J. For. Res. DOI 10.1007/s11676-017-0397-4
ORIGINAL PAPER
Optimal management of Korean pine plantations in multifunctional forestry Xingji Jin1 • Timo Pukkala2 • Fengri Li1 • Lihu Dong1
Received: 15 October 2016 / Accepted: 15 November 2016 Northeast Forestry University and Springer-Verlag Berlin Heidelberg 2017
Abstract Korean pine is one of the most important plantation species in northeast China. Besides timber, it produces edible nuts and plantations sequester carbon dioxide from the atmosphere. This study optimized the management of Korean pine plantations for timber production, seed production, carbon sequestration and for the joint production of multiple benefits. As the first step, models were developed for stand dynamics and seed production. These models were used in a simulation–optimization system to find optimal timing and type of thinning treatments and optimal rotation lengths. It was found that three thinnings during the rotation period were optimal. When the amount or profitability of timber production is maximized, suitable rotation lengths are 65–70 years and wood production is 5.5–6.0 m3 ha-1 a-1. The optimal thinning regime is thinning from above. In seed production, optimal rotation lengths are over 100 years. When carbon sequestration in living biomass is maximized, stands should not be clear-cut until trees start to die due to senescence. In the Project funding: This research was financially supported by the National Natural Science Foundation of China (31600511), and the Fundamental Research Funds for the Central Universities of the People’s Republic of China (2572017CA04). The online version is available at http://www.springerlink.com Corresponding editor: Hu Yanbo. & Fengri Li
[email protected] 1
Department of Forest Management, School of Forestry, Northeast Forestry University, Harbin 150040, Heilongjiang, People’s Republic of China
2
University of Eastern Finland, P.O. Box 111, 80101 Joensuu, Finland
joint production of multiple benefits, the optimal rotation length is 86 years if all benefits (wood, economic profits, seed, carbon sequestration) are equally important. In this management schedule, mean annual wood production is 5.5 m2 ha-1 and mean annual seed yield 141 kg ha-1. It was concluded that it is better to produce timber and seeds in the same stands rather than assign stands to either timber production or seed production. Keywords Carbon sequestration Edible seeds Multiobjective optimization Pine nuts Pinus koraiensis
Introduction Korean pine (Pinus koraiensis Siebold and Zucc.) is one of the most important conifers in northeast China and native to eastern Asia. The species also occurs in natural forests where it can reach 50 m in height and more than 1 m trunk diameter (Zheng and Fu 1978). Korean pine timber is soft, straight-grained and easy to work with in sawmills and carpentry (Zheng and Fu 1978). It is used for many purposes, for sawn wood, veneer, plywood, particleboard, telecommunication poles, and in the pulp and paper industry. Its resin can be used to produce turpentine and other products (Li and Lo¨fgren 2000; Rang et al. 2012). In China, Korean pine forests have been over-exploited because of their edible nuts and high quality timber (Meng et al. 2008). Degradation of natural stands has been partially addressed by establishing plantations. In the Heilongjiang province of China, the plantation area of Korean pine is around 172,400 hectares, which is 63.3% of the total area of Korean pine plantations in Northeast China (State Forestry Administration 2014). Korean pine has been planted for timber production but also for its nutrient-rich
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seeds, which are harvested and sold as ‘‘pine nuts’’. The pine nut oil contains up to 20% of pinolenic acid which is believed to have positive health effects, including the suppression of hunger and helping with weight loss (Zheng and Fu 1978). Korean pine plantations—as all tree plantations—sequester CO2 from the atmosphere and mitigate the effects of climate change. Increasing the carbon sequestration of forests is a part of the current forest policy of China (National Development and Reform Commission (NDRC) 2007). The origins of most Korean pine plantations in Heilongjiang province may be traced back to the Great Reforestation Project by the State Forestry Administration of China which took place mainly in the 1960s. Therefore, the age of most planted stands range from 40 to 55 years, which is less than the currently recommended 80-year rotation age for Korean pine. The management of stands in Heilongjiang is based on experience and silvicultural research (State Forestry Administration 2011). Some plantations are designated for seed production while others are for maximum timber production. However, separate stands for different products may not be the optimal way to maximize outputs; it may be more efficient to optimize the joint production of timber and pine nuts in the same stands (Pasalodos-Tato et al. 2016). According to the eighth forest resource survey report (State Forestry Administration 2014), the quality of many Korean pine plantations is poor, and with a mean volume of 85.6 m3 ha-1. Productivity is low as the mean annual volume increment is less than 2 m3 ha-1. The current unsatisfactory condition in many plantations is partly because of insufficient knowledge of their optimal management. Most previous studies have focused on growth and yield models (Wang et al. 2006; Owari et al. 2015), on biomass or carbon (Li et al. 2011; Dong et al. 2014), or on the effects of various forest operations and silvicultural activities on the structure and functions of these ecosystems (Zhao et al. 2013, 2014; Hao et al. 2006). There is relatively little science-based information on optimal rotation lengths and optimal thinning regimes of and even less information on the influence of nontimber objectives on optimal management. In the case of Korean pine, it is also necessary to know the trade-offs between different management objectives, especially between timber production, seed yields and carbon sequestration. The objective of this study was to find the optimal management system for Korean pine plantations in Heilongjiang province for timber production and in multifunctional forestry. Before determining the optimizations, the required models for optimization were developed.
