Cross-sectional interpolation of annual rings within a 3D root model

Ring width of a given year can be highly variable throughout the cross section of a stem. This is especially true for roots. Therefore, the entire circumference of tree rings is often needed for studies focusing on specific reactions of individual trees on certain environmental conditions. Also, ring reconstructions are of interest for biomass calculations estimated by the cross-sectional area. The aim of the study is thus to reconstruct tree rings of cross sections within a 3D root-surface model, which will be the basis for an upcoming 3D root-development model. A FARO ScanArm was used for the acquisition of the 3D root structure (Technologies Inc., 2010). Afterwards ring-width data was measured along 4 radii per cross section and the resulting ring boundaries were integrated into the 3D root model. A weighted interpolation algorithm was used to reconstruct entire ring-width profiles of the cross sections. The algorithm considered the ring-width variations of the adjacent radii as well as the outer shape of the cross section. Hence, the intention was to estimate ring width around the root circumference using ring widths measured along 4 radii and the surface dimensions of roots. Interpolated ring-width data was compared to the measured tree-ring data as a control for the developed interpolation algorithm. Comparisons between modelled and empirical values showed a mean absolute error of about 0.06 mm deviation, and with a few exceptions the growth patterns could be accurately simulated. This has permitted additional radii measurements to be replaced by model interpolations.     

Incorporating 2D tree-ring data in 3D laser scans of coarse-root systems

In times of global change biomass calculations and the carbon cycle is gaining in importance. Forests act as carbon sinks and hence, play a crucial role in worlds and forests carbon budgets. Unfortunately, growth models and biomass calculations existing so far mainly concentrate on the above-ground part of trees. For this reason, the aim of the present study is to develop an annually resolved 3D growth model for tree roots, which allows for reliable biomass calculations and can later be combined with above-ground models. A FARO scan arm was used to measure the surface of a tree-root segment. In addition, ring-width measurements were performed manually on sampled cross sections using WinDENDRO. The main goal of this study is to model root growth on an annual scale by combining these data sets. In particular, a laser scan arm was tested as a device for the realistic reproduction of tree-root architecture, although the first evaluation has been performed for a root segment rather than for an entire root system. Deviations in volume calculations differed between 5% and 7% from the actual volume and varied depending on the used modeling technique. The model with the smallest deviations represented the structure of the root segment in a realistic way and distances and diameter of cross sections were acceptable approximations of the real values. However, the volume calculations varied depending on object complexity, modeling technique and order of modeling steps. In addition, it was possible to merge tree-ring borders as coordinates into the surface model and receive age information in connection with the spatial allocation. The scan arm was evaluated as an innovative and applicable device with high potential for root modeling. Nevertheless, there are still many problems connected with the scanning technique which have an influence on the accuracy of the model but are expected to improve with technical progress.     

Preparing micro sections of entire (dry) conifer increment cores for wood anatomical time-series analyses

The type of samples most commonly used in dendro sciences are increment cores of conifers. These cores allow for an easy determination and measurement of ring-width variations over long time periods. For wood anatomical analyses, the cores have to be split into pieces to enable the preparation of high quality micro sections for detailed measurements of cell properties. A major drawback of this procedure is the fact that it is labor intensive and time consuming. We present a new technique enabling the preparation of micro sections of entire increment cores up to a length of 40 cm. For that purpose we combined standard wood-anatomical techniques with the application of Mowiol glue and common Tesa tape. We tested the introduced method on increment cores of Larix decidua Mill. sampled years ago for ring-width analyses to reanalyze them on a microscopic level. The ability to cut these long sections will tremendously reduce the time needed to prepare micro sections. This is of special interest for wood anatomical image analyses of cores used before to create long ring-width chronologies for any kind of environmental reconstructions.     

Multiple dendrochronological responses to the eruption of Cinder Cone,Lassen Volcanic National Park,California

Two dendrochronological properties – ring width and ring chemistry – were investigated in trees near Cinder Cone in Lassen Volcanic National Park, northeastern California, for the purpose of re-evaluating the date of its eruption. Cinder Cone is thought to have erupted in AD 1666 based on ring-width evidence, but interpreting ring-width changes alone is not straightforward because many forest disturbances can cause changes in ring width. Old Jeffrey pines growing in Cinder Cone tephra and elsewhere for control comparison were sampled. Trees growing in tephra show synchronous ring-width changes at AD 1666, but this ring-width signal could be considered ambiguous for dating the eruption because changes in ring width can be caused by other events. Trees growing in tephra also show changes in ring phosphorus, sulfur, and sodium during the late 1660s, but inter-tree variability in dendrochemical signals makes dating the eruption from ring chemistry alone difficult. The combination of dendrochemistry and ring-width signals improves confidence in dating the eruption of Cinder Cone over the analysis of just one ring-growth property. These results are similar to another case study using dendrochronology of ring width and ring chemistry at Parícutin, Michoacán, Mexico, a cinder cone that erupted beginning in 1943. In both cases, combining analysis with ring width and ring chemistry improved confidence in the dendro-dating of the eruptions.     

