Spherical Leaf Angle Distribution Research Articles

Narrow but robust advantages in two-big-leaf light use efficiency models over big-leaf light use efficiency models at ecosystem level

This study aims to (1) investigate whether two-big-leaf light use efficiency (LUE) models (TL) outperform big-leaf LUE models (BL) by incorporating different gross primary productivity (GPP) responses in sunlit and shaded leaves; (2) explore the robustness of using the leaf area index (LAI), clumping index (Ω) and spherical leaf angle distribution to partition canopies into sunlit and shaded leaves across canopy architectures; (3) identify optimal light response forms in LUE models. To exclude influences of drivers of GPP other than radiation, we collected various formulations of GPP response functions to temperature, vapor pressure deficit, CO2, soil water supply, light intensity and cloudiness index to construct 5600 BLs and 1120 TLs. These models were evaluated at 196 globally-distributed eddy covariance sites from the FLUXNET observational network using the Nash-Sutcliffe model efficiency (NSE), root mean squared error and Bayesian information criterion. Across all sites, the best big-leaf model (BL*; NSE=0.82) was statistically equal to the best TL (TL*; NSE=0.84). However, daily dynamics in GPP under hot and dry conditions were best described using TL* in 17% of sites, highlighting the local importance in separating sunlit and shaded leaves. Across approaches to represent effective LAI, the best approach relies on using normalized difference vegetation index with a spherical or flexible leaf angle distribution across sites rather than satellite LAI and Ω. We also observed similar performance between non-rectangular hyperbola and reciprocal light response functions across TLs. Models degrade when the maximum LUE is not differentiated between sunlit and shaded leaves, but not when light saturation levels are the same. Despite functional differences, the best five TLs agree in a larger contribution of shaded leaf area to total GPP, resulting from higher LAI and LUE. Overall, these results suggest marginal but robust selection of TL compared to BL.

Leaf area index estimation of a row-planted eggplant canopy using wide-angle time-lapse photography divided according to view-zenith-angle contours

In year-round horticultural fruit production, the leaf area index (LAI; L) is a useful indicator for proper crop management. In this study, wide-angle time-lapse digital cameras were applied to estimate the L of a row-planted eggplant canopy throughout an entire growth period. Six wide-angle time-lapse cameras were placed above the canopy; three cameras pointed to the nadir, and the other three pointed at 57.5°-tilted angles from the nadir with different azimuthal orientations (i.e., along the row, at a 40° angle from the row, and perpendicular to the row). L was estimated based on the gap-fraction theory using three methods: (1) the crop method, in which only a part of each photograph was used to calculate L, (2) the whole-image method, in which the entirety of each photograph was used to calculate L, and (3) the contour method, in which each photograph was divided into zones according to the view-zenith-angle contours and L was estimated through weighted averaging of the zonal Ls. The L values estimated using the crop method were heavily biased depending on the camera position and orientation, whereas the values obtained with the other two methods were less affected by the camera position and orientation, indicating the advantage of a wide viewing angle. Compared to the whole-image method, the contour method improved the L estimation accuracy. Under the assumption of a spherical leaf-angle distribution, nadir-looking photography tended to overestimate L, whereas 57.5°-angled photography was more consistent with the allometrically obtained reference L value. The accuracy of the L estimations obtained using nadir-looking photography was improved considerably by applying the beta leaf-angle distribution function with optimized parameters. This study highlights the (1) applicability of wide-angle photography for estimating the L of a row-crop canopy, (2) advantage of the contour method, and (3) importance of using a proper leaf-angle distribution.

Leaf inclination angle and foliage clumping in an evergreen broadleaf

How leaves are presented affects interaction of atmospheric CO2, energy (light), and plant physiology. Plant productivity is primarily determined by the amount of leaf area, leaf orientation and distribution in space. Not much attention has been paid to possible changes in leaf orientation and distribution with elevated CO2, but its effect on plant growth could alter the proportions of sunlit and shaded leaf areas and feedback on carbohydrate available for further growth. We report on first measurements of leaf inclination angle distribution and foliage clumping in a native evergreen Eucalyptus woodland in ambient CO2 and under +150 ppm elevated CO2. We found that a spherical leaf angle distribution was not an appropriate supposition for present species (Eucalyptus tereticornis Sm.) at this site. Our measurements of leaf inclination angles from imagery indicated an erectophile, highly skewed unimodal leaf inclination angle distribution function. We conclude that despite the measured steeper angles under elevated CO2 concentrations, the leaf angle change is not significant and falls within the expected natural variability and uncertainties connected with the measurement method. The lack of a clear response of leaf orientation and foliage clumping to elevated CO2 concentration indicates that the previously produced datasets of leaf inclination angles and foliage clumping maps with Earth observation data may be suitable while modelling carbon and water cycles under climate change.

