Mutual Shadowing Research Articles

Extending the GOSAILT Model to Simulate Sparse Woodland Bi-Directional Reflectance with Soil Reflectance Anisotropy Consideration

Anisotropic canopy reflectance plays a crucial role in estimating vegetation biophysical parameters, whereas soil reflectance anisotropy affects canopy reflectance. However, woodland canopy bidirectional reflectance distribution function (BRDF) models considering soil anisotropy are far from universal, especially for the BRDF models of mountain forest. In this study, a mountain forest canopy model, named geometric-optical and mutual shadowing and scattering from arbitrarily inclined-leaves model coupled with topography (GOSAILT), was extended to consider the soil anisotropic reflectance characteristics by introducing the simple soil directional (SSD) reflectance model. The modified GOSAILT model (named GOSAILT-SSD) was evaluated using unmanned aerial vehicle (UAV) field observations and discrete anisotropic radiative transfer (DART) simulations. Then, the effects of Lambertian soil assumption on simulating the vi-directional reflectance factor (BRF) were evaluated across different fractions of vegetation cover (Cv), view zenith angles (VZA), solar zenith angles (SZA), and spectral bands with the GOSAILT-SSD model. The evaluation results, with the DART simulations, show that the performance of the GOSAILT-SSD model in simulating canopy BRF is significantly improved, with decreasing RMSE, from 0.027 to 0.017 for the red band and 0.051 to 0.037 for the near-infrared (NIR) band. Meanwhile, the GOSAILT-SSD simulations show high consistency with UAV multi-angular observations (R2 = 0.97). Besides, it is also found that the BRF simulation errors caused by Lambertian soil assumption are too large to be neglected, with a maximum relative bias of about 45% for the red band. This inappropriate assumption results in a remarkable BRF underestimation near the hot spot direction and an obvious BRF overestimation for large VZA in the solar principal plane (PP). Meanwhile, this simulation bias decreases with the increase of fraction of vegetation cover. This study provides an effective technique to improve the capability of the mountain forest canopy BRDF model by considering the soil anisotropic characteristics for advancing the modeling of radiative transfer (RT) processes over rugged terrain.

New approach to calculating tree height at the regional scale

BackgroundDetermining the spatial distribution of tree heights at the regional area scale is significant when performing forest above-ground biomass estimates in forest resource management research. The geometric-optical mutual shadowing (GOMS) model can be used to invert the forest canopy structural parameters at the regional scale. However, this method can obtain only the ratios among the horizontal canopy diameter (CD), tree height, clear height, and vertical CD. In this paper, we used a semi-variance model to calculate the CD using high spatial resolution images and expanded this method to the regional scale. We then combined the CD results with the forest canopy structural parameter inversion results from the GOMS model to calculate tree heights at the regional scale.ResultsThe semi-variance model can be used to calculate the CD at the regional scale that closely matches (mainly with in a range from − 1 to 1 m) the CD derived from the canopy height model (CHM) data. The difference between tree heights calculated by the GOMS model and the tree heights derived from the CHM data was small, with a root mean square error (RMSE) of 1.96 for a 500-m area with high fractional vegetation cover (FVC) (i.e., forest area coverage index values greater than 0.8). Both the inaccuracy of the tree height derived from the CHM data and the unmatched spatial resolution of different datasets will influence the accuracy of the inverted tree height. And the error caused by the unmatched spatial resolution is small in dense forest.ConclusionsThe semi-variance model can be used to calculate the CD at the regional scale, together with the canopy structure parameters inverted by the GOMS model, the mean tree height at the regional scale can be obtained. Our study provides a new approach for calculating tree height and provides further directions for the application of the GOMS model.

Kirigami‐Based Compliant Mechanism for Multiaxis Optical Tracking and Energy‐Harvesting Applications

Kirigami‐based structures and materials have recently emerged with a variety of geometric transformation capabilities in applications such as flexible electronics, soft robotics, nanophotonics, energy harvesting, and others. Herein, a 2D pattern of cuts (kirigami) that transform into a 3D, one‐piece compliant mechanism that allows for optical tracking over a solid angle sweep of over 110° in two axes is presented. This structure is scaled to an arbitrarily large array, yet the displacement required to achieve the angular sweep remain compact and independent of the number of elements and areal extent of the array. One of the applications of this mechanism is in solar concentration and dual‐axis tracking. Using practical dimensions, 80‐fold or greater concentration is realized. Mutual shadowing of nearby concentrators is assessed along with thermal effects of optical concentration that limit photovoltaic (PV) cell efficiency. The significant reduction in semiconductor usage along with the multiaxis tracking ability reduces the overall cost of solar PV panels. This is projected to make them competitive with stationary silicon panels capable of satisfying the household daily average energy requirement.