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Materials and methods Modelling stand dynamics The first part of the study consisted of fitting models for simulating the stand dynamics of Korean pine. The simulation tool was similar as used in Jin et al. (2016). It uses individual tree models for diameter increment, height and survival (Jin et al. 2016). In addition, a model for site index was required. A taper model was developed for partitioning harvested trees into different timber assortments. In addition, biomass models for different components were required for calculating dry biomass which was then converted into carbon stock, assuming that approximately 50% of dry mass is carbon. Site index modelling was based on the guide curve approach as repeated height measurements from the same plots were not available (Clutter et al. 1983). The guide curve gives the average temporal height development of the plantations which reflects average site fertility. Multiplying the guide curve by constants different from one gives the heights for other site classes. The data for guide curve modelling were collected in 57 temporary sample plots. Additional diameter-height data from tree analyses were used to confirm that the fitted guide curve model was logical. This checking was done because the modelling dataset did not include very young stands. Mean tree height was used in the model instead of the more common dominant height because dominant height data were not available; mean height at index age is commonly used in China to describe site productivity (see e.g. Lou et al. 2016; Jin et al. 2016). Another dataset was used to model the relationship between dbh and individual tree height. This dataset consisted of 2898 diameter and height measurements from 330 plots. The selected height curve model was proposed by Na¨slund (1937) which, according to Mehta¨talo et al. (2015), is quite often the best model amongst the formulas in the literature. The model is as follows: h ¼ 1:3 þ
d2
ð1Þ
ða þ b d Þ2
where h is height (m), d is dbh (cm), and a and b are parameters. To describe the change of the height curve along with stand development, parameters a and b were made dependent of the mean height of the stand (H): h ¼ 1:3 þ
d2 ða1 þ a2 ln H þ ðb1 þ b2 ln HÞ dÞ2
ð2Þ
Data for diameter increment and survival modelling came from 229 inventory plots; the number of observations was 3162 for 5-year-diameter increment modelling and 3
Optimal management of Korean pine plantations in multifunctional forestry
301 for 5-year survival modelling. Variables describing site productivity (site index), tree size (dbh) and competition (stand basal area, basal area in larger trees) were used as predictors. Since the plantations were relatively young, it was not possible to model the influence of senescence on mortality. Therefore, an expert model, based on the literature (Omelko et al. 2016) and the professional experience of the authors was used for predicting the effect of age on tree survival. This model has no effect on the economic optimization of timber production but it does prevent the selection of illogically long rotation lengths, for example, when the size of the carbon stock is maximized. The number of stem diameters for taper modelling was 816, measured from 48 trees. The model proposed by Kozak (2004) was selected based on the literature (Kozak 2004; Heiðarsson and Pukkala 2011; de Miguel et al. 2012) and preliminary analyses. The allometric model was used to describe the dependence of biomass on dbh and tree height. Measurements from 60 trees were available for modelling. To allow for the optimization of multifunctional management (the production of both timber and seeds), a model was developed to predict annual seed yields. Because the empirical data on seed yields represented a very narrow age range, the model was adjusted based on expert knowledge, letting the data determine the average level of yield. Expert knowledge was used also to determine the influence of mean tree size and stand density on seed yields.
