Application of process-based models to forest management: experience with PROMOD, a simple plantation productivity model.

Process-based growth models are rarely used as a basis for decisions in forest management. Reasons for this are discussed and the development and application of PROMOD, a simple process-based plantation productivity model designed to meet the needs of managers, is described. In particular,PROMOD is intended for screening prospective plantation sites on the basis of readily available input data, including site latitude, soil characteristics, and long-term climate data. Originally developed for use with Eucalyptus globulus Labill., PROMOD has since been parameterized also for Eucalyptus nitens (Deane & Maiden) Maiden and Pinus radiata D. Don. We discuss the adaptation of PROMOD to new environmental conditions and species; the sensitivity of the model's predictions to changes in model structure, the values of its physiological parameters and the accuracy and resolution of site survey information; and the use of the model both in assessing the profitability of plantation irrigation in semi-arid regions, and for generating broad-area productivity maps.

A wide-angle gradient index optical model of the crystalline lens and eye of the octopus.

Cephalopods and fish have had no common ancestor since the Cambrian, and their eyes are a classic example of convergent evolution. The octopus has no cornea, and immerson renders the trout cornea optically ineffective. As a result, the nearly spherical lens is responsible for all refraction in these eyes. In spite of the fact that the octopus lens consists of two joined parts, while the trout lens consists of one part, we show here that their optical properties are very similar. An index gradient bends rays within these lenses, adding power and correcting spherical aberration. High spherical symmetry in both lenses strongly reduces other monochromatic aberrations and yields a wide field of vision, advantageous in attack and evasion. The octopus Mattheissen's ratio, 2.83, an inverse measure of light-gathering power, lies above the trout value of 2.38 but within the range of values reported for fish. Strong uncorrected longitudinal chromatic aberration is nearly identical in both animals as a result of similar lens protein optical properties, and will limit resolution. We discuss how animal lifestyle requirements and lens material properties influence the design of these eyes.

Modeling the effect of physiological responses to green pruning on net biomass production of Eucalyptus nitens.

Green pruning of Eucalyptus nitens (Deane and Maiden) Maiden increases instantaneous rates of light-saturated CO(2) assimilation (A), and changes patterns of total leaf area and foliage distribution. We investigated the importance of such changes on the rate of recovery of growth following pruning. A simple process-based model was developed to estimate daily net biomass production (G(d)) of three-year-old plantation-grown trees over a 20-month period. The trees had been pruned by removal of 0, 50 or 70% of the length of green crown, equivalent to removal of 0, 55 or 88% of leaf area, respectively, when the plantation verged on canopy closure. Total G(d) was reduced by only 20% immediately following the 50%-pruning treatment, as a result of both the high leaf dark respiration and low A in the portion of the crown removed compared to the top of the crown. Pruning at the time of canopy closure preempted a natural and rapid decline in G(d) of the lower crown. Although leaf area index (L) was approximately 6.0 at the time of pruning, high light interception (95%) occurred with an L of 4.0. The 50%-pruning treatment reduced L to 3.5, but the physiological responses to pruning were sufficient to compensate fully for the reduction in intercepted radiation within 110 days of pruning. The 70%-pruning treatment reduced L to 1.9, and reduced G(d) by 77%, reflecting the removal of branches with high A in the mid and upper crown. Physiological responses to the 70%-pruning treatment were insufficient to increase G(d) to the value of unpruned trees during the study. Model sensitivity analysis showed that increases in A following pruning increased G(d) by 20 and 25% in the 50- and 70%-pruned trees, respectively, 20 months after pruning. Changes in leaf area/foliage distribution had a greater effect on G(d) of 50%-pruned trees (47% increase) than did changes in A. However, the reduction in photosynthetic potential associated with the 70%-pruning treatment resulted in only small changes in leaf area/foliage distribution, which consequently had little effect on G(d). The effects of physiological processes occurring within the crown and in response to green pruning on G(d) are discussed with respect to pruning of plantations.

Freezing behaviors in leaf buds of cold-hardy conifers visualized by NMR microscopy.

