A spectral directional reflectance model of row crops
Feng Zhao a,b, Xingfa Gu b,⁎, Wout Verhoef c, Qiao Wang d, Tao Yu b, Qiang Liu b, Huaguo Huang e,Wenhan Qin f, Liangfu Chen b, Huijie Zhao a
a Key Laboratory of Precision Opto-Mechatronics Technology, Ministry of Education, School of Instrument Science and Opto-Electronics Engineering, Beijing University of Aeronautics andAstronautics, Beijing, 100191, PR Chinab State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing Applications (IRSA), Chinese Academy of Sciences, Beijing, 100101, PR Chinac National Aerospace Laboratory (NLR), Emmeloord, The Netherlandsd Environmental Satellite Center of Ministry of Environmental Protection, PR Chinae Key Laboratory for Silviculture and Conservation, Ministry of Education, College of Forestry, Beijing Forestry University, Beijing, 100083, PR Chinaf SSAI/NASA Goddard Space Flight Center, Greenbelt, Maryland, United States
⁎ Corresponding author. State Key Laboratory of RemoRemote Sensing Applications, Chinese Academy of Scien
A computationally efficient reflectance model for row planted canopies is developed in this paper throughseparating the contributions of incident direct and diffuse radiation scattered by row canopies. The rowmodel allows calculating the reflectance spectrum in any given direction for the optical spectral region. Theperformance of the model is evaluated through comparisons with field measurements of winter wheat aswell as with an established 3D computer simulation model. Especially the systematic comparisons with thecomputer simulation model demonstrate that the model can adequately simulate the characteristicdistribution of directional reflectance factors of row canopies, which is shown in the polar map of reflectanceas a high or low value stripe approximately parallel to the row orientation, besides the hotspot effect.Physical mechanisms causing the dynamics were proposed and supported by comparison studies. Thefeatures of reflectance distributions of row canopies, which are distinctively different from those ofhomogeneous canopy, imply that it is problematic to use one-dimensional radiation transfer model tointerpret radiation data and estimate the structural or spectral parameters of row canopies from reflectancemeasurements. Finally, further improvements needed for the current model are briefly discussed.
te Sensing Science, Institute ofces, Beijing, 100101, PR [email protected] (X. Gu),
Agricultural crops are important but complex targets for remotesensing instruments. They are important because of the need for theidentification of crops and acreage early in the growing season, theearly assessment of crop conditions, prediction of final crop yields,and the possibility of irrigation scheduling based on remote sensinginputs (Jackson et al., 1979; Moran et al., 1997). Much of thecomplexity arises because crops are usually planted in rows, whichmeans that, for a considerable time during the early part of thegrowing season, the stripes of bare soil seen between rows form animportant contribution to canopy reflectance. This contribution isdetermined by the row orientation, row structure, crop architecture,viewing direction, and sun position, and therefore it is much morecomplex than in the case of homogeneous canopies (Suits, 1983). Thisis even more so when the soil reflectance shows strongly anisotropicbehavior affected by factors like soil roughness, moisture content,
organic matter content, and particle size distribution, etc. (Irons et al.,1992). Experimental and/or modeled results of solar radiationinterception for row canopies (Annandale et al., 2004; Bégué et al.,1994; Cohen et al., 1987; Ganis, 1997; Jackson & Palmer, 1972) havedemonstrated that the assumption of the crop being horizontallyhomogeneous may cause large errors in estimating light penetration,distribution and absorption when plant canopies are planted indistinct row structure. Field measured directional reflectance data ofrow canopies (Goel & Grier, 1986; Nilson & Kuusk, 1989; Verhoef &Bunnik, 1976) and computer simulated reflectance data of row crops(Qin et al., 1996) show that RT models developed for homogeneouscanopy layers are no longer applicable to horizontally discontinuousrow canopies.
There have been some studies of canopy reflectance models toinclude the effect of row crops in the early growing stages. Verhoefand Bunnik (1976) developed a row effect model by extending theone-layer Suits model (Suits, 1972) with a few extra geometricalparameters related to the row structure. They assumed that thevegetation canopy along rows is formed by periodic rectangularprisms of plant material, with bare soil in between the prisms. Therow effect is described by modifying the gap probabilities and thecoefficients in the Suits model for a homogeneous canopy. By
b Row width.h Row height.d Row distance.L Leaf area index.D Foliage area volume density, equals (Ld) /(bh) for row
canopies.θ Zenith angle.φ Azimuth angle.α The inclination angle projected in the perpendicular
plane of the row, with the relation: tanα= tanθsinφ.Ωs Solar direction, also can be expressed as (θs, φs).Ωo Viewing direction, also can be expressed as (θo, φo).ξ The angle between Ωs and Ωo.R Directional reflectance factor.rso Single-scattering contribution of the directional re-
flectance factor.rm Multiple-scattering contribution of directional reflec-
tance factor, including within-row part rwithin-row andbetween rows part rbetween-rows.
rsd Hemispherical reflectance for direct sunlight.rdo Directional reflectance for diffuse skylight.rl Leaf hemispherical reflectance.tl Leaf hemispherical transmittance.rs Soil hemispherical reflectance.reff Effective reflectance of the row.Sλ/Qλ The proportion of direct solar spectral irradiance to the
total solar irradiance in a horizontal plane above theplant canopy.
Es Direct solar flux density on a horizontal plane.E− Diffuse downward irradiance.E+ Diffuse upward irradiance.Eo Flux-equivalent radiance in viewing direction, equals
πLo, where Lo is the radiance in the observer'sdirection.
Ei Total irradiance at the top of row canopy, equalsEs(0)+E−(0).
a Attenuation coefficient for diffuse flux.k Extinction coefficient for direct flux in the direction of
the sun.K Extinction coefficient for direct flux in the direction of
the observer.s Scattering coefficient from Es to E+.s′ Scattering coefficient from Es to E−.v Scattering coefficient from E− to Eo.v′ Scattering coefficient from E+ to Eo.w Bidirectional scattering coefficient from Es to Eo.σ Scattering coefficient from E− to E+, or from E+ to E−.G(θ) The projection of a unit leaf area onto the surface
normal to the direction θl(Ω, z) The effective path length in the direction of Ω passing
through the canopy at the height of z.lso The difference between incident solar and viewing
path length.P(Ω,z) Gap fraction in the direction of Ω at the height of z.Pso(Ωs,Ωo,z) The joint probability of the existing free lines of
sight at the depth z of the canopy in the solardirection (Ωs) and the viewing direction (Ωo).
CHOTSPOT Hotspot correction function.kl Hotspot parameter, equals 1/sL, sL is the characteristic
linear dimension of foliage elements.
Kopen The fraction of the sky seen from a point on the rowwallor background, without being interrupted by the row.Withdifferent subscripts used inAppendixB, this symbolmeans openness of different parts of the row area.