timber assortments and their minimum dimensions are shown in Table 1. Optimization Management was optimized by determining the most effective combination of thinning years, thinning intensities and rotation lengths, separately for different numbers of thinning treatments. The number of thinnings was increased until the increase no longer improved the objective function value. Thinning intensities and types were defined using the following thinning intensity curve (Pukkala et al. 2014; Pukkala 2015): pðdÞ ¼
•
For each thinning: •
Economic parameters •
Table 1 Minimum dimensions of timber assortments and their stumpage prices
Assortment
ð3Þ
where p(d) is the proportion of harvested trees when dbh is d cm, and a1 and a2 are parameters to be optimized. Parameter a2 gives the diameter at which thinning intensity is 0.5, and a1 defines the type of thinning. A negative value of a1 results in thinning from below and a positive value in thinning from above. When a1 is equal to 0, thinning is uniform (thinning intensity is the same in all diameter classes). The optimized variables were:
• •
Even-aged management was optimized in this study. Simulations were started from a 20-year-old initial stand with mean diameter of 9 cm and stand density equal to 2000 trees per hectare. When calculating the net present value (NPV), all costs and revenues were discounted to the beginning of the rotation. The NPV was calculated to infinity by assuming an infinite sequence of equal rotations. The following stand establishment costs were based on interviews of local forest managers: site preparation 2000 RMB/ha and planting 5000 RMB/ha in year 0, and a tending treatment 1500 RMB/ha in year 10. Incomes from timber sales were calculated using stumpage prices. The
1 1 þ expða1 ða2 dÞÞ
Number of years since planting (1st thinning) or previous thinning (other thinnings) Parameter a1 of the thinning intensity curve Parameter a2 of the thinning intensity curve
For the final harvest: •
Number of years since the last thinning
As a result, the number of optimized variables was NThin 9 3?1 where NThin is the number of thinnings. The objective function was a utility function: U ¼ w1 ðNPV=NPVmax Þ þ w2 ðWP=WPmax Þ þ w3 ðC=Cmax Þ þ w4 ðS=Smax Þ
ð4Þ
where wi is the weight of the objective variable i, NPV, WP, C and S are, respectively, net present value, mean annual harvest, mean carbon stock and mean annual seed yield of the treatment schedule. All weights (wi) were 0.25.
Minimum top diameter (cm)
Minimum log length (m)
Stumpage price (RMB/m3)
Medium log
18
4
950
Small log
12
4
800
Pole
6
4
650
Firewood
1
0.5
200
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NPVmax gives the net present value when NPV is maximized as the only objective. WPmax, Cmax and Smax were calculated similarly by maximizing WP, C or S as the only objective. Therefore, all objective variables were divided by their highest possible value, which removed the effect of different units. The direct search method of Hooke and Jeeves (1961) was used to perform the optimizations.
Results Models for stand dynamics The following model proposed by Rickhards (1959) describes the relationship between stand age and mean tree height on average sites (Fig. 1): Hguide ¼ 17:997 ð1 expð0:052TÞ2:025
ð5Þ
where Hguide is the mean height (m) and T stand age (years). The R2 of the model was 0.857 and the RMSE (square root of the mean of squared errors) 2.67 m. The index age was selected as 40 years and hence site index (SI) was defined as the mean tree height at 40 years. The SI of a plot with known mean height (H) and stand age (T) is: SI ¼
HðTÞ Hguide ð40Þ Hguide ðTÞ
ð6Þ
After knowing the site index, mean height at age T is obtained from HðTÞ ¼
SI Hguide ðTÞ Hguide ð40Þ
ð7Þ
The model for tree height is as follows:
25
þ
d2 ð1:039 0:205 ln H þ ð0:598 0:130 ln HÞ d Þ2 ð8Þ
where H is the mean height of the stand (R2 0.751, RMSE 1.61 m). Figure 2 shows that the height curve climbs as the stand ages and its mean height increases. An individual at a certain dbh is therefore taller in older stands than in younger ones. The model for diameter increment was: d22 d12 ¼ y ¼ expð2:051 þ 1:27 lnðd1 Þ 0:018d1 0:041G 0:080BAL= lnðd1 þ 0:01Þ ð9Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi id ¼ ðy þ d12 Þd1
