Review of methods for in situ leaf area index (LAI) determination: Part II. Estimation of LAI,errors and sampling

The theoretical background of modeling the gap fraction and the leaf inclination distribution is presented and the different techniques used to derive leaf area index (LAI) and leaf inclination angle from gap fraction measurements are reviewed. Their associated assumptions and limitations are discussed, i.e., the clumping effect and the distinction between green and non-green elements within the canopy. Based on LAI measurements in various canopies (various crops and forests), sampling strategy is also discussed.     

Slope correction for LAI estimation from gap fraction measurements

Digital hemispherical photography poses specific problems when deriving leaf area index (LAI) over sloping terrain. This study proposes a method to correct from the slope effect. It is based on simple geometrical considerations to account for the path length variation within the canopy for cameras pointing vertically. Simulations over sloping terrain show that gap fraction increases up-slope while decreasing down-slope. As a consequence of this balance between up- and down-slope effects, effective LAI estimates derived from inversion of the Poisson model are marginally affected for low to medium slopes (<25°) and LAI (LAI < 2). However, for larger slopes and LAI values, estimated LAI values may be strongly underestimated. The proposed correction was evaluated over four forested sites located over sloping terrain. Results indicate that in these conditions (LAI between 0.6 up to 3.0, clumped canopies with relatively erectophile leaf distribution), the effect of the slope (between 25° and 36°) was moderate as compared to other potential sources of problems when deriving LAI from gap fraction measurements, including clumping, leaf angle inclination and spatial sampling.     

Foliage area and architecture of plant canopies from sunfleck size distributions

A Poisson model is developed to describe sunfleck or gap size distributions beneath clumped plant canopies. This model is based on the assumption that foliage clumps are randomly distributed in space and foliage elements are randomly distributed within each clump. Using this model, the foliage clumping index, leaf area index (L), clump area index, element area index in each clump, and element and clump widths were successfully derived for two artificial canopies and a thinned and pruned Douglas-fir forest stand. It is shown that existing theories for deriving L from measurements of canopy gap fraction have limitations, and the use of canopy architectural information derived from canopy gap size distribution can substantially improve the technique for indirectly measuring L of plant canopies.     

The computation of foliage clumping index using hemispherical photography

Hemispherical photography (HP) is extensively used for both canopy architecture such as leaf area index (LAI), and solar radiation regime determinations under forest canopies. This is done mainly by assuming that foliage elements occur in a spatially random manner. However, the majority of world forests occur in heterogeneous ecosystems and topography with rather complex canopy architecture. To improve the estimates of canopy structures and solar radiation regimes, a non-random spatial distribution parameter called clumping index (CI) has been used. We compared varying methodologies of CI determination on real HP acquired in contrasting forest types growing on sloping ground, and on simulated HP representing different aggregation levels of foliage elements. The major aim was the comparative analysis of the effects of forest types, forest density, slope and gap fraction acquisition accuracy on estimation of CI using the five different approaches. The result indicated that CI estimates based on gap size distribution approaches performed the best and were less affected by topography and forest density compared to approaches based on solely logarithmic gap averaging techniques.     

Optically-based methods for measuring seasonal variation of leaf area index in boreal conifer stands

The feasibility of detecting the seasonal variation in leaf area index (LAI) in boreal conifer forests is investigated using optical instruments. The LAI of six stands was measured. They include young and old jack pine (Pinus banksiana) and old black spruce (Picea mariana) located near the southern border (near Prince Albert, Saskatchewan) and near the northern border (near Thompson, Manitoba) of the Canadian boreal ecotone. LAI values of the stands are obtained by making several corrections to the effective LAI measured from the LI-COR LAI-2000 Plant Canopy Analyzer (PCA). The corrections include a foliage element (shoot) clumping index (for clumping at scales larger than the shoot) measured using the optical instrument TRAC (Tracing Radiation and Architecture of Canopies) developed by Chen and Cihlar (Chen, J.M. and Cihlar, J., 1995a, Plant canopy gap size analysis theory for improving optical measurements of leaf area index of plant canopies, Appl. Opt., 34: 6211–6222), a needle-to-shoot area ratio (for clumping within the shoot) obtained from shoot samples, and a woody-to-total area ratio obtained through destructive sampling of trees. It is found that the effective LAI varied about 5% to 10% in the growing season and the element clumping index remained almost unchanged. The needle-to-shoot area ratio varied the most, about 15% to 25%, which is of the same order of magnitude as the expected seasonal variability in LAI. This demonstrates that most of the seasonal variation information is contained in the needle-to-shoot area ratio, which can not be measured indirectly using in situ optical instruments and has to be obtained from a large quantity of shoot sample analysis which is laborious and error-prone. Based on our experience, an improved and convenient shoot sampling strategy is suggested for future studies. The optically-based LAI values were compared with destructive sampling results for three of the stands. Based on error analysis, we believe that optical measurements combined with shoot sample analysis can produce LAI values for conifer stands which are more accurate than destructive sampling results.     