MtreeRing: An R package with graphical user interface for automatic measurement of tree ring widths using image processing techniques

Accurate measurements of ring-width series are essential for dendrochronological analyses. We present an R package MtreeRing for ring-width measurements on scanned digital images. A morphological alternate sequential filter is used for noise reduction in the original image. Ring boundaries are determined by the steepest negative slopes in the light reflectance of latewood-earlywood transitions. To automatically identify tree rings, the package provides three alternative methods (watershed-based segmentation, Canny edge detector, and a linear detection algorithm), each with advantages and disadvantages and suited to different wood anatomical features. The user can also manually mark tree rings on species with complex anatomical structures. The arcs of inner-rings and angles of successive inclined ring boundaries are used to correct ring-width series. Differences in ring-width measurements between MtreeRing and WinDENDRO in a given coniferous species (Larix gmelinii) were assessed, and no significant difference between programs was found. Furthermore, the package provides an R-based web application which was developed using the Shiny framework. This beginner-friendly application allows viewing and interacting with tree ring images. It requires no programming experience and can run on either a local computer or a remote server.     

ONTOGENETIC ANALYSIS OF TREE ROOTS IN ACER RUBRUM AND BETULA PAPYRIFERA

The development of long (6-20 m) tree roots was reconstructed from serial transverse sections taken 10-20 cm apart. Measurements of primary xylem diameter showed that the tips of long roots of red maple (Acer rubrum L.) and paper birch (Betula papyrifera Marsh.) are initially small, but they increase in diameter with increasing distance from the stem. A repeating pattern of the width of the first annual ring marks length increments of long roots. The pattern of ring width is paralleled by a pattern of primary xylem diameter. Our interpretation is that primary xylem diameter increases during spring and early summer, stays constant during late summer and decreases in autumn. After injuries to large root tips, new large lateral tips are formed that replace the parent tip. Thus, a single long root is actually formed by a succession of these replacement roots. In a series of sections there may be sudden changes in primary xylem diameter as the successive sections pass from parent root to replacement root at points of injury. These changes in birch are associated with changes in a number of protoxylem poles.     

Comparison of radial increment and volume growth in stems and roots of Quercus petraea

Dendrochronological studies dealing with roots, stems and branches are very rare or often take the form of short notes. The difficulties of detecting rings and of quantifying the radial growth in roots have already been described for various species. In oak the anatomical root structure differs from stemwood. The roots are radial-porous or diffuse-porous, and there is often no clear distinction between individual rings. In our study visual and radiographic techniques were used to examine radial increment in roots of sessile oak (Quercus petraea L.) which was compared with radial growth in branches and along the stem. Coarse roots were cut from four 30- to 34-year-old trees that had been uprooted mechanically and disks were taken at different distances from the stem-root base. Ring widths were measured in the stem at height of 0.3 m, at breast height (1.3 m), beneath the crown, in branches of the crown, and in roots every 20 cm. The ring widths were cross-dated, and the heterogeneity of growth within a root and within the root system were analysed. Asymmetric growth frequently occurred in roots so that ovals, I-beam and T-beam shapes were developed. With the method used in our study the annual growth layers close to the central cylinder could be distinguished as well as beneath the bark. Pointer years were detected in all sections of the tree and permitted correction of ring widths in roots. Root system, stem and branch showed a basic similarity in their radial sequence of ring width. The annual biomass increment was weaker and more variable with several consecutive changes in the roots than in the stems. The root/shoot ratio reached a minimum rather early, beginning at the cambial age of 20 years. This revised version was published online in June 2006 with corrections to the Cover Date.     