266 F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
introducing the concept of density modulation to more flexiblyaccount for the architecture of the row canopy, Suits (1983) as wellmade an extension of his model to include the effects of crops plantedin rows. These two models using the Suits model as their basis toinclude row effects have the major deficiency that Suits's approach oftaking horizontal and vertical leaf area projections to calculate thescattering and extinction coefficients is too drastic (Verhoef, 1984).Based on Suits's row model, Goel and Grier (1986) added two newfeatures: (1) vegetation elements are allowed to have an arbitrary(azimuthally symmetric) inclination angle distribution, like in theSAIL model (Scattering by Arbitrarily Inclined Leaves, Verhoef, 1984),and (2) the row subcanopy shape is described by an ellipse function soas to dynamically mimic the canopy shape during various stages ofgrowth. This type of rowmodel which takes consideration of both thegeometrical shape of row canopies and radiation transfer within therow canopy are hybrids of the geometrical and turbidmediummodels(GORT). However, these row models stemmed from the classicaltheory of radiation transfer in turbid media, and therefore cannotrepresent special phenomena such as the hotspot, which resultsexplicitly from the mutual shading of scatters (e.g. leaves) of finitesize (Jupp & Strahler, 1991; Kuusk, 1991; Qin & Goel, 1995; Qin &Xiang, 1994). What's more, to solve the differential equations, in therow models of Suits (1983), and Goel and Grier (1986), the diffusefluxes E− and E+ are assumed to be approximately laterally uniformin the calculation of the contribution of the diffuse fluxes, even withthe density modulation. In the second and higher-order scatteringevents the row structure is ignored, which may cause considerableerrors in canopies with distinct geometrical structure (Chen &Leblanc, 2001), for example row crops with a clear row structure inthe early growing season and in widely spaced orchards. Besides theabove mentioned models, which are mainly based on radiativetransfer theory while considering the geometric structure of rowcrops, another significant branch adopts the theory of geometricaloptics to calculate the sunlit and shadowed regions to determine theradiation regime in the row canopies. Jackson et al (1979) and laterKimes and Kirchner (1982) abstracted the rows as extendedrectangular solids which have no gaps, and calculated the proportionsof projected surface area of four surfaces (sunlit and shadedvegetation and soil). With these four proportions and correspondingrepresentative reflectance and temperature for each surface, com-posite reflectance and temperature of the row crops were simulated.These GO modeling approaches are straightforward and can welldescribe the angular variations of canopy reflectance as a function ofrow orientation, crop dimensions, soil background and shadow effectswith different sun-viewing geometries. They were successfullyapplied in the red spectral region, where the contrasts of sunlit andshaded components are large, and later extended into the thermalinfrared band with some modifications (Caselles et al., 1992; Chenet al., 2002; Kimes, 1983; Norman&Welles, 1983; Sobrino et al., 1990;Yan et al, 2003; Yu et al., 2004). GOmodels represent the row crops asopaque rectangular solids and do not simulate radiation transferwithin the canopy. As a result, the accuracy of the GO modelingapproach deteriorates at near-infrared (NIR) wavelengths because ofthe poor modeling of the multiple-scattering contributions to canopyreflectance.
Up to now, few simple analytical models have been reported tostudy row crops' directional reflectance while also considering thehotspot effect and reasonably modeling the multiple scatteringcontributions simultaneously. In this paper, a new row model for
267F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
the calculation of the reflectance anisotropy of row crops, based onthemodernizedmathematical treatment of four-stream SAILmodel, isdeveloped. In this model, row canopy structure, leaf inclinationdistribution, the problem of numerical singularities in the calculationof directional reflectance by the original SAIL model, the canopyhotspot effect and multiple scattering contributions within row andbetween rows are properly taken into account. Firstly, a generaldescription of the new model is presented, and then the validation ofthe row model is performed using the experimental reflectance dataof winter wheat collected in the Xiaotangshan experimental area, nearBeijing, China. The performance of the rowmodel is further evaluatedthrough detailed comparisons with an established 3D computersimulation model under the identical spectral and illuminationconditions based on the same 3D vegetative scenes. The paper endswith a brief conclusion and a discussion of improvements of thecurrent model. Derivation of the analytical equation for computationof the directional reflectance factor (DRF) and the multiple scatteringbetween rows are reported in the Appendices.
2. Description of the model
For operational applications in remote sensing, an ideal canopyreflectance model should have a reasonable compromise between theadequacy to describe the dependence of canopy reflectance on itsgeometrical structure and optical properties and the computerefficiency to simulate canopy reflectance and further retrievestructural parameters (Kuusk, 1995; Nilson, 1991; Qin & Jupp,1993). Based on this principle and concerned with the characteristicof row canopy's structure, the following two approximations aremade in the row model.
First, similar to most of above mentioned studies, the concept ofthe hedgerow with rectangular cross-section configuration, which isporous so that light beams can penetrate the canopy rows throughgaps within the hedgerows, is chosen to describe the most significantclumping pattern of leaves in row crop canopies. This simplification ofrow canopy structure is also justified by the fact that under thisassumption we can use simple analytical formulas of effective pathlength passing through the row canopies from any solar or viewingdirections (Gijzen & Goudriaan, 1989), which greatly facilitates thecomputation of gap probabilities. The row geometry and itscoordinate system in a cross-row section are shown in Fig. 1. Theorigin of x is at the footprint of the left corner of one hedgerow; b isthe row width; h is the row height; d is the row distance. Within thehedgerow, leaves are randomly distributed, with a two-parameterleaf inclination distribution function (LIDF) (Verhoef, 1998; Wang
Fig. 1. Sketch map of the row geometry and the coordinate system in a cross-rowsection.
et al., 2007) to represent the leaf angle distribution. The solar andviewing directions projected in the plane perpendicular to the rowsare represented by their inclination angles αs and αo respectively.They have the following relationship
tanα = tan θ sinφ ð1Þ
where θ and φ are the zenith and azimuth angles defining the solar orviewing direction. With this relationship, the calculation of effectivepath length of row crops can be converted into the plane X–Z.
Second, the contributions of first-order scattering and multiplescattering by row canopies are separately evaluated. With thisgenerally accepted and widely used approximation (e.g., Hapke,1981; Marshak, 1989; Nilson & Kuusk, 1989; Nilson, 1991; Liang &Strahler, 1993; Qin & Jupp, 1993; Kuusk, 1995; Gobron et al., 1997;Kuusk, 2001), DRF (the directional reflectance factor for arbitraryillumination conditions) of the row canopy is calculated as a sum ofsingle and multiple scattering components,
R = ðSλ =QλÞrso + rm ð2Þ
where rso is the single scattering contribution to the DRF, rm is thecontribution of multiple scattering, and Sλ/Qλ is the proportion ofdirect solar spectral irradiance to the total spectral solar irradiance in ahorizontal plane above the plant canopy, which is wavelength-dependent. The calculations of rso and rm will be given later. Eq. (2)can also be derived from the four-stream differential equation givenbelow. This derivation is included in Appendix A.
Our model is based upon the SAIL (Verhoef, 1984, 1985 and 1998)model for homogeneous canopies, in which the four-stream differ-ential equation of radiative transfer in a layer is given in matrix–vector notation by (Verhoef, 1985, 1998):
dLdz
EsE−
Eþ
Eo
0BB@
1CCA =
k−s′ a −σs σ −aw v v′ −K
0BB@
1CCA
EsE−
Eþ
Eo
0BB@
1CCA ð3Þ
Here z is the relative optical height coordinate, which runs from−1 at the bottom of the layer to 0 at the top, and L is the leaf areaindex (LAI). The coefficients in the matrix are the extinction andscattering coefficients. The coefficients k and K are the extinctioncoefficients for direct flux in the directions of the sun and theobserver, respectively. The other coefficients (explained in nomen-clature table) describe the scattering of incident fluxes, except for theattenuation coefficient a, which includes the extinction of diffuseincident flux. These coefficients are comprehensively described inVerhoef (1984). Empty places in the matrix indicate zeros. The fourfluxes (streams) are the direct solar irradiance on a horizontal planeEs, the downward and upward diffuse fluxes E− and E+, and the flux-equivalent radiance Eo=πLo, where Lo is the radiance in the observer'sdirection.