ð10Þ
where d1 is dbh at the first measurement (cm), d2 is dbh 5 years later (cm), G is stand basal area (m2 ha-1), BAL is basal area of trees larger than the one for which growth is predicted (m2 ha-1) and id is the 5-year diameter increment. The R2 of Eq. (9), calculated for d22-d21, was 0.441 and the mean of squared errors (MSE) was 0.474, corresponding to RMSE of 0.688. The rate of diameter increment is greatest with trees at 15–25 cm diameters (Fig. 3). When competition (BAL) increases, diameter increments decrease. Site index was not a significant predictor of diameter increment, most probably because of insufficient variations in site productivity in the modelling data. Therefore, the diameter increment model should be used only for stands that represent average or typical growing sites for Korean pine. The logistic model used to describe the influence of tree size and competition on survival is:
Data Guide curve (SI = 13.7 m) Analytic trees SI = 18 m SI = 10 m
20
30
15
25 10
Height, m
Mean height, m
h ¼ 1:3
5
0
0
10
20
30
40
50
60
Stand age, years Fig. 1 Data points (large open circles) used in guide curve modelling (thick line). The small dots are age-height observations from tree analyses. They were used to confirm that the relationship shown by the guide curve is logical for young stand ages. The thinner lines show the mean height development for site indices 10 and 18 m
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20 15 10 5 0
0
10
20
30
40
Hmean=20
Hmean=25
Dbh, cm Hmean = 10
Hmean= 15
Fig. 2 Height curves for different mean tree heights (Hmean) according to the individual-tree height model
Optimal management of Korean pine plantations in multifunctional forestry
G = 25 m2/ha
Survival probability
Diameter increment, cm
G = 25 m2/ha 2.5 2 1.5 1 0.5 0
1 0.95 0.9 0.85 0.8 0
0
5
10
15
20
25
BAL=10
BAL=1
BAL=15
3 2 1 0
5
10
15
BAL=5
BAL=10
20
25
BAL=10
BAL=15
BAL=20
0.96 0.94 0.92 0.9
0
5
10
15
20
25
30
Basal area, m2/ha BAL=1
BAL=15
BAL=5
BAL=10
BAL=15
BAL=20
BAL=20
1 s¼ 1 þ exp½ð6:578 þ 0:149d 1:366lnG 0:167BAL= lnðd þ 0:01ÞÞ
ð11Þ where s is the probability that the tree survives for 5 years. The Negelkerke R2 of the survival model was 0.242 and the percentage of correct predictions in the modelling data was 95.9. As with the diameter increment model, SI was not a significant predictor of tree survival. The model indicates that the probability of survival increases with increasing dbh (Fig. 4). Increasing stand basal area (G) and basal area of larger trees (BAL) decrease the survival rate. Since the dataset did not allow for modelling the influence of senescence (old age or large size) on mortality, the following model was assumed in optimizations. The model is based on the maximum age of Korean pine (Omelko et al. 2016): 1 1 þ exp½ð5:00 0:01T Þ
BAL=5
30
Fig. 3 Relationships between 5-year diameter increments, dbh, stand basal area and basal area of larger trees (BAL) according to the diameter increment model
ssenescence ¼
30
0.98
Basal area, m2/ha BAL=1
25
1
4
0
20
Dbh = 20 cm
Dbh = 15 cm
5
15
BAL=20
Survival probability
Diameter increment, cm
BAL=5
10
Dbh, cm
Dbh, cm BAL=1
5
30
Fig. 4 Dependence of 5-year survival probabilities on dbh, stand basal area and basal area of larger trees (BAL) according to the survival model
The following allometric model was used for the biomass of different components: bm ¼ a db
ð13Þ
where bm is dry biomass (kg), d is dbh (cm) and a and b are parameters (Table 2) of the models for different biomass components. The proportion of carbon in dry biomass was 0.49 for all four components. The taper model fitted for Korean pine was as follows (Kozak 2004): di ¼ 0:8620 d 0:9827 h0:0841 XB B ¼ 0:6036 q4 0:5505= expðd=hÞ þ 0:4813 X 0:1
ð14Þ
Q
0:8524=d þ 0:0101 h 0:0482 X where di is diameter (cm) at height hi (m), d is dbh (cm), h is total tree height (m), q is hi/h, X is (1-q1/3)/(1-(1.3/
ð12Þ
where T is stand age (years). This model shows that 100-year-old trees survive with 98.3% probability, 200-year-old trees with 95.3% probability and 300-yearold trees with 88.1% probability for the following 5 years. The product of the two survival probabilities (s and ssenescence) gives the total 5-year survival probability of the tree.
