Comparative Analysis on Cutting Possibilities Derived from Different Allowable Cut Indicators in Slovakia

This paper examines the issue of forecasting growing stock development and cutting possibilities based on the actual regeneration period of individual forest stands. These cutting possibilities represent a harvest level that is sustainable in light of forest stand regeneration. A survey was conducted using two groups of forest stands taken from the Forest Management Plan database at the Training Forest Enterprise of the Technical University in Zvolen, Slovakia. We compare the growing stock and harvest levels estimated by considering the actural regeneration period with those estimated by the following indicators of allowable cut: analytical cutting percentage, empirical cutting percentage, 1/20 of standing volume of forest stands in the two oldest age-classes and older, and 1/30 of standing volume of forest stands in the three oldest age-classes and older. The results indicated that cutting possibilities estimated by considering the actual regeneration period can be used as the judging criterion for selecting the most suitable allowable indicator to the target forest management unit. For our experiments, the empirical cutting percentage outperformed the other indicators on the basis of suitability of the derived cutting possibilities.


Introduction
The prediction of growing stock development, age structure, and cutting possibilities is an important component of selecting allowable cut indicators for a particular forest management unit (FMU). The previous method for predicting growing stock development was based on the expected allowable cut without considering some important silvicultural elements, which could influence forest harvest in Slovakia. Many researchers have tackled on developing a solution to these problems, and have proposed a new methodology for calculating the expected growing stock (see Greguš, 1989;Marušák, 1998;Marušák, 1999;Burgan, 2002). The current method uses model increments represented by the expected growing stock coefficients to predict timber volume according to age-classes for individual tree species.
In today's practical forest management planning, forecasting growing stock development is indispensable for selecting allowable cut (harvesting) indicators.
The current Slovak forestry Act number 453/2006 Coll., related to forest management and forest protection, stipulates that only one of five possible allowable cut indicators can be applied, so that the selection method for the indicators needs to be as objective as possible. The current allowable cut indicators are: (i) analytical cutting percentage, (ii) empirical cutting percentage, (iii) final mean increment, (iv) 1/20 of timber volume of forest stands in the two oldest age-classes and older, and (v) 1/30 of timber volume of forest stands in the three oldest age-classes and older.
Prediction of growing stock development and harvest levels determined by allowable cut indicators plays an important role in selecting the most suitable indicator. From the practical viewpoint, such an allowable cut indicator that ensures cutting sustainability and evenness should be selected and used. That is, the selected indicator should consider the age and growing stock structures in order to maintain equitable harvest levels over the longest possible period. Practically, when applying the indicator, the expected timber volume development needs to be favoured. The initial growing stock markedly affects the harvest level, and the harvest level conversely affects the expected growing stock. These two variables cannot be separated, as those expressly depend upon each other. It is commonly noticed that the analytical cutting percentage and the empirical cutting percentage are the most suitable for the calculation of the expected timber volume because they provide the expected harvest level in each age-class separately. Other allowable cut indicators determine the cutting amount as a whole.
The calculation of the expected timber volumes and harvest levels in Slovakia has historically been associated with the analytical cutting percentage. The analytical cutting percentage, however, assumes 100% cut in the oldest age-classes whose trees are generally older than the rotation period plus half the regeneration period, which violates the regeneration rules. Meeting this analytical cutting percentage is problematic because these age-classes also include forest stands that cannot be regenerated in the first decennium because of the silvicultural requirements. In other words, the regeneration of these forest stands would require two or more decennia in order to satisfy such silvicultural requirements as the regeneration element width and area cut in the applied silvicultural system and harvesting criteria.
In the renewal process of the forest management plan, the remaining regeneration period (RRP) for each forest stand is determined by the number of years required for regeneration on the basis of the harvesting regime. Based on the regeneration rules, regeneration has to be completed by the year of the rotation period plus half of the regeneration period. In theoretical terms, with a rotation period (RP) of 110 years and a regeneration period (ReP) of 30 years, given 10 years for one age-class, regeneration has to be completed within the age range from 95 to 125 years. Thus, regeneration starts for forest stands with age 95 years in age-class 10. Since forest stands in age-class 10 are from 91 to 100 years old, they should have RRP of 25-30 years, while forest stands in age-class 11 should have RRP of 15-20, in age-class 12 they should have RRP of 5-10 years, and those in age-class 13 have RRP less than 5 years. There should not be any forest stands in higher ageclasses (14 and higher in this example). In reality, however there are still some forest stands remained with RRP over 5-10 years, even in these higher age-classes.
Given the mean regeneration period, it is possible to determine cutting possibilities in each age-class. This information can also be used to select an appropriate allowable cut indicator by comparing the derived cutting possibilities with the planned cutting amount estimated by the selected allowable cut indicator. It is subsequently possible to decide if the selected allowable cut indicator is feasible for FMU.
When the cutting possibilities for FMU become greater than the planned harvesting level, the harvesting requirement is fulfilled. If there is a large surplus for the cutting possibilities, the regeneration period must be extended. In the opposite case, when the planned harvesting level is greater than the cutting possibilities, the mean regeneration period must be shortened. Otherwise, this could result in violation of the area cut limits requried by the silvicultural system.
The objective of this work is two-fold; (1) to estimate cutting possibilities based on the regeneration period established by the actural requiremens from the forest stand management and (2) to compare the derived cutting possibilities with the harvest level derived by allowable cut indicators in order to judge which allowable cut indicator is the most realistic and suitable.