Preliminary study on integrated wireless smart terminals for leaf area index measurement

The last few decades have seen the emergence of many new methods for measuring leaf area index (LAI). One attractive method is to measure LAI by using a readily available simple instrument, such as a smartphone, as an alternative to traditional complicated and thus costly commercial instruments. We designed a novel integrated LAI measurement system, LAISmart, which is implemented by using two smart terminals communicating through a wireless connection in an integrated support infrastructure. The LAI is calculated by using the Beer gap fraction model on the assumption of spherical leaf angle distribution that takes the G value (the projection of unit foliage area on the plane perpendicular to the view direction θ) as constant at 0.5. The gap fraction is calculated by segmenting the image pixel into canopy and background. For the selection of image segment features, LAISmart provides two options, greenness index and blue band, which may be suited to different vegetation types. The proposed LAISmart was validated by measurements on four types of vegetation, i.e., Evergreen Needleleaf Forest (ENF), Deciduous Broadleaf Forest (DBF), Deciduous Needleleaf Forest (DNF), and broadleaf crop, on which 114 LAI values were calculated in the eight datasets. A pairwise comparison between LAISmart and LAI-2000 showed that the LAI values derived from LAISmart correlated strongly with those of the LAI-2000, with an R2 value of 0.97, and had high accuracy in total, with a root–mean–square error (RMSE) of 0.45m2/m2. The validation results revealed that the overestimation on LAI caused by underestimation of the G value might complement the bias caused by misclassification. Moreover, although there is no limitation on the shooting angle of LAISmart, it is recommended that LAISmart be used at the low zenith angle mode, e.g., upward- or downward-looking mode, rather than at the large zenith angle. Further validation will focus on other vegetation types such as grass and shrubs in order to improve the performance of LAISmart for different vegetation types.

Efficiency of chlorophyll in gross primary productivity: A proof of concept and application in crops

One of the main factors affecting vegetation productivity is absorbed light, which is largely governed by chlorophyll. In this paper, we introduce the concept of chlorophyll efficiency, representing the amount of gross primary production per unit of canopy chlorophyll content (Chl) and incident PAR. We analyzed chlorophyll efficiency in two contrasting crops (soybean and maize). Given that they have different photosynthetic pathways (C3 vs. C4), leaf structures (dicot vs. monocot) and canopy architectures (a heliotrophic leaf angle distribution vs. a spherical leaf angle distribution), they cover a large spectrum of biophysical conditions. Our results show that chlorophyll efficiency in primary productivity is highly variable and responds to various physiological and phenological conditions, and water availability. Since Chl is accessible through non-destructive, remotely sensed techniques, the use of chlorophyll efficiency for modeling and monitoring plant optimization patterns is practical at different scales (e.g., leaf, canopy) and under widely-varying environmental conditions. Through this analysis, we directly related a functional characteristic, gross primary production with a structural characteristic, canopy chlorophyll content. Understanding the efficiency of the structural characteristic is of great interest as it allows explaining functional components of the plant system.

Mapping urban forest leaf area index with airborne lidar using penetration metrics and allometry

In urban areas, leaf area index (LAI) is a key ecosystem structural attribute with implications for energy and water balance, gas exchange, and anthropogenic energy use. In this study, we estimated LAI spatially using airborne lidar in downtown Santa Barbara, California, USA. We implemented two different modeling approaches. First, we directly estimated effective LAI (LAIe) using scan angle- and clump-corrected lidar laser penetration metrics (LPM). Second, we adapted existing allometric equations to estimate crown structural metrics including tree height and crown base height using lidar. The latter approach allowed for LAI estimates at the individual tree-crown scale. The LPM method, at both high and decimated point densities, resulted in good linear agreement with estimates from ground-based hemispherical photography (r2=0.82, y=0.99x) using a model that assumed a spherical leaf angle distribution. Within individual tree crown segments, the lidar estimates of crown structure closely paralleled field measurements (e.g., r2=0.87 for crown length). LAI estimates based on the lidar crown measurements corresponded well with estimates from field measurements (r2=0.84, y=0.97x+0.10). Consistency of the LPM and allometric lidar methods was also strong at 71 validation plots (r2=0.88) and at 450 additional sample locations across the entire study area (r2=0.72). This level of correspondence exceeded that of the canopy hemispherical photography and allometric, ground-based estimates (r2=0.53). The first-order alignment of these two disparate methods may indicate that the error bounds for mapping LAI in cities are small enough to pursue large scale, spatially explicit estimation.