A calibration curve was established to convert plant area index of Eucalyptus nitens (Deane and Maiden) Maiden, assessed with a Li-Cor LAI-2000, to leaf area index, LAI. Based on a comparison of this calibration curve with existing calibration curves for other species, we concluded that a generic calibration curve may be applicable for the assessment of LAI in eucalypt plantations. The Li-Cor LAI-2000 measurements were used to correlate the equilibrium LAI of E. nitens plantations with mean annual temperature. These and other data were then combined to develop relationships between LAI in both E. nitens and E. globulus Labill. plantations and mean annual temperature and water stress. In plantations of both species, LAI declined linearly with water stress. However, marked differences in the effect of suboptimal growth temperatures on LAI were observed between species: on cold sites, LAI of E. nitens was markedly higher than LAI of E. globulus. A simple analytic model of net primary production (NPP) was developed. In this model, increasing LAI increased light interception and hence dry matter production, but simultaneously increased canopy respiration. Consequently, for a given light utilization coefficient (epsilon), there was a value of LAI that maximized NPP. The model was parameterized for E. globulus and used to investigate the influences of water stress and mean annual temperature on LAI through their effects on epsilon. The model indicated that the value of LAI that was predicted to maximize NPP under various water and temperature stress regimes was similar to the value of LAI observed in the field under similar conditions only if leaf longevity was linked to water and temperature stress.

A wide-angle gradient index optical model of the crystalline lens and eye of the rainbow trout.

Trout lens external shape and internal refractive index gradient structure were measured and used to construct an optical lens model that predicts by ray tracing the average longitudinal spherical and chromatic aberration, focal length and image quality. The nearly spherical shape of the lens was measured from photographs, and the internal refractive gradient structure was measured directly with a special Pulfrich areal refractometer. Longitudinal spherical aberration and back focal length were measured using a simplified Hartmann test using laser beams and a Schlieren test which additionally made refractive index gradient fine structure visible and detected scattering, axial symmetry and structural irregularity. Axial focus shift caused by longitudinal chromatic aberration was measured using a star test. The model lens was then incorporated into a model trout eye based on vertical and horizontal eye frozen sections. Calculated model function yields insight into the relation between eye and lens structure and optical behaviour. Semi-random secondary structural features act as perturbations on the basic model, and will result in point image fine structure.

Refractive index within the lens of a goldfish eye determined from the paths of thin laser beams.

The paths of 15 micron diameter laser beams traversing goldfish eye lenses were photographed. Measurements of these photographs gave experimental data for the distance of the exit point of each ray from the lens axis as a function of the corresponding entrance distance. A number of mathematical models with distinct distributions of refractive index within the lens were analysed by tracing rays to simulate the experimental data. The only distributions for which the simulated and experimental data were in agreement have a refractive index N which varies continuously with distance r from the lens center in a manner consistent with that originally proposed by Matthiessen: N2 = a - br2. Estimates for the central (1.55-1.57) and surface (1.35-1.38) refractive indices of the goldfish eye lens are derived from the preferred model, but these differ from those previously given by Matthiessen for other species. The optical performance of the lens models is also compared by third-order analyses.

Classification scheme and nomenclature for refractive-index distributions.

A classification scheme and nomenclature for inhomogeneous refractive-index distributions is proposed which is consistent, unambiguous, and appeals to intuition. The classification is based on (1) the generic shape of the isoindicial surfaces, (2) the detailed dependence of the index on some position coordinate characterizing the isoindicial surfaces, and (3) whether the index distribution is given by N or N2 as some function of position. The scheme is illustrated by distributions which are of technological or physiological interest.

Aberration coefficients and unusual coordinates for specifying rays.

The aberration coefficients of Buchdahl have been used almost exclusively in situations where rays are specified by their points of intersection with a pair of planes in the object space of the system. A simple method is presented in this paper whereby rays may be specified by their points of intersection with a pair of not necessarily plane surfaces situated in quite distinct parts of the system. The manner in which existing schemes for computing the aberration coefficients must be modified in order to accommodate the new coordinates is considered in detail. They stem basically from the need to reinterpret the intermediate coefficients appearing in the iteration equations and include modifications to the identities between the coefficients. Three examples of the new coordinates are discussed, namely: the case where the object surface is a surface of revolution about the optic axis, and the cases where rays are specified by their points of intersection with the (physical) aperture stop of the system (aperture oordinates) or with an ideal spherical wave surface in the image space of the system (W(o) coordinates).