Estimating leaf area distribution in savanna trees from terrestrial LiDAR measurements

Vegetation structure parameters are key elements in the study of ecosystem functioning and global scale ecosystemic interactions. The detailed retrieval of many of these parameters by direct measurements is impractical due to the quantity of plant material in trees. Terrestrial LiDAR Scanners (TLSs) have been shown to hold great potential as an indirect means of estimating plant structure parameters with a high level of detail, while some studies identified a number of challenges inherent to this approach. In this study we investigate the use of a voxel-based approach to retrieve leaf area distribution of individual trees. The approach is based on the contact frequency method applied to co-registered TLS returns from two or more scanning positions. The contact frequency was computed for voxels being 10, 30, and 50 cm in size and subsequently corrected for the influence of occlusion effects, leaf inclination, the presence of non-photosynthetic material, and the laser beam size. The leaf area of voxels for which occlusion effects were too pronounced was estimated using modeled values based on the availability of light. We compared the TLS derived leaf area estimates against direct measurements, obtained by the harvesting of leaves, in a broad-leaved savanna of central Mali. The measured leaf area values of the sampled trees ranged from 30 to 530 m², and crown LAI values between 0.8 and 7.2. The leaf area estimates lay on average 14% from the reference measurements (general bias). Our method provides vertical as well as radial distributions of leaf area in individual trees, and lends itself to the estimation of savanna vegetation structural parameters with a high level of detail.     

Simulation of statistical characteristics of gap distribution in forest stands

An estimate of the required amount of LAI-2000 or digital hemispheric image measurements to ensure the desired accuracy of the leaf area index value derived from optical analyser measurements by inversion of gap fraction data is given. The estimate is based on a theoretical model of the second order statistics of gap occurrence in forest canopies. The main attention is paid to gap fractions averaged over the angular rings similar to the LAI-2000 instrument. Nilson's (1999) forest gap fraction model is first extended to simulate the bidirectional gap fraction and next the approximate equations for the standard deviation of gap fraction, correlation matrix of gap readings in different LAI-2000 angular rings, standard deviation of the LAI value as determined by the inversion of gap fraction data are derived. The results of simulation are compared with those obtained by LAI-2000 instrument and digital hemispheric photographs in three mature forests from Järvselja, Estonia. The comparison shows an acceptable agreement between the simulated and measured second order statistical characteristics. The distance from the observation height to the crowns and crown dimensions appear to be important in determining the magnitude of variance. When the LAI-2000 instrument is used together with a view-cap, the angular size of the view-cap has an effect on the second order statistics and on the value of apparent clumping index. A computer program has been written to calculate the second-order gap statistics.     

