- freely available
Forests 2017, 8(9), 307; doi:10.3390/f8090307
2. Materials and Methods
2.1. The Markov Chain Model
2.1.1. General Description
2.1.2. Application of the EFDM for the Simulations of Any-Aged Forest Management
2.2. Steps of the Analysis
- Preparing the initial forest inventory data and pairwise observations for modeling the transitions (Section 2.3);
- Parameterizing the EFDM model with respect to the initial state space, transition and activity probabilities, and output coefficients (Section 2.4);
- Running the EFDM with scenario assumptions specified in Section 2.5.
2.3. Forest Inventory Data
2.3.1. An Overview of Parameterizing the EFDM with the Input Data
- Two alternative data sets were used to derive the pairwise observations to model the transitions due to natural processes. The data sets were permanent NFI10-11 and temporary NFI11 plots, which slightly differ in terms of estimating the pairwise observations, as detailed in Section 2.3.3 and Section 2.4.2 with respect to estimation and EFDM-specific formatting, respectively. The two plot types were used to derive two distinct sets of transition probabilities, which were switched as the input data when running the analyses, but the permanent and temporary plots were never merged when modeling the transitions. Notably, the transitions estimated based on both the permanent and temporary plot data included only growth and not potential reductions due to calamities or natural disturbances , for example. Including these effects is discussed in Section 4 and Section 5.
- A simulator was implemented to derive the pairwise observations from situations before and after thinning treatments. The thinnings took place in the beginning of each simulation period and the growth of the thinned forests in that period was simulated applying the transition probabilities of forests not managed. The forests affected by final fellings were forced to transit to the beginning of the even-aged rotation. The data processing involved the initial estimation (Section 2.3.3) and formatting the data for the EFDM (Section 2.4.2).
- The activity probabilities, which give the proportion of different types of forests to be managed, were defined in two steps with two assumptions. First, the initial allocation of the harvests to the different types of forests was assumed to follow either the proportion of harvests realized during the most recent five-year period (“business-as-usual allocation”, ABAU) or the proportion of forests that should be harvested strictly according to the instructions of forest management  (“schoolbook allocation”, ASB). Second, the final values for the activity probabilities of both the allocations were obtained by iteratively adjusting the initial probabilities to produce the harvesting levels aimed at in the future large-area scenarios. The data processing related to both the steps is explained in detail in Section 2.4.3 and Section 2.5.
- Output coefficients were prepared to translate the areas in different volume, age, and stem number classes to timber assortment and total volumes. The related steps are explained in Section 2.4.4.
2.3.2. Measurements and Estimation Principles of the NFI Data
2.3.3. Pairwise Observations
- Deriving the growth observations is explained separately for the two alternative data sets, namely (a) permanent and (b) temporary NFI plots:
- Permanent NFI sample plots, which were matched between data sets with certainty and had no treatments between the two subsequent inventories, were identified from the data. The positive differences in the total volumes between NFI10 and NFI11 were recorded as the pairwise data.
- Pairwise observations were derived from temporary NFI11 plots using the increment estimates. In the NFI, every seventh tree (continuously over plot clusters) is measured for diameter and height increment, from which a volume growth percent was estimated following Tomppo et al. . Due to the low number of observations, the percent was estimated at the level of sampling regions and the percent computed for a sampling region was applied for all plots in the region. This percent was used to estimate the difference of volumes between the two subsequent inventories for the plots without treatments, i.e., the pairwise observations were obtained as the difference between the observed volume and that deducted by the estimated growth.
- To determine transitions due to management by thinning treatments, a plot-level simulator was implemented to assess the proportion of the total and assortment volume to be removed in future thinning treatments. The NFI11 plots were used as the input data. The simulator determined the thinning removal following two types of instructions:
- A thinning from below corresponding to traditionally applied instructions for forest management  was simulated according to thinning curves downloaded from the repository of the SIMO software (Simosol Py, Riihimäki, Finland, ). The curves predict the thinning limit and remaining basal area as the function of tree species, site type and dominant height (estimated as mean stand height +1.75 m ). The lower curves of two available thinning intensity levels were used and the harvesting removal was determined as the difference between the thinning need and remaining basal area.
- A thinning from above was simulated by predicting the remaining basal area using the plot-level forest attributes as predictors of Equation (2) of Pukkala et al. . The thinning intensity is determined in terms of interest rate used as a predictor of the aforementioned equation. We used the curves corresponding to an interest rate of 3% and determined the harvesting removal as the difference between the initial and remaining basal area.
2.4. Parameterization of the Markov Model
2.4.1. State Space
- Known land-use restrictions: FAWS, FRAWS, FNAWS
- Forest ownership: private, public + other (cf. ).
- Site fertility: altogether, five categories corresponding to four taxation classes traditionally used in Finland + fifth class including all poorly productive forest land.
- Dominant species: pine, spruce, deciduous trees.
- In the input data for the simulations, every plot representing even-aged forest had a value of 0 as the stem number class and the values of age and volume ranged according Appendix A. Every plot representing uneven-aged forest had a value of 0 as the age class and the values of stem number and volume ranged according to Appendix A.
- In the input data for modeling the transition probabilities, the set of plots with pairwise observations was duplicated. Thus, every plot was included twice with either the age or stem number class set as 0, i.e., the data to model the transitions of both Age-Vol or N-Vol were always the same except for the variable combination.
2.4.2. Transition Probabilities
2.4.3. Activity Probabilities
2.4.4. Output Coefficients
2.5. Harvesting Scenarios Used in the Simulations of Any-Aged Forest Management
3.1. Effects of the Parameterization of the EFDM on the Projections
3.2. Results of the Scenario Analyses
4.1. Parameterization of the Markov Model for the Simulations of Any-Aged Forest Management
4.2. On the Use of the EFDM Approach for Projecting Future Wood Supply
4.3. Recommendations for Further Research
Conflicts of Interest
|Volume Classes 1||Age Classes 1|
|1. (∞, 0.0000)||1. (∞, 0)|
|2. (0.0000, 10.5884)||2. (0, 5)|
|3. (10.5884, 29.8618)||3. (5, 10)|
|4. (29.8618, 51.3846)||4. (10, 15)|
|5. (51.3846, 73.6844)||5. (15, 20)|
|6. (73.6844, 96.5440)||6. (20, 25)|
|7. (96.5440, 122.8744)||7. (25, 30)|
|8. (122.8744, 153.2864)||8. (30, 35)|
|9. (153.2864, 191.3348)||9. (35, 40)|
|10. (191.3348, 248.0352)||10. (40, 45)|
|11. (248.0352, 303.3532)||11. (45, 50)|
|12. (303.3532, ∞)||12. (50, 55)|
|13. (55, 60)|
|Stem number classes 1||14. (60, 65)|
|1. (∞, 0.0000)||15. (65, 70)|
|2. (0.0000, 69.8725)||16. (70, 75)|
|3. (69.8725, 330.6332)||17. (75, 80)|
|4. (330.6332, 509.0106)||18. (80, 85)|
|5. (509.0106, 676.9061)||19. (85, 90)|
|6. (676.9061, 875.1651)||20. (90, 95)|
|7. (875.1651, 1108.6395)||21. (95, 100)|
|8. (1108.6395, 1384.8279)||22. (100, 105)|
|9. (1384.8279, 1754.0609)||23. (105, 110)|
|10. (1754.0609, 2398.5651)||24. (110, 115)|
|11. (2398.5651, 2975.8412)||25. (115, 120)|
|12. (2975.8412, ∞)||26. (120, ∞)|
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