Volume 7
Issue 1
Forestry
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Available Online: http://www.ejpau.media.pl/volume7/issue1/forestry/art01.html
OPTIMALIZATION OF THE NUMBER AND SIZE OF SAMPLE PLOTS FOR ESTIMATION OF THE QUALITY STRUCTURE OF STANDING SPRUCE TIMBER
Anna Barszcz, Krzysztof Michalec
The present study concerns the determination of variability of spruce timber as a basis of optimalization of the number and size of sample plots. The plots might be used to estimate the quality structure of spruce timber for both scientific and practical purposes. Research was conducted at 6 onehectare sample plots, divided into subplots, in the province of the Beskid Żywiecki Mts. in the Carpathian Region. The features under analysis showed considerable variability, particularly in the case of the least numerous classes and groups of timber. The analysed dependencies were described by means of expotential equations.
Key words: Norway spruce, timber quality, variability coefficients, number and size of sample plots.
Standing timber assessment is the first task with regard to forest utilization which is performed in field. The data collected constitutes the basis for making plans of harvesting and transport costs, as well as preparing sale offers of timber at forest inspectorates. The results of the assessments are important for preparing the national balance of timber and constitute the basis for planning industrial production using timber. Since the traditional methods, especially the method of assessment of every single tree, carried out over the whole stand area, are very timeconsuming, there is a need for simpler solutions, which could be used as an alternative. Sample plots which could serve not only for current assessment but also for analysis of the quality and size of timber bases may turn out to be such a solution in large areas with the predominance of singlespecies forest stands with little diversification of age. Assessment of quality and value of the volume of standing timber is becoming a more and more significant issue in the market economy. The aim of the present research was to determine the optimum number of sample plots with regard to their size, as a basis for assessment of the quality structure of timber of the forest timber base. The scope of the present research was limited to mature spruce stands in the Beskid Żywiecki Mts.
In accordance with the nature and forest regionalization [8], the sample plots were located in the 4^{th} Province of the Beskid Żywiecki Mts, in the VIII Carpathian Natural Forest Region. The area is built of magura and submagura beds (sandstone, shale and marl). It constitutes the highest situated part of the Beskidy Mts, and is characterized by the socalled topographic adolescence (deep valleys and steep river gradient). The area under research includes the mountain group of the Babia Góra (1725 m above sea level), the highest in the Outer Western Carpathian Mts; with Wielka Racza Mt (1234 m above sea level) to the southwest and the group of Pilsko Mt (1557 m above sea level) in between. Forests take up about 64% of this area. They are characterized mainly by mountain broadleaved forest sites and mixed mountain broadleaved forest sites, with a small share of mixed mountain coniferous forest sites as well as mixed upland forest sites and upland forest sites.
The research here was carried out at six sample plots located in spruce stands, three of which were set up in Myślenice Forest Inspectorate (the Regional Directorate of State Forests in Cracow) and the remaining three in Jeleśnia Forest Inspectorate (the Regional Directorate of State Forests in Katowice). The characteristics of the sample plots, according to the data from forest management plans [4, 5], are provided in Table 1.
Table 1. Characteristics of sample plots 
Forest 
Altitude 
Exposure 
Age 
Site type 
Stand quality class 
Forest 
Stand 
Average breast height diameter 
Average height 
Technical quality 
Myślenice 
950 
W 
90 
LMG 
II 
1.1 
full 
33 
28 
1 
Myślenice 
10251050 
N 
100 
BMG 
II.5 
1.1 
full 
39 
27 
2 
Myślenice 
1075 
E 
90 
BMG 
II.5 
1.3 
full 
26 
25 
1 
Jeleśnia 
1150 
N 
110 
BMG 
II 
0.8 
intermittent 
36 
31 
2 
Jeleśnia 
950 
N 
110 
LMG 
I 
0.8 
intermittent 
43 
35 
2 
Jeleśnia 
1025 
SW 
115 
LMG 
II.5 
0.9 
moderate 
35 
29 
3 
Explanations: LMG mixed mountain forest BMG mixed mountain coniferous forest 
Preliminary choice of stands for the purpose of the present research was made on the basis of forest management plans [4, 5]. Mature spruce stands aged 90 or older were selected. The decisive factor was good technical quality of stands, stated in forest management plans, which suggested the occurrence of greater variety of classes and groups of size and quality of timber, including high quality timber. Next, three stands were chosen at random in each of the two Forest Inspectorates.
Sample plots with the area of 1ha and a square shape (100 x 100 m) were located in the places most representative for the conditions in the stands with relation to stand density index, timber quality and species composition. Each plot was then divided into 100 subplots, every of 0.01 ha which were numbered and marked in their corners in field. The numbers followed along isohypses; and each following group of ten located below the previous one began on the same side of the large, onehectare plot.
The following measurements and assessments were carried out, according to the rules of standing timber assessment [6, 1012]:
measurement of each tree of 7 or more cm thick in the breast height diameter;
measurement of the height of each tree;
assessment of standing timber in order to determine the class or group of the butt log according to size and quality.
The data was recorded according to the divisions into the small, oneare subplots.
For the purpose of the present research, the 0.01 ha plots, which are to be used in the future for other analyses of timber quality, were grouped by joining each consecutive five plots (i.e. plots from 1 to 5, from 6 to 10 etc.). As a result, each large, onehectare plot was divided into twenty 0.05 ha units.
The trunk of every tree noted in the newlyformed 0.05 ha units underwent a simulated division into classes and groups of quality and size, possible to be distinguished along the whole tree up to its top. The starting point of the bucking was the quality and size class of the timber in the butt log, assessed during field work. Radwańskis tables [7] were used for this purpose, which made it possible to determine the size and volume of each particular section of the stem in the course of bucking on standing trees.
