Leaf Angle Distribution Function Research Articles

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.

Retrieving Corn Canopy Leaf Area Index from Multitemporal Landsat Imagery and Terrestrial LiDAR Data

Leaf angle is a critical structural parameter for retrieving canopy leaf area index (LAI) using the PROSAIL model. However, the traditional method using default leaf angle distribution in the PROSAIL model does not capture the phenological dynamics of canopy growth. This study presents a LAI retrieval method for corn canopies using PROSAIL model with leaf angle distribution functions referred from terrestrial laser scanning points at four phenological stages during the growing season. Specifically, four inferred maximum-probability leaf angles were used in the Campbell ellipsoid leaf angle distribution function of PROSAIL. A Lookup table (LUT) is generated by running the PROSAIL model with inferred leaf angles, and the cost function is minimized to retrieve LAI. The results show that the leaf angle distribution functions are different for the corn plants at different phenological growing stages, and the incorporation of derived specific corn leaf angle distribution functions distribute the improvement of LAI retrieval using the PROSAIL model. This validation is done using in-situ LAI measurements and MODIS LAI in Baoding City, Hebei Province, China, and compared with the LAI retrieved using default leaf angle distribution function at the same time. The root-mean-square error (RMSE) between the retrieved LAI on 4 September 2014, using the modified PROSAIL model and the in-situ measured LAI was 0.31 m2/m2, with a strong and significant correlation (R2 = 0.82, residual range = 0 to 0.6 m2/m2, p < 0.001). Comparatively, the accuracy of LAI retrieved results using default leaf angle distribution is lower, the RMSE of which is 0.56 with R2 = 0.76 and residual range = 0 to 1.0 m2/m2, p < 0.001. This validation reveals that the introduction of inferred leaf angle distributions from TLS data points can improve the LAI retrieval accuracy using the PROSAIL model. Moreover, the comparations of LAI retrieval results on 10 July, 26 July, 19 August and 4 September with default and inferred corn leaf angle distribution functions are all compared with MODIS LAI products in the whole study area. This validation reveals that improvement exists in a wide spatial range and temporal range. All the comparisons demonstrate the potential of the modified PROSAIL model for retrieving corn canopy LAI from Landsat imagery by inferring leaf orientation from terrestrial laser scanning data.

Rapid measurement of the three-dimensional distribution of leaf orientation and the leaf angle probability density function using terrestrial LiDAR scanning

At the plant or stand level, leaf orientation is often highly anisotropic and heterogeneous, yet most analyses neglect such complexity. In many cases, this is due to the difficulty in measuring the spatial variation of the leaf angle distribution function. There is a critical need for a technique that can rapidly measure the leaf angle distribution function at any point in space and time. A new method was developed and tested that uses terrestrial LiDAR scanning data to rapidly measure the three-dimensional distribution of leaf orientation for an arbitrary volume of leaves. The method triangulates laser-leaf intersection points recorded by the LiDAR scan, which allows for easy calculation of normal vectors. As a byproduct, the triangulation also yields continuous surfaces that reconstruct individual leaves. In order to produce a probability density function for leaf orientation from triangle normal vectors, it is critical that the proper weighting be applied to each triangle. Otherwise, results will heavily bias toward normal vectors pointed toward the the LiDAR scanner. The method was validated using artificially generated LiDAR data where the exact leaf angle distributions were known, and in the field for an isolated tree and a grapevine canopy by comparing LiDAR-generated distribution functions to manual measurements. The artificial test cases demonstrated the consistency of the method, and quantitatively showed that errors in the predicted leaf angle distribution functions decreased as scan resolution was increased or as the density of leaves was increased. The isolated tree field validation showed qualitatively similar trends between manual and LiDAR measurements of distribution functions. Manual measurements of leaf orientation in the vineyard were shown to have large errors due to high leaf curvature, which illustrated the benefits of the more detailed LiDAR measurement method.