Modeling directional forest reflectance with the hybrid type forest reflectance model FRT

The directional multispectral hybrid type forest radiative transfer model FRT by Kuusk and Nilson (2000) was compared using directional reflectance factor of high angular resolution measured over three mature hemiboreal forest stands in Estonia. The model systematically underestimated backward scattering even in the case of the best available input data, especially in coniferous stands. The measured BRF distribution could be reproduced if the spherical leaf angle distribution was replaced by erectophile in order to better model the angular dependence of gap fraction, and the Ross–Nilson area scattering phase function was replaced by significantly more asymmetric Henyey–Greenstein phase function. The limited amount of available data does not allow deciding how universal are the applied asymmetry parameter values. The asymmetry of the phase function may depend on the species composition, stand age, and site type.

Effects of canopy architectural parameterizations on the modeling of radiative transfer mechanism

In most of the ecological models, simplified methods are still being used to describe the canopy radiative transfer mechanism (CRTM). Largest uncertainties in the conceptualization of CRTM lies in the adequate description of the two main canopy architectural parameters: (1) the projection function (G) that describes the foliage inclination distribution in space and (2) the clumping function (Ω) that describes the aggregative nature of canopy elements. Herein, we explore the effects of different (simple to complex) representations of the G and Ω functions on simulations of photosynthetically active radiation (PAR) transmitted through a middle-aged maritime pine canopy, using a scenario-based numerical experiment.Initially we studied the nature of different G and Ω functions for a maritime pine stand using the data obtained using a cohort of ground-based instruments that measures canopy architecture (LAI-2000, TRAC, Digital Hemispherical Photography (DHP)). Further, we evaluated the performances of 15 CRTM scenarios that had various combinations of the G and Ω functions (or values) to predict the transmitted PAR below the overstory canopy (Runder). The performances of the scenarios were explored by comparing the simulated and measured daily average Runder for 293 days in 2008. We found that the best performance was showed by scenario S6 (bias +1%, RMSE=32.42μmolm−2s−1, NSE=0.90) wherein the Ω function was described using the empirical function derived using the TRAC data, and the G function calculated using a leaf angle distribution function (LADF) employing the Goel and Strebel (1984) approach. The scenarios that used the Ellipsoidal LADF for the G-function showed a general tendency to overestimate Runder with poorer performances. Assumption of a spherical leaf angle distribution (G=0.5) along with a Ω function developed by Kucharik et al. (1999) (scenario S3) showed a rather satisfying performance (bias=2% RMSE=33.31μmolm−2s−1, NSE=0.89). The scenario (S4) that assumed a random foliage distribution (Ω=1) and a spherical leaf angle distribution (G=0.5), the most common method used in ecological models, showed the worst performance to predict the Runder (bias −34%, RMSE=72.8μmolm−2s−1, NSE=0.40). With these observations we suggest that the dynamics of G and Ω function be explicitly defined in the CRTM modules that are used within ecological models.

Is the spherical leaf inclination angle distribution a valid assumption for temperate and boreal broadleaf tree species?

Angular distribution of leaves is an important parameter determining the transmission and reflection of radiation by vegetation canopies. When inverting canopy transmittance measurements for estimating the leaf area index or canopy clumping, incorrect assumptions on leaf angles may lead to considerable errors. To address this issue, we measured an extensive data set of leaf angle distributions for 58 deciduous broadleaf tree species commonly found in temperate and boreal ecoclimatic regions. Additionally, a small subset of species was sampled several times during the growing season. We found that reliable estimates of leaf angle distributions at the level of a whole tree can be obtained by measuring the leaf inclination angles of 75 leaves distributed across the vertical tree profile using a simple technique based on digital photography. According to our measurements, the common assumption of a spherical leaf angle distribution often used when no measurement data is available is not a valid assumption for most of the studied tree species. Our multitemporal measurements indicated no seasonality of leaf inclination angles of the selected tree species, except directly after budburst. Finally, using a gap fraction model, we illustrate the influence of different leaf angle distributions on the clumping factor and leaf area index. We advocate the use of species-specific leaf angle distributions from actual leaf inclination measurements. However, a planophile or a plagiophile leaf angle distribution appears to be a more appropriate assumption than a spherical one for modeling radiation transmission through temperate and boreal broadleaf stands when no leaf inclination angle measurements are available.