a) Single-scattering contribution
For a homogeneous canopy, the single-scattering contribution toDRF is given by the following equation (Nilson & Kuusk, 1989;Verhoef, 1998; the derivation also can be found in Appendix A):
rso = w⋅L⋅∫0−1
PsoðΩs;Ωo; zÞdz + rsPsoðΩs;Ωo;−1Þ ð4Þ
where w is the bidirectional scattering coefficient of Eq. (3), and rs isthe reflectance of the soil. Pso(Ωs,Ωo,z) is the joint probability of theexisting free lines of sight at the depth z of the canopy in the solardirection (Ωs) and the viewing direction (Ωo), and Pso(Ωs,Ωo,−1) isthe probability of seeing sunlit soil. The first and second terms inEq. (4) are the single scattering contributions from leaves and soil
268 F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
respectively. If the gap probabilities Ps(Ωs,z) and Po(Ωo,z) areindependent, we get
PsoðΩs;Ωo; zÞ = PsðΩs; zÞ⋅PoðΩo; zÞ ð5Þ
For a discontinuous canopy, the gap probability P(Ω,z) can bemodeled as a function of path length (Li & Strahler, 1988)
PðΩ; zÞ = e−GðθÞ⋅D⋅lðΩ;zÞ ð6Þ
where G(θ) is the projection of a unit leaf area onto the surface normalto the direction θ, which equals k cosθ (or K cosθ, depending onwhether it is the solar or the viewing direction). D, the foliage areavolume density, equals (Ld)/(bh) for row canopies, in units of m−1.l(Ω, z) is the effective path length in the direction of Ω passingthrough the canopy at the height of z. For row canopies, l also dependson the horizontal position with respect to the row x in a row unit,which is given by analytical formulas as a function of row structureand sun or viewing direction (Gijzen & Goudriaan, 1989).
But in real plant canopies these gap probabilities, Ps(Ωs,z) andPo(Ωo,z) are at least partly dependent, mostly due to the finite size ofthe canopy elements. This dependence gives rise to the so-calledcanopy hotspot effect. With the theory proposed by Kuusk (1991), thestatistical dependence of gap probabilities Ps(Ωs,z) and Po(Ωo,z) in thedirections Ωs and Ωo respectively, may be explained by the correctionfunction CHOTSPOT(ξ, z):
In Eq. (8), kl=1/sL, and sL is the characteristic linear dimension offoliage elements. lso is the vectorial difference between incident solarand viewing path length:
For row canopies, Pso in Eq. (4) is a function of both the depth z andthe horizontal positionwith respect to the row x. Then Eq. (4) becomes:
rso =1d⋅½w⋅D⋅ ∫
0
−1
∫b
0PsoðΩs;Ωo; x; zÞdxdz + rs⋅∫
d
0PsoðΩs;Ωo; x;−1Þdx�
ð11Þ
In the above equation, the single scattering contribution wasdivided by the row distance d so as to normalize it for a row unit.Given row structure and sun-observing geometry, Pso(Ωs,Ωo,x,z) canbe determined by Eqs. (6) to (10). Eq. (11) is numerically solved bydividing the row height and row distance into proportional intervals.Next, the bidirectional gap probability at every point in the row can becalculated and the integration in Eq. (11) is resolved.
b) Multiple-scattering contribution
rm is the multiple-scattering contribution to DRF. In the rowreflectance GORT models mentioned above, rm is simplified to thecomputation of the contribution of diffuse fluxes from within-rowcanopies, and themultiple scattering processes between the row crop'swalls and the soil background are ignored. But because of the rowcanopy's distinct geometrical structure, its influence on the second-order and higher order scattering still remains. Here the researchmethod on the effective directional emissivity of the V-shaped valley(Su, 2000; Su et al., 2003) and of row crops (Yang, 2001) are adoptedand improved for the situation of this study. In this new rowmodel, thecomputation of rm includes two parts: within-row and between rows
rm = rwithin�row + rbetween�rows ð12Þ
Here rwithin-row is the multiple-scattering part of within-rowcanopies, and rbetween-rows is that of between the rows.
In the SAIL model the diffuse fluxes of multiple scattering and ofthe sky are considered together with the four-stream approximation,which is a very rational treatment used to compute the total multiple-scattering contributions of the canopy (Kuusk, 1995). Then for a rowcanopy rwithin-row is given by:
rwithin�row =1d⋅ 1Ei⋅f ∫0
−1
∫b0D⋅½v′EþðzÞ + vE−ðzÞ�⋅PoðΩo; x; zÞdxdz
+ rs⋅∫b0PoðΩo; x;−1Þ⋅E−ð−1Þdxg
ð13Þ
where Ei is the total irradiance at the top of row canopy, and E+(z)and E−(z) are the upward and downward diffuse fluxes at the heightz respectively. The first term in Eq. (13) is the contribution of multiplescattering from within-row canopies and the second is from the soilunder the row canopy. To avoid the possible problem of mathematicalsingularities with the regular solution of Eq. (3), a numerically stablealgorithm is applied (Verhoef et al., 2006) to compute the diffusefluxes. With the boundary conditions
E−ð0Þ = 1−Esð0Þ ð14Þ
Eþð−1Þ = ½E−ð−1Þ + Esð−1Þ�⋅rs ð15Þ
rwithin-row can be numerically solved similar to Eq. (11).rbetween-rows is the contribution of diffuse fluxes reflected from the
void area of the row structure, or ‘U-shaped’ area, which consists of therow walls of two adjacent row canopies, and the void soil surfacebetween them. rbetween-rows includes two parts: hemispherical reflec-tance for direct sunlight rsd and directional reflectance for diffuseskylight rdo over the U-shaped area. The calculation of rsd for theU-shaped area can be simplified as summations of several geometricseries with a reasonable approximation. Here the main principles areintroduced, and the derivation is given in the Appendix B.
Fig. 2.Measured versus simulated DRF distributions in PP and CP for the red (a) and NIR(b) bands. SZA and SAA were 45°, 134° for PP, and 44°, 136° for CP, respectively.
Fig. 3. Measured versus simulated DRF distributions in AR and CR for the red (a) andNIR (b) bands. SZA and SAA were 43°, 138° for AR, and 42°, 139° for CR, respectively.
Fig. 4.Measured versus simulated DRF distributions in PP and CP for the red (a) and NIR(b) bands. SZA and SAA were 39°, 132° for PP, and 38°, 134° for CP, respectively.
Fig. 5.Measured versus simulated DRF distributions in PP and CP for the red (a) and NIR(b) bands. SZA and SAA were 37°, 136° for AR, and 36°, 137° for CR, respectively.
269F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
Fig. 6. Four scenes of row canopies at different growing stages: a) stage-1; b) stage-2; c) stage-3; and d) a homogeneous canopy. All row canopies are north–south oriented.
270 F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
When direct sunlight impinges on the U-shaped area, it can bereflected, absorbed, or transmitted into the row canopy. The photonswhich are directly scattered out of the canopy belong to the first orderscattering and have been calculated by Eq. (11). Those scattered morethan once in the U-shaped area and that ‘escaped’ out of the U-shapedarea form diffuse radiation. The quantity of escaped diffuse radiationis partly determined by the fraction of the sky visible from the point inthe U-shaped area. We introduce the concept of openness for rowcanopies: the fraction of the sky seen from a point on the row wall orthe background, without being interrupted by the row, represents theopenness of this point. Then the mean openness of the row walls andthe void soil surface, or parts of them can be computed by thegeometric structure of row canopy.With the openness, the probabilityof photons impinging on those surfaces and then scattered out of theU-shaped area is established. The reflectance of the row wall, calledeffective reflectance of the row reff, is parameterized as a function ofrow width, row height, LAI, leaf inclination distribution, and leafhemispherical reflectance. Through analyzing all cases of scatteringevents of photons, we find that the fraction of total photons scattered outof theU-shaped area can be expressed by several geometric series. Finally,the analytical formula of hemispherical reflectance for direct sunlight rsd
Table 3Structural and optical parameters of four scenes.