Table 2 Parameters of biomass equation of different tree components (Eq. 13) Biomass component
a
b
R2
RMSE
Stem
0.08814
2.2705
0.957
0.14
Branches
0.00131
3.2250
0.935
0.26
Foliage
0.00507
2.5952
0.929
0.22
Roots
0.04175
2.1982
0.875
0.27
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h)1/3), and Q is 1-q1/3 (R2 0.9859, RMSE 0.7882). The model was used to calculate the volumes of different timber assortments.
reasonable to assume that too low or too high a stand density decreases the seed yield of a stand. Optimal management
Seed yield model Effect of discount rate Because of the high annual variation in seed yield and because the empirical seed yield data represented a narrow range of stand age and mean tree size, expert knowledge supported by empirical data was used to develop the following model, which shows the influence of tree size and stand density on seed yield. Seeds ¼ 1500 0:03 Dq expð0:03 DqÞ 0:002 N expð0:002 NÞ ð15Þ where Seeds is the annual seed yield of the stand (kg/ha), Dq the quadratic mean diameter (cm) and N stand density (trees/ha). The model was calibrated to give the same mean seed yield for the observations (dots in Fig. 5) as their observed mean yield (160 kg/ha). The model modifies the expected mean annual yield (160 kg/ha) of Korean pine based on mean tree size and stand density, and on the fact that young stands do not produce much seed and senescence probably also decreases seed yields. It is also
700
Seed yeald, kg/ha
600 500 400 300 200 100 0
0
10
20
30
40
50
Stand management for timber production was optimized by maximizing the net present value of timber production with 0, 1, 2, 3 and 4 thinning treatments and using different discount rates. The results show that increasing the number of thinnings increased the NPV (Fig. 6). However, the increase was slower after 2 thinnings. Taking into account that the results were calculated using stumpage prices which were independent of harvested volume, it was concluded that three thinning treatments during the rotation period were sufficient. Increasing the number of thinnings would lead to smaller harvests and higher harvesting costs per cubic meter, decreasing economic profitability. Therefore, all the remaining optimizations in this study used three thinning treatments during the rotation period. Optimizations with three thinnings led to rotation lengths ranging from 52 to 69 years (Table 3). Lower discount rates resulted in longer optimal rotations. Wood production and mean annual net income of the optimal management schedule decreased slowly with increasing discount rates. Seed production was not sensitive to discount rates but the average carbon stock of the stand decreased. Figure 7 depicts the optimal schedule obtained with a 2% discount rate. It shows that the most valuable assortment—medium-sized log—was removed in every thinning, leading to high incomes. All thinnings were from above, and the second and third thinnings were close to dimension cutting, removing all trees with dbh larger than 17 cm (second thinning) or 19 cm (third thinning).
