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Articles by Tron Eid

Category: Research article

article id 1347, category Research article
Paulo Borges, Even Bergseng, Tron Eid, Terje Gobakken. (2015). Impact of maximum opening area constraints on profitability and biomass availability in forestry – a large, real world case. Silva Fennica vol. 49 no. 5 article id 1347. https://doi.org/10.14214/sf.1347
Highlights: We solved a large and real world near city forestry problem; The inclusion of maximum open area constraints caused 7.0% loss in NPV; Solution value at maximum deviated 0.01% from the true optimum value; The annual energy supply of 20–30 GWh estimated from harvest residues could provide a small, but stable supply of energy to the municipality.

The nature areas surrounding the capital of Norway (Oslomarka), comprising 1 700 km2 of forest land, are the recreational home turf for a population of 1.2 mill. people. These areas are highly valuable, not only for recreational purposes and biodiversity, but also for commercial activities. To assess the impacts of the challenges that Oslo municipality forest face in their management, we developed four optimization problems with different levels of management constraints. The constraints consider control of harvest level, guarantee of minimum old-growth forest area and maximum open area after final harvest. For the latter, to date, no appropriate analyses quantifying the impact of such a constraint on economy and biomass production have been carried out in Norway. The problem solved is large due to both the number of stands and number of treatment schedules. However, the model applied demonstrated its relevance for solving large problems involving maximum opening areas. The inclusion of maximum open area constraints caused 7.0% loss in NPV compared to the business as usual case with controlled harvest volume and minimum old-growth area. The estimated supply of 20-30 GWh annual energy from harvest residues could provide a small, but stable supply of energy to the municipality.

  • Borges, Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, P.O. Box 5003, 1432 Aas, Norway ORCID ID:E-mail: paulo.borges@nmbu.no (email)
  • Bergseng, Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, P.O. Box 5003, 1432 Aas, Norway ORCID ID:E-mail: even.bergseng@nmbu.no
  • Eid, Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, P.O. Box 5003, 1432 Aas, Norway ORCID ID:E-mail: tron.eid@nmbu.no
  • Gobakken, Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, P.O. Box 5003, 1432 Aas, Norway ORCID ID:E-mail: terje.gobakken@nmbu.no
article id 418, category Research article
Tron Eid. (2004). Testing a large-scale forestry scenario model by means of successive inventories on a forest property. Silva Fennica vol. 38 no. 3 article id 418. https://doi.org/10.14214/sf.418
Modellers of large-scale forestry scenario models face numerous challenges. Information and sub-models from different disciplines within forestry, along with statistical and mathematical methodology, have to be considered. The individual biological sub-models (i.e. models for recruitment, growth and mortality) applied in large-scale forestry scenario models are in general well documented and extensively evaluated. However, evaluations by means of full-scale comparisons of observed and predicted values for continuous forest areas, where the totality of the large-scale forestry scenario model including interactions between sub-models and other parts of the model, are considered, have rarely been seen. The aim of the present work was to test the totality of the Norwegian large-scale forestry scenario model AVVIRK-2000, and thereby evaluate the applicability of the model for use in management planning. The test was done by means of successive inventories and accurate recordings of treatments over a period of 30 years for a property comprising 78.5 ha forest-land. Seen in the perspective of management planning, the differences between observed and predicted values for potential harvest level, growing stock and growth were small, e.g. a difference between observed growing stock in year 2000 and growing stock in the same year predicted from 1970 of 2.6%. The model may therefore be applied for practical purposes without any fundamental changes or calibrations of the biological model basis. However, the present test should be seen as an example that failed to falsify the model, rather than a final validation. As long as the model is in practical use, further evaluations should continue and subsequent possible calibrations should be performed.
  • Eid, Agricultural University of Norway, Dept of Ecology and Natural Resource Management, P.O. Box 5003 NO-1432 Ås, Norway ORCID ID:E-mail: tron.eid@ina.nlh.no (email)
article id 583, category Research article
Hans Fredrik Hoen, Tron Eid, Petter Økseter. (2001). Timber production possibilities and capital yields from the Norwegian forest area. Silva Fennica vol. 35 no. 3 article id 583. https://doi.org/10.14214/sf.583
How intensely should a forest be grown? This is a fundamental question in the process of formulating policy guidelines for the management of a forest area, both at the individual property level as well as at the national level. The question is related to a number of factors; the objective(s) of the forest owner, the productivity of the forestland, the initial growing stock, the accessibility within the forest, assumptions regarding future prices and costs and the required real rate of return. This paper presents an applied analysis with the objective of mapping possible future paths for the growing stock on, and timber harvest from the productive forest area in Norway. The analysis is deterministic. The regeneration strategy is a key factor for the long run development of a forest and is thus given particular attention. The analysis is restricted to deal with timber production only and maximisation of the net present value of the forest area is used as the objective function. The required real rate of return is varied and used as the driving force to find the best (optimal) level of intensity in silvicultural management and thus optimal paths for harvesting and growing stocks.
  • Hoen, Agricultural University of Norway, Dept. of Forest Sciences, P.O. Box 5044, N-1432 Ås, Norway ORCID ID:E-mail: hans.hoen@isf.nlh.no (email)
  • Eid, Agricultural University of Norway, Dept. of Forest Sciences, P.O. Box 5044, N-1432 Ås, Norway ORCID ID:E-mail:
  • Økseter, Agricultural University of Norway, Dept. of Forest Sciences, P.O. Box 5044, N-1432 Ås, Norway ORCID ID:E-mail:
article id 633, category Research article
Tron Eid. (2000). Use of uncertain inventory data in forestry scenario models and consequential incorrect harvest decisions. Silva Fennica vol. 34 no. 2 article id 633. https://doi.org/10.14214/sf.633
Uncertainty in long-term timber production analyses usually focus success of regeneration, growth/mortality of trees and future fluctuations of timber prices/harvest costs, while uncertainty related to inventory data is paid less attention. At the same time, evaluations of inventory methods usually stop when the error level is stated, while the uncertainty accompanied by using the data is seldom considered. The present work addresses uncertain inventory data in long-term timber production analyses. Final harvest decisions, i.e. possible outcome intervals with respect to timing and expected net present value-losses due to incorrect timing, were considered. A case study was presented where inventory data errors according to different error levels were generated randomly. The selected error levels were based on observations from practical forest inventories in Norway. The analysis tool was GAYA-JLP. The impact of errors on decisions was derived through repeated computations of management strategies maximising net present value without harvest path constraints. A real rate of discount of 3% and an error level of 15% resulted in expected net present value-losses of 1 NOK ha–1 for basal area, 63 NOK ha–1 for mean height, 210 NOK ha–1 for site quality, 240 NOK ha–1 for stand age, and 499 NOK ha–1 when random errors occurred simultaneously for all these variables. The expected net present value-losses varied considerably. The largest losses appeared for stands with ages around optimal economical rotation ages. The losses were also relatively large for young stands, while they were relatively low for overmature stands. The experiences from the case study along with considerations related to other sources of uncertainty may help us to get a more realistic attitude to the reliability of long-term timber production analyses. The results of the study may also serve as a starting point in a decision oriented inventory planning concept, in which alternatives for inventory design and intensity are based on considerations with respect to inventory costs as well as net present value-losses.
  • Eid, Department of Forest Sciences, Agricultural University of Norway, P.O. Box 5044, N-1432 Ås, Norway ORCID ID:E-mail: tron.eid@isf.nlh.no (email)

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