Detection and Localization of Overlapped Fruits Application in an Apple Harvesting Robot

For yield measurement of an apple orchard or the mechanical harvesting of apples, there needs to be accurate identification of the target apple fruit. However, in a natural scene, affected by the apple’s growth posture and camera position, there are many kinds of apple images, such as overlapped apples; mutual shadows or leaves; stems; etc. It is a challenge to accurately locate overlapped apples. They will influence the positioning time and recognition efficiency and then affect the harvesting efficiency of apple-harvesting robots or the accuracy of orchard yield measurement. In response to this problem, an overlapped circle positioning method based on local maxima is proposed. First, the apple image is transformed into the Lab color space and segmented by the K-means algorithm. Second, some morphological processes, like erosion and dilation, are implemented to abstract the outline of the apples. Then image points are divided into central points; edge points; or outer points. Third, a fast algorithm is used to calculate every internal point’s minimum distance from the edge. Then, the centers of the apples are obtained by finding the maxima among these distances. Last, the radii are acquired by figuring out the minimum distance between the center and the edge. Thus, positioning is achieved. Experimental results showed that this method can locate overlapped apples accurately and quickly when the apple contour was complete; and this has certain practicability.

Secret Image Sharing with Dealer-Participatory and Non-Dealer-Participatory Mutual Shadow Authentication Capabilities

A ( k , n ) threshold secret image sharing (SIS) method is proposed to divide a secret image into n shadows. The beauty of this scheme is that one can only reconstruct a secret image with k or more than k shadows, but one cannot obtain any information about the secret from fewer than k shadows. In the ( k , n ) threshold SIS, shadow authentication means the detection and location of manipulated shadows. Traditional shadow authentication schemes require additional bits for authentication; need much information to be public; or need to put each shadow into a host image, utilizing the information hiding technique, which makes the generation, recovery and authentication complexity higher. Besides, most existing schemes work when a dealer participates in recovery. Our contribution is that we propose a SIS method for a ( k , n ) threshold with dealer-participatory and non-dealer-participatory mutual shadow authentication capabilities which integrates polynomial-based SIS and visual secret sharing (VSS) through using the result of VSS to “guide” the polynomial-based SIS by a screening operation. In our scheme, when an authentication image is public, all involved actors (participants and dealer) can mutually authenticate each other by exchange the lowest level plane instead of the whole shadow. Our scheme is suitable for the case with and without a dealer participate recovery. In addition, the proposed scheme has characteristics of low generation and authentication complexity, no pixel expansion, 100% detection rate and lossless recovery.

A Radiative Transfer Model for Patchy Landscapes Based on Stochastic Radiative Transfer Theory

The availability of global high-resolution land cover maps provides promising a priori knowledge for characterizing subpixel heterogeneity and improving predictions of directional reflectance of coarse-resolution pixels. Due to mutual shadowing and sheltering effects between the adjacent forest and cropland patches, the spectral nonlinear mixing of patchy ecotones is significant, especially when the sun illuminates the ecotone from the forest side with high solar zenith angle. The spectral linear mixture (SLM) approach leads to overestimation of the bidirectional reflectance factor (BRF) in the red band in the principal plane (PP), with a maximum absolute error (MAE) of 0.0063 and a maximum relative error (MRE) of 52.5%, and to underestimation in the near-infrared band in PP with an MAE of 0.0940 and an MRE of 14.5%. In a scenario with randomly distributed boundary orientations, the overestimation of SLM increases with the degree of fragmentation and the view zenith angle. We propose a Radiative Transfer model for patchy ECotones (RTEC). which improves $R^{2}$ from 0.61 to 0.94 in the red band of Landsat-8 directional reflectance at the validation site. The RTEC model provides an efficient and analytical approach for directional reflectance predictions over heterogeneous patchy landscapes at coarse resolution and will be used for biophysical parameter retrievals [e.g., the leaf area index (LAI)] in future applications.