Evaluation in field conditions of a three-dimensional architectural model of the maize root system: Comparison of simulated and observed horizontal root maps

Most existing water and nutrient uptake models are based on the assumption that roots are evenly distributed in the soil volume. This assumption is not realistic for field conditions, and significantly alters water or nutrient uptake calculations. Therefore, development of models of root system growth that account for the spatial distribution of roots is necessary.The objective of this work was to test a three dimensional architectural model of the maize root system by comparing simulated horizontal root maps with observed root maps obtained from the field. The model was built using the current knowledge on maize root system morphogenesis and parameters obtained under field conditions. Simulated root maps (0.45 × 0.75 m) of horizontal cross sections at 3 depths and 3 dates were obtained by using the model for a plant population. Actual root maps were obtained in a deep, barrier-free clay-loamy soil by digging pits, preparing selected horizontal planes and recording root contacts on plastic sheets.Results showed that both the number of cross-sections of axile roots, and their spatial distribution characterized with the R-index value of Clark and Evans (1954), were correctly accounted for by the model at all dates and depths. The number of cross-sections of laterals was also correctly predicted. However, laterals were more clustered around axile roots on simulated root maps than on observed root maps. Although slight discrepancies appeared between simulated and observed root maps in this respect, it was concluded that the model correctly accounted for the general colonization pattern of the soil volume by roots under a maize crop.     

Unusual Fine Root Distributions of Two Deciduous Tree Species in Southern France: What Consequences for Modelling of Tree Root Dynamics?

The spatial distribution of fine roots of two deciduous tree species was investigated in contrasting growing conditions in southern France. Hybrid walnut trees (Juglans regia×nigra cv. NG23) and hybrid poplars (Populus euramericana cv. I214) were both cultivated with or without annual winter intercrops for 10 years on deep alluvial soils. Soil samples for measuring the fine root distribution of both trees and crops were obtained by soil coring down to 3-m depth at several distances and orientations from the tree trunk. The distribution of live fine roots from walnut and poplar trees was patchy and sometimes unexpected. In the tree-only stands, fine root profiles followed the expected pattern, as fine root density decreased with increasing depth and distance from the tree trunk. However, many fine root profiles under intercropped trees were uniform with depth, and some inverse profiles were observed. These distributions may result from a high degree of plasticity of tree root systems to sense and adapt to fluctuating and heterogeneous soil conditions. The distortion of the tree root system was more pronounced for the walnut trees that only partially explored the soil volume: in the tree-only stand, the walnut rooting pattern was very superficial, but in the intercropped stand walnut trees developed a deep and dense fine root network below the crop rooting zone. The larger poplars explored the whole available soil volume, but the intercrop significantly displaced the root density from the topsoil to layers below 1 m depth. Most tree root growth models assume a decreasing fine root density with depth and distance from the tree stem. These models would not predict correctly tree–tree and tree–understorey competition for water and nutrients in 3D heterogeneous soil conditions that prevail under low-density tree stands. To account for the integrated response of tree root systems to such transient gradients in soils, we need a dynamic model that would allow for both genotypic plasticity and transient environmental local soil conditions.     

A density-based approach for the modelling of root architecture: application to Maritime pine (Pinus pinaster Ait.) root systems

Root morphology influences strongly plant/soil interactions. However, the complexity of root architecture is a major barrier when analysing many phenomena, e.g. anchorage, water or nutrient uptake. Therefore, we have developed a new approach for the representation and modelling of root architecture based on branching density. A general root branching density in a space of finite dimension was used and enabled us to consider various morphological properties. A root system model was then constructed which minimizes the difference between measured and simulated root systems, expressed with functions which map root density in the soil. The model was tested in 2D using data from Maritime pine Pinus pinaster Ait. structural roots as input. We showed that simulated and real root systems had similar root distributions in terms of radial distance, depth, branching angle and branching order. These results indicate that general density functions are not only a powerful basis for constructing models of architecture, but can also be used to represent such structures when considering root/soil interaction. These models are particularly useful in that they provide a local morphological characterization which is aggregated in a given unit of soil volume.     

Temporal variability and scaling behaviour in the fine-root system of kiwifruit (Actinidia deliciosa)

We show that temporal variability in root populations can depend upon the scale of measurement (particularly the sampled soil volume). The presence of roots in a range of volumes of soil was studied using perspex tubes installed horizontally into the soil around three mature kiwifruit vines. Roots intercepting lines scored on the tubes were counted using a periscope. For small volumes of soil (c. 2–4 cm³) the root counts varied with time in a very irregular manner, and as the interval between measurements increased the autocorrelation between the measurements decayed rapidly. At about half of the locations monitored there was no significant autocorrelation between measurements 27 d apart. Linear interpolation in these time series was unreliable, and where the correlation dimension could be resolved it was usually non-integer (suggesting chaotic behaviour). The time series measured at different locations were poorly correlated, indicating weak coordination. As the observed soil volume increased, the coordination between locations improved, the autocorrelation function increased, and linear interpolation errors decreased (although these remained substantial). Clearly there are considerable fundamental constraints on our ability to predict the root behaviour of kiwifruit vines at scales that are appropriate for mechanistic models of nutrient and water uptake. We discuss the need for a new conceptual model of the fine-root systems of kiwifruit and similar species.     