Materials and Methods
The development of cutting possibilities using the remaining regeneration period was assessed in two groups of forest stands, created from the original primary management group of stands at the Training Forest Enterprise of the Technical University in Zvolen, Slovakia. The first group represents state-owned forest stands (3,252.82 ha) and the second group consists of forest stands owned by multiple nonstate owners (919.16 ha). In both cases, the mean rotation period and the regeneration period are 110 and 30 years, respectively. Hereafter, these stands are designated by FMU1 and FMU2, respectively. Databases of two groups were retrieved from the original forest management plan database prepared for the period 1993-2002.
The calculation of cutting possibilities was conducted with the mean value of the remaining regeneration period calculated for individual forest stands, as specified by the forest management plan (FMP) on the basis of the established regeneration procedures.
To estimate possible harvest levels easier, let the remaining regeneration period (o) be expressed in tens of years. By using the mean remaining regeneration period, o ti , for age-class i in period t, the corresponding harvest level, T ti , is calculated by, where V ti is the timber volume from age-class i in period t. The mean remaining regeneration period in equation [1] is the weighted average of RRP, where the target harvesting area is used as weighting.
The mean remaining regeneration period for the second decennium, ( 2i o ), is calculated in a similar manner. Only forest stands with the remaining regeneration period greater than 10 years at the beginning of the first planning period are included in the calculation. For the third decennium, the mean, ( 3i o ), is calculated using forest stands with the remaining regeneration period greater than 20 years. The mean regeneration period for each planning period is calculated by, where ti p is the cutting possibility in period t of age-class i with considering the regeneration period. In forecasting, it was assumed that age-classes for regeneration in the second or third decennium would be subject to cutting 1/3 (33%) of the timber volume in each decennium. Such an age-class in our case was currently age-class 9 in the second and third decennium, where 2,9 o = 3 ( 2,9 p = 33), 3,9 o = 3 ( 3,9 p = 33), and age-class 8 in the third decennium, where 3, The expected timber volume was calculated through predicting the growing stock of individual tree species with the corresponding increment percentage (Marušák 1999(Marušák , 2001. The harvest levels by other allowable cut indicators were also predicted. The estimated cutting possibilities from allowable cut indicators were: (1) analytical cutting percentage (denoted by CP), (2) empirical cutting percentage (denoted by ECP), (3) 1/20 of the growing stock of forest stands in the two oldest age-classes and older (denoted by 1/20), and (4) 1/30 of growing stock forest stands in the three oldest age-classes and older (denoted by1/30). Note that prediction by these indicators did not consider incidental harvesting due to difficulty of objectively determining it within FMU. Table 1 shows the number and area of forest stands with respect to RRP and age-class in FMU1. The total of 88 stands was considered as mature (older than age-class 10), and it covered 522.50 ha. Only 18 forest stands out of them covered 173.31 ha (33%) (expressed by bold in the table), and they could be regenerated in time with the stated rotation period (RP) and the regeneration period (ReP). RRP in age-class 12 has to be 10 years, while it should be no more than 20 years in age class 11, and 30 years in age-class 10. They were in the first mature age-class.

