Clumping effect denotes the nonrandomness of foliage. It deviates from the random distribution assumption of Beer’s law which is usually applied to leaf area index (LAI) retrieval from large-footprint full-waveform light detection and ranging (LiDAR). Some studies correct for large gaps-induced between-crown clumping, yet ignore the within-crown clumping. The error of LAI caused by these clumping effects and the influence of the forest structure parameters on them have not been quantitatively studied. This study quantified the between-crown, within-crown, and total clumping indices through a theoretical derivation, clarifying the mechanism of clumping; we used airborne LiDAR point clouds data in 11 290 footprints (diameter = 25 m) to estimate these indices in real forests. We found that: 1) the underestimation of LAI caused by directly applying Beer’s law could be up to 93%, and it decreases with fractional crown coverage but increases with crown length and leaf area density; 2) the method of correcting between-crown clumping improves LAI retrieval for cylindrical canopies effectively; however, 3) considerable underestimation (up to 58%) exists if we neglect the within-crown clumping for other canopies, which has not been realized before; and 4) both the between-crown and the within-crown clumping can be the dominant contributor, and the within-crown clumping was greater than the between-crown clumping in 47% of the studied footprints. In the two physically based LAI retrieval methods, Beer’s law has been commonly used due to its simplicity. Pathways to improve future LAI retrieval would be instrument improvement to capture the between-crown gaps and method study to correct the within-crown clumping further.

Remote sensing estimation based on the dimidiate pixel model (DPM) using vegetation indices (VIs) is a common approach for mapping fractional vegetation cover (FVC). The major drawback of DPM is that it does not consider real endmember conditions and multiple scattering between soil and vegetation. An analysis of FVC uncertainties caused by these model deficiencies is still lacking. Here, we first calculated the FVC theoretical uncertainty caused by reflectance uncertainties based on the law of prapagation of uncertainty (LPU). Then, we tested the performance of DPM using six VIs over 3-D forest scenes. We simulated both Aqua-MODIS and Landsat-OLI surface reflectance (SR) at their corresponding spatial resolutions and spectral response functions (SRFs) using a well-validated 3-D radiative transfer (RT) model which helps to separate the model and input uncertainties. We found that ratio vegetation index (RVI)- and enhanced vegetation index (EVI)-based models were most affected by sensors, followed by the normalized difference vegetation index (NDVI)-, enhanced vegetation index 2 (EVI2)-, renormalized difference vegetation index (RDVI)-, and difference vegetation index (DVI)-based models. Without considering SR uncertainties, the DVI-based model performed best (FVC absolute difference < 0.1); however, the commonly used NDVI model reached a maximum difference of 0.35. At the same time, input uncertainty increased the uncertainty of FVC retrieval. We noticed that the increase of solar zenith angle (SZA) resulted in a clear increase of retrieved FVC under the uniform distribution, which can be explained by the increased shadow proportion. Besides, model accuracy was dominated by the purity of soil (vegetation) endmember in low (high) vegetation cover area. This study provides a reference for the selection of the optimal VI for FVC retrieval based on the DPM.

Bidirectional reflectance distribution function (BRDF) models are used to correct surface bidirectional effects and estimate land surface albedo. Many operational BRDF/albedo algorithms adopt a Roujean linear kernel-driven BRDF (RLKB) model because of its simple form and good performance in fitting multidirectional surface reflectance values. However, this model does not explicitly consider topographic effects, resulting in errors when applied over rugged terrain. To address this issue, we proposed a hybrid algorithm suitable for both flat and rugged terrain, called topographical kernel-driven (Topo-KD). First, we constructed a linear kernel-driven BRDF model considering terrain (LKB_T) which describes the topographic effects with a mountain radiative transfer (MRT) model. Then, the Topo-KD algorithm adaptively selects the most suitable model (RLKB or LKB_T) according to the terrain conditions and fitting residuals. The performances of Topo-KD and RLKB using the RossThick–LiSparseReciprocal (RTLSR) kernel are compared using simulated data sets and moderate-resolution imaging spectroradiometer (MODIS) observations. The results show that the BRDF of the pixel is affected by topography. But the RTLSR model does not specifically account for it, resulting in larger biases over rugged terrain than the Topo-KD algorithm in both the red and near-infrared (NIR) bands. The experiment using MODIS data sets demonstrates that the Topo-KD algorithm reduces fitting residuals in the red and NIR bands by 21.5% and 27.4% compared with the RTLSR model. These results indicate that the Topo-KD algorithm can be a better choice for retrieving land surface parameters and describing the radiative transfer process in mountainous areas.

Occlusion effect, an inherent problem of terrestrial laser scanning (TLS) measurements, limits the potential of TLS data in tree attribute estimation. Multiple scans seek to mitigate this effect to provide enhanced scan completeness. However, the numbers and locations of the scans (i.e., the scan design) are usually determined via a subjective assessment of the tree density, spatial patterns of trees, and attributes to be derived. These could cause suboptimal scan completeness and limit tree attribute estimation. This study proposed an iterative-mode scan design to minimize the occlusion effect. First, we introduced a PoTo index based on visibility analysis to evaluate how many trees can be scanned from a location and to select effective candidates for the optimal TLS location. Second, we introduced a cumulative degree of ring closure (CDRC) to quantify the scan completeness for each candidate and determine the optimal TLS location. The TLS data sets of virtual forests with field-measured and synthetic plot parameter settings were simulated according to iterative- and regular-mode designs by using a Heidelberg light detection and ranging (LiDAR) Operations Simulator (HELIOS). The results demonstrated that an iterative-mode design can improve the scan completeness of trees compared to the regular-mode design. The tree attribute (diameter at breast height (DBH), tree height, stem curve, and crown volume) estimates of the iterative-mode design were less erroneous than those of the regular-mode design (e.g., the root-mean-square error (RMSE) could decrease the stem curve estimation by 38% and the crown volume estimation by 15%). This study suggests that the iterative-mode design can obtain an improved quality of the TLS data, especially for dense stands.