Light Induced Inverse-Square Law Interactions between Nanoparticles: "Mock Gravity" at the Nanoscale.

The interaction forces between identical resonant molecules or nanoparticles, optically induced by a quasimonochromatic isotropic random light field, are theoretically analyzed. In general, the interaction force exhibits a far-field oscillatory behavior at separation distances larger than the light wavelength. However, we show that the oscillations disappear when the frequency of the random field is tuned to an absorption Fröhlich resonance, at which the real part of the particle's electric polarizability is zero. At the resonant condition, the interaction forces follow a long-range gravitylike inverse square distance law which holds for both near- and far-field separation distances.

Bimodal Porosity and Stability of a TiO2 Gig-Lox Sponge Infiltrated with Methyl-Ammonium Lead Iodide Perovskite.

We created a blend between a TiO2 sponge with bimodal porosity and a Methyl-Ammonium Lead Iodide (MAPbI3) perovskite. The interpenetration of the two materials is effective thanks to the peculiar sponge structure. During the early stages of the growth of the TiO2 sponge, the formation of 5–10 nm-large TiO2 auto-seeds is observed which set the micro-porosity (<5 nm) of the layer, maintained during further growth. In a second stage, the auto-seeds aggregate into hundreds-of-nm-large meso-structures by their mutual shadowing of the grazing Ti flux for local oxidation. This process generates meso-pores (10–100 nm) treading across the growing layer, as accessed by tomographic synchrotron radiation coherent X-ray imaging and environmental ellipsometric porosimetry. The distributions of pore size are extracted before (>47% V) and after MAPbI3 loading, and after blend ageing, unfolding a starting pore filling above 80% in volume. The degradation of the perovskite in the blend follows a standard path towards PbI2 accompanied by the concomitant release of volatile species, with an activation energy of 0.87 eV under humid air. The use of dry nitrogen as environmental condition has a positive impact in increasing this energy by ~0.1 eV that extends the half-life of the material to 7 months under continuous operation at 60 °C.

Modeling Discrete Forest Anisotropic Reflectance Over a Sloped Surface With an Extended GOMS and SAIL Model

Topographic effects on canopy reflectance play a pivotal role in the retrieval of surface biophysical variables over rugged terrain. In this paper, we proposed a new canopy anisotropic reflectance model for discrete forests, Geometric Optical and Mutual Shadowing and Scattering-from-Arbitrarily-Inclined-Leaves model coupled with Topography (GOSAILT), which considers the effects of slope, aspect, geotropic nature of tree growth, multiple scattering, and diffuse skylight. GOSAILT-simulated areal proportions of four scene components (i.e., sunlit crown, shaded crown, sunlit background, and shaded background) were evaluated using the Geometric Optical model for Sloping Terrains (GOST) model. The canopy reflectances simulated by GOSAILT were validated against two reflectance data sets: Discrete anisotropic radiative transfer (DART) simulations and wide-angle infrared dual-model line/area array scanner (WIDAS) observations. Compared with a horizontal surface, the forest canopy reflectance over a steep slope (60°) is significantly distorted with absolute (relative) bias values of 0.048 (79.60%) and 0.056 (12.02%) for the red and near-infrared (NIR) bands, respectively. The GOSAILT-simulated component areal proportions show close agreements with GOST. Moreover, GOSAILT simulations have high overall accuracy (red band: coefficient of determination (R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) = 0.96; root-mean-square error (RMSE) = 0.003; and mean absolute percentage error (MAPE) = 3.91%; and NIR band: R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 0.78, RMSE = 0.019; MAPE = 3.94%) when compared with the DART simulations. These extensive validations indicate good performances of GOSAILT in canopy reflectance simulations over sloped surfaces.

A New Photovoltaic Arrays Fixed Reconfiguration Method for Reducing Effects of One- and Two-Sided Mutual Shading

Low distance between photovoltaic (PV) arrays can lead to the mutual shading between them. This can lead to significant power losses. Usually, these shadows can be seen in PV plants with limited land such as buildings' roof. In this paper, a PV arrays fixed reconfiguration method is presented in order to reduce the effects of one- and two-sided mutual shadings in total cross tied (TCT) arrangements. Two-sided mutual shading appears when the array is shaded in two separate areas, while there is only one shaded part in the array in one-sided mutual shading. In this method, the physical locations of the modules are rearranged without changing the electrical interconnections. To reduce the effects of these shadings, first, their important features are explained. Then, the optimal array rearrangement is determined by considering all possible mutual shadows (MSHs). In mutual shading conditions, the obtained arrangement is capable of equally dispersing shaded modules in different array rows, while there is no need to add any additional switches or sensors. Due to this equal dispersion, there is no need to use the bypass diodes for maximum power extraction in this condition. The simulation results validate the effectiveness of this method.

