4.1. Robust and Stochastic Approach Lead to Similar Results
As our approach includes deadwood targets in a risk-considering optimization tool on enterprise level, the tool decides about the types of assortments, stands, and the time horizon to achieve the desired deadwood targets. This enables the possibility to compare the effects of several optimised strategies. To model the deadwood amount, we use an exponential decay function. Another approach would be the use of linear decay models ([
31], for an overview cf. Mackensen and Bauhus [
22]). The ostensible advantage of linear models is that they seem to explain data from measurements of deadwood amounts in forests quite well. In contrast, exponential models lead to relative long decay times that seem not be confirmed by experimental data. However, experimental data often underestimate small scale fragments of deadwood as they are easily overseen on the forest floor making exponential models yet the better choice.
Furthermore, we used a stochastic as well as a robust optimization approach for the investigation. The results showed that the robust approach and the stochastic approach deliver similar results. As described in the method section the robust optimization skips the information of the functional distribution of the assumed uncertainties. Consequently, its advantage is that less data are needed to collect or assume, making it an easier method to apply in forestry where data collection is typically very time and money consuming. However, the results of
Table 6 show that the stability against random realizations of the unknown returns is raised by the robust solution. Comparing the values of the returns between the both optimization approaches shows that the robust means are generally below the stochastic means but closer to the individual baseline. Therefore, the robust system leads to more stable results over all deadwood scenarios.
The derived costs are given as annuity losses on the enterprise level. This implies that the results are valid for enterprises consisting of pure stands of the individual species. To relate them to a real enterprise, the figures have to be reduced by the actual proportion of beech or spruce stands. If there are different deadwood objectives planned for different stand classes, the costs have to be reduced to the area of that particular stand class (for example if one wants to achieve a deadwood target of 40
in beech stands older than 140 years only, cf. BaySF [
76]).
4.2. Some Results Are Comparable to Other Studies
The basic patterns of the results are reasonable. Higher costs with increasing deadwood amounts have been shown by other studies [
43]. The authors present costs as net present values of 301
for 5
of deadwood to around 2034
for 48
of deadwood. The equivalent annuities are 9
and 59
. While the costs at the low end correspond to our results, the higher costs differ ( 59
compared for example to 179
for 40
of spruce deadwood within 5 years in “Neureichenau”). This is caused by the different assumptions about the timber prices and the different growth conditions. While Santaniello et al. [
43] calculate with average prices of
for spruce, we assumed 83
for sawlogs of diameter class 20 cm to 24 cm and 50
for pulpwood. Furthermore, their study region is a low-productivity forest in Scandinavia while our results are derived from high-productivity forests in Central Europe. Additionally, our study integrates the dynamics of the deadwood decay as we derived costs for maintaining a certain amount of deadwood instead of providing it once in time.
Wikström and Eriksson [
38] calculated relative net present value losses of up to about 5%, 10% and 25% for deadwood amounts of 10
, 20
and 40
, respectively, in single stands that are mixed of birch and Norway spruce of low diameters at breast height (average between 8 cm and 11 cm). Their results are not comparable with ours as they defined these deadwood amounts as the total sum over a time horizon of 100 years. Furthermore, their model did not include any decay functions.
Tikkanen et al. [
41] derived net present values of 62
for providing spruce deadwood. Assuming a deadwood objective of 40
, this is equivalent to 90
. Their simulation is based on stands with an age from between 30 to 40 years, so the results are comparable to our deadwood target within 30 years. In that case, we derived comparable 86
in “Neureichenau” and 102
in “Eichelberg” for the total tree strategy.
Jonsson et al. [
40] present costs for different deadwood treatments in Sweden. They derived net present values of around 219
(2191 SEK ha
) for an increase of
of spruce deadwood assuming a retention area of 5% in stands in Southern Sweden. This is equivalent to about 8
and, therefore, comparable to our findings for the 5
scenarios in the large enterprise “Neureichenau”.
Jacobsen et al. [
42] derived a net present value reduction of up to 10% due to deadwood management in NATURA 2000 areas. Compared with our results for deadwood objectives in “Eichelberg” within 5 years, this is true for objectives up to 20
of spruce deadwood and up to 40
of beech deadwood.
Ekvall et al. [
44] derived an average net present value of 15
(146.80 SEK m
) for a mix of different deadwood strategies on enterprise level using a risk-free linear programming model. On average, their scenario adds 15
of deadwood. The calculated costs are equivalent to only
. This result can be explained by their approach of combining different deadwood strategies to achieve the additional deadwood amount, and by starting with an initial volume of 20
.