Leaf area index measurements at Fluxnet-Canada forest sites

Leaf area index (LAI) measurements made at 17 forest sites of the Fluxnet Canada Research Network are reported here. In addition to LAI, we also report other major structural parameters including the effective LAI, element clumping index, needle-to-shoot area ratio, and woody-to-total area ratio. Values of the fraction of photosynthetically active radiation (FPAR) absorbed by green leaves in these stands at noon of 15 August are also provided, and a procedure is suggested for using the effective LAI for estimating FPAR at various times of the day and year. Labour-intensive laboratory measurements of the needle-to-shoot area ratio were made for five conifer sites. For each site, 45 shoot samples were measured at three heights from three trees. LAI-2000, TRAC and digital hemispherical photography (DHP) were used in the field, and good agreements between these techniques were obtained. In particular, the low cost DHP technique agreed within 21% of LAI-2000 in terms of effective LAI measurements and 12% of TRAC in terms of element clumping index measurements, suggesting a possibility of using DHP alone for indirect LAI measurements. However, LAI-2000 and TRAC are still found to be more reliable than DHP because of some remaining technical issues with DHP. We confirm the correct method for determining the photographic exposure proposed in previous studies and suggest optimum zenith angle ranges in photograph processing to estimate the effective LAI and the clumping index.     

Change in radiation penetration of mechanically-injured maize

Abstract

The aim of the study was to provide new information about those environmental processes, mainly in radiation, which lead to production decrease in mechanically- and hail-injured maize. The size of the leaf area and its vertical distribution were used to describe the stand. In place of direct leaf angle measurements the extinction coefficient was used to characterize the modification that resulted from leaf laceration. In the course of the investigations it was found that while healthy plant stands allowed 30.6% of the total incident radiation to reach the ground, this figure was 41% for hail-damaged stands. There was little difference in the quantity of radiation measured on sunny and shaded patches in the two stands, but the ratio of sunny to shaded patches was altered. The radiation intensity reaching the soil surface in the lacerated stand increased despite the very slight difference in leaf area index (LAI). Extra radiation input in the soil of hail-damaged stand was a consequence of modification in the leaf angle.     

Estimation, variation and importance of leaf curvature in Zea mays hybrids

Maize leaves are curved but this curvature cannot be described by a single system of equations based on conic sections. We made comparisons of curvature between hybrids, leaf positions and planting density using measures of maximum leaf height and leaf tip:maximum leaf height ratio. With these measures a modern hybrid released in 1991 (Pioneer 3394) shows less curvature compared with hybrids released in 1963 (Pioneer 3306) and 1936 (Pioneer 307). The greater uprightness of 3394's leaves was apparent for all leaves measured. Curvature is a plastic character. While all hybrids developed less curvature in higher density plantings the effect was greatest for 3394. 3394 had shorter, more lanceolate leaves with smaller leaf area, a lower estimated torque around the point of leaf attachment to the stem, and a significantly smaller auricle base and smaller angle between the leaf blade and auricle base. These results support suggestions that the pattern of curvature may be produced by the progression of irreversible bending during leaf development. We found no consistent relationships between differences in curvature and measurements of leaf midrib morphology or anatomy.A frequently used approach in modeling foliage area distribution by angle is to use an approximation provided by the angular distribution of an ellipsoid. We show that for leaves in this study this approach is biased and that a Richards function describes the cumulative frequency distribution of leaf area by inclination angle more effectively. The importance of an unbiased estimator is discussed in relation to the variation in photon flux density received by surfaces of different inclinations.     

Estimating the three-dimensional structure of canopy foliage based on the light measurements in a Betula ermanii stand

In order to more accurately evaluate the functional activity of forest stands by canopy production and evapotranspiration, we improved the methods for field measurements and statistical modeling to estimate foliage configuration (spatial distribution of leaves) while simultaneously reconstructing the three-dimensional photosynthetically active photon flux density (PPFD) distribution (PPFD pattern) in a forest canopy. By using a sensor (photodiode) array, a PPFD pattern was observed in summer 2002 under the canopy in an even-aged, pure stand of Japanese mountain birch Betula ermanii Cham. (17-years old) in Hokkaido, northern Japan. A Markov chain Monte Carlo (MCMC) sampling technique is developed such that a set of foliage configurations generated by the model referred to as the Gibbs foliage canopy (GFC) approximates the field-measured PPFD pattern. The posterior distribution of the foliage configurations is generated by the parallel tempering MCMC of eight independent series of foliage configurations. The GFC model generated the posterior distribution of the LAI estimates (mean 4.56) that appeared to be appropriate in comparison to other LAI estimates of the B. ermanii stand based on the indirect and nondestructive methods by LAI-2000 (LAI = 3.43) and litterfall traps (LAI = 5.56) because they could be under- and overestimated, respectively. Our evaluations of the canopy production and evapotranspiration rates suggest that the relationship between LAI and canopy functions was not very simple because it depended on the nonlinear functional forms of the leaf responses of photosynthesis and transpiration to PPFD. The current study demonstrates an application of MCMC techniques that can generate a set of possible structures of unobserved/unobservable objects based on the high-resolution dataset obtained by some indirect (or remote-sensing) methods.     