Optimization of the Sudoku based reconfiguration technique for PV arrays power enhancement under mutual shading conditions

The low relative position of the fixed PV arrays can lead to the mutual shading between them. This shading decreases the overall energy produced by PV systems due to the mismatch losses. In this paper, the fixed reconfiguration technique is optimized bases on Sudoku puzzle pattern to reduce the effects of this shading. In the optimized technique, the physical location of modules in a total cross tied (TCT) connected PV array are rearranged based on new modified Sudoku dispersion rules. For this purpose, the mutual shadow (MSH) pattern is initially determined in the PV plants that have collectors with the same tilt and direction. Then, the weaknesses of the usual Sudoku dispersion rules against these shadows are explained and the MSHs that can lead to the non-optimal conditions are presented. For optimization of the Sudoku-based reconfiguration technique, the new rules will be merged to the usual Sudoku dispersion rules. Finally, the improvement resulting from the modified technique with respect to the non-modified and some other methods is demonstrated by extensive simulation results.

Canopy Light Interception Conversion in Upright Fruiting Offshoot (UFO) Sweet Cherry Orchard

<abstract> The sun‘s position varies throughout the day. The changes in time and/or location cause different angles between the sunbeam and tree canopy (sunbeam-canopy angle, θ). Canopy light interception, the fractional interception of photosynthetically active radiation (PAR), varies as θ changes, resulting in a different measurement basis of light interception if light interception is measured at different θ. This situation is more noticeable in planar tree architecture, such as upright fruiting offshoot (UFO) architecture. This study aimed to develop a conversion method to provide a common basis for determining canopy light interception at different sun positions for such architectures. In addition to sun azimuth and zenith angles (α and β, respectively), conversion inputs included canopy dimensions, orchard configuration, canopy light interception, and canopy ground occupation porosity (the fraction of non-shaded area). Field data collection was conducted at 18 different times within a time window of ±2.50 h from solar noon (no mutual shadows were cast between adjacent rows) with 0.25 h intervals for eight sample blocks. The conversion method was able to convert canopy light interception with an overall root mean square error (RMSE) of 0.03 and mean absolute percentage error (MAPE) of 7.85%. Based on the overall accuracies when using a different basis and using different measured values in this study, conversion is recommended when θ is greater than 8°. In addition, we recommend conducting conversion with canopy projection from the same side to avoid the influence of asymmetrical canopies.

Modifying Geometric-Optical Bidirectional Reflectance Model for Direct Inversion of Forest Canopy Leaf Area Index

Forest canopy leaf area index (LAI) inversion based on remote sensing data is an important method to obtain LAI. Currently, the most widely-used model to achieve forest canopy structure parameters is the Li-Strahler geometric-optical bidirectional reflectance model, by considering the effect of crown shape and mutual shadowing, which is referred to as the GOMS model. However, it is difficult to retrieve LAI through the GOMS model directly because LAI is not a fundamental parameter of the model. In this study, a gap probability model was used to obtain the relationship between the canopy structure parameter nR2 and LAI. Thus, LAI was introduced into the GOMS model as an independent variable by replacing nR2 The modified GOMS (MGOMS) model was validated by application to Dayekou in the Heihe River Basin of China. The LAI retrieved using the MGOMS model with optical multi-angle remote sensing data, high spatial resolution images and field-measured data was in good agreement with the field-measured LAI, with an R-square (R2) of 0.64, and an RMSE of 0.67. The results demonstrate that the MGOMS model obtained by replacing the canopy structure parameter nR2 of the GOMS model with LAI can be used to invert LAI directly and precisely.