In accordance with the Polish standards [6, 10], the following border values were adopted: for largesized wood: minimum 14 cm under bark in the upper end; for middlesized wood: from 14 cm under bark in the lower end to 5 cm under bark in the upper end. Large sizedwood and middlesized wood together constituted commercial boles. Largesized wood consisted of the following classes: WA0 and WB0, which comprised the best quality saw timber; WB1 matchwood and WC0 average quality saw timber. Middlesized wood comprised only group S2 pulpwood as well as a small amount of timber of group S1 mine timber and S4 fuel wood. The analysed material did not contain class WD low quality saw timber or S3 wood for making poles.
The received data was used to determine sums of volume of class and group according to quality and size as well as sums of commercial boles and of volume of whole trees within the 0.05 ha units. These units were then joined into larger ones, sized 0.10, 0.20, 0.30 and 0.50 ha. In the course of summing done within each onehectare plot, the rules employed were the same as with the joining of the 0.01 ha units, i.e. they were joined consecutively along isohypses.
For the following sums of volume: of whole trees, of commercial boles and of timber classes and groups, obtained from all of the 0.05 ha units in both Forest Inspectorates taken together, KołmogorowSmirnow test was carried out to check whether the distribution of the sums of volume remains in accordance with the normal distribution on the significance level p=0.05. Mean values and standard deviations of the analysed parameters of timber were used to calculate variability coefficients. For each series, the coefficients were the basis for the determination of the minimum number of sample plots sized, consecutively: 0.05, 0.10, 0.20, 0.30 and 0.50 ha, to be set up in field in order to determine the sum of volume of whole trees, sum of volume of commercial boles or sum of volume of timber classes and groups, taking into consideration the assumed error. The errors were assumed on the level of 3, 5 and 10%, i.e. they reflected the precision which is most often required in scientific research and in practice [1]. The analysis was based on the following equation [2]:
where:
n the minimum number of sample plots of a given size;
t the coefficient in the tables of normal distribution for the assumed confidence level of 0.95;
v variability coefficient (%) for the volume of the analyzed feature on sample plots of a given size;
p the assumed error.
The results of calculations were used to make tables and a series of graphs. The graphs allowed for the extension of the data received in the course of research. Additionally, they made it possible to find out, by way of extrapolation, the number of 1ha plots which should be set up in order to calculate the volume of whole trees or of timber classes and groups depending on the assumed error. The dependency between the size and number of plots was described by an expotential model with the function y = a × e ^{(b} × x), where y the number of sample plots with the assumed error; a and b coefficients describing the course of the curves; e the basis of the natural logarithm; x plot size. The model was adjusted on the basis of the determination coefficient R^{2}. In all stages of the analyses, timber of groups S1 and S4 was ignored due to its scarce occurrence. These groups were included in middlesized wood considered as a whole.
The next stage was to determine the parameters of a series of equations allowing for the determination of the necessary number of sample plots, depending on their size and the assumed error, and taking into account timber classes and groups. These dependencies were also described by the expotential model because it provided the most precise reflection of the analysed dependencies. In these equations: y symbolizes the number of plots; x the assumed error. In the case of the volume of a whole tree and the volume of commercial boles, the dependencies were additionally shown on graphs.
In the analysed spruce timber the variability coefficients of the sums of volume of whole trees, of commercial boles and particular classes and groups of quality and size are very varied (Table 2). The highest values occur in the following classes: WA0, WB0, WB1, in grup S2 and also at some points which result from joining classes or groups of timber. Small variability is shown by the volume of largesized timber treated jointly, by the volume of commercial boles and by the volume of a whole tree, while the values of these coefficients are close to each other. The conclusion is that an analysis of these features of spruce timber would require setting up only a small number of sample plots. In the area under present research, depending on the size of a plot, and assuming the 10% error (accepted in practice), the number of plots would range from three 1 ha plots to thirtytwo 0.05 ha plots. Variability coefficients decrease steadily as the size of plots increases. As an exception, class WB1 does not show this dependency; the coefficients are generally very high and range from 63.30% to 69.93%. The explanation might be a sporadic occurrence of timber of this class (special, high quality timber), noted only at certain sample plots, and a great range of sizes and volume of trees whose butt logs were classified as timber WB1. As a result, high values of coefficients and large variability of fractions of timber were obtained by joining classes WB0 and WB1. For 1 ha plots, where the data was obtained by extrapolation, for analyses of volume of whole trees, commercial boles and largesized timber it would be enough to set up, depending on the assumed error, only from 3 to 59 plots, though their number would increase considerably if timber classes and groups are considered. The greatest number of plots, as many as 2168, should be set up for the purposes of research on the volume of class WB1 with the error of 3%. The course of these dependencies is shown on the example of a whole tr ee and a commercial bole (Fig. 1 and 2). Determination coefficients for these curves ranged between 0.66 and 0.98.
Table 2. Minimum number of sample plots depending on their size and assumed error 