Estimation of downward shortwave radiation (DSR) is of great importance in global energy budget and climatic modeling. Although various algorithms have been proposed, effective validation methods are absent for rugged terrains due to the lack of rigorous methodology and reliable field measurements. We propose a two-step validation method for rugged terrains based on computer simulations. The first step is to perform point-to-point validation at local scale. Time-series measurements were applied to evaluate a three-dimensional (3-D) radiative transfer model. The second step is to validate the DSR at pixel-scale. A semiempirical model was built up to interpolate and upscale the DSR. Key terrain parameters were weighted by empirical coefficients retrieved from ground-based observations. The optimum number and locations of ground stations were designed by the 3-D radiative transfer model and Monte Carlo method. Four ground stations were selected to upscale the ground-based observations. Additional three ground stations were set up to validate the interpolated results. The upscaled DSR was finally applied to validate the satellite products provided by MODIS and Himawari-8. The results showed that the modeled and observed DSR exhibited good consistency at point scale with correlation coefficients exceeding 0.995. The average error was around 20 W/m2for the interpolated DSR and 10 W/m2for the upscaled DSR in theory. The accuracies of the satellite products were acceptable at most times, with correlation coefficients exceeding 0.94. From an operational point of view, our method has an advantage of using small amount of ground stations to upscale DSR with relatively high accuracy over rugged terrains.

Terrain affects surface solar radiation (SSR) of mountainous area greatly. However, reliable observational data and methods are absent in mountainous areas. The stations located in these areas, typically built on flat places equipped with horizontal radiometers, are hard to capture the topographic effects. We proposed a tilted SSR observation group for mountainous areas based on ground stations. In 2015 and 2016, the method was tested in Chengde, China. Five ground stations were built on hilltop, valley, and three slopes to measure SSR. The radiometers on slopes and hilltop were set up parallel to the ground surfaces, while the radiometer in the valley was set horizontally to compare with the tilted observation method. A topographic radiation model along with a 12.5m digital elevation model (DEM) data was used to simulate the downward SSR and compare with observations. The result showed good consistency with the observations on slopes with R2values as high as 0.99, but relatively big deviations were found at the hilltop and valley stations, caused by the slope calculation errors and unsuitable observational method. The results demonstrate the fact of that the topographic radiation model should be validated using proposed method with high accuracy DEM.

Land-surface bidirectional reflectance distribution function (BRDF) models are used for the description of surface bidirectional effects and the estimation of surface albedo. The semi-empirical linear kernel-driven BRDF model is one of them which has been adopted by the moderate resolution imaging spectroradiometer (MODIS) operational BRDF/Albedo algorithm, due to its briefness and well-fitting ability. However, this model does not consider the topography factors, and will lead to errors over rugged terrains. However, researches seldom analyze the models' uncertainties caused by rugged terrains quantitatively, as it is difficult to directly validate models over mountain areas at coarse resolution. This letter proposes a forward topographic BRDF simulation method by combining a canopy radiative transfer model (SAILH) and a mountain radiative transfer (MRT) model to investigate the uncertainty and sensitivity of the kernel-driven model over mountain areas theoretically. Results show that the topographic effects can cause over 20% uncertainties on both red and NIR bands. Topography leads to the asymmetry of BRDF distributions on azimuth, which cannot be captured by kernel-driven model at 1km scale. Both DEM types and observation situations influence the retrieval accuracy significantly. Therefore, this work is meaningful to study the optimal inversion scale and observation requirements depending on the topography.

Estimation of daily downward shortwave radiation (DSR) is of great importance in global energy budget and climatic modeling. The combination of satellite-based instantaneous measurements and temporal extrapolation models is the most feasible way to capture daily radiation variations at large scales. However, previous studies did not pay enough attention to topographic effects and simple temporal extrapolation methods were applied directly to rugged terrains which cover a large amount of the land surface. This paper, divided into two parts, aims at analyzing the topographic uncertainties of existing models and proposing a better method based on a mountain radiative transfer (MRT) model to calculate daily DSR. As the first part, this paper analyze the spatiotemporal variations of DSR influenced by topographic effects and checks the applicability of three temporal extrapolation methods on cloud-free days. Considering that clouds also have a strong influence on solar radiation, cloud-free days are chosen for targeted analysis of topographic effects on DSR. Three indices, the coefficient of variation, entropy-based dispersion coefficient (CH), and sill of semivariogram, are put forward to give a quantitative description of spatial heterogeneity. Our results show that the topography can dramatically strengthen the spatial heterogeneity of DSR. The index, CH, has an advantage for quantifying spatial heterogeneity as it offers a tradeoff between accuracy and efficiency. Spatial heterogeneity distorts the daily variation of DSR. Application of extrapolation methods in rugged terrains leads to overestimation of daily average DSR up to 60 W/m2 and a maximum 200 W/m2 error of instantaneous DSR on cloud-free days. This paper makes a quantitative analysis of topographic effects under different spatiotemporal conditions, which lays the foundation for developing a new extrapolation method.