Gentan probability is defined as the distribution of survival time for a forest stand until being harvested after a plantation. The original method to estimate Gentan probability is based on derivation of the gamma distribution from an average and variance of harvest timing. Given that a forest stand is not harvested up to a certain age, a new method is proposed to estimate Gentan probability by means of the Laplace transformation of the distribution of survival time. The method is to estimate the distribution of survival time, i.e., Gentan probability, through an average, variance and skewness of the tree life span from an existent harvest statistical data.

In this paper, three approaches for forest capital valuation are discussed. The first approach is a profit-based approach, where capital value is estimated in terms of the product of the average lifetime of capital and annual profit from capital. The second one is a cost-based approach with a use of costs inherited to forest productivity. Capital value in the second approach is the product of the average lifetime of a forest (or average rotation age) and annual costs. For the second approach, we compare these methodologies to estimate forest productivity based on the widely defined concept of normal forests and Hirata’s concept. As the last approach, we propose a new capital valuation approach by incorporating fuzzy phenomena on nature or economy into Hirata’s cost-based capital concept. The proposed approach is characterized by combining valuations derived from the two viewpoints of planning and fluctuation.

In this paper, we propose a log production model for 150-year rotation forest stands. In the proposed model, tree volume growth along with growth of the corresponding occupied space, W², increases tree diameter on the ground, D, tree height, H, and its occupied width, W. Except the early stage of growth, it is shown that the annual growth of tree basal area has 40cm²/year as a upper bound, and that a lower bound for the annual growth of tree diameter, △D_minis 0.25cm/year. Assuming that the annual growth of volume is greater than or equal to the product of the surface area of a log (proportional to height times diameter) and △D_min/2, we estimate W/D>11 as an index for volume productivity 20m³/ha/year. As one of the tasks for forest stand management for 150 rotation age, it would be of importance to maintain enough space for individual trees as tree diameter and height grow, and to utilize most from the forgone trees over the time horizon.

In this paper, new price models are developed for small-end-diameter logs, and their applicability is examined. In general, with a increase in diameter, a price of logs tends to be higher within a certain diameter range suitable for a pillar use. This relation between price and diameter can be expressed by a model with one peak in a price-diameter curve. Two types of the functional form are proposed for the function with a peak, i.e., the peak function. Applicability of these models is examined with use of five data sets for the price-diameter relationship of Ate lumber and sugi lumber from Noto district in Ishikawa prefecture, and hinoki lumber at Izumo district in Shimane prefecture. Our results show that these models fit the data well and are reliable for describing the relationship.

This report intends to analyze the forest grazing system, and to develop a yield production model for managing forest stands along with grazing. The forest grazing system is governed by three main factors, i.e., forest stands, cattle, and grass. The relationship of these factors plays an important role in constructing the model. It is shown that there is a correlation between Ry(yield index) and grazing capacity, and that grazing becomes possible under Ry less than or equal to 0.5. There is also a correlation between the size of grazing area and capacity. Combining these results and system yield tables, a yield prediction model for forest grazing is developed.

In this paper, a stochastic control model is constructed by incorporating geometric Brownian motion to capture uncertain price dynamics into a one-stage and two-state stochastic dynamic programming model. The proposed model is to search for optimal harvest timing under price uncertainty without considering other forestry operations, e.g., thinning. We consider an additional option to replant a forest stand or to abandon the management for another use of a forest land besides harvesting. Our experimental analysis shows that optimal harvest timing under stochastic log prices is delayed when the price level is crucial to maintain the management. It is also showed that when the current log price is sufficiently high, optimal harvest timing from the stochastic and the deterministic approach becomes the same. With a downward trend on price dynamics, optimal harvest timing tends to be hastened overall. This stems from the fact of a depreciation effect on the future return, which stimulates harvesting at an earlier period.

Following the history of forest inventory, the outline of recent trends and characteristics is reported. As an example, for Shikoku regional forest planning units, local forest growth models are derived and their applicability for precise prediction over the long term horizon is discussed by using growth data from permanent and temporary plots. For the use in regional forest planning, conjunction with various sampling and yield plots data is recommended with these local models as a basic model. It would be applied to multi-regional planning, and fill information gaps.

The transition of the stand density is studied with high density and old-age yield experimental plots for hinoki (Chamaecyparis obtusa) in Kyushu district. As a measurement for the stand density, tree density, basal area density, relative spacing and a yield index are analyzed. The relative spacing at unthinned hinoki stands is perceived to approach asymptotically to 10%, which is similar to sugi (Cryptomeria japonica) stands. There exist some plots whose density is above the full density curve from the stand density control diagram of hinoki in Kyushu district. This implies a need for reconstruction of the stand density control diagram.

Advanced technology is necessary to express the growth process of forest structures visually. Recently, the development of the visualization system of the growth progress becomes possible even with the diffusion type personal computer and operating system. The case study is conducted on the stand structure analysis in two beech forests under different snow environments. Also, significance of the dynamic analysis of the stand space structures is pointed out. For the dynamic analysis the three-dimensional visual system "Forest Window" for the stand structure is shown to be useful. It is also shown that together with annual ring information the system can be applied for analysis on dynamic change in the stand structure.

Because of the substitutional relationship between the domestic and the imported timber for the use of construction materials, the timber market structure has changed over the last several decades. The foreign timber was initially introduced in order to fulfil a shortage of the domestic timber supply. Approximately 80% of the Japanese timber market is currently occupied by the imported timber. The two major foreign timber supplies are the U.S. and Canada. In this paper, we analyse a change of substitution between the domestic and the imported timber in terms of price elasticity of timber demand and supply. Econometric models for timber demand and supply are constructed with use of the log-transformed linear function. The Japanese timber market is divided into the following eight regions, Tohoku, Kanto, Hokuriku, Chubu, Kinki, Chugoku, Shikoku and Kyushu. Our analysis shows that in such a major timber consumption region as Kanto, Chubu and Kinki, timber demand is elastic to price. It is also shown that the domestic lumber supply is inelastic to price in each region, while the import lumber supply is slightly elastic to price.

FAO developed a forest product trade model by applying GFPM (Global Forest Product Model) to trading fifteen products among sixteen nations in Asia and other seven nations over the time horizon till 2020. At this moment, there remain some problems on this kind of the modeling approach to policy analysis from the viewpoint of comparative dynamics. This paper is to clarify possibility and limitation of such a model for policy analysis on timber trade by reviewing the report from USTR on the tariff liberalization of forest products with a use of GFPM and CGTM (CINTRAFOR Global Trade Model).