Explanations: Symbols of timber classes and groups according to the quality and size classification (6, 10, 11) *  values read from diagrams 
Fig. 1. Dependency between size and number of sample plots in analysis of volume of a whole tree 
Fig. 2. Dependency between size and number of sample plots in analysis of volume of commercial boles 
The next stage of research was drawing the curves which showed the dependency between the value of error from 1% to 10% and the number of sample plots (Fig. 3 and 4). The diagrams concern only the volume of a whole tree and of a commercial bole. For the remaining classes and groups of quality and size a table was created which contains parameters of equations describing the course of the curves (Table 3). Determination coefficients for this series of curves remained within the range of 0.55 to 0.81. Using the general formula provided in Methods as well as the parameters contained in the table, it is possible to calculate the number of plots depending on their size and on the error assumed to be any value within the range of 1 to 10%. The situation of the curves clearly depends on the size of a plot. The highest curve corresponds to 0.05 ha plots, while the lowest curve corresponds to 1 ha plots. The course of the curves shows tha t, up to the values of error amounting to 4 5%, the curves presenting the volume of a whole tree and the volume of a commercial bole go down rapidly, especially in the case of small plots. Further on the curves approach each other and, starting from the 7 8% error, are arranged almost parallel to the horizontal axis. This indicates the necessity of setting up a large number of sample plots for a high required precision of results. Their number increases dynamically with a decreasing size of plots.
Fig. 3. Number of sample plots depending on the assumed error for the calculation of the volume of a whole tree 
Fig. 4. Number of sample plots depending on the assumed error for the calculation of the volume of commercial boles 
Table 3. Parameters of expotential equations for particular classes and groups of timber depending on size of sample plots 
Timber class or group 
Parameter 
0.05 ha 
0.1 ha 
0.2 ha 
0.3 ha 
0.5 ha 
1 ha 
WA0 
a 
3903.134 
2361.764 
1665.105 
1298.435 
971.461 
536.46 
b 
0.335 
0.335 
0.335 
0.335 
0.335 
0.417 