60
Dq, cm
1
1%
0.9
600
Relative NPV
Seed yield, kg/ha
700
500 400 300 200
2% 0.8
4% 6%
0.7
100 0
0
500
1000
1500
2000
N, trees/ha Fig. 5 Effect of mean tree size (Dq) and stand density (N) on annual seed production. The line gives the model prediction and the dots are measured seed yields
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0.6
0
1
2
3
4
Number of thinnings Fig. 6 Effects of the number of thinning treatments during rotation on the net present value when maximized with different discount rates. Note that the y axis is cut at 0.6
Optimal management of Korean pine plantations in multifunctional forestry Table 3 Effect of discount rate on optimal rotation lengths, wood production, mean annual net income, seed yield and average carbon stock when the management schedule includes three thinning treatments NPV, RMB/ha
Wood production, m3 ha-1
Net income, RMB/ha
Carbon stock, Mg/ha
Seed yield, kg/ha
1%
69
382,390
5.92
4903
46
119
2%
62
147,190
5.9
4825
43
111
4%
55
42,208
5.81
4525
38
113
6%
52
14,049
5.42
4121
33
113
200 180 160 140 120 100 80 60 40 20 0
1
Total Medium log Small log Pole
Thinning intensity
Fig. 7 Development of total growing stock volume and assortment volumes in the optimal management schedule when NPV is maximized with 2% discount rate (left) and the optimal harvest percentage in different diameter classes (right)
Volume, m3/ha
Rotation length, years
0.8 0.6 1st 0.4
2nd 3rd
0.2
Firewood 0
0
20
40
60
80
5
10
15
Stand age, years
Effect of silvicultural recommendations
Effect of management objective Optimizations were also carried out for management objectives other than NPV. When NPV was the only
25
30
Relative NPV, %
120 100 80 60 40 20 0
1%
2%
4%
6%
Discount rate No constraints
Max thinning 45%
Forced low thinning
80
Rotation length, years
A commonly applied practical rule in the management of tree plantations in China is that thinning intensity must not exceed 45%. It has also been common to apply only thinning from below or forced low thinning. To see the effects of these recommendations, optimizations were repeated by implementing first the maximum thinning intensity constraint and then the additional constraint of forced low thinning, implemented by fixing parameter a1 of the thinning intensity curve (Eq. 3) to -1. Figure 8 illustrates that both restrictions decrease the economic profitability of timber production. Their relative effect increases with increasing discount rates. When both constraints are used, the net present value of the optimal management schedule decreases by 15 to 25%. Both constraints tend to shorten the optimal rotation length (Fig. 8, bottom) which is logical, since removing the smallest trees from the stand increases the average financial maturity of the remaining trees (Pukkala 2015). Restricting the maximum thinning intensity to 45% slightly decreased seed yields (because of shorter rotations) but forced low thinning increased seed yields (because of larger average tree sizes in the remaining stand). The effects of both management directions were less than 10% of the seed yields of unconstrained optima.
20
Dbh, cm
70 60 50 40 30 20 10 0
1%
2%
4%
6%
Discount rate No constraints
Max thinning 45%
Forced low thinning
Fig. 8 Effects of silvicultural constraints on the net present value and rotation length of the optimal management schedule. ‘‘Max thinning 45%’’ means that the maximum percentage of removed trees is 45% of stand basal area, and ‘‘Forced low thinning’’ means that only thinning from below is allowed
objective or one of several, it was calculated with a 2% discount rate. Multi-objective optimization maximized the utility function, which consisted of NPV, wood production (mean annual harvest during the rotation), mean carbon stock of the stand during the rotation, and mean annual seed yield (Eq. 4).
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The results (Table 4) show that maximizing wood production increased production only slightly as compared to maximizing profitability with a 2% discount rate (from 5.9 to 6.01 m3 ha-1 a-1). Rotation length was extended by three years. The effect of maximizing income instead of NPV led to a 10-year longer rotation, but its effect on the other objective variables was small compared to the maximum profit schedule. The effects of choosing other objective functions were greater. Logically, maximizing carbon stock led to long rotation lengths with significantly reduced timber production and economic profitability. Seed production was maximized when the rotation length was 109 years. This led to significant reductions in NPV and timber production. The multi-objective optimum had thinning treatments at 35, 50, and 65 years, and final harvest at 86 years (Fig. 9, left). Thinnings removed the largest trees from the stand Table 4 Optimal rotation lengths and quantities of different outputs in singleobjective optimization (NPV, WP, Net income, Carbon, Seed) and in multi-objective optimization (Utility); the results for NPV are repeated from Table 3 for easier comparison