4.3. Other Results Reveal Additional Important Aspects of Deadwood Management
Another relation exists between sinking costs and longer time horizons. For example, a deadwood target of 20 within 5 years leads almost to the same costs as a target of 40 within 30 years. This effect is caused by the increasing flexibility to achieve the deadwood target within a longer time range and the discount effect. Reaching and maintaining a deadwood objective farer in the future affects the decision maker today much less than a short time goal. This result shows, that not only the actual deadwood amounts have to be chosen carefully, but also in which time period these targets must be reached. This aspect has yet rarely been investigated.
Increasing the rate of segregation leads to more cost-effective solutions, as the deadwood amounts can be selected more effective from stands of the most appropriate timber dimensions and age. The more integrative approaches imply an additional restriction, as they force to distribute the deadwood provision into stands less suitable for that purpose – in economic terms. Another aspect that has not been investigated so far.
Besides these general findings, the results show that they are influenced by the actual state of the forests in the given enterprise. One aspect is the relationship between the costs of using either beech or spruce. In the case of “Eichelberg” spruce is the cheaper solution, while in the case of “Neureichenau” the costs are equal or slightly lower for beech. An explanation is the age distribution of the stands. For “Eichelberg” the mean age of beech stands is 59 years in the first simulation period, with a range from 24 to 92 years. In the case of “Neureichenau” the mean age is at 79 years, with a range from 34 to 173 years. Therefore, “Neureichenau” starts with already more mature stands, implying the following aspects: The average overall volume of the beech stands is higher, as well as the mean volume of the trees. The older trees have bigger crowns and provide more crown material in total as well as per tree. Therefore, the costs of the crown material strategy will decrease, as bigger amounts can be provided by cutting down fewer trees which can be selected from a bigger population. Therefore, the cost advantage of using low-valued assortments joined to economically mature trees with valuable roundwood segments comes into effect without being foiled by the disadvantage of needing a lot of trees to provide the overall deadwood volume. This explains, why the crown material strategy shows reduced costs in the case of the older beech stands in “Neureichenau”, compared to the heavy timber strategy, and compared to the younger stands in “Eichelberg”.
In general, the results for the crown material strategies might be overestimated, due to the tree models available. As there is no model or sorting algorithm known to us, that simulate side branches with large diameters, that are common for older beech crowns, the overall amount of crown material in real forests may be higher than simulated. To compensate this effect to some extent, we increased the maximum diameter of logs for beech that are considered as being part of the crown (cf.
Section 1.2). Despite this adjustment, there may be situations in forest enterprises with mainly old growth beech stands, where crown material strategies will be the most economic choice.
The relation of the costs for the spruce strategies can be explained the same way. The mean age of the stands in “Eichelberg” is 74 years (ranging from 44 to 91 years) and 62 years for “Neureichenau” (ranging from 11 to 146 years). The bigger amount of non-mature spruce stands increases the costs of providing deadwood from these stands—especially for the higher deadwood targets—despite the large overall area of spruce stands (13,288 ha).
The pattern within the spruce strategies can be explained by timber prices and timber volumes. Using crown material has the advantage of being a cheap option. As these amounts may only be used as fuelwood, they cannot be sold for a high price. The disadvantage of this strategy is, that a single softwood tree does not provide a large volume of crown material, due to its natural habit. Therefore, the advantage of being a cheap option can be used only for low deadwood targets up to 5 . Higher volumes can only be reached for the sake of high costs that follow from cutting non-mature trees. The results show that in the case of “Eichelberg” the provision of heavy timber is cheaper than that of total trees for smaller targets up to 20 . This can be explained again with the structure of the timber prices and the age distribution of the spruce stands. The high amount of mature stands makes it cheaper to use some heavy timber trunks of bad quality for the provision of low deadwood amounts and selling the remaining better assortments of the tree than using the total tree for deadwood. This is a special case for “Eichelberg” and no general rule as this pattern cannot be seen in the case of “Neureichenau”.
In a similar way, the more diverse pattern of the beech strategies are explained. The higher timber volume of beech crowns provides the cost advantage of this option, as long as there are enough beech stands to use flexibly from. In that combination, this option can be more cost-effective than the heavy timber approach. For targets of 20 and 40 within 20 years or more, it is the cheapest method. This advantage cannot be realized, if there are not enough mature beech stands available, like in the case of “Eichelberg”, where only 48 of beech stands with an average age of 59 years exist.
The results for deadwood amounts of 5 with beech in “Neureichenau” show an anomaly, as the crown material strategies have the highest costs. This can be explained with the contradicting mechanisms mentioned above. In this case, the low overall deadwood volume can be reached by using total trees or heavy timber logs. Contrary to the other scenarios, the limitation of using only crown material is a more severe restriction than the heavy timber strategy. In the first simulation period, in which the deadwood target fully applies, are necessary to build up the deadwood from crown material, while the heavy timber strategy uses and the total tree option of beech stands. While the model accounts for the selling of the remaining assortments, almost doubling the size of the deadwood area causes heavy losses in selling non-mature timber.