can be derived. Then, for given a viewing direction, the diffuse reflectancefor specular incidence over the U-shaped area r′sd equals
r′sd =d−bd
⋅ SλQλ
rsd ð16Þ
According to the reciprocity principle, the directional reflectancefor diffuse skylight rdo equals rsd for the corresponding zenith angle.But note here that rsd should include first order scattered radiation.Then, for the given viewing direction, the directional reflectance fordiffuse incidence over the U-shaped area r′do equals
r′do =d−bd
⋅1−SλQλ
rsd ð17Þ
Thus, we get the contribution of diffuse fluxes reflected from theU-shaped area rbetween-rows:
rbetween�rows = r′sd + r′do ð18Þ
IDF.b rl rs tl
Red NIR Red NIR Red NIR
.36 0.079 0.431 0.163 0.209 0.036 0.53
.41
.38
.36
271F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
3. Model evaluation
The adequacy of the row model can be evaluated by comparisonswith field multiangular measurements and matching spectral andstructural data of the row canopy required by the model. Since suchdata sets may be costly and difficult to acquire accurately for naturalrow canopies, comparisons can also be made with a ‘validated’computer simulation model under identical structural, spectral andillumination conditions. In this section, firstly some simulated resultsare compared with measured DRF data acquired in the Xiaotangshanexperimental area. Then systematic comparisons with the 3D Radio-sity-Graphics combined Model (RGM) were performed, not only forthe total DRF simulations but also for single scattering contributions(especially around the hotspot) and the multiple-scattering.
The input parameters for the row model are grouped as follows:
a) Sun and viewing geometrical parameters: sun zenith angle (SZA orθs), sun azimuth angle (SAA or φs), viewing zenith angle (VZA orθo) and viewing azimuth angle (VAA or φo).
b) Canopy geometry parameters: row distance d; row width b; rowheight h; dimension of foliage elements kl; Leaf Area Index (L); leafarea distribution parameters LIDF.a and LIDF.b, and row orientation.In the implementation of the rowmodel, b and d are normalized by h.
c) Optical parameters: hemispherical reflectance rl and transmittancetl of leaf, hemispherical reflectance of soil rs, the ratio of direct to totalirradiance at the given wavelength Sλ/Qλ at the top of the canopy.
3.1. Comparisons with field measurements
A series of comprehensive field experiments were carried out in2004 at the China National Experimental Station for PrecisionAgriculture in Xiaotangshan county, which is located in the ChangpingDistrict, Beijing (40°11′N, 116°27′E), China. The experimental sitemainly consisted of north–south row-planted winter wheat, which isone of the most important agricultural crops in Northern China. Rowdistance (d) of the mechanically sowed wheat canopy was 15 cm.Three kinds of data used in this study are as follows.
a) Optical parameters
Hemispherical reflectance and transmittance measurements ofwheat leaves were conducted on the sample leaves with a Li-CorIntegrating Sphere (Li-Cor, Inc., Lincoln, NE, USA) in the 350–2500 nmspectral range. Soil reflectance was measured under clear skyconditions at nadir from a height of 1.3 m by using an ASD FieldSpecPro spectrometer (Analytical Spectral Devices, Boulder, CO). Adetailed measurement protocol and computation method to acquirethe reflectance factor from raw data can be found in Ranson et al.(1991) and Sandmeier et al. (1998).
b) Canopy hyperspectral DRF
A goniometric instrument was used to measure canopy multi-angular radiation. Two arms are connected perpendicularly to eachother with the longer one fixed onto the track and the shorter onekept at horizontal position on top of which ASD spectrometer can bemounted. Pictures of this device can be found in Huang et al. (2006).Using this device, we carried out the spectral and multiangularmeasurements with viewing zenith angles from −60° (opposite tothe sun: forward direction) to 60° (backward direction) at 5° or 10°intervals in the principal plane (PP, viewing azimuth angle alignedwith solar azimuth angle), the cross plane (CP), the along row plane(AR, the plane along row direction), and the cross row plane (CR, theplane perpendicular to the row direction) in a short time.
c) Canopy structural parameters
While conducting the spectral measurement, crop structuralparameters, such as LAI, leaf angle distribution, coverage, row
width, average canopy height etc., were concurrently measured.Detailed measurement methods of LAI and the leaf angle distributioncan be found in Huang et al. (2006). The row structure parameters,rowwidth and row height, are the effective lengths, as shown in Fig. 1.
Before the soil ground was fully covered by the wheat canopy, twodays of comprehensive field experiments were conducted in 2004, onApril 1 and April 17. Here we chose two characteristic spectral bandsof vegetation, red (666 nm) and NIR (850 nm), to compare themeasured data and modeled results. The structural and opticalparameters are listed in Tables 1 and 2 respectively. The hotspotparameter kl is difficult to determine for the wheat canopy from themeasured data, so its value is estimated by the agreement betweenmeasured and model results.
The wheat canopy on April 1, 2004 was in the reviving stage, andhad a clear row structure. Themeasured average leaf inclination angleis 29.57° with a standard deviation of 24.99°. Figs. 2 and 3 show thecomparisons of measured and modeled profiles in four viewingazimuth planes, with correlation coefficient of 0.788 and 0.562 for redand NIR bands respectively. The root mean square error (RMSE)betweenmeasured and simulated DRF is 0.014 for red band, and 0.046for NIR band. From these figures, notable difference betweenmeasured and modeled data appeared around the nadir viewingdirection. Multiangular measurements began from the nadir direc-tion, then to backward viewing direction until 60°. After the backwarddirection was finished, the sensor measured again in nadir directionand started the forward-direction observation. In this process, cloudsmight appear and their shade fell on the canopy, which may have ledto fluctuations of the reflectance at the nadir direction. Another reasonmay be that the target observed changed between backward andforward observations because of the heterogeneity in the wheat field.In the principal plane (Fig. 2), the hotspot reflectance cannot beadequately acquired by the sensor in the field experiment because ofself-shading and large field-of-view (FOV, 25°). Therefore, a remark-able discrepancy is displayed for the two curves around hotspotdirection. In these figures, further away from the nadir viewingdirection, there generally exists poor agreement. The footprint areaand the mode of the ASD sensor may explain the larger deviation athigher viewing zenith angles. 1.6m above the canopy with a field-of-view 25°, the footprint area of the sensor pointed in the nadirdirection is a circle on the ground with the diameter of about 0.7m,which can cover approximate four rows in the cross-row section.Away from the nadir direction, the footprint area is an ellipse. Thehigher the viewing zenith angles, the more the footprint area of thesensor departs from the regular row structure supposed in the rowmodel. Therefore, the agreement is poorer for higher viewing zenithangles. In addition, the agreement is somewhat less in the along-rowplane (Fig. 3). This is mainly due to a lack of multiangularmeasurements of the soil. In the experiment, only the nadir radiationfor bare soil was measured. But the influence of anisotropy of the soilreflectance is considerable in the along-row plane for early growingwheat. Further improvement of the row model to incorporate adirectional soil model is necessary.
The wheat canopy on April 17, 2004 was in the elongation stage,close to the full cover of wheat canopies. The measured average leafinclination angle is 70.85° with a standard deviation of 16.32°. Theagreement between measured data and simulated results is betterthan on April 1, with correlation coefficients of 0.928 and 0.898 for redand NIR bands respectively, although the discrepancy around thehotspot direction and for high viewing zenith angles still exists. TheRMSE betweenmeasured and simulated DRF is 0.005 for the red band,and 0.04 for the NIR band. There is an obvious improvement in thealong-row plane (Fig. 5). The reason is partly that the influence ofanisotropy of the soil reflectance is minimal because of the densecanopy. With the increase of biomass, the row structure effect on thedirectional reflectance weakens. This is manifested in the CP (Fig. 4),AR and CR planes (Fig. 5). Profiles measured and modeled in these
272 F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
Fig. 8. DRF distributions by RGM and the row model in four viewing planes: PP (a), CP (b), AR (c) and CR (d) in the red band.