(Fig. 9, right), and the diameters at which thinning intensity was 50% were 14.5 cm in the first thinning, 20.0 cm in the second, and 23.5 cm in the third. The difference to the max NPV schedule (Fig. 7) was that trees that contained medium-sized logs were not completely removed in the second and third thinnings. The economic profitability of the multi-objective optimum was 10% lower than in the max NPV schedule, and wood production was 8% lower. Average carbon stock was 50% of the maximum carbon schedule, and seed production 74% of the maximum seed schedule. Therefore, the multi-objective schedule may be regarded a good compromise in the production of goods and services other than for carbon stock. Compared to the max NPV schedule, the multi-objective schedule increased seed yield by 27% and average annual carbon stock by 21%. Wood production decreased by 6% and NPV by 10%. Figure 10 shows that the main reason for
Objective function NPV (2%)
WP
Net income
Carbon
Seed
Utility
Rotation length, years
62
65
72
244
109
86
NPV (2%), RMB/ha
147,190
146,552
142,863
20,245
45,539
132,574
Wood production, m3/ha
5.90
6.01
5.84
1.27
3.32
5.53
Net income, RMB/ha
4825
4852
4926
1074
2844
4722
Carbon stock, Mg/ha
43
44
46
104
77
52
Seed yield, kg/ha
111
117
116
163
191
141
The value of the maximized variable is in boldface Fig. 9 Development of total growing stock volume and assortment volumes in the optimal management schedule when multi-objective utility function is maximized (left), and the optimal harvest percentage in different diameter classes (right)
1
200
Thinning intensity
Volume, m3/ha
250
Total 150
Medium log Small log
100
Pole 50
Firewood
0.8 0.6 1st 0.4
0
10 20 30 40 50 60 70 80 90
3rd
0.2 0
0
2nd
5
10
80
20
25
30
250
70 60 50 40
NPV 2%
30
Multi
20 10 0
Annual seed yield, kg/ha
Carbon stock, Mg/ha
15
Dbh, cm
Stand age, years
200 150 NPV 2%
100
Multi 50 0
0
20
40
60
Stand age, years
80
100
0
20
40
60
80
100
Stand age, years
Fig. 10 Development of carbon stock (left) and mean annual seed yield (right) when the NPV of timber production is maximized (NPV 2%) or when the multi-objective utility function is maximized (Multi)
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Optimal management of Korean pine plantations in multifunctional forestry
increased carbon stock and seed yield is increasing rotation length. The trade-off curves between the NPV of timber production versus carbon stock or seed production were produced by including the two analyzed objective variables in the utility function, changing the weights of the objective variables, and optimizing the management schedule after every change (dots in Fig. 11). The trade-off curve between timber benefit (NPV) and carbon stock was more linear than that for timber benefit versus seed yield (Fig. 11). The optimization selected either carbon-oriented management with a long rotation length and low profitability, or profitability-oriented management with much shorter rotation length and low average carbon stock. This result and the shape of the trade-off curve indicate that it is difficult to find compromise schedules for economic profitability and high carbon stock. The situation was different for timber profit versus seed yield, for which it was easy to find compromise schedules depending on the importance of the two management objectives. The shape of the trade-off curve suggests that the production of seed and timber NPV is maximized when both are produced in the same stands, instead of devoting separate stands for seed and for timber production.
sensitivity of the results to these economic parameters was analyzed by first increasing the costs or prices by 50% and then increasing them by 100%, as compared to the baseline optimizations. Increasing stand establishment costs led to longer rotation lengths (Table 5), which is logical since it is optimal to postpone the final felling if the establishment of a new stand is costly. Decreasing timber prices also increased rotation lengths. Wood production, average annual carbon stock and seed yield were not much affected. Since the changes made in silvicultural costs and timber prices were substantial, it may be concluded that the results of this study are not sensitive to the cost and price levels used in the calculations. Instead of timber prices, it would also have been possible to analyze the effect of the minimum dimensions of different timber assortments, or to change the price of only one timber assortment at a time. However, this would have greatly increased the number of analyses.
Sensitivity of results to economic parameters
The empirical dataset to fit the models for stand dynamics were rather small. There were few observations from very young and very old stands. However, the data sets represent reasonably well those ages and stands used in the
Discussion Analysis of the methods
Since there is much uncertainty about the future level of silvicultural costs and timber prices in China, the
Carbon-or ientedd
Profit-orie ntedd
6HHG\LHOGNJKD
&DUERQVWRFN0JKD
Fig. 11 Trade-off curves of timber benefits versus carbon stocks (left) and timber benefits versus seed production (right)
139 50%KD
139 50%KD
Table 5 Effect of silvicultural costs and timber prices on optimal rotation lengths and amounts of different products and services
Silvicultural cost multiplier Timber price multiplier
Rotation length, years
NPV (2%), RMB/ha
Wood production, m3/ha
Net income, RMB/ha
Carbon stock, Mg/ha
Seed yield, kg/ha
0.5
60
153,137
5.88
4853
42
114
1
62
147,190
5.9
4825
43
111
2
65
136,562
5.89
4724
44
121
0.5
65
68,281
5.89
2362
44
121
1 2
62 60
147,190 306,274
5.9 5.9
4825 9706
43 42
111 114
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X. Jin et al.