Estimation of canopy properties in deciduous forests with digital hemispherical and cover photography

Rapid, reliable and meaningful estimates of forest canopy are essential to the characterization of forest ecosystems. In this paper the accuracy of digital hemispherical (DHP) and cover (DCP) photography for the estimation of canopy properties in deciduous forests was evaluated. Leaf area index (LAI) estimated from both these photographic methods and from light transmittance data derived from DHP were compared with direct measurements obtained by litter traps (LAILT) and an AccuPAR ceptometer. Also, comparison with different gap fraction methods used to calculate LAI in DHP and LAI-2000 PCA were performed.We applied these methods in four forest stands of Quercus cerris, two stands of Castanea sativa and four stands of Fagus sylvatica, the most common deciduous species in Italy, where LAILT ranged from 3.9 to 7.3. Both photographic methods provided good indirect estimates of LAILT. The DCP method provided estimates of crown porosity, crown cover, foliage cover and the clumping index at the zenith, but required assumptions about the light extinction coefficient at the zenith (k), to accurately estimate LAI. Cover photography provided good indirect estimates of LAI assuming a spherical leaf angle distribution, even though k appeared to decrease as LAI increased, thus affecting the accuracy of LAI estimates in DCP. In contrast, the accuracy of LAI estimates in DHP appeared insensitive to LAILT values, but the method was sensitive to photographic exposure and more time-consuming than DCP.The studied stands were characterized by higher within-crown clumping than between-crowns clumping; only the segmented analysis of gap fraction for each ring of the fisheye images was found to provide reliable and useful clumping index in DHP. The 1-azimuth segment method employed in PCA poorly detected clumping in dense canopies.The correlation between transmittance estimates by DHP with values measured at noon with the AccuPAR ceptometer was linear and significant, although the variability observed in reference measures suggested that results obtained with the ceptometer should be treated with caution.We conclude both photographic methods are suitable for dense deciduous forests. Cover photography holds great promise as a means to quickly obtain inexpensive estimates of LAI over large areas. However, in situations where no direct reference measurements of k are available, we recommend using both DHP and DCP, in order to cross-calibrate the two methods; DCP could then be used for more routinely indirect measurement and monitoring of LAI.

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 ( r 2 = 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 r 2 of 0.78 at an area of 900 m 2. 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.

Comparison and sensitivity analysis of instruments and radiometric methods for LAI estimation: assessments from a boreal forest site

Retrievals of LAI from inversion of canopy radiometric measurements, using the Li-Cor LAI-2000 Plant Canopy Analyzer and the Decagon AccuPar Ceptometer (a linear quantum probe) were analyzed and compared. Field data were collected from 34 sites in the boreal forest of interior Alaska, and sensitivity tests were conducted to estimate the effect of a variety of measurement conditions on the LAI retrievals. We also tested the response of estimated LAI to different values of the theoretical parameters in the retrieval algorithms. Uncertainty in the incident radiation level was magnified by the LAI retrieval, meaning that even small errors in this measurement significantly affected the LAI estimates. Changes in solar zenith angle over long data acquisition times also contributed to the errors. The most important quality control factors for accurate retrieval of LAI from field measurements were the incident radiation and solar zenith angle. A series of sensitivity tests showed that extreme values of leaf angle distribution could change LAI estimates, but our multi-angle measurements produced results consistent with a spherical leaf angle distribution. Alternative methods taken from the literature for post-processing of the data from the two instruments produced similar results for the LAI-2000, but widely different results for the Decagon AccuPar. Retrievals from the two instruments had an overall correlation coefficient r=0.88,( P<0.01). Agreement was considerably better in aspen stands ( r=0.85, P<0.01, N=43) than in spruce ( r=0.56, P<0.05, N=22). Some of the variability was attributed to spatial heterogeneity within stands, particularly sparse spruce canopies. Overall, our results suggest the retrievals were robust, and largely comparable between instruments over a range of measurement conditions, provided variability in measurement conditions was adequately characterized.

Modelling the effect of diffuse light on canopy photosynthesis in controlled environments.

A layered canopy model was used to analyze the effects of diffuse light on canopy gross photosynthesis in controlled environment plant growth chambers, where, in contrast to the field, highly diffuse light can occur at high irradiance. The model suggests that high diffuse light fractions (approximately 0.7) and irradiance (1400 micromoles m-2 s-1) may enhance crop life-cycle canopy gross photosynthesis for hydroponic wheat by about 20% compared to direct light at the same irradiance. Our simulations suggest that high accuracy is not needed in specifying diffuse light fractions in chambers between approximately 0.7 and 1, because simulated photosynthesis for closed canopies plateau in this range. We also examined the effect of leaf angle distribution on canopy photosynthesis under growth chamber conditions, as these distributions determine canopy extinction coefficients for direct and diffuse light. We show that the spherical leaf angle distribution is not suitable for modeling photosynthesis of planophile canopies (e.g., soybean and peanut) in growth chambers. Also, the absorption of the light reflected from the surface below the canopy should generally be included in model simulations, as the corresponding albedo values in the photosynthetically active range may be quite high in growth chambers (e.g., approximately 0.5). In addition to the modeling implications, our results suggest that diffuse light conditions should be considered when drawing conclusions from experiments in controlled environments.

