Akio Inoue

Calibrating view angle and lens distortion of the Nikon fish-eye converter FC-E8

Recently, an inexpensive digital camera that can equip with a fish-eye converter lens, FC-E8, has been available from Nikon. The converter has more than 180° view angle and lens distortion. The objectives of the present study were to develop a procedure for calibrating the view angle and lens distortion of the fish-eye converter, and to examine the effect of the calibration on light environment estimates. Based on unpublished data provided by the Electric Image Technical Center of Nikon, a 12-order poly-nomial expression for the calibration was derived. The expression enabled us to calibrate the view angle and lens distortion for all selectable resolution digital images. Using a Nikon Coolpix 990 digital camera with the fish-eye converter, 105 hemispherical photographs were taken in 15 stands, and then the canopy cover and weighted openness were measured as the light environment estimates. The calibrated estimates were significantly higher than uncalibrated ones, but the differences were comparatively small, with the average differences being 0.658% for canopy cover and 0.344% for weighted openness. A strongly positive correlation between calibrated and uncalibrated estimates was observed. Both slope and intercept of the regression lines of the calibrated estimate against the uncalibrated one were significantly different between canopy cover and weighted openness, suggesting that the calibration effect would be different among light environment estimates. In conclusion, we should pay attention to the view angle and lens distortion of the fish-eye converter in estimating light environments using the Coolpix digital camera.

Effects of residual trees on tree height of 18- and 19-year-old Cryptomeria japonica planted in group selection openings

This study examined the effects of residual trees on the height of 18- and 19-year-old Cryptomeria japonica planted in group selection openings of about 0.1u2009ha at Yufuin in Oita Prefecture in southern Japan. We first developed a general model expressing variation in the height for all of the planted trees within the openings from indices of both between-cohort competition (the effects of residual trees) and within-cohort competition (among the even-aged planted trees). The between-cohort competition index was calculated both with and without taking into account the direction that residual trees were positioned from subject trees. The two models suggested that residual trees located near the northern edge of the opening were not effective competitors for light for the planted trees within the opening. In addition, our results indicated that both between-cohort competition and within-cohort competition are important for explaining tree height in closed stands within group selection openings. Using the general model, we then estimated the potential loss of height growth for locally dominant trees within the openings that could be attributed only to the influence of residual trees. These results indicated that in addition to the effect of opening size, both the degree of crowding and the direction of residual trees from the planted trees are important factors affecting the height of individual trees planted in group selection openings.

Relationships of stem surface area to other stem dimensions for Japanese cedar (Cryptomeria japonica D. Don) and Japanese cypress (Chamaecyparis obtusa Endl.) trees

I investigated the relationships between stem surface area outside bark and other stem dimensions for Japanese cedar (Cryptomeria japonica D. Don) and Japanese cypress (Chamaecyparis obtusa Endl.) trees. The stem dimensions used here were the basal area and the product of diameter at breast height (dbh) and total tree height. The regression equation of the stem surface area s against basal area g was s = 184.216u2009g for the cedar trees and s = 156.878u2009g for the cypress trees. The slope of the equation was significantly different between the two species. For the same dbh, the cedar trees tended to have a higher total tree height than the cypress trees. The cedar trees also had a larger surface area of relative stem form than the cypress trees. These results indicated that the difference in the slope was produced by the differences in both the stem slenderness and tapering between the two species. On the other hand, the regression equation between the stem surface area and the product of dbh and total tree height dh was s = 1.937u2009dh for the cedar trees and s = 1.921u2009dh for the cypress trees, whereas no significant difference in the slope was found. The obtained slopes for the cedar and cypress trees seemed to be in accord with that for other coniferous species reported in earlier studies, suggesting that the variation in the slope among coniferous species would be small. The estimation from the basal area would provide a simpler means for estimating the stem surface area and would be useful in obtaining an approximation of the surface area. By contrast, the estimation from the product of dbh and total tree height would provide a more accurate and precise estimate as well as a wider applicable range, i.e., a parameter for physiological growth models. In conclusion, it could not be judged which regression equation examined in the present study was superior to the other, and thus it was important to select an appropriate equation depending both on the purpose and on the time and labor available.

A model for the relationship between form-factors for stem volume and those for stem surface area in coniferous species

A model that describes the relationship between the form-factors for stem volume and those for stem surface area in coniferous species is proposed. The model is derived assuming that the stem form of a tree can be expressed by Kunzes equation. The model indicated that the form-factor for stem surface area was directly proportional to the square root of the form-factor for stem surface volume, independent of the stem position. The proposed model expressed the relationship of the form-factors for Japanese cedar (Cryptomeria japonica D. Don) and Japanese cypress (Chamaecyparis obtusa Endl.) trees well. Therefore, the form-factors for stem surface area could be estimated from those for stem volume. No significant difference in the coefficient was found between Japanese cedar and Japanese cypress trees, indicating that the proportional coefficient would be common between the two species. Many studies have shown that the form-factors for stem volume at 0.7 and 0.5 in relative height were, respectively, almost steady at 0.7 and 1.0, independent of species, district, density control, and growth stage. Substituting these universal values into the proposed model, the form-factors for stem surface area at 0.7 and 0.5 in relative height were estimated to be 0.730 and 0.873, respectively. The estimated values of the form-factors for stem surface area would be universal for coniferous species. The proposed model also showed that the breast height form-factor for stem surface area decreased sharply with the increase in total tree height, when the height was less than 10u2009m. However, after the tree attained the total height of 10u2009m, the breast height form-factor gradually decreased with the total tree height approaching its asymptotic value of 0.605. In conclusion, the model proposed here can be used to describe the relationship between form-factors for stem volume and those for stem surface area successfully.