Assessing the share of regeneration periods in mature age-classes
Regeneration could be completed earlier in 11 stands (41.54 ha (8%)), and the remaining 59 stands (307.65 ha (59%)) needed more time to regenerate than required.
FMU2 was also dominated by forest stands with a long RRP (

Development of cutting possibilities
The mean remaining regeneration period was calculated for the nearest three decennia ( 1 2 3 , ,  Table 3 along with analytical cutting percentage (denoted by CP) for the comparison purpose. From the results in Table 3, it is noted that with respect to the mean remaining regeneration periods, the planned cutting measures were only associated with the balanced withdrawal of growing stock in the current age-class 10. On the contrary, over-mature age-classes 14 and 15+, and age-class 13 that represented the last mature age-class, required more than one decennium for additional harvesting. In age-class 13, it was possible to harvest only 45 % in the first decennium because the age-class contained 17 stands with the remaining regeneration period over 10 years (Table 1). The mean remaining regeneration period of these stands was 2.2 decennia in the first planning period, and it would be   Table 4. As in FMU1, ageclass 10 in Table 4 was the most favourable for the even-withdrawal of timber volume. Forest stands in age-class 12 at the beginning of the first decennium required two decennia to regenerate, and stands in age-classes 13 and 14 would regenerate in three decennia. Unlike FMU1, forest stands in age-class 15+ would be harvested in the first decennium. The amount of the possible cutting (PC) was used as the basis for realistic suitability of the indicators. It was calculated in each age-class with the corresponding mean regeneration period, which represented the cutting possibilities of forest stands with respect to the determined regeneration procedure. The results are shown in Table 5. In the first period, the cutting possibilities by PC in FMU1 amounted to the total amount of 126,843 m³, the lowest value calculated for any of the allowable cut indicators. In the event that harvest levels for FMU1 were determined by one of these allowable cut indicators, the prescribed cut would exceed the capacity of individual stands. Assuming that the cutting possibilities need to meet certain regeneration procedures, increasing the harvest level would become only possible by violating the area cut limits requried by the silvicultural system. Therefore, the analytical cutting percentage (CP) with a value of 179,153 m³ became unrealistic for FMU1. This was also observed for the results in Table 6, which showed the values through PC and CP in each age-class. It showed that the cutting possibilities by PC were much lower than those by CP in most age-classes. A similar result can be seen in the allowable cut indicator of (1/20). The empirical cutting percentage (ECP) with a value of 131,576 m³ was lower by 3.7% from those of PC. With comparison of PC with each allowable cut indicator in the second and third decennium, we can conclude that ECP was the best allowable cut indicator for FMU1 because it best mimiced the cutting possibilities of the forest stands derived by PC. The next appropriate indicator is (1/30).  In FMU2, CP became inconvenient because its value for the first decennium was 81,109 m³ (Table 5), 50% more than that determined by PC (54,100 m³). This trend can also be seen in CP by most age-classes in Table 7. The 1/20 allowable cut indicator exceeded PC in the first decennium by 5% and its value in the following two periods was lower than those of PC. Allowable cut indicators ECP and 1/30 exhibited lower values than PC in all three periods, implying that they can be achieved and are suitable for FMU2.

Development of expected timber volume
The planned harvest levels affect the predicted timber volume. Using CP and 1/20 allowable cut indicators in FMU1, the timber volume expected in the following decennia became 5% lower than that predicted by PC on average using high values for these indicators (Figure 1). Conversely, the expected timber volume development using the ECP and 1/30 allowable cut indicators was very similar to that predicted by PC, implying that these allowable cut indicators would be suitable for FMU1.
In FMU2, with cutting possibilities by PC higher than some allowable cut indicators, the highest increase in the timber volume was predicted through ECP and 1/30 indicators (Figure 2). The highest values were achieved by the 1/30 indicator with the expected timber volume higher at the end of the predicted period (at the beginning of the fourth decennium) than that calculated by PC. The difference was 8% using ECP.