Modeling Solar Radiation in the Forest Using Remote Sensing Data: A Review of Approaches and Opportunities
Solar radiation, the radiant energy from the sun, is a driving variable for numerous ecological, physiological, and other life-sustaining processes in the environment. Traditional methods to quantify solar radiation are done either directly (e.g., quantum sensors), or indirectly (e.g., hemispherical photography). This study, however, evaluates literature which utilized remote sensing (RS) technologies to estimate various forms of solar radiation or components, thereof under or within forest
... r within forest canopies. Based on the review, light detection and ranging (LiDAR) has, so far, been preferably used for modeling light under tree canopies. Laser system's capability of generating 3D canopy structure at high spatial resolution makes it a reasonable choice as a source of spatial information about light condition in various parts of forest ecosystem. The majority of those using airborne laser system (ALS) commonly adopted the volumetric-pixel (voxel) method or the laser penetration index (LPI) for modeling the radiation, while terrestrial laser system (TLS) is preferred for canopy reconstruction and simulation. Furthermore, most of the studies focused only on global radiation, and very few on the diffuse fraction. It was also found out that most of these analyses were performed in the temperate zone, with a smaller number of studies made in tropical areas. Nonetheless, with the continuous advancement of technology and the RS datasets becoming more accessible and less expensive, these shortcomings and other difficulties of estimating the spatial variation of light in the forest are expected to diminish. Light intensity in the forest is mainly affected by canopy structure, site characteristics, atmospheric conditions and solar elevation [13,      . These factors produce complex understory light patterns that express not only horizontal heterogeneity, but also the vertical variation at any given time  . Both solar elevation and atmospheric conditions are primarily dependent on the geographical location of the specified site. Thus, the discussions of these factors were deliberately excluded. The remaining factors: canopy structure and site characteristics are often represented and described with the use of remote sensing (RS) data [21, 22, 24, 25] . Among others, canopy closure, canopy cover or canopy height are proxies of structural and geometrical information of leaves and branches, which are important variables characterizing light conditions inside the stand [6, 9, 19,     . Such information carries critical parameters that can only be described effectively in a 3D space. In addition, site characteristics, such as micro relief, aspect, slope, and height above sea level, can be derived from an accurate high-resolution digital elevation model (DEM) acquired with the use of an active system, such as the light detection and ranging (LiDAR) [30, 31] . Clearly, the remote sensing technology can be a very useful and important source of information for light condition inside the forest    . Existing comprehensive reviews on quantifying forest light environment have been published so far by Lieffers et al.  , Comeau , and Promis  . The authors showed the nature and properties of the different instruments used, methods applied, the accuracies, as well as the associated costs. The use of handheld instruments, called ceptometers, and other quantum-equipped sensors as part of direct measurements, was widely mentioned, while hemispherical photography is considered the most common indirect way. Nonetheless, what was not considered in the scope of the three reviews, was the utilization of RS technology and other allied sciences. Combined with field data, RS provides a handful of benefits, such as the generation of continuous spatial information with an effective cost on a wider scale. Modeling with the use of geographic information system (GIS), for example, can be used in lieu of field-recorded data for areas where field data is not available, or would be too expensive to record  . With this strategy, a continuous map of light conditions can be delivered as a final result. While a passive optical sensor in two-dimensional format proved to be useful in various forestry applications, three-dimensional data may offer even more canopy details and a better understanding of the forest's structure    . Aside from that, it overcomes some of the disadvantages of passive remote sensing, such as cloud-cover issues and vegetation index saturation problems  . A wide-ranging description of available airborne and satellite sensors and their capabilities, in general, could be referred to in the publications by Wang et al.  , Brewer et al.  and, more recently, by Toth and Jozkow  , with the latest discussions not only on sensors, but on platforms as well. This paper, however, evaluates published articles that used or have at least a component of remote sensing in the context of solar radiation at forest stands in various scales. The aim of this study is to (i) synthesize the studies to determine how and what has been done with this state-of-the-art technology, and (ii) detect gaps in methodology or specific technology used to address improvements in the future. The first section of the review presents the physical concepts of solar radiation, and how it transmits through the canopy. The second section focuses on the different techniques and modeling approaches done by researchers on analyzing subcanopy solar radiation with the use of RS data. The next section discusses what we think are the critical issues that came out after synthesizing the articles, and selects papers that stand out and demonstrate novel approaches that only RS technology could offer. Lastly, conclusions and recommendations are laid down on how to improve future directions of similar studies. Overview of Concepts Scientists estimate that roughly 1368 watts m −2 , averaged over the globe and over several years, illuminates the outermost atmosphere of the Earth  . This value is known as solar constant or the total solar irradiance (TSI), which is the maximum possible power that the sun can deliver to the Earth at the mean distance between them [23, 46] . Only about 1 4 of the TSI that is considered the incoming Remote Sens. 2018, 10, 694 3 of 22 solar radiation, collectively called shortwave radiation, enters the top of Earth's atmosphere . Out of this proportion, approximately 20% and 30% is absorbed by the atmosphere and reflected back to space, respectively . The remaining 50% penetrates the atmosphere, and is taken in by the land and the oceans . Gibson  said that about half of the shortwave radiation is in the visible region (0.4-0.7 µm) of the electromagnetic spectrum, and the other half is mostly in the near-infrared (0.7 µm-100 µm). Ultraviolet radiation (0.01-0.4 µm) makes up only a little over 8% of the total . The entire spectrum of the absorbed radiation drives photosynthesis, fuels evaporation, melts snow and ice, and warms the Earth . Once the shortwave radiation touches the Earth's surface, there are three forms of interactions that take place-absorption, transmission, and reflection . Their proportions depend on the wavelength of the energy, and the material and condition of the feature . According to Brown and Gillespie  , a single layer of leaf will generally absorb 80% of incoming visible radiation, whilst reflecting 10% and transmitting the remaining 10%. Approximately 20% of infrared is absorbed, with 50% reflected and 30% transmitted. These interactions may be modified considering the heterogeneous spatiotemporal characteristics of canopy based on the type of leaf, arrangements, density, and the angle of incidence which determines the projected ("shadowed") leaf area in the direction of the radiation [8, 50, 51] . Furthermore, in a subcanopy environment, the direct component of radiation is more heterogeneous than the diffused light. A predominantly direct-beam radiation that passes through openings in the forest canopy is called sunfleck  . The amount of sunfleck in the understory depends on different, often interacting factors: the coincidence of solar path with a canopy opening, the movement of clouds that obscure or reveal the sun, and the wind-induced movement of foliage and branches  . On the other hand, the penetration of the diffuse light is less variable, as it depends on the level of sky brightness, and the number, size, and spatial distribution of canopy openings, the canopy geometry, and the spatial distribution and optical characteristics of the forest biomass  . Generally, solar radiation below the canopy and on the forest floor has been expressed as transmittance, which depends on (1) the density and thickness of the vegetation layer, (2) the terrain, and (3) the position of the sun [36, 55] . Comeau  defined transmittance as the ratio of solar radiation that reaches a sampling point within a forest to the incident radiation measured in the open or over the canopy at the same time. A widely accepted theory on light transmission in the forest is used by treating the canopy as a turbid medium [34, 35] . This equation is called the Beer-Lambert-Bouguer law, or simply, Beer's law [6, 56] : where: I = below-canopy light intensity I 0 = incident radiation at the canopy top k = extinction coefficient L = leaf area index (LAI) The extinction coefficient which corresponds to an optical depth per unit leaf