Evaluation of an algorithm for predicting albedo in heliotropic crops

Albedo (the fraction of reflected incoming solar radiation in the 400–3000 nm range) is of critical importance in crop simulation studies because it determines how much solar radiation is available for carbon uptake, crop water use, and ultimately productivity and yield. However, many crop simulation models do not place as much emphasis on albedo as is warranted given its importance in determining these crop processes. In addition, prediction of albedo in crop simulation models dealing with heliotropic crops (their leaves follow the sun) has received relatively little attention. An albedo algorithm based on a spherical leaf angle distribution was modified to predict albedo in two heliotropic crops, alfalfa ( Medicago sativa L.) and soybean ( Glycine max (L.) Merr.). Since no analytical expression exists for the heliotropic leaf angle distribution, linear relationships were developed to predict the albedo of these heliotropic crops from the albedo of a crop with a spherical leaf angle distribution. These relationships were developed from field data and tested on independent field measurements. Albedo was measured over soybean for a wide range of leaf area indices and leaf optical properties and between two cuttings in alfalfa. The normalized mean absolute error was used to compare predicted and measured values. There was good agreement between predicted and measured values except under foggy conditions when the direct beam fraction was zero and when water droplets on leaf surfaces may have influenced leaf optical properties.

Vertical point quadrat sampling and an extinction factor to calculate leaf area index

The appropriateness of a correction factor to derive leaf area index (LAI) from contact frequency using vertically-inserted point quadrat sampling was investigated. Point quadrat data were collected in a grid pattern over 72 individual shrubs and grass plots comprising eight common Great Basin scrub species of widely divergent ecology and canopy form. Destructive sampling and intercept measurements were used to determine LAI values. Extinction coefficients were then calculated from paired LAI and contact frequency. For all eight species, this extinction coefficient was statistically equivalent to 0·5 as a result of spherical leaf angle distribution, permitting LAI estimation simply by multiplying contact frequency by 2.

The bare bones of leaf-angle distribution in radiation models for canopy photosynthesis and energy exchange

The effects of leaf-angle distribution in radiation models for canopy photosynthesis and energy exchange can be accurately described by using as few as three leaf-angle classes (0–30°, 30–60° and 60–90°). On this basis, simple equations have been developed and tested for reflectance, extinction and distribution of radiation in leaf canopies. In these equations the spherical leaf-angle distribution, default in most models, serves as a point of reference.

Extinction coefficients for radiation in plant canopies calculated using an ellipsoidal inclination angle distribution

Equations used to calculate extinction coefficients for radiation in plant canopies tend either to be too simple to describe canopy radiation accurately, or too complex for convenient computation. An equation has been derived using the assumption that the angular distribution of leaf area in a canopy is similar to the distribution of area on the surface of a prolate or oblate spheroid. This is therefore a generalization of the spherical leaf angle distribution which is frequently used for plant canopies. Simulated leaf angle distributions generated using this model closely approximate measured leaf angle distributions for plant canopies. Extinction coefficients calculated from the model give values which are virtually identical to those calculated using six leaf angle classes.

Leaf area estimates from measurements of photosynthetically active radiation in wheat canopies

Transmission of photosynthetically active radiation (PAR) measured with quantum sensors in three wheat cultivars during periods of clear sky were used to indirectly determine the leaf area index (LAI). The exponential description of direct and diffuse radiation penetration, which depends on leaf inclination, was correlated to the transmission measurements at various solar zenith angles. The highest correlations were found for fixed leaf inclinations of 60 and 75°, and for the spherical leaf angle distribution. Angular shape coefficients corresponding to these leaf inclinations were then used to solve the exponential equation for LAI taking incoming PAR to be direct. This was shown to be an acceptable approximation when the proportion of direct radiation in the incoming PAR was higher than 0.85. Predictions of LAI were found to be within 0.7 units for a range of LAI from 1.5 to 5.0. A statistical analysis of the results indicated that the most suitable leaf inclination was a combination of 60 and 75° fixed angles, and spherical distribution.