农作物秸秆皮带输送量的影响因素分析

该文以农作物秸秆的皮带输运特性为研究对象,以玉米秸秆为例,分析了秸秆全水分、粒度分布,以及皮带输送倾角和皮带速度对质量输送量的影响规律。结果表明,玉米秸秆的质量输送量和堆积密度随全水分的增加近乎线性增加,干物质的质量输送量呈线性下降;全水分增加时,质量输送量随着堆积密度的增加,其变化率逐渐减小;粒度对质量输送量和动堆积角的影响较大;带速在临界速度1.6 m/s前后,质量输送量的趋势发生明显变化。同时,该文对小麦秸秆、甜高粱秸秆进行了试验规律验证,发现输送规律基本一致,仅小麦秸秆在输送倾角变化时的质量传输规律略有差异,充分显示生物结构特征相似的秸秆具有相同的传输规律。试验证实,流态化临界角与各粒度区间的动堆积角满足线性加权关系,为其他农作物秸秆的皮带输送提供了必要的研究方法。     

鲁西北平原作物群体几何性状研究

作物群体几何性状用叶倾角和叶方位角表示。叶倾角的大小主要决定于作物品种的遗传特性，受种植方式的影响较小。叶倾角大的作物品种，群体叶面积大；叶倾角小的作物品种，群体叶面积小。叶方位角的分布主要受种植方式的影响。     

Documenting improvement in leaf area index estimates from MODIS using hemispherical photos for Australian savannas

This paper compares estimates of Leaf Area Index (LAI) obtained from the MODIS (Moderate Resolution Imaging Spectroradiometer) collections 4.8 (MC4) and 5.0 (MC5) with ground-based measurements taken along a 900 km north-south transect through savanna in the Northern Territory, Australia. There was excellent agreement for both the magnitude and timing in the annual variation in LAI from MC5 and biometric estimates at Howard Springs, near Darwin, whereas MC4 overestimated LAI by 1-2 m² m⁻² for the first 200 days of the year. Estimates of LAI from MC5 were also compared with those obtained from the analysis of digital hemispherical photographs taken during the dry season (September 2008) based on algorithms that included random and clumped distribution of leaves. Linear regression of LAI from MC5 versus that using the clumping algorithm yielded a slope close to 1 (m = 0.98). The regression based on a random distribution of leaves yielded a slope significantly different from 1 (m = 1.37), with higher Mean Absolute Error (MAE) and bias compared to the clumped analysis. The intercept for either analysis was not significantly different from zero but inclusion of five additional sites that were visually bare or without green vegetation produced a statistically significant offset of +0.16 m² m⁻² by MC5. Overall, our results show considerable improvement of MC5 over MC4 LAI and good agreement between MC5 and ground-based LAI estimates from hemispherical photos incorporating clumping of leaves.     

Comparison of marker- and pedigree-based methods for estimating heritability in an agroforestry population of Vitellaria paradoxa C.F. Gaertn. (shea tree)

We implemented a regression-based method between pairwise relatedness estimated from markers and phenotypic similarity to estimate heritability of traits related to leaf size and morphology in a wild tree population (Vitellaria paradoxa C.F. Gaertn.: shea tree). We then compared the results with heritability estimated with a classical pedigree-based method. We tested both approaches in an agroforestry population of this tree species, a very important one and abundant in the Sudano-Sahelian zone of Africa. Twelve microsatellite loci were used to estimate pairwise relatedness after selection of estimator coefficients based on Monte Carlo simulation. The regression-based method applied to 200 individuals did not display a significant trend with physical distance between trees for relatedness as well as for actual variance of relatedness. In consequence, estimates of narrow-sense heritability of traits related to leaf size were not significant. The pedigree-based method using a progeny test with 39 families and 15 individuals per family from the same population showed high and significant estimates of narrow-sense heritability for the same traits (h² = 0.36–0.95), demonstrating a marked genetic variation within the population. This discrepancy between methods stresses the poor performance of the molecular marker-based method. This can be explained by the absence of fine-scale structure within the agroforestry population of shea trees, other parameters being consistent with recommended values. The regression-based method does not seem well adapted to the agroforestry tree population. New experiments in tree populations and theoretical approaches are needed to evaluate the real potential of the marker-based methods.     