273F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
three planes show almost symmetric shapes between backward andforward observations, as opposed to the notable differences in thesame three planes on April 1, both in values and in general shape,because of the clear row structure.
3.2. Comparison with a 3-D computer simulation model
According to Nicodemus et al. (1977), Schaepman-Strub et al.(2006) and Milton et al. (2009), field multiangular measurementswith a finite FOV measure hemispherical–conical reflectance factors(HCRF), and they are different from DRF especially when within thefield of view directional effects are present and the target isheterogeneous. Besides this inconsistency between measured andmodeled quantities, measurement uncertainties and errors, thestructural difference between the natural wheat canopy and thegeometry supposed by the row model may also contribute to thediscrepancies between the two datasets. To clarify the uncertaintiesand further evaluate the performance of the rowmodel, we comparedit with the 3-D Radiosity-Graphics combined Model (RGM, Qin &Gerstl, 2000), which has participated in three phases of the radiationtransfer model intercomparison exercises (RAMI, Pinty et al., 2001,2004; Widlowski et al., 2007), and showed good agreement withother three-dimensional radiative transfer models.
In a radiosity-graphics basedmodel like RGM, a 3-D architecturallyrealistic canopy is firstly generated where vegetation components aresimulated by a number of polygons (triangular or 4-sided polygon).
Fig. 7. Polar plots of DRFs in the red band by RGM (left panels) and the row model (right(c, d), stage-3 (e, f), and homogeneous canopy (g, h). In the polar map, the distance fromdirection with a viewing azimuth angle of 0°, and in clockwise direction angles for east, south“N” with an arrow means the row is north–south oriented. “PP” with a dashed line indicate
By using computer graphics techniques and radiosity analysis, thevisibility of polygons along a given direction (solar or viewing) andmultiple scattering between polygons can be determined, so that thehotspot effect and multiple scattering are automatically taken intoaccount in the canopy reflectance factors' computation. Rationale anddetailed procedures for implementing the radiosity-graphics methodcan be found in Borel et al. (1991) and Goel et al. (1991). Here only theparts that entail the comparison of structural parameters, DRF, thesingle scattering and multiple scattering contributions between RGMand the row model are described.
3.2.1. Canopy scene generationIn the rowmodel, row canopies are parameterized as a rectangular
cross-section configuration with a two-parameter LIDF and the LAIdescribing the attenuation of light by randomly distributed leaveswithin the hedgerows. To generate such a canopy scene, a represen-tative square background area which can accommodate several (sayfour) rows is selected. Then, according to the designed row structureconfiguration (row width, row distance and row height), four virtualrectangular parallelepipeds are set up to encircle the random leaves(with a given leaf inclination distribution function), whose number isdecided by LAI and the polygon's area. In this study, leaves wererepresented by isosceles triangles with adjustable sides. By changingthe row structure configuration, row canopy scenes at differentgrowing stages can be generated. When the boundaries of the virtualrectangular parallelepipeds within the square background area are
panels). The top two panels (a, b) correspond to stage-1, in ascending order: stage-2the origin represents the off-nadir viewing angle. North is designated as the originaland west are 90°, 180° and 270° respectively. In the upper left corner of each polar plot,s the solar principal plane.
274 F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
Fig. 10. DRF distributions by RGM and the row model in four viewing planes: PP (a), CP (b), AR (c) and CR (d) in NIR band.
275F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
eliminated, a homogeneous canopy scene can be generated. So in thismanner, canopies from sparse row structure to homogenousvegetation can be simulated through statistical parameters such asLAI, LIDF, and the row structure parameters. Once 3-D structures ofcanopy over a certain background area are generated, a procedure ofduplication of this finite canopy is used to generate an infinite canopybefore the implementation of the radiosity-graphics method (Goelet al., 1991). Then RGM can be used to calculate DRF, single-scatteringand multiple-scattering contributions. In this paper, three typicalgrowing stages of row canopies were chosen to evaluate theperformance of the row model, and a homogeneous canopy scenewas generated to compare its DRF shape to that of a row canopy andto test the row model's capability to converge to the 1-D RT modelwhen the space between the rows disappears.
Three growth stages of row canopies with north–south orienta-tion, representing a gradual growth from the early stage to a moreadvanced phase of a typical row crop, for instance wheat and sugarbeet, are simulated as shown in Fig. 6(a–c). Though theymay not be asrealistic as natural row canopies, the main characteristics arepreserved, for example the row structure, and the proportionalincrease of height and width of the crop during the growing season. Ahomogeneous canopy scene of a canopy height, leaf inclinationdistribution and leaf size comparable to those of the third stage(Fig. 6c) has been generated (Fig. 6d). Statistical parameters of thefour scenes needed to drive the row model are listed in Table 3, with“Stage-” and a number showing the corresponding stage in Fig. 6, and‘Homo’ for homogeneous canopy. Here b and d are normalized by h.As opposed to the distinct variations of LAI and row structure, LIDF
Fig. 9. Polar plots of DRFs in NIR band by RGM (left panels) and the row model (right p(c, d), stage-3 (e, f), and homogeneous canopy (g, h). Symbols as in Fig. 7.
and leaf size (triangle area) were kept almost constant to focus thestudy on the key row structure parameters. Relatively less variableparameters of the LIDF represent an erectophile type with an averageleaf inclination angle of around 62.5°, and a standard deviation ofaround 29.6°. Though the mean leaf size remains constant for the fourscenes, the hotspot parameter kl increases gradually because it isrelevant for the ratio of leaf size to the canopy height (Qin & Goel,1995). During the comparisons of the two models, Eq. (19) gave anexplicit estimation of kl:
where H is the canopy height and SΔ is the area of a leaf triangle. Amore accurate kl can be determined by improving reflectance factors'agreement (especially for single-scattering contributions around thehotspot directions) between these two models, since all otherstructural and optical parameters are already known. Optical para-meters of leaf and soil in the red and NIR bands are shown in Table 3.
For all four canopies, the single scattering contributions in the redband dominate the DRF with a share of at least 90%. So for the redband only DRF comparisons were given. However in the NIR band,because the multiple scattering contributions are of the same order ofmagnitude as the single scattering contributions, the comparisons of DRF,single scattering and multiple scattering contributions between the twomodels were carried out separately. For the row model, the singlescattering contribution of the direct sunlight can be extracted from thetotal DRF. However this separation can not to be done for the diffuse
anels). The top two panels (a, b) correspond to stage-1, in ascending order: stage-2
276 F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
Fig. 12. Single-scattering contributions' distributions by RGM and the row model in four viewing planes: PP (a), CP (b), AR (c) and CR (d) in NIR band.
277F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
skylightbecause the scatteringofdiffuse skylight contributes to thediffusefluxes and belongs to multiple scattering. Nevertheless, the singlescattering contributions of direct and diffuse sunlight for RGM can becalculated separately. To facilitate the comparisons of the differentcontributions for these two models, we assume that the irradiance issolely composed of the direct component. Under this condition, thereflectancequantitywe shoulduse is BRF, andDRF equals BRF. But to keepthe consistency of the notations, still DRF is used here. For all thecomparisons below, SZA and SAAwerefixed at 40° and140°, respectively.