Assessing bias in diameter at breast height estimated from tree rings and its effects on basal area increment and biomass

Above-ground forest productivity can be reliably estimated from tree-ring width measurements. In doing so, annual growth is linked to the tree’s basal area increment (BAI), which is the change in cross-sectional area associated with each annual ring. When BAI is estimated from ring-width series, a value for the diameter of the tree is required. This diameter is ideally measured in the field, but can also be estimated as the sum of the annual ring widths. Tree biomass can also be estimated directly from the diameter estimates derived from tree-rings. Summing the ring widths, however, typically underestimates the tree’s true diameter. To evaluate this potential bias in diameter, we compared field-measured diameter and diameter estimated from the sum of the ring widths using tree-ring chronologies for seven common species in the eastern United States. We then evaluated the impacts of using the biased diameter estimates on derived BAI and biomass values. To simulate field-sampling error (i.e., failure to reach the pith when obtaining a core sample), we re-calculated BAI and biomass after removing a portion of the innermost rings from each tree. Comparisons of these various methods quantify the substantial and consistent underestimations in forest productivity estimates. To reduce the bias in diameter when using ring widths, we developed a regression model to adjust the diameter using core samples. This model is predicated on having some field-measured diameter values available at a site to calibrate and validate the model, but it can then be used to produce estimates at similar sites with similar species where no field-measured diameter values are available. Values of BAI and biomass derived from model-estimated diameter were more accurate at representing absolute growth than values produced by using the sum of the ring widths. Assessing the interannual variations in tree-growth is dependent on having metrics that accurately reflect the area and mass of wood produced. Our results suggest that published estimates of BAI and biomass using the sum of the ring widths to estimate diameter have substantially underestimated these productivity metrics. Our new procedure allows for more reliable estimates of productivity metrics that use diameter-at-breast height derived from tree rings.     

How do trees grow? Response from the graphical and quantitative analyses of computed tomography scanning data collected on stem sections

Tree growth, as measured via the width of annual rings, is used for environmental impact assessment and climate back-forecasting. This fascinating natural process has been studied at various scales in the stem (from cell and fiber within a growth ring, to ring and entire stem) in one, two, and three dimensions. A new approach is presented to study tree growth in 3D from stem sections, at a scale sufficiently small to allow the delineation of reliable limits for annual rings and large enough to capture directional variation in growth rates. The technology applied is computed tomography scanning, which provides – for one stem section – millions of data (indirect measures of wood density) that can be mapped, together with a companion measure of dispersion and growth ring limits in filigree. Graphical and quantitative analyses are reported for white spruce trees with circular vs non-circular growth. Implications for dendroclimatological research are discussed.     

Variation of different tree-ring parameters in samples from each terminal shoot of a Norway spruce tree

Variability of wood parameters in a tree is sometimes a rather nebulous concept since variability is evident within single cells, from early to latewood, from pith to bark and from stem base to the top of a tree. So far, stem analyses have been done using a restricted number of parameters, mostly ring-width, and using a restricted number of samples in the longitudinal direction. This study analyses a number of parameters from a single tree. An 81-year-old spruce tree was felled and internodial discs were taken from each annual terminal shoot. All tree rings in each disc were measured and a whole-stem analysis was completed for the following parameters: ring-width, mean ring density, maximum density, percentage of latewood, type of transition from early to latewood, intra-annual density fluctuation, number of resin ducts per tree-ring and position of resin ducts within the tree-rings. All parameters showed calendar-year patterns, visible as lines parallel to the bark. The most clear calendar-year pattern was seen for the type of transition from early to latewood and for intra-annual density fluctuations. The strongest inter-series correlation between calendar rings was seen for ring-width. None of the parameters showed significant inter-series correlations for cambial rings. These results may help us to understand how cores or discs taken at breast height represent the entire tree.     

河北省年均降水量插值方法比较

以河北省及临近区域120个气象观测站点1971～2000年均降水量数据为基础,选择其中的40个作为检验站点,其余站点分别取80、40、20个作为插值站点,采用局部插值、整体插值、多元线性回归、综合模拟等多种插值模型讨论了降水空间插值问题,主要结论如下:插值站点数、模型类型、模型参数都会影响插值精度.局部插值模型相对误差最小值出现在Spline、IDW模型中,其次为Kridging模型,而整体模型Trend、多元线性回归模型误差均较大,但综合了局部插值模型和统计模型的综合模型一定程度上能改善插值精度及误差分布.河北省80和40个站点的最优插值模型为综合模型,20个站点的最优插值模型为IDW2.     

