lands, in a flat surface about 3 km from the Órbigo River, the plots were planted with 2-year old saplings of Populus × euroamericana (Dode) Guinier, clonal variety I-214. In March 2006, trees were planted in a 5 × 5 m spacing, with a total of 404 trees planted. Trees were tended as usual in the region (localized fertilization in plantation in year 2 combined with chemical herbicide and pesticide), followed by manual removal of weeds with scythe each summer, and irrigation in June and August each summer. Trees were pruned in plantations in years 3 and 5.

2.2. Measurements and Data Analysis

Diameters at breast height (1.30 m, DBH) were measured annually in August for each tree every year using a tree caliper and estimated as the average of two perpendicular measurements. Tree heights were measured for each tree annually in August using an ultrasonic hypsometer (Vertex IV, —Haglöf, Sweden), and estimated as the average of six measurements. Individual tree volume was estimated using the volume equation by [3].

Data were tested for normality with the Shapiro-Wilk and Kolmogorov–Smirnov tests. Homoscedasticity was tested with the Levene and Bartlett tests. As data passed both tests, regressions between tree height and DBH, and between DBH and tree volume were carried out using linear, polynomial, and power functions [4].

3. Results

Tree diameter at breast height (DBH) in 2019 (at plantation age 13 years) ranged from 12.8 to 39.1 cm, but most of trees were close to an average diameter of ~25 cm (

Table 1. Summary data for the measured trees in 2019 (n = 404, averages ± error standard).

Variable	Value
DBH (cm)	24.78 ± 0.605
Height (m)	21.67 ± 0.423
Slenderness index (m/m)	88.85 ± 1.45
Tree volume (m3)	0.458 ± 0.029
Basal area (m2 ha−1)	23.004 ± 0.855
Volume with bark (m3/ha)	233.840 ± 17.698

). Tree heights ranged from 11.93 to 37.17 m, with an average of ~22 m. Therefore, trees were quite slender, with slender indexes (height/diameter) close to 100. Tree volume was variable (ranging from 0.038 to 1.343 m³) with an average value close to 0.458 m³ (Table 1). For stand-level variables, basal area was approximately 23 m² ha⁻¹, whereas volume reached 233.840 m³ ha⁻¹ (Table 1).

An average growth per tree of 1.66 cm year⁻¹ in diameter, 1.52 m year⁻¹ in height, and 0.03 m³ year⁻¹ in volume was estimated, which translated into annual volume growth of 13.02 m³ ha⁻¹ year⁻¹. However, annual volume growth was different among plots due to their fertility, with two plots reaching maximum growth around 13 years of tree age and another at 15 years, encompassing the typical productivity range in plantations in this region. Such data allowed developing simple lineal, power, and polynomic equations (Equation (1)–(4)) to estimate height and volume, explaining 75% to 97% of the observed variability (Figure 1).

$$H\left(m\right)=2.1061\times D{\left(cm\right)}^{0.7356}{\mathrm{R}}^2=0.7575$$

(1)

$$H\left(m\right)=0.4433+1.1472 D\left(cm\right)+0.0102\times D^2\left(cm\right){\mathrm{R}}^2=0.760$$

(2)

$$\left(m^3\right)=0.000056\times D{\left(cm\right)}^{2.7473}{\mathrm{R}}^2=0.9709$$

(3)

$$V\left(m^3\right)=-0.0308-0.0088\times D\left(cm\right)+0.0011\times D^2\left(cm\right){\mathrm{R}}^2=0.9782$$

(4)

4. Discussion

Relationships among tree attributes are determined by tree architecture and growing conditions. As seen in this work, some poplar trees planted in the Duero Basic can reach commercial (harvesting) sizes (DBH > 30 cm) 13 years after planting, but with the recorded annual growth rates (1.66 to 2.39 cm⁻¹ year⁻¹), these stands may need 15.2–16.1 years to reach commercial size (DBH > 30 cm) on average. Long rotation times for a fast-growing species, such as hybrid poplar, are typical for this region, reaching an annual productivity considered as good [5]. However, the lengthy plantation time and dense plantation spacing can make trees quite susceptible to windthrow, as indicated by the slender index close to 100 [6]. Trees broken or fallen by wind are clear economic losses that may cancel the benefit of extending rotation times. Therefore, after passing 13–14 years since plantation, owners in this region must evaluate the potential benefit of letting trees grow another year (about 2.0 cm potential DBH increase) versus losses by wind.

To make such decisions, it is crucial for the forest owner to know how much the timber price stands at the time of harvest, but what is even more important is to know how much standing volume is present in the plantation. There are several volume equations for poplar plantations in Spain [7,8,9,10], but they all use two or more tree attributes (e.g., diameter and height). As tree height is difficult to be precisely measured without specific equipment (usually expensive, such hypsometers), two-variable equations, are out of reach in practical terms for forest owners (most of the seniors).

In contrast, the equations provided here show a very high predictive capacity (R² values in the 75–97% range), more than enough to provide volume estimations adequate to make such decisions. In addition, the equations provided here are simple enough that they can be written in any smart phone equipped with a calculator app. This allows the forest owner to measure the tree with a regular measuring tape, introduce the circumference in the calculator and just converting it into diameter and then into tree volume. Such simple calculations will provide a forest owner with the capacity to initiate negotiations with timber companies on the time and cost of plantation harvesting from a much stronger position than if the volume estimation is left in the hands of the same company that has to harvest the trees.