3.2.2. Row structure canopiesa) Red band
In Fig. 7 and the remaining polar plots, the center of the plotrepresents the nadir viewing direction, and outward from the center,the numbers above the contours indicate the VZAs. North isdesignated as the original direction with a VAA of 0°, and in clockwisedirection angles for east, south and west are 90°, 180° and 270°respectively. PP (and CP) was (were) indicated for DRF (and singlescattering contributions) distributions in the polar maps to assist inreading them. Based on this polar coordinate system, the samplingstrategy of the DRF and the single scattering and multiple scatteringcontributions for bothmodels toplot thepolarmapswas chosen thisway:from0° to 350°with a stepof 10° forVAA, and from0° to 70°with a stepof5° for VZA. Besides this strategy, a denser sampling was adopted aroundthe hotspot directions: within 10° of the PP, the steps are 1° and 0.5° forthe azimuth and zenith angles, respectively. For instance, when SAA
Fig. 11. Polar plots of single-scattering contributions in the NIR band by RGM (left panels)ascending order: stage-2 (c, d), stage-3 (e, f), and homogeneous canopy (g, h). “CP” with a
equals 140° and SZA 40°, in the range of 130° and 150° for VAA, the step is1°; in the rangeof 30° and50° forVZA, the step is 0.5°. In thisway, a total of1386 values for each reflectance quantity by everymodel were computedand compared. The manner of arrangement for the comparisons of thesetwo models in these figures (Figs. 7, 9, 11 and 13) is as follows: The leftpanels correspond to simulated results of RGM, and right to the rowmodel; top panels indicate results of these two models for stage-1, andtheygradually increase to stage-3 inascendingorder, at lasthomogeneouscanopy for the bottom panels.
Fig. 7 shows the comparison results of the DRFs for three stages andhomogeneous canopies in redbandbetweenRGMand the rowmodel.Wecan see the shapes of the DRF distributions for all four canopies agree veryclosely. For example, for the distinctive row structure canopies (stage-1, 2and 3), a maximum value at the sun's position (due to the hotspot effect)is found, in addition to a high value stripe nearly parallel to the roworientation, which is obviously conditioned by the row structure ofcanopy. The following mechanisms cause such distributions. For along-rowornear-along rowazimuthangles,more sunlit soil betweenrows, andmore sunlit leaves at all height levels are visible through the void spacebetween rows, with the maximum probabilities at the hotspot direction.As a result, a high value stripe approximately parallel to the roworientationwithmaximumvalues at the sun position appears in the polarmap. For homogeneous canopy (Fig. 7g–h), DRFs show an almostsymmetrical distribution about the PP, and the above distributioncharacteristics are absent. To more clearly examine the agreementsbetween these twomodels,DRFs in four viewingplanes: PP, CP, ARandCR
and the row model (right panels). The top two panels (a, b) correspond to stage-1, indashed line indicates the solar cross plane. Other symbols as in Fig. 7.
278 F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
279F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
areplotted inFig. 8. (InPP, valuesofVZAwith the stepof5° areplotted, not0.5°, otherwise they are indiscernible. The comparisons specifically in thehotspot directions are given below. AR and CR are meaningless forhomogeneous canopy, and here just the same sun-viewing geometryrelationships are used to plot the results.) Simulated DRFs from bothmodels decrease with the growth of the row canopies due to soil and leafreflectance contrast in the red band. In PP, the hotspot effects for the twomodels are evident and fit well with each other. In CP and CR (Fig. 7b–d),DRF distributions for row canopies show bell shapes with protrusions inbackwarddirections,which are regulatedby the rowstructure, in contrastto the symmetry about nadir in CP and a gentle slope in CR forhomogeneous canopy. For stage-3, the agreements around the nadirdirection in the fourplanes arenot sogood. The reasonmight lie in the3-Dscene itself, but this is difficult to validate because the scenes generated bythe same statistical structural parameters are different owing to therandomness during the scene generation.
b) NIR band
Fig. 9 shows the polarmaps of DRF in the NIR band computed by thetwo models. Similar to those in the red band, the general shapes of theDRF distributions for all four canopies still agree closely, although theshapes are different from those in the red band. The discrepanciesmainly appear at high viewing zenith angles. The comparisons in fourviewing planes (Fig. 10) confirm this point, and show a tendency thatwith the growth of the row canopies, the discrepancies at high VZAs(larger than 40° in backward directions and less than−40° in forwarddirections) become larger. In Fig. 10, the discrepancies of DRFs'distributions are noticeable for row canopy stage-3 and its counterpart,homogeneous canopy. Except in AR, higher reflectance anisotropies areobserved for the row canopy, though they both show bowl shape(Fig. 10a, b and d). Since these two canopies have comparable structuralparameters and the same spectral properties, the only reason inducingthe discrepancies lies in the row structure. For homogeneous canopy,the DRFs in four viewing planes are larger than those for the rowmodel(or SAILH here), which is consistent with the comparison results inRAMI Phase 2 for the case of homogeneous canopy with an erecophileleaf angle distribution (Fig. 4 in Pinty et al., 2004). Because in the NIRband both single scattering and multiple scattering contributions playimportant roles in the formation of the DRF shapes, it is important tocompare theagreements for both contributionsandanalyze thephysicalmechanisms behind the DRF distribution shapes.
Single scattering contributions of four scenes are shown in Fig. 11.Peculiar phenomena appear: clear row canopies (stage-1 and 2, a–b andc–d in Fig. 11) show two low value stripes approximately parallel to therow orientation with their centers roughly appearing in CP (SAA=50°and 230°), and a high value stripe approximately parallel to the roworientation being cut off by CP, though themaximumvalue still appearsat the hotspot direction. With the growth of the canopies, the two low-value centers begin to approach to each other (stage-3, e–f in Fig. 11),and finally they merge into one low-value center in the forwarddirection near nadir for homogeneous canopy (g–h in Fig. 11). Thecomparisons of single-scattering contributions' distributions for rowcanopies and homogeneous canopy facilitate understanding the causeof the formation of peculiar shapes for the former. For the homogeneouscanopy without row structure, the low value center of the singlescattering contribution should appear at nadir or around nadirdirections (here for erectophile canopies), because in these directionsmost shaded soil and leaves will be visible, plus the effect of higher leafreflectance and transmittance than the reflectance of the soil. Forrelatively sparse canopies in early stages (stage-1 and 2, a–b and c–d inFig. 11), a substantial proportion of soil and leaves is directly sunlit andvisible around nadir directions, so single-scattering contributions in
Fig. 13. Polar plots of multiple-scattering contributions in NIR band by RGM (left panels) aascending order: stage-2 (c, d), stage-3 (e, f), and homogeneous canopy (g, h). Symbols as
these directions are not so weak. In CP, the contribution of singlescattering is small because the joint gap probability between illumina-tion and viewing directions (Eq. (7)) is minimum. Besides, leavesclumping in the rows reduce the probability of seeing sunlit leaves andsoil for near along-row azimuth angles, which jointly formed two low-value stripes approximately parallel to the row directionwith centers inCP at high VZAs. Relatively speaking, the single scattering contributionson the samesideof the sunposition relative to the rowdirection (we canterm this as the ‘backward’ direction) are higher than these of other halfcorresponding VZAs in CP, because for these viewing directions, moresunlit soil and sunlit leaves at all height levels are visible through thevoid space between the rows. This phenomenon is absent forhomogeneous canopies where forward and backward directions aresymmetrical and there is no need to distinguish them (g–h in Fig. 11).Then the joint of these two low value centers cut off the high valuestripe.With the increases of rowwidth, rowheight and LAI (stage-3, e–fin Fig. 11), the single-scattering contributionaround thenadir directionsdecreases. On the other side, the increase of leaf area leads to theenhancement of single scattering at high VZAs by erectophile leaves. Bythe above combined effects, the two low-value centers begin to movetowards the nadir direction. For homogeneous canopies, they mergeinto one low-value center in the forward direction near nadir (g–h inFig. 11).