area  is determined by a number of factors, such as leaf angle distribution, canopy structure, and clumping level  . Depending on the type of vegetation, it usually varies between 0.3 and 0.6    . For an assumed spherical leaf angle distribution, k is approximated as a function of the solar zenith angle θ [23,58]: The LAI which represents a structure parameter in the vertical direction is defined as the total one-sided area of leaf tissue per unit ground surface area (m 2 m −2 ) [51, 57] . Nearly all vegetation and land-surface models include parameterizations of LAI, as it characterizes the canopy-atmosphere interface, where most of the energy fluxes exchange [57, 60] . Estimation of the LAI can be derived Remote Sens. 2018, 10, 694 4 of 22 from light transmission applying Beer's law, where the fraction of light that is intercepted (T) changes exponentially as the layer of leaves increases : So, with a theoretical value of 0.5 for k, an LAI of 1, 3, 6, and 9 intercepts, respectively, 39, 78, 95, and 99% of the visible light  . In addition, Nyman et al.  describes another way to measure transmittance as a function of the path length (P), based on the earlier work of Seyednasrollah and Kumar  . In this approach, the density of the vegetation and the extinction coefficients are combined into a single parameter which describes the rate of absorption per unit path length. Path length of the direct beam is computed as the ratio of canopy height and cosine of solar zenith angle (Figure 1 ). The probability of attenuation of an incident radiation is directly proportional to the path length itself, leaf density (ratio of LAI and canopy height) and the leaf area facing the beam of light, or the leaf normal oriented in the light's direction  . Remote Sens. 2018, 10, x FOR PEER REVIEW 4 of 23 So, with a theoretical value of 0.5 for k, an LAI of 1, 3, 6, and 9 intercepts, respectively, 39, 78, 95, and 99% of the visible light  . In addition, Nyman et al.  describes another way to measure transmittance as a function of the path length (P), based on the earlier work of Seyednasrollah and Kumar  . In this approach, the density of the vegetation and the extinction coefficients are combined into a single parameter which describes the rate of absorption per unit path length. Path length of the direct beam is computed as the ratio of canopy height and cosine of solar zenith angle (Figure 1 ). The probability of attenuation of an incident radiation is directly proportional to the path length itself, leaf density (ratio of LAI and canopy height) and the leaf area facing the beam of light, or the leaf normal oriented in the light's direction  . Solar radiation energy is often measured as an energy flux density (watts per square meter), and is appropriate for energy balance studies because watt is a unit of power [23, 64] . But for studies of light interception in relation to plant's health and growth, the photon density is better suited because the rate of photosynthesis depends on the number of photons received, rather than photon energy  . The specific range of 400 to 700 nm wavelength is where photosynthesis is active, and so it is called the photosynthetically active radiation or PAR region [64, 65] . Owing to its similarity to spectral range, PAR is often used synonymously with visible light [28, 66] . Energy in the PAR region is referred to as photosynthetic photon flux density (PPFD), with units in µmol m −2 s −1 . Modelling Approaches Using RS Technology Based on the selected scientific literatures, a schematic diagram (Figure 2 ) was created to illustrate how the authors made use of RS technology in building their models. Airborne laser scanning (ALS) and terrestrial laser scanning (TLS) are the two commonly used systems, while additional information was taken from optical images either from satellites or UAV-based digital cameras. Point clouds from either ALS or TLS were processed and transformed into voxels, where transmission model was applied. Most of the voxel modeling relied on Beer-Lambert-Bouguer law, where attenuation of sunlight is calculated as a function of vegetation structure. Generation of LiDAR metrics, such as canopy height or canopy density, was also observed, then used as inputs for further analysis. Others used it in ray-tracing model or as a substitute to LAI, particularly in Equation (1) . For simulation of light regime, reconstruction of the canopy was performed especially from the TLS dataset. Letters (a) and (b) of Figure 2 illustrate how laser pulses best represent the direct beam of sunlight hitting various parts of Remote Sens. 2018, 10, 694 5 of 22 the canopy, as well as the ground. Detailed discussions on how these techniques were executed are given in the subsequent section.