Effects of light and microsite conditions on tree size of 6-year-old Cryptomeria japonica planted in a group selection opening

We examined the extent to which direct and indirect measures of light and microsite conditions could explain variation in tree height and diameter at the base of 6-year-old Cryptomeria japonica trees planted in a group selection opening of about 0.32u2009ha on a steep slope at Shiiba, Miyazaki Prefecture, southern Japan. We first used the gap light index (GLI) and soil thickness (ST) as directly measured indices. For an indirect measure of light, we used a between-cohort competition index (BCI) estimated from the position and total height of residual trees. For indirect measures of microsite, we examined topographic indices (slope, plan and profile curvature, average slope gradient, and relative elevation) derived from digital elevation models (DEMs) with different resolutions ranging from 2 to 10u2009m. The multiple linear regression using GLI and ST explained about 45% of variation in tree size, while simple regression using only GLI explained about 35%. The contribution of ST was about half of GLI. The multiple regressions using BCI and the topographic indices did not explain any more variation than using BCI alone (R2 of about 0.26). We conclude that microsite conditions with shallower soil and steeper slope have negative effects on tree growth in group selection openings, although the relative importance is smaller than light conditions. More comprehensive studies considering several openings with more heterogeneous topography including different species are needed to generalize our growth prediction using the indirect measures, which are useful for practical forest management.

Allometric model of the Reineke equation for Japanese cypress (Chamaecyparis obtusa) and red pine (Pinus densiflora) stands

An allometric model that explains the mechanism of the difference in the slope of the Reineke equation (A) among species was proposed based on the allometric relationships of mean tree height (H) to quadratic mean diameter D (H ∝ Dθ) and stand density N (H ∝ Nδ), i.e., A = θ/δ. The proposed model was fitted to Japanese cypress (Chamaecyparis obtusa Endl.) and red pine (Pinus densiflora) stands. The allometric exponents θ and δ were, respectively, 0.8995 and −0.5000 for cypress and 0.8612 and −0.6619 for pine. The difference between cypress and pine was significant for δ but not for θ. Inserting the exponents into the model resulted in predicted slopes of −1.7991 for cypress and −1.3011 for pine. The difference in the slope of the Reineke equation between the two species was produced by characteristics related to the tree crown, rather than characteristics related to stem slenderness. The proposed model enables us to estimate the slope of the Reineke equation from commonly measured stand attributes, such as mean tree height and quadratic mean diameter. Therefore, the proposed model is expected to be practical and convenient for estimating the slope of the Reineke equation and for explaining the mechanism of its variation among species. The model should be also accepted as a generalized model of the stand density versus quadratic mean diameter relationship, whereas the original Reineke equation should be seen as a specific case of this model.

Allometric model of the height—diameter curve for even-aged pure stands of Japanese cedar (Cryptomeria japonica)

We derived an allometric model of the height–diameter curve for even-aged pure stands, which was a modification of the earlier model proposed by Inoue (2000a). An individual-dependent allometric equation was used as the height–diameter curve. Using the discriminant analysis method, all trees composed of a stand were stratified into upper and lower trees. It was assumed that both relationships between mean tree height Hm and upper tree height Hu and between mean DBH Dm and mean DBH of upper trees Du could be described by the time-dependent allometric power equations. The height–diameter curve showed an average relationship between tree height and DBH of a given stand at a given time, and hence it could be assumed that the height–diameter curve contained two points (Dm, Hm) and (Du, Hu). With these assumptions, we derived an allometirc model of height–diameter curve, which allowed the coefficients of the curve to be estimated from mean tree height and mean DBH. The proposed model was fitted to Japanese cedar (Cryptomeria japonica D. Don) data. The error ratio of the allometric model ranged from 2.254% to 13.412% (mean = 6.785%), which was significantly smaller than that of the earlier model. When the error of mean tree height was ±1.0u2009m or less, the effect of the error of mean tree height on the error ratio was comparatively small. This suggested that the error of ±1.0u2009m in mean tree height could be accepted in the estimation of height–diameter curve using the allometric model. These features enable us to combine the allometric model with Hirata’s vertical angle-count sampling or growth models. In conclusion, the allometric model would be one of the most practical and convenient approaches for estimating the height–diameter relationship of even-aged pure stands.