The intensity of the field generated by a point source and reflected from a rough surface

This paper studies the intensity of the acoustic field generated by a point source above a rough surface with the Dirichlet or Neumann boundary conditions. The derived equations are valid for arbitrary distances between the source, receiver and rough surface, including the case when these distances are smaller than the correlation radius of the surface roughness. It is believed that the proposed method is an improvement of the more conventional approach, which is based on integration over individual areas of the rough surface and that is valid when the source, receiver, and surface are at large distances from each other. The main limitation in deriving the expressions for the acoustic field intensity is the condition that the mutual shadowing of the surface points is small, which is close to the small slope approximation for the rough surface profile. The derivation includes the limiting cases which lead to the traditional small perturbation method and Kirchhoff approximation.

Cost of energy and mutual shadows in a two-axis tracking PV system

The performance improvement obtained from the use of trackers in a PV system cannot be separated from the higher requirement of land due to the mutual shadows between generators. Thus, the optimal choice of distances between trackers is a compromise between productivity and land use to minimize the cost of the energy produced by the PV system during its lifetime. This paper develops a method for the estimation and optimization of the cost of energy function. It is built upon a set of equations to model the mutual shadows geometry and a procedure for the optimal choice of the wire cross-section. Several examples illustrate the use of the method with a particular PV system under different conditions of land and equipment costs. This method is implemented using free software available as supplementary material.

Estimation of forest canopy leaf area index using MODIS, MISR, and LiDAR observations

A new approach for determining the forest leaf area index (LAI) from a geometric-optical model inversion using multisensor observations is developed. For improving the LAI estimate for the forested area on rugged terrain, a priori information on tree height and the spectra of four scene components of a geometric-optical mutual shadowing (GOMS) model are extracted from airborne light-detection and ranging (LiDAR) data and optical remote sensing data with high spatial resolution, respectively. The slope and aspect of the study area are derived from digital elevation model data. These extracted parameters are applied in an inversion to improve the estimates of forest canopy structural parameters in a GOMS model. For the field investigation, a bidirectional reflectance factor data set of needle forest pixels is collected by combining moderate-resolution-imaging-spectroradiometer (MODIS) and multiangle-imaging-spectroradiometer (MISR) multiangular remote sensing observations. Then, forest canopy parameters are inverted based on the GOMS model. Finally, the LAI of the forest canopy of each pixel is estimated from the retrieved structural parameters and validated by field measurements. The results indicate that the accuracy of forest canopy LAI estimates can be improved by combining observations of passive multiangle and active remote sensors.

A three‐dimensional analytic model for the scattering of a spherical bush

Advanced climate models require a more realistic description of canopy radiation with reasonable computational efficiency. This paper develops the mathematics of scattering from a spherical object conceptualized to be a spherical bush to provide a building block that helps to address this need of climate models. It is composed of a homogeneous distribution of individual smaller objects that scatter isotropically. In the limit of small optical depth, incident radiation will scatter isotropically as the sum of that scattered by all the individual scatterers, but at large optical depth the radiation leaving the spherical bush in a given direction is reduced by mutual shadowing of the smaller objects. In the single scattering limit, the scattering phase function and so the albedo are obtained by simple but accurate analytic expressions derived from analytic integration and numerical evaluation. Except in the limit of thin canopies, the scattering and hence albedos are qualitatively and quantitatively different than those derived from 1‐D modeling.

Improved topographic correction of forest image data using a 3‐D canopy reflectance model in multiple forward mode

In most forestry remote sensing applications in steep terrain, simple photometric and empirical (PE) topographic corrections are confounded as a result of stand structure and species assemblages that vary with terrain and the anisotropic reflective properties of vegetated surfaces. To address these problems, we present MFM‐TOPO as a new physically‐based modelling (PBM) approach for normalising topographically induced signal variance as a function of forest stand structure and sub‐pixel scale components. MFM‐TOPO uses the Li‐Strahler geometric optical mutual shadowing (GOMS) canopy reflectance model in Multiple Forward Mode (MFM) to account for slope and aspect influences directly. MFM‐TOPO has an explicit physical‐basis and uses sun‐canopy‐sensor (SCS) geometry that is more appropriate than strictly terrain‐based corrections in forested areas since it preserves the geotropic nature of trees (vertical growth with respect to the geoid) regardless of terrain, view and illumination angles. MFM‐TOPO is compared against our recently developed SCS+C correction and a comprehensive set of other existing PE and SCS methods (cosine, C correction, Minnaert, statistical‐empirical, SCS, and b correction) for removing topographically induced variance and for improving SPOT image classification accuracy in a Rocky Mountain forest in Kananaskis, Alberta Canada. MFM‐TOPO removed the most terrain‐based variance and provided the greatest improvement in classification accuracy within a species and stand density based class structure. For example, pine class accuracy was increased by 62% over shaded slopes, and spruce class accuracy was increased by 13% over more moderate slopes. In addition to classification, MFM‐TOPO is suitable for retrieving biophysical parameters in mountainous terrain.

