Multifunctional Forestry & Interaction With Site Quality

Several studies have shown the economic value of various ecosystem services provided by the forest. However, the economic value of how site-specific ecological conditions interact with other functions provided by the forest. As a result, a numerical discrete dynamic optimisation model was constructed to estimate the economic value of site quality, taking into account its interaction with timber value and carbon sequestration, in Swedish forests. By Ing-Marie Gren, Swedish University of Agricultural Sciences and Franklin Amuakwa-Mensah, University of Gothenburg


Multifunctional forestry can be regarded as the ability of the forest to provide multiple and interconnected outputs or services, which can be either positive or negative, intended or unintended, complementary or substitute, and marketable or non-marketable. 

Ecosystem services provided by the forest, besides the traditional timber provision includes recreation and ecotourism, erosion control from land-slides and wind, flood protection and benefits to water quality, and climate regulation through carbon sequestration. 

Furthermore, the presence of below-ground micro-organisms, mostly fungi diversity, plays an important role in enriching the site conditions of the forest as it helps in regulating ecosystem processes. This role becomes apparent as below-ground organisms drive, or control, mineral and energy cycling within the ecosystems.

The productivity of the forest and the ability of the forest to provide essential ecosystem services are mostly driven by management practices and prevailing ecological quality at the site (site quality for short), which in most cases are determined by environmental, biophysical, and climate conditions. 

These site-specific ecological conditions have a tendency to interact with ecosystem services provided by the forest, which affects the economic value of the forest. 

In spite of the potential benefits of site-specific ecological conditions in enhancing forest growth, there are no studies addressing the economic impacts of site quality on forest management. 

Therefore, the purpose of this study is to examine the economic effects of site quality in forest management when including both timber values and non-market services, in terms of carbon sequestration. This objective is achieved by constructing a discrete dynamic optimisation problem, where the forest manager maximises his/her net present values (NPV) of both timber and carbon sequestration subjected to the development in the standing biomass volume, which is dependent on-site quality.

Following the work by Gren and Amuakwa and earlier studies, we used site index as a proxy for site productivity or quality. According to Skovsgaard and Vanclay, site index shows the potential of tree growth under ideal conditions, and is usually measured as the biomass potential at a certain age of a tree species. 

Moreover, Stokland et al. asserts that site index usually reflects the quality of the forest soil in terms of potential forest productivity. Our evaluation of site quality is analyzed by considering the effect of site quality on forest growth rate.


Dynamic Programming Model

The optimal forest management in the presence of site-specific ecological conditions and the economic evaluation of these in Swedish forest is calculated based on a non-linear discrete-time dynamic programming model. 

The level of site quality in time t + 1 is assumed to be determined by site quality in the earlier period, and by harvest. Harvest creates disturbance in the soil, mainly in terms of carbon losses, which affects the level of the quality. As shown by Diochon et al., carbon losses can occur decades after the harvesting of spruce, but can also recover after an even longer period due to the carbon content in intact forests. 

However, there is insufficient information on the impact of harvest on the more general site quality indicator used in this study, which includes multiple environmental factors at the site. 

In the present study, only above ground carbon sequestration is included, which depends on the forest biomass growth. In addition, the net removal depends on the use of forest products. 

Depending on the impact of harvesting on standing biomass growth and carbon sequestration, the marginal user cost can either be positive or negative. In situations where the average forest stand is young with relatively low growth, for each additional unit of standing volume harvested today, there is an associated cost. 

This is because the average age and standing biomass volume falls in the next period, which implies a lower growth in standing volume, given that the average forest stand is young. 

As a result, marginal user cost is positive. On the other hand, in situations where the average forest stand is old with relatively low growth, for each additional unit of standing volume harvested today, there is an associated benefit. This is because the average forest age falls in the next period, which implies a higher growth in standing volume, given that the average forest stand is old. In this case, the marginal user cost is negative.

Assuming that the marginal user cost of forest biomass is positive, Equation shows that neglecting any of the future impact on forest biomass or site quality will result in too high harvest volumes. In this case, the total marginal cost is reduced, which implies higher harvest in early periods. This, in turn, implies lower profit during the entire period.

In order to calculate the role of site quality, data are needed for parameterising the growth and other functions. The analysis considers the entire productive forest of Sweden without particular emphasis on tree species since there is no specific biomass growth function for various tree species.

We use a site index for Swedish forests which is based on statistical assessments of multiple effects of different environmental factors at a site. According to Bontemps and Bouriaud, the index can indicate the constraints of the ecological niche and distribution of tree species, and thus can portray biodiversity. 

As suggested by Stokland, site quality can be an indicator of this type of diversity, since it usually reflects the quality of the forest soil in terms of potential forest productivity. It has also been found to be correlated with fungi diversity in forest soil in Sweden.

And besides, the data were obtained from the Swedish Forest Agency that measures and reports site quality index for different parts of Sweden, the calculation of which is based on Hägglund and Lundmark. 

The value of the index ranges between 2.6 and 8.9 for different time periods and forest regions in Sweden, with the highest in the regions in the south of Sweden. Because of the time series nature of the harvest and site quality data, fully modified ordinary least squares estimation techniques were used in order to address the problems of serial correlation, stationarity, and endogeneity. 


NPV Of Forest Management

Based on the parameter values from the biological and economic models shown, the optimal time path for harvesting, carbon benefit, profit, and the economic value of site quality is generated through simulation for a period of 100 years. 

The numerical models are solved using the mathematical programming code in GAMS, using the year 2015 as the baseline period and making simulations for a 100-year period. 

A stepwise method was followed in this analysis, in order to ascertain the economic value of various ecosystem services from the forest. 