Evaluation of six leaf angle distribution functions in the Castillo® coffee variety

The study was conducted at the "Estación Central Naranjal Ce-nicafé" (National Coffee Research Center, Chinchina, Caldas, Colombia) on Coffea arábica L. variety Castillo® to find the leaf angle distribution function that best described the tilt of the angles present in the canopy. Leaf angles were recorded for 1,559 leaves located in the upper, middle and lower profiles of the canopy. The observed leaf angle distribution was compared with the Beta, ellipsoidal and four de Wit distribution functions. The fit between comparisons was determined by the Pearson X2 test and its significance, the regression coefficient statistically equal to one and the RMSE. Likewise, the leaf angle distribution recorded in the field per profile and their combination was described based on three angle classes (1stclass: 0°-30°; 2nd class: 30°-60°; and 3rd class: 60°-90°) according to the Goudriaan criterion. Generally, the leaf angle distribution present in the canopy of Castillo® coffee variety is adequately described by the Beta function with two parameters and the ellipsoidal function based on the adjustment provided by the statistical tests.

A simulation model for predicting canopy structure and light distribution in wheat

Quantitative simulation of architectural structure and light distribution within a crop canopy is important for photosynthesis estimation and virtual construction. This study was undertaken to simulate the leaf curve, canopy structure and light distribution in winter wheat (Triticum aestivum L.). The field experiments with different plant types and sowing densities were carried out, and the time-course changes in canopy structure and light distribution were measured in winter wheat. The leaf curvature in wheat canopy increased with increasing sowing density and the leaf curve could be simulated with a quadratic function and its varied forms. The maximal value of leaf curvature was considered as a cultivar parameter reflecting the genetic characteristics, and the plant number per unit area was used to quantify the effects of sowing density on leaf curvature. Based on the simulated canopy structure, the leaf angle distribution function (f(θL)), extinction coefficient (K(θ)) and leaf area index (LAI) of the canopy were directly calculated by dividing leaf inclination angle into tiny units and accumulating the corresponding leaf areas. Then, the vertical distribution of photosynthetic photon flux density (PPFD) in a canopy could be simulated by using the Beer’s law. The models were validated with the independent dataset from the field experiment of different wheat cultivars. The average relative root mean square error (RRMSE) between the estimated and observed values were 17.44% for layered LAI and 19.35% for PPFD. These results indicated that the present model could effectively predict the growth dynamics of structure and of light distribution within wheat canopies, which would be useful for structural visualization or photosynthesis simulation.

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.

Continental‐scale multiobservation calibration and assessment of Colorado State University Unified Land Model by application of Moderate Resolution Imaging Spectroradiometer (MODIS) surface albedo

This study attempts to establish the first continental‐scale multiobservation calibration and assessment of a land surface model (LSM) over the conterminous United States by using the Colorado State University Unified Land Model (CSU ULM) within the NASA GSFC's Land Information System and the Parameter Estimation (PEST) model. This study aims to calibrate the vegetation and soil optical parameters in different landcover classes by comparing model‐predicted surface albedo and those derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) (including black‐ and white‐sky albedo for visible and near‐infrared band). The sum of squared deviations (Ψ) between model‐ and MODIS‐derived albedo is iteratively reduced via the Gauss‐Marquardt‐Levenberg (GML) algorithm. The first calibration process (1) reduced Ψ by about 80% for noncalibrated as well as calibrated seasons and years, (2) revealed the functional biases related to diffuse‐radiation upscattering parameters in two‐stream canopy radiation scheme (which was fixed before the second calibration), and (3) shows that the parameter related to the leaf angle distribution function could not be tuned. The second calibration was implemented from the lessons learned from the first calibration, and results in the more realistic convergence of the parameters. After calibration, the summertime surface energy budget simulated by offline ULM changed significantly over the less vegetated regions; for example, net shortwave radiation and available energy increased by more than 40 W m−2 and radiative temperature increased by more than 1.6 K in the postcalibrated experiment.

Comparison of leaf angle distribution functions: Effects on extinction coefficient and fraction of sunlit foliage

Leaf angle distribution is a key parameter to characterize canopy structure and plays a crucial role in controlling energy and mass balance in soil-vegetation-atmosphere-transfer system. Several leaf angle distribution functions found in literature have been proposed to account for the non-random distribution of leaf inclination angle with one or two parameters. In this paper, these leaf angle distribution functions (Beta distribution function, ellipsoidal function, rotated-ellipsoidal function, Verhoef's algorithm and de Wit's functions) were compared with field data collected in the First ISLSCP Field Experiment (FIFE) project and two sites within Ku-ring-gai Chase National Park, Sydney, Australia. All functions performed reasonably well. However, the comparison showed that the two-parameter functions including the Beta distribution function and Verhoef's algorithm commonly were more consistent predictors than one-parameter functions. G-statistics and χ 2 test applying to the estimates of leaf angle distribution demonstrated that Beta function presented more robustness over other functions, even the ellipsoidal leaf distribution function which has been widely used. Furthermore, the predictions of leaf angle distribution by these functions were used to calculate extinction coefficient and to separate foliage into sunlit and shaded parts. The results suggested that, ellipsoidal function may be suitable to be retrieved with remotely-sensed data and to compute extinction coefficient and fraction of sunlit foliage because this function requires only a single parameter, namely the ratio of the horizontal semi-axis length to the vertical semi-axis length of an ellipsoid. Finally, the comparison of three approaches (Nilson's, Fuchs’ and Ross–Goudriaan's algorithms) for computing extinction coefficient indicated that, there was no significant difference between the three approaches.