采用3D几何特征的草莓叶片含水率监测与试验验证

为实现植物水分状况的实时在线监测，该研究采用非接触式双目摄像仪获取草莓叶片的深度图像并转换为点云数据，从中抽取叶片三维（Three-Dimension, 3D）形态信息，用以建立草莓叶片含水率的预测模型。采用随机采样一致算法与整体最小二乘法相结合的点云平面拟合方法拟合叶片平面从而获取叶倾角，采用代数拟合球面法以估计叶片的拟合球半径，从而可以定量分析草莓叶片的几何参数与不同含水率的关系。在建模集的一元线性回归分析中，叶倾角与叶片含水率、余弦值与叶片含水率、球半径与叶片含水率均线性相关，决定系数分别为0.842 9、0.854 6 和 0.880 8；采用多元线性回归分别分析了球半径和叶倾角、球半径和余弦值与叶片含水率，两者与叶片含水率之间关系都十分显著，修正决定系数分别为0.914 3和0.912 9。对所建立的单变量含水率预测模型和双变量预测模型在验证集上进行了验证，结果表明，利用球半径和叶倾角建立的回归模型预测叶片含水率效果最好，均方根误差仅为0.015 8，决定系数高达0.953 4。该试验研究结果可以快速检测草莓叶片含水情况，为草莓含水状况的非接触式测量提供一种有效的方法，为农情信息精准获取提供技术支持。     

Estimating nitrogen transfer by foliar 15N-labelling in legume – non-legume associations

We examined the basis for estimating the transfer of legume N to companion cereals or grasses in intercropping or pature systems using the foliar ¹⁵N-labelling technique. Published data from three pot experiments were used to illustrate different methods for estimating N transfer. Yield-dependent and yield-independent methods based on measurement of the ¹⁵N enrichment of the whole legume biomass at harvest overestimate N transfer. Estimates of N transfer using a yield-independent method based on the ¹⁵N enrichment of the legume roots at harvest were inconsistent with estimates based on the isotopic composition of the whole plant. We propose a new mathematical concept for estimating the transfer of legume N based on measurement of the ‘mean pool abundance’ of the legume biomass during the period of N transfer. Received: 7 January 1996     

Modeling approaches to estimate effective leaf area index from aerial discrete-return LIDAR

Leaf area index (LAI) has traditionally been difficult to estimate accurately at the landscape scale, especially in heterogeneous vegetation with a range in LAI, but remains an important parameter for many ecological models. Several different methods have recently been proposed to estimate LAI using aerial light detection and ranging (LIDAR), but few systematic approaches have been attempted to assess the performance of these methods using a large, independent dataset with a wide range of LAI in a heterogeneous, mixed forest. In this study, four modeling approaches to estimate LAI using aerial discrete-return LIDAR have been compared to 98 separate hemispherical photograph LAI estimates from a heterogeneous mixed forest with a wide range of LAI. Among the four approaches tested, the model based on the Beer–Lambert law with a single parameter (k: extinction coefficient) exhibited highest accuracy (r² = 0.665) compared with the other models based on allometric relationships. It is shown that the theoretical k value (=0.5) assuming a spherical leaf angle distribution and the zenith angle of vertical beams (=0°) may be adequate to estimate effective LAI of vegetation using LIDAR data. This model was then applied to six 30 m × 30 m plots at differing spatial extents to investigate the relationship between plot size and model accuracy, observing that model accuracy increased with increasing spatial extent, with a maximum r² of 0.78 at an area of 900 m². Findings of the present study can provide useful information for selection and application of LIDAR derived LAI models at landscape or other spatial scales of ecological importance.