A monotonous bowl shape appears for the homogeneous canopy(plus a hotspot in PP) (Fig. 12), while the shapes for row canopiesshowmuch more variations under influence of the row structure. Thecomparisons in four viewing planes show good agreement betweenthese two models' results except for stage-3 in AR (Fig. 12c). So thediscrepancies at high VZAs observed in Figs. 9 and 10 were not mainlycaused by the single scattering contributions, and we should comparethe agreement of the multiple scattering contributions between thetwo models.
Symmetric features along the row direction for row canopies(Fig. 13a–c) and azimuthally symmetric bowl centered around nadir forhomogeneous canopy (Fig. 13d) appear in the polar-contourmaps for themultiple scattering contributions. Low-value stripes ofmultiple scatteringcontributions with their centers in nadir directions emerge along the roworientation because of the large gap probability near this azimuth angle.Away from the nadir direction,multiple-scattering contributions increasesteadily with the increase of VZAs because more vegetation is visiblewhich enhances the multiple-scattering process. Though the generalshapes of the multiple-scattering contributions for four canopies by therowmodel are consistentwith the correspondingonesby theRGMmodel,the discrepancies in values between these two models for four viewingplanes (Fig. 14), especially at high VZAs and in (near) AR plane, areevident. Except in (near) AR plane, the agreements at low VZAs (nothigher than 40°here) are persistently good for all three growing stages.However, the accordance deteriorates for VZAs of 40° and above,with thetendency of increasing disagreement at higher VZAs. Similar phenomenaoccur for homogenous canopy. So maybe it is the systematic deviationbetween RGM and the base model SAILH for the multiple-scatteringcontributions that partly caused the discrepancies between RGM and therowmodel in theNIR for rowcanopies. Therefore, thoughwe can expect ahigh accuracy of themultiple-scattering contributions in the NIR band forsmall VZAs by the row model, further efforts to investigate thediscrepancies for high VZAs are needed.
Near the AR planes, except for the single-scattering contributions forstage-1 and 2 (Fig. 12c), the agreement of the two models in the NIR ispoor, especially for themultiple-scattering contributions (Fig. 14c),wherethere is a tendency that with the growth of the row canopy thediscrepancies become larger. This phenomenon can be attributed to thestructural difference between the designed row structure configuration
nd the row model (right panels). The top two panels (a, b) correspond to stage-1, inin Fig. 7.
Fig. 14. Multiple-scattering contributions' distributions by RGM and the row model in four viewing planes: PP (a), CP (b), AR (c) and CR (d) in NIR band.
280 F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
whose parameters (row width, row distance and row height) were usedby the row model and the actual generated scene. As described above,these configuration parameters were used to encircle the randomlydistributed leaves. But there was always a certain number of leaves thatpartially crossed the boundaries, which causes the structural difference.Themore leaves generated (with the growth of row canopies), the largerthe numbers of boundary-crossing leaves are. So with the growth of thecanopy, the correspondence of the two models deteriorated. Adjustmentof the row parameters for the near-AR planes can improve the agreementbetween the two models. But to maintain the consistency of the inputparameters for all viewing planes, the originally designed row configu-ration parameters were used. This may also suggest an azimuth-dependent clumping effect for row canopies, which needs further study.
As a result, the DRFs in the NIR band by the collective effects of single-scattering and multiple-scattering contributions displayed a low valuestripe approximately parallel to the row direction with the minimumappearing at lowVZAs or nadir in forwarddirections for the rowcanopies.
a) Hotspot direction
Comparison of denser sampled single-scattering contributions forfour canopies in both the red and the NIR bands in PP by these twomodels are shown in Fig. 15. Minor differences are acceptableconsidering the semi-empirical nature of the hotspot model weadopted and the difference in shape between the generated (isoscelestriangle) and the one supposed by the hotspot model (disk). For rowcanopies, two levels of hotspot effect should be present: the canopylevel, which is related to the row structure, and the leaf level, which isdetermined by the ratio of leaf size and canopy height. In Fig. 15,evident phenomena appear for both bands and both models: theangular width of the hotspot effect depends on the row structure,narrowing with the growth of the row canopy. In particular, thehotspot effect is broader for sparse row canopies than for dense row
canopies, which is expected since for the former the hotspot feature isdominated by the geometry of the rows, soil background and the gapsbetween them, and for the later it is dominated by the relative size ofthe leaves. This latter point is confirmed by the comparisons betweenstage-3 and the homogeneous canopy, especially in NIR band wherethe angular width is almost identical (Fig. 15b), which indicates therelative size of the leaves dominates the hotspot effect for densecanopies.
3.2.3. Summary of comparison results with RGMTo further evaluate the performance of the row model, systematic
comparisons between the row model and the 3-D computersimulation model RGM were carried out under identical spectraland illumination conditions based on the same 3-D vegetation scenesat different growing stages for row canopies and for a homogenouscanopy with respect to DRF, the single-scattering contribution(especially around the hotspot direction) and the multiple-scatteringcontribution. In fact, the validation/evaluation of a numerical model isvery difficult, especially in the context of Earth sciences, because anabsolute reference per se cannot be established (Pinty et al., 2001).This is a reason why the RAMI exercises were initiated and are still anongoing activity to intercompare RT models. In accordance with threephases of results of RAMI exercises in which RGM has participated, itagreed reasonably well with other 3-D computer simulation models.So here RGM served as a surrogate for the unknown truth. Anotherproblem we should point out is that the reflectance output by RGM isbased on a scene that is generated by the statistic parameters ofcanopy structure as only one realization. Ideally, we should generateseveral scenes (say five or more) based on the same statisticparameters and compute the reflectance quantities of the sceneseach time. Then the averages of them should be used for thecomparison with the row model. But the complexity to run RGM
Fig. 15. Single-scattering contributions' distributions by RGM and the rowmodel in redband (a), and NIR band (b) around hotspot direction in PP.
281F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
and the time to compute such a large number of quantities are a majorconcern. Fortunately, the results by RGM for different scenes based onthe same statistic parameters are stable according to our tests. However,this deficiency may explain the discreteness in the polar plots by RGM.
Table 4 gives the statistics of these two models' fitting resultswhichwere correspondingly established on the 1386 values under thesame sun and viewing geometries for each canopy scene. The highcorrelation coefficients (r, with minimum being 0.9790 for DRF atstage-1 in the NIR band) and the low RMSE (with the maximum being0.0025 for DRF at stage-3 in the red band, and 0.0168 for themultiple-scattering contribution for the homogeneous canopy in the NIR band)show the good agreement between the two models.
Table 4Statistical results of correlation between RGM and the row model for four scenes.
Homo r 0.9912 0.9912 0.9869 0.9939 0.9967RMSE 0.0023 0.0022 0.0152 0.0065 0.0168
aHere the statistical parameters used are the correlation coefficient (r) and the rootmean square error (RMSE).b, cR_s_red and R_s_NIR stand for single-scattering contributions in the red and NIRbands, respectively.dR_m_NIR stands for multiple-scattering contributions in NIR band.
Bothmodels display the characteristics of the radiance distributionfor row canopies. In the red band, this effect is shown as a high valuestripe approximately parallel to the row orientation with maximumvalues in the hotspot direction in the polar map. In the NIR band, bothsingle-scattering and multiple-scattering contributions play impor-tant roles in the formation of the DRF shapes, which results in a lowvalue stripe approximately parallel to the row direction with theminimum being near nadir viewing direction in forward directions.