Variation of different tree-ring parameters in samples from each terminal shoot of a Norway spruce tree

Variability of wood parameters in a tree is sometimes a rather nebulous concept since variability is evident within single cells, from early to latewood, from pith to bark and from stem base to the top of a tree. So far, stem analyses have been done using a restricted number of parameters, mostly ring-width, and using a restricted number of samples in the longitudinal direction. This study analyses a number of parameters from a single tree. An 81-year-old spruce tree was felled and internodial discs were taken from each annual terminal shoot. All tree rings in each disc were measured and a whole-stem analysis was completed for the following parameters: ring-width, mean ring density, maximum density, percentage of latewood, type of transition from early to latewood, intra-annual density fluctuation, number of resin ducts per tree-ring and position of resin ducts within the tree-rings. All parameters showed calendar-year patterns, visible as lines parallel to the bark. The most clear calendar-year pattern was seen for the type of transition from early to latewood and for intra-annual density fluctuations. The strongest inter-series correlation between calendar rings was seen for ring-width. None of the parameters showed significant inter-series correlations for cambial rings. These results may help us to understand how cores or discs taken at breast height represent the entire tree.     

TRAP: a modelling approach to below-ground carbon allocation in temperate forests

Tree root systems, which play a major role in below-ground carbon (C) dynamics, are one of the key research areas for estimating long-term C cycling in forest ecosystems. In addition to regulating major C fluxes in the present conditions, tree root systems potentially hold numerous controls over forest responses to a changing environment. The predominant contribution of tree root systems to below-ground C dynamics has been given little emphasis in forest models. We developed the TRAP model, i.e. Tree Root Allocation of Photosynthates, to predict the partitioning of photosynthates between the fine and coarse root systems of trees among series of soil layers. TRAP simulates root system responses to soil stress factors affecting root growth. Validation data were obtained from two Belgian experimental forests, one mostly composed of beech (Fagus sylvatica L.) and the other of Scots pine (Pinus sylvestris L.). TRAP accurately predicted (R = 0.88) night-time CO₂ fluxes from the beech forest for a 3-year period. Total fine root biomass of beech was predicted within 6% of measured values, and simulation of fine root distribution among soil layers was accurate. Our simulations suggest that increased soil resistance to root penetration due to reduced soil water content during summer droughts is the major mechanism affecting the distribution of root growth among soil layers of temperate Belgian forests. The simulated annual rate of C input to soil litter due to the fine root turnover of the Scots pine was 207 g C m^–2 yr^–1. The TRAP model predicts that fine root turnover is the single most important source of C to the temperate forest soils of Belgium.     

Three-dimensional modeling of the cochlea by use of an arc fitting approach

Purpose: A cochlea modeling approach is presented allowing for a user defined degree of geometry simplification which automatically adjusts to the patient specific anatomy. Model generation can be performed in a straightforward manner due to error estimation prior to the actual generation, thus minimizing modeling time. Therefore, the presented technique is well suited for a wide range of applications including finite element analyses where geometrical simplifications are often inevitable. Methods: The method is presented for n=5 cochleae which were segmented using a custom software for increased accuracy. The linear basilar membrane cross sections are expanded to areas while the scalae contours are reconstructed by a predefined number of arc segments. Prior to model generation, geometrical errors are evaluated locally for each cross section as well as globally for the resulting models and their basal turn profiles. The final combination of all reconditioned features to a 3D volume is performed in Autodesk Inventor using the loft feature. Results: Due to the volume generation based on cubic splines, low errors could be achieved even for low numbers of arc segments and provided cross sections, both of which correspond to a strong degree of model simplification. Model generation could be performed in a time efficient manner. Conclusion: The proposed simplification method was proven to be well suited for the helical cochlea geometry. The generated output data can be imported into commercial software tools for various analyses representing a time efficient way to create cochlea models optimally suited for the desired task.     

Determination of age in the Japanese monkey from growth layers in the dental cementum

The teeth of 14 Japanese monkeys (Macaca fuscata) were examined to establish an exact method of determining age by histological observation of dental cementum. The cementum showed annual growth layers, which were especially remarkable in the incisor root and in the molar cementum deposited at the junction of the roots. The layer of cementum formed in winter appears as a dark layer in stained sections and as a translucent layer in unstained ground sections. In the incisor the first dark and light layers are formed at the age of three years, whereas in the molar they do not appear at a definite age. The layers are thick and clear in the upper medial incisor. As a result, the age of a Japanese monkey can be determined by adding two to the number of dark layers and an outer light layer. It is interesting that the formation of the cementum of the first molar begins a few years after its eruption. The relation between this fact and the pressure of occlusion is discussed.