WB0 
a 
4159.24 
3916.457 
3780.345 
3691.2 
3328.61 
2778.835 
b 
0.335 
0.335 
0.335 
0.335 
0.335 
0.332 

WB1 
a 
4319.39 
3852.1 
4634.326 
3947.61 
4574.383 
5056.16 
b 
0.335 
0.335 
0.335 
0.335 
0.335 
0.332 

WB0+WB1 
a 
4320.045 
3416.175 
2960.88 
2869.37 
2845.235 
2673.863 
b 
0.335 
0.335 
0.335 
0.335 
0.335 
0.365 

WC 
a 
1217.726 
835.372 
603.425 
466.17 
434.334 
284.574 
b 
0.335 
0.335 
0.337 
0.338 
0.333 
0.42 

W jointly 
a 
799.772 
539.236 
395.292 
315.138 
264.113 
174.977 
b 
0.335 
0.339 
0.342 
0.343 
0.332 
0.413 

S2 
a 
2046.347 
1555.94 
1340.007 
1190.92 
1192.56 
468.689 
b 
0.335 
0.334 
0.336 
0.335 
0.335 
0.172 

S jointly 
a 
1881.115 
1339.786 
1091.606 
997.618 
970.612 
302.738 
b 
0.335 
0.334 
0.335 
0.337 
0.335 
0.127 
Explanations: Symbols of timber classes and groups according to the quality and size classification [6, 10, 11] 
The problem of determination of an optimum amount of material necessary to determine quality features of timber was discussed previously in a large number of studies. The paper by Barszcz and Rutkowska [1], discussed only parameters of wood defects occurring on standing trees in mature spruce stands of the Beskidy Mts. The variability of these features and the assumed level of error allowed for the determination of the minimum number of trees to be considered in order to characterize their timber with relation to defects occurring in it. The values of variability coefficients of timber defects were very varied in the research mentioned above. They often exceeded the level of 100%. Depending on the assumed error (3 or 5%) and the kind of defect, the minimum number of model trees required to analyse timber defects ranged from 17 to 938.
Research on the optimalization of the number and size of sample plots in spruce stands, which was similar to the present research, was carried out by Leśniak [3]. Its scope was, however, much smaller (one sample plot of 1ha) so the computed coefficients of variability of volume of timber classes and groups were, as a result, much lower. Moreover, in Leśniaks research, the variability of class WA0 was higher in comparison with WB0 and WB1 as opposed to the present study.
Unique research, due to special features of the area, was conducted by Zygmunt [12] in the Olkusz Industrial District. Assuming a constant size of sample plots (0.05 ha), which were also used for the purposes of inventory of stand, he only optimalized their number. His analysis concerned volume of trees and value of timber, based on the classification of quality and size. Calculations allowed for correction of the assumed variability coefficients as well as for determination, depending on the required precision of results, of the number of sample plots necessary for analysis of volume and value of timber in industrial districts. It is worth emphasizing here that the coefficient of variability of volume of whole trees calculated by Zygmunt for mature stands of Olkusz Industrial District amounted to 33%, which was very close to the value obtained in the present research (28.57% for a 0.05 ha sample plot).
Due to a large and usually unknown variability of quality of timber, any research carried out with the use of sample plots requires the determination of their optimum size and number, necessary to obtain results on the required level of precision.
An analysis of variability coefficients of timber quality conducted in the mature spruce stands of the Beskid Żywiecki Mts showed that the minimum number of sample plots clearly increases with the increasing required precision of calculations. This tendency is present in most classes or groups distinguished according to quality and size of timber, independently of the size of sample plots. As an exception, this dependency was not confirmed for the timber of class WB1.
The largest number of sample plots was calculated for high quality timber of class WB1, which may be explained by a sporadic occurrence and a wide range of sizes of the trees belonging to this class in the stands under research. The smallest number of sample plots (3 every time) can be assumed, with the error of 10% and plot size of 1 ha, for an analysis of volume of: largesized wood of all quality classes jointly, commercial boles and a whole tree.
Dependencies between the size and the required number of sample plots were described (assuming the error of 3, 5 and 10%) by equations of regression, assuming the expotential model as the best adjusted one. The expotential model was also used to construct equations which allowed for the calculation of the minimum number of sample plots (sized from 0.05 to 1 ha), depending on the assumed error. The course of these curves indicates a dynamically increasing number of plots, especially the small ones, when the error was lower than 45%.
Due to the lack of more precise data concerning the variability of quality of Norway spruce timber, the obtained results may be used as approximations in research on the quality of this species in its southern natural range in Poland. The results may also constitute the basis for similar approximations in preliminary stages of research on the quality and size structure of this timber in other parts of the country, including the northern range of spruce.
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Zygmunt R. 2003. Ocena zmian wielkości zasobów drzewnych oraz próba ich wartościowania w lasach Olkuskiego Okręgu Przemysłowego. [Estimation of changes in the size of timber resources and an attempt at its valuation in the forests of Olkusz Industrial Region. Praca dokt. Akad. Roln. H. Kołłątaja w Krakowie [in Polish].
Anna Barszcz, Krzysztof Michalec
Department of Forest and Wood Utilization
Agricultural University of Cracow
Al. 29 Listopada 46, 31425 Cracow, Poland
phone: (012) 662 50 96
email: rlbarszc@cyfkr.edu.pl,
kmichalec@op.pl
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