First, the optimisation process was made, considering only timber output of the forest. In the second step, optimisation was made over timber and site quality interaction; and the third step considered both timber and carbon values, without site quality interaction. The final step considers timber and carbon values together, with the interaction of site quality.

In order to evaluate the impact of different parameter values on the maximum NPV, sensitivity analyses were performed where the levels of the discount rate, impact of site quality on biomass growth rate, and intrinsic growth rate of biomass were changed.

The NPV of forest management under the four different cases (timber with and without carbon sequestration, and with and without site quality interaction) is represented. As expected, accounting for the non-timber value of the forest increases the NPV.

The results show that the NPV of forest management more than doubled when considering carbon sequestration; it increased from 190,042 SEK per hectare to 396,940 SEK per hectare. 

The impact of site quality was more modest; where the NPV for timber and site quality interaction, and timber, carbon sequestration, and site quality interaction are 192,239 SEK (solid volume excluding bark) per hectare and 403,152 SEK per hectare, respectively. 

The value of site quality can then be calculated as the difference in NPV with and without the consideration of site quality in the optimisation, which gives 2197 SEK/ha with timber as output, and 6212 SEK/ha with timber and carbon sequestration.

There are small differences in the optimal time path of harvest between the scenarios. In all cases, the harvest path shows a similar trend where it rises during initial years, remains relatively constant over a long period, and rises sharply during the later years. 

Comparing the harvest path for the case where only timber value is optimised with that of timber and carbon sequestration, the volume of harvest when only timber is optimised is higher at the initial years until the end of the period. This finding corroborates that of, where it was observed that accounting for carbon value in the optimisation process reduces the volume of harvest at initial years. Similarly, also conclude that the inclusion of carbon sequestration and other ecosystem benefits of the forest in the optimisation process results in longer rotation age.


Analysis Of Sensitivity Analysis

The results in the base case indicated relatively small effects on the maximum NPV of the impact of site quality on forest growth. Therefore, calculations were made for a high increase in this parameter value, at 0.5 instead of 0.023 in the base, to examine the impact on NPV. 

Similarly, calculations are made for a relatively large decrease in the price of carbon sequestration. In the base case, the Swedish tax on carbon dioxide emissions (SEK 1130/ton CO2) was used, which is a relatively high value of the social cost of carbon. 

Therefore, calculations were made using the equilibrating price at the EU emission trading system (ETS) as the price of carbon, which was SEK 73/ton CO2 in 2015. Impacts on NPV were also calculated for large changes in the discount rate, from 3 percent in the base case, to 1 percent and 6 percent. 

On the other hand, calculations were made for a relatively small change in the intrinsic forest growth rate, at 0.16 instead of 0.13 in the base case. Despite the large increase in the impact of site quality on forest growth, the effects on maximum NPV is in the same order of magnitude as the increase in the forest growth rate.

The NPV for timber, both timber and carbon interactions, with high impact of site quality is 238 thousand SEK per hectare and 454 thousand SEK per hectare, respectively. The corresponding site quality values are then 48 thousand SEK per hectare and 57 thousand SEK per hectare for interactions with timber only, and both timber and carbon, respectively. 

A high intrinsic growth rate allows for higher harvest levels and carbon sequestration, and NPV increases for all combinations of the ecosystem services. The values of site quality are in the same order of magnitude as the case with high impact of site quality on forest growth.

As expected, NPV is sensitive to the price of carbon and discount rate. A decrease in the price of carbon from the Swedish tax to the EU ETS price of carbon reduces the NPV by almost 40 percent. An increase in the discount rate to 6 percent leads to a drastic decrease in the NPV. In relation to site quality value, an inverse relationship between site quality and the discount rate. 

Thus, at a lower discount rate, site quality value is higher than at a higher discount rate. The calculated NPV is also sensitive to the assumed values of timber prices, but the magnitude of the impacts of these parameters is smaller than that for the parameters included in the present study.

Given the multifunctionality of forests in providing both timber and non-timber services, several studies have attempted to quantify the economic value of non-timber services provided by forests. 

However, no study has examined implications of the interactions of the services provided by the forest with site specific ecological conditions. As such, using a numerical discrete dynamic optimisation model, we estimated the economic value of site quality, taking into account that harvest has a negative impact on forest biomass and site quality growth. 

The contribution of site quality becomes apparent as it facilitates biomass growth. With high growth, there is an increase in timber yield, which is eventually sold for more net revenue. In addition, higher biomass growth increases the carbon sequestration potential of standing biomass, and this increases the non-timber benefits of the forest to the manager. However, the interaction also implies that the marginal cost of harvest increases, due to the negative effect on site quality and associated effects on future biomass growth.

The empirical application to the forests in Sweden showed that the value of site quality ranges between 2197 SEK per hectare and 6212 SEK per hectare depending on assumed interactions with timber and carbon sequestration. 

Given that the productive forest area in Sweden is about 22.7 million hectares, the value of site-specific ecological conditions in Swedish forests ranges between approximately SEK 50 billion and SEK 141 billion, which correspond to approximately 0.1 percent–0.2 percent of the gross domestic product in 2015. The value increases considerably when the impact of site quality on forest growth increases.

However, the empirical calculations rest on simplified assumptions, in particular, on the impacts of harvest on site quality and on the effect of site quality on forest growth. 

This points to the need for more empirical analyses of these relations. The empirical results also showed that the NPV of forest management can be doubled when considering the value of carbon sequestration, which is demonstrated in several other studies. 

The results therefore indicate a need for careful analyses of the economic role of site quality and carbon sequestration of Swedish forests. A materialisation of these values would require the implementation of an appropriate incentive structure for the forest managers. 

The approach used in this presented study could then be a useful tool for deriving the effects of different incentive structures.

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