schedules that maximized wood production or NPV. Additional data and model visualization were used to check that the models were biologically consistent. The models do not describe the influence of the site because site variation in the empirical modeling data was too small to reveal statistically significant effects. Therefore, only one site was analyzed which represented average site conditions in the plantations. This does not decrease the value of the results for forest managers, since the results represent conditions under which most of the current Korean pine plantations are growing. However, the study does not provide information for those who desire management support for plantations established on poorer or better sites. The results are less reliable for the multi-objective cases since seed production and carbon sequestration in biomass call for longer rotations, which were not covered well in our modelling data. In addition, the model for seed yield is based on observations from a very narrow range of stands. Despite this, the model used, which combines empirical data and expert knowledge, is reasonable. The overall level of seed production is based on 157 measured seed yields. It is known that young stands do not produce significant quantities of seed, and it is reasonable to assume that seed yields begin to decline at older ages. In a seed yield model for another pine nut species, Pinus pinea L., seed yields reached their maximum at a stand age of about 100 years, after which yields slowly declined (Pasalodos-Tato et al. 2016). The overall behavior of our model is similar as the Spanish model for Pinus pinea. The weakest component of the simulation–optimization system was the model for age-dependent survival. However, mortality rates increased only after 100 years of age and at 300 years, the 5-year survival probability was still 0.9. Therefore, the effect of this model on the results was small. The exception is the carbon balance results which greatly depend on the assumed life span of the trees. On the other hand, without senescence-related mortality, the optimal rotation for maximal carbon stock had been much longer than the maximum recorded age of Korean pine. Despite a number of limitations with the modelling data, we are confident that the trends indicated by our optimization results are correct, although there are some inaccuracies. Due to the urgent need for guidelines for the management of Korean pine plantations, we believe that presenting results calculated with the current data is better than waiting for many years for improved modelling datasets. Analysis of the results The results show that thinning from above was more profitable than thinning from below. Many earlier studies
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have led to similar conclusions (e.g., Pukkala et al. 2014). If the natural regeneration of Korean pine is satisfactory, it may be worthwhile to switch to continuous cover management in a part of the plantations (Pukkala et al. 2014, 2015). However, numerical analysis of this option would require regeneration or ingrowth models for planted Korean pine stands. Such models are not available at the moment. Aiming for maximum seed production led to a 47-year longer optimal rotation compared to the schedule which maximized NPV of the timber. The effect of seed production on optimal management is similar as obtained recently for Pinus pinea in central Spain (Pasalodos-Tato et al. 2016). Increasing rotation length is also common in the joint production of timber and mushrooms (Palahı´ et al. 2009); timber and wild berries (Miina et al. 2010, 2016) and timber and pine honey (de Miguel et al. 2014). The shape of the trade-off curve between seed production and timber benefits suggests that joint production is more efficient than devoting different stands for different purposes. On the other hand, high carbon stock is difficult to combine with good profitability of timber production, or high wood production or income. Carbon sequestration in living biomass is less in conflict with seed production. This study proposes a multi-objective management schedule as a compromise between profitable timber production and other benefits. This schedule uses an 86-year rotation with three thinning treatments at 15-year intervals, starting at stand age of 35 years. If this management schedule is used in all stands, wood production will be 134%, NPV of timber production 148%, carbon sequestration 78% and seed production 97%, as compared to a situation where 25% of stands are managed for maximal profitability, 25% for maximal wood production, 25% for maximal carbon stock, and 25% for maximal seed yield. This calculation shows that the joint production of different products and services in the same stand is a good option for benefits other than for carbon sequestration. However, it should be noted that maximum carbon stock in living biomass does not reflect the total carbon sequestration in forests because carbon pools of dead organic matter and wood-based products are ignored as is reduced carbon emissions from fossil fuels due to the use of wood. If all these are taken into account, this research shows that regular cutting may lead to better long-term carbon balances than letting the forest go unmanaged (Werner et al. 2010; Pukkala 2017). Therefore, without further available information, we recommend that the optimal schedule for multifunctional management should be applied to current Korean pine plantations.
Optimal management of Korean pine plantations in multifunctional forestry
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