Leaf orientation and distribution in a Phaseolus vulgaris L. crop and their relation to light microclimate.

Changes in canopy structure parameters (leaflet orientation, leaflet inclination and leaf area index) were measured in crops of beans (Phaseolus vulgaris L.) in the field as the canopy developed between July and October. These changes were compared with the corresponding changes in seasonal light transmission. The beans showed clear heliotropic behaviour, with preferential orientation of leaflets towards the sun's beam, especially on sunny days. Nevertheless a significant proportion of the leaves pointed in other directions, with as much as 20% oriented towards the north. The highest proportion of leaf inclinations was in the range 30-40 degrees on cloudy days and between 40 degrees and 50 degrees on sunny days. Two methods were compared for assessing changes in light transmission: (a) the use of a Sunfleck Ceptometer and (b) the use of continuous records obtained with sensors installed in the canopy. Over the growth period studied, the total of the leaf plus stem area indices (L(S)) increased from 0.26 to 5.2 with the transmission coefficient (tau) for photosynthetic photon flux density (PPFD), obtained using the Ceptometer, correspondingly decreasing from 0.72 to 0.05, and the canopy extinction coefficient decreasing from 1.4 to 0.62. The continuous records of light transmission gave generally similar estimates of tau. Some contrasting leaf angle distribution functions were compared for estimation of L(S) from the light measurements. The best leaf angle function to predict L(S) from the observed light transmission was a conical function corrected by the degree of heliotropism.

Inversion of Monte Carlo model for estimating vegetation canopy parameters

The Monte Carlo technique for estimating model parameters is presented. The bidirectional reflectance factor is calculated by the Monte Carlo method of solving the integral equation of radiation transfer in plant canopies. A general inversion technique for the estimation of canopy parameters is considered. The method of calculating derivatives of the bidirectional reflectance factor with respect to unknown parameters using the same photon trajectories as in the solution of the direct problem is developed. The leaf dimensions are taken into account using a new extinction coefficient. Finally, numerical results for estimating three optical canopy parameters (coefficients of leaf reflectance, transmittance, and soil albedo) and four geometrical canopy parameters (leaf area index, two parameters of leaf angle distribution function, and leaf size parameter) are briefly discussed.

A method for simulating the direct solar radiation regime in sunflower, jerusalem artichoke, corn and soybean canopies using actual stand structure data

A method has been developed to incorporate actual canopy architecture in radiation models. The mathematical procedure involved, introduces a leaf angle and azimuthal distribution function, and yields an integrated extinction coefficient which can be substituted into basic light extinction formulae.Leaf angle and azimuthal distribution functions were determined for sunflower (Helianthus annuus), Jerusalem artichoke (Helianthus tuberosus), corn (Zea mays) and soybean (Glycine max var. Amsoy). A special computer program was written to calculate the extinction coefficients for each canopy at a number of solar elevations.Applying these coefficients in the extinction formulae for direct solar radiation, the influence of the four stand structures on penetration, interception, absorption and sunlit leaf area index was evaluated. The variation of these variables with time of the day is influenced by the leaf angle distribution function, while the non-random azimuthal distribution is reflected in an upper and lower limit for each variable. The span of this variation increases with low solar elevations and with higher ratios of maximum and minimum azimuthal density.Although the four crops displayed an almost equal daily absorption of direct solar radiation, it was shown that erectophile plant stands are more efficient in their light intercepting capacity than planophile canopies.An error analysis indicates considerable deviation on the prediction of the radiation regime, when calculations are based on a uniform leaf inclination. Deviations on extinction coefficient, interception and sunlit leaf area index are expected to be 10 to 20% at low solar elevations.