Saturn’s Rings at True Opposition

ABSTRACTOn 2005 January 14, the Saturn system was observed at true opposition with the planetary camera of the Wide Field Planetary Camera 2 (WFPC2) on the Hubble Space Telescope. This was the culmination of nearly a decade of similar UBVRI observations, yielding a uniform set of over 400 high spatial resolution and photometrically accurate radial profiles of the rings that spans the full range of ring inclinations and solar phase angles accessible from the Earth. Using a subset of these images at similar effective ring opening angles Beff∼ -23°, we measured the normalized ring reflectivity I/F over broad regions of the A, B, and C rings as a function of solar phase angle and wavelength. There is a strong surge in brightness near opposition. To measure the width and amplitude of the opposition effect, we fitted two models to the observations: a simple four‐parameter linear‐exponential model and a more complex model (B. Hapke) that incorporates a wavelength‐dependent description of the coherent backscatter opposition effect, as well as the shadow‐hiding opposition effect by a particulate surface. From fits to the linear‐exponential model, the half‐width at half‐maximum for the rings is ∼0.1° at BVRI wavelengths, increasing to ∼0.16° and ∼0.19° for the A and B rings, respectively, in the U filter (338 nm). To assess the contribution of the shadowing of ring particles by each other to the opposition surge, we used Monte Carlo simulations of dynamical models of the rings for a variety of optical depths and particle size distributions, both with and without self‐gravity. Multiple scattering is very weak at low phase angles, and thus these simulations are nearly wavelength independent. The interparticle shadow‐hiding opposition surge increases in strength with ring optical depth and with broadened size distributions. Self‐gravity produces wakes that somewhat complicate the picture, because mutual shadowing by wakes is strongly dependent on illumination and viewing geometry. The observed opposition surge in the rings is much stronger and narrower than that caused by interparticle shadowing. We examined regional variations in the opposition surge across the A, B, and C rings using linear‐exponential model fits. Some of these are most easily explained on the basis of optical depth, volume filling factor, and the relative width of the particle size distribution. The opposition effect for the A, B, and C rings is substantially narrower than for two nearby icy satellites, Mimas and Enceladus, indicating that they have distinctly different surface properties.

Scattering and radiative properties of complex soot and soot-containing aggregate particles

We use the superposition T-matrix method to compute the scattering matrix elements and optical cross-sections for a variety of complex soot and soot-containing aggregate particles in random orientation at a visible wavelength 0.628 μm. It is shown that random variations in the geometrical configuration of monomers in a soot cluster for fixed fractal dimension and prefactor, monomer size, and number of monomers have a rather weak effect on scattering and absorption, at least in the visible part of the spectrum. Thus, the electromagnetic scattering and absorption characteristics of a single cluster realization are sufficient to represent the mean values obtained by averaging over many realizations of the “equivalent” clusters generated for the same fractal parameters. However, the results for the soot clusters differ fundamentally from those calculated for the volume-equivalent soot sphere and for the corresponding external mixture of soot monomers, assuming that there are no electromagnetic interactions between the monomers. We also compute and analyze the scattering and absorption properties of aerosols formed by semi-external aggregation of larger ammonium sulfate, silica, or dust particles with soot clusters as well as semi-external aggregates consisting of several components with different sizes and refractive indices. Depending on its chemical composition and size, the larger particle that is in touch with a soot cluster can strongly influence, or even dominate, the overall optical characteristics of the aggregate. Aggregation can result in stronger extinction, absorption, and scattering cross-sections relative to those computed for the corresponding external mixture. Possibly owing to mutual shadowing, the optical cross-sections of multi-component aggregates are smaller than those of their externally mixed counterparts, but by no more than ∼20%. Implications of our study for analyses of remote sensing observations and atmospheric radiation balance computations are discussed.