Do trees have constant branch divergence angles?

Many herbaceous plants feature remarkably regular arrangements of lateral organs along the central axis. These phyllotactic patterns are generated by a constant divergence angle between successive buds (or whorls thereof) that first appears at the shoot apircal meristem and is maintained across later ontogentic stages when it can be observed at the macroscopic scale. Do the branches along a tree trunk exhibit similar patterns? Here we use branch skeleton data derived from terrestrial laser scans to empirically estimate the distributions of the divergence angles between successive branches along the trunks of mature European beech, Norway spruce, and Scots pine trees. We find that rather than clustering around a particular value, species-specific branch divergence angles feature statistical properties characteristic of a uniform distribution. We hypothesise this to be the result of the stochasticity in bud development and branch shedding, and provide a rigorous mathematical proof that even when the divergence angle between successive lateral buds is constant, the observed distribution of branch divergence angles will approximate a uniform distribution if bud mortality and branch shedding rates are high.

Acceleration of the rotation of asteroid 1862 Apollo by radiation torques.

The anisotropic reflection and thermal re-emission of sunlight from an asteroid's surface acts as a propulsion engine. The net propulsion force (Yarkovsky effect) changes the orbital dynamics of the body at a rate that depends on its physical properties; for irregularly shaped bodies, the propulsion causes a net torque (the Yarkovsky-O'Keefe-Radzievskii-Paddack or YORP effect) that can change the object's rotation period and the direction of its rotation axis. The Yarkovsky effect has been observed directly, and there is also indirect evidence of its role in the orbital evolution of asteroids over long time intervals. So far, however, only indirect evidence exists for the YORP effect through the clustering of the directions of rotation axes in asteroid families. Here we report a change in the rotation rate of the asteroid 1862 Apollo, which is best explained by the YORP mechanism. The change is fairly large and clearly visible in photometric lightcurves, amounting to one extra rotation cycle in just 40 years even though Apollo's size is well over one kilometre. This confirms the prediction that the YORP effect plays a significant part in the dynamical evolution of asteroids.

Absolute radiometric calibration of Als intensity data: effects on accuracy and target classification.

Radiometric calibration of airborne laser scanning (ALS) intensity data aims at retrieving a value related to the target scattering properties, which is independent on the instrument or flight parameters. The aim of a calibration procedure is also to be able to compare results from different flights and instruments, but practical applications are sparsely available, and the performance of calibration methods for this purpose needs to be further assessed. We have studied the radiometric calibration with data from three separate flights and two different instruments using external calibration targets. We find that the intensity data from different flights and instruments can be compared to each other only after a radiometric calibration process using separate calibration targets carefully selected for each flight. The calibration is also necessary for target classification purposes, such as separating vegetation from sand using intensity data from different flights. The classification results are meaningful only for calibrated intensity data.

Uncertainty in multispectral lidar signals caused by incidence angle effects.

Multispectral terrestrial laser scanning (TLS) is an emerging technology. Several manufacturers already offer commercial dual or three wavelength airborne laser scanners, while multispectral TLS is still carried out mainly with research instruments. Many of these research efforts have focused on the study of vegetation. The aim of this paper is to study the uncertainty of the measurement of spectral indices of vegetation with multispectral lidar. Using two spectral indices as examples, we find that the uncertainty is due to systematic errors caused by the wavelength dependency of laser incidence angle effects. This finding is empirical, and the error cannot be removed by modelling or instrument modification. The discovery and study of these effects has been enabled by hyperspectral and multispectral TLS, and it has become a subject of active research within the past few years. We summarize the most recent studies on multi-wavelength incidence angle effects and present new results on the effect of specular reflection from the leaf surface, and the surface structure, which have been suggested to play a key role. We also discuss the consequences to the measurement of spectral indices with multispectral TLS, and a possible correction scheme using a synthetic laser footprint.

Non-intersecting leaf insertion algorithm for tree structure models.

We present an algorithm and an implementation to insert broadleaves or needleleaves into a quantitative structure model according to an arbitrary distribution, and a data structure to store the required information efficiently. A structure model contains the geometry and branching structure of a tree. The purpose of this work is to offer a tool for making more realistic simulations of tree models with leaves, particularly for tree models developed from terrestrial laser scanning (TLS) measurements. We demonstrate leaf insertion using cylinder-based structure models, but the associated software implementation is written in a way that enables the easy use of other types of structure models. Distributions controlling leaf location, size and angles as well as the shape of individual leaves are user definable, allowing any type of distribution. The leaf generation process consist of two stages, the first of which generates individual leaf geometry following the input distributions, while in the other stage intersections are prevented by carrying out transformations when required. Initial testing was carried out on English oak trees to demonstrate the approach and to assess the required computational resources. Depending on the size and complexity of the tree, leaf generation takes between 6 and 18 min. Various leaf area density distributions were defined, and the resulting leaf covers were compared with manual leaf harvesting measurements. The results are not conclusive, but they show great potential for the method. In the future, if our method is demonstrated to work well for TLS data from multiple tree types, the approach is likely to be very useful for three-dimensional structure and radiative transfer simulation applications, including remote sensing, ecology and forestry, among others.

Bayes Forest: a data-intensive generator of morphological tree clones.

Detailed and realistic tree form generators have numerous applications in ecology and forestry. For example, the varying morphology of trees contributes differently to formation of landscapes, natural habitats of species, and eco-physiological characteristics of the biosphere. Here, we present an algorithm for generating morphological tree "clones" based on the detailed reconstruction of the laser scanning data, statistical measure of similarity, and a plant growth model with simple stochastic rules. The algorithm is designed to produce tree forms, i.e., morphological clones, similar (and not identical) in respect to tree-level structure, but varying in fine-scale structural detail. Although we opted for certain choices in our algorithm, individual parts may vary depending on the application, making it a general adaptable pipeline. Namely, we showed that a specific multipurpose procedural stochastic growth model can be algorithmically adjusted to produce the morphological clones replicated from the target experimentally measured tree. For this, we developed a statistical measure of similarity (structural distance) between any given pair of trees, which allows for the comprehensive comparing of the tree morphologies by means of empirical distributions describing the geometrical and topological features of a tree. Finally, we developed a programmable interface to manipulate data required by the algorithm. Our algorithm can be used in a variety of applications for exploration of the morphological potential of the growth models (both theoretical and experimental), arising in all sectors of plant science research.

Aperture size effects on backscatter intensity measurements in Earth and space remote sensing.

Most materials show a peaked intensity versus phase (light-source-target-detector angle) curve. For nonnegligible angular apertures of the source and/or the detector, the measured intensity at and near zero phase (backscatter) is lower than the real one. We derive an averaging aperture integral that represents this effect, and with it we invert measured intensity values to obtain the actual intensity curve. We also give a practical formula for estimating the magnitude of the aperture effect in zero-phase intensity measurements and show that only two such measurements made at different apertures are sufficient for deriving the real intensity. These corrections are needed in the comparison of measured reflectances in an increasing number of validation efforts for remote sensing applications requiring ground truth measurements.

Small-angle goniometry for backscattering measurements in the broadband spectrum.

We present experiments on spectral bidirectional reflectance distribution function (BRDF) effects at backscatter and discuss the feasibility of new methods for laboratory and field simulations of remote sensing of land surfaces. The extreme sharpness of the intensity peak allows both directional and comparative experimental spectral studies of hot spots. We demonstrate wavelength-dependent features in the hot-spot reflectance signatures that facilitate extension of spectral and directional BRDF measurements of natural targets (such as forest understories and ice surfaces) into retroreflection to exploit their hot-spot characteristics in the interpretation of spaceborne and airborne data.