Though the row effect may be different according to the rowstructure, LIDF, component optical parameters etc., the row modelis expected to faithfully reproduce the distributions of DRFs inmost cases. Another advantage of the row model is its capability ofnaturally converging to the SAILH model when the space between therows disappears and it tends to become homogenous without extramodification.
4. Conclusion and discussion
To quantitatively utilize the information content of the remotelysensed data for crop yield prediction, living status assessment, andirrigation scheduling, the mechanism of radiative transfer by row-planted crops must be fully understood. The new hybrid geometricoptical and radiative transfer row model in this study was developedto fulfill this objective. This computationally efficient row reflectancemodel permits calculation of the directional reflectance factor of arow-structured canopy with hyperspectral resolution for the entireoptical spectral region. The model can be used for the theoreticalanalysis of the mechanism of a row canopy's angular and spectralreflectance, the sensitivity to optical and structural parameters ofcanopy reflectance, and further for inference of these parametersusing remotely sensed data. The main conclusions are as follows.
1. In this new computationally efficient model, the row canopystructure, the leaf inclination distribution, the problem of numer-ical singularities, the canopy hotspot effect and multiple scatteringwithin rows and between rows are taken into account. Evaluationresults, especially the systematic comparisons between RGM andthe row model, show that the row model has the ability toreproduce the angular distribution of the canopy DRFs as a whole.
2. The features of the DRF distribution of row canopies (termed as therow effect) were revealed, and underlying physical mechanismswere proposed and supported by comparison studies. For a row-structured canopy, more sunlit soil between rows and more sunlitleaves at all height levels are visible through the void spacebetween the rows than for homogenous canopies. The effectscaused by the row structure, along with the leaf angle distribution,the optical properties of the leaf and soil, result in a bright stripeapproximately parallel to the row orientation with maximumvalues at the hotspot direction in the red band, and a dark stripeapproximately parallel to the row direction with the minimumappearing at low VZAs or nadir in forward directions in the NIRband in the polar map.
Generally speaking, the row model captures the basic character-istics of a row canopy's DRF distributions such as the row effect andthe hotspot effect. Another advantage of the row model is itscapability of naturally converging to the SAILH model when rowcanopies tend to be homogenous, because they are based on the samemodeling framework. Therefore, this computationally efficient modelextends the SAILH model to row-planted canopies, and is suitable forretrieval of agricultural parameters and other crop managementapplications. With respect to the inversion of the row model, a prioriknowledge of the row canopy should be fully available, since themodel needs over ten input parameters (though we limited thenumber of parameters). Among the sources of prior knowledge of thecanopy, the species can not only supply the information of rowdistance (mechanically sowed), but also a priori constraints of some
Fig. A1. Sketch map of the U-shaped area.
282 F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
structural and optical parameters, for example row height, LIDF, rl, tl,and rs, with the auxiliary information of growing season and opticaldatabase. The inversion of the row model will be a research topic inour follow-up work.
However, further improvement needed of the current model isnecessary. A directional soil reflectance model should be incorporatedto describe the non-Lambertian reflection of the soil, which isespecially important for early growing row canopies. Evidentdiscrepancies compared with RGM come from themultiple-scatteringcontribution. Though it is unclear whether it is caused by thedifference of the RT formulations between the radiosity-based RGMand the four-stream SAIL model or not, further study and improve-ment of this part are needed. Also the parameterization of clumpingeffects along the row direction should be improved.
Acknowledgements
This work was supported by the Knowledge Innovation Programof the Chinese Academy of Sciences (Grant No. kzcx2-yw-303),the National High Technology Research and DevelopmentProgram of China (863 program) (Grant No. 2006AA12Z113 and2008AA121102), the State Key Laboratory of Remote Sensing Science(2009kfjj022), and the Chinese Natural Science Foundation underProject 40901156. We thank the reviewers' constructive reviewsthat markedly improved this paper. Much of the work was carriedout at IRSA, CAS, when Dr. Feng Zhao was a PhD candidate. And hewould like to thank Tian Qiyan, Chen Min, Dr. Huang Jianxi, Dr.Huang Wenjiang, Prof. Wang Jindi, Dr. Yang Hua, Dr. Xie Donghui,Dr. Song Jinling, Dr. Du Yongming, Yu Shanshan, Dr. Yao yanjuan,Wang Jiangeng, Chen Xinfeng and Zang Wenqian for their help tothis paper. Dr. Wout Verhoef was funded by NLR's own researchprogramme.
Appendix A. The computation of DRF from thedifferential equation
Starting with the last differential equation of Eq. (3)
dLdx
Eo = wEs + vE− + v′Eþ−KEo ðA1Þ
One can first differentiate EoeKLx (Verhoef, 1998), which yields
dLdx
EoeKLx = KEoe
KLx + eKLxdLdx
Eo ðA2Þ
Substitution of Eq. (A1) gives
dLdx
EoeKLx = eKLxðwEs + vE− + v′EþÞ ðA3Þ
The solution of Eq. (A3) is given by
EoeKLx = ∫
x
−1
eKLxðwEs + vE− + v′EþÞLdx + c ðA4Þ
With the lower boundary condition
Eoð−1Þ = ½E−ð−1Þ + Esð0Þe−kL�⋅rs
The constant c in Eq. (A4) can be determined
c = rsE−ð−1ÞPoð−1Þ + rsEsð0ÞPsoð−1Þ ðA5Þ
With Eq. (A4) and (A5), we can get the flux-equivalent radiancefor the top of the canopy in the viewing direction
πLo = Eoð0Þ = ∫0
−1
½wEsð0ÞPsðxÞ + vE− + v′Eþ�LPoðxÞdx
+ rsE−ð−1ÞPoð−1Þ + rsEsð0ÞPsoð−1Þ
ðA6Þ
Rearranging Eq. (A6) and separating the contribution of directsunlight due to single scattering and the contribution due to multiplescattering of diffuse fluxes, we get
πLo = Esð0Þ½ ∫0
−1
wLPsoðxÞdx + rsPsoð−1Þ�
+ ∫0
−1
ðvE− + v′EþÞLPoðxÞdx + rsE−ð−1ÞPoð−1Þ
ðA7Þ
Then canopy directional reflectance factor R equals
where Es(0)+E−(0)=Ei is the total irradiance at the top of therow canopy. By supposing Ei equals unity and by replacing Es(0)/[Es(0)+E−(0)], the single scattering part and the multiple scatteringof diffuse fluxes part, with Sλ /Qλ, rso and rm, respectively, one obtainsEqs. (2) and (4).
Appendix B. Computation of the contribution of diffuse fluxesfrom the between rows
Calculation of the openness:Openness (Kopen): the fraction of the sky seen from a point on the
row wall or background, without being interrupted by the row,represents the openness of this point. However, we are moreinterested in the openness of the whole surfaces (A, B, and C, asshown in Fig. A1) or part of them. The aim of computing the opennessof the whole surfaces A, B and C or parts of them is to estimate theprobability that photon escapes from the U-shaped area. Allthe computations are performed in perpendicular plane of rows,and the transforming relation from zenith and azimuth angles toinclination angle in the two-dimensional X–Z coordinate system isgiven by Eq. (1). In the following derivations, we suppose surface A isdirectly illuminated (0°≤φs<180°). Since surface B is symmetricwith surface A, the derivations can also be applied for surface B.
We define the inclination angle of the sunlight passing through theupper corner point q on surface B and the lower corner point g onsurface A as ‘critical angle’, namely ∠jgq in Fig. A1. And ∠jgq=arctan[(d−b)/h] (in radian). Then the openness of point g is: kg=arctan[(d−b) /h] /π. From the point g upward, the openness linearly
283F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
increases, and reaches the maximum at the peak point j, which equalsπ /2/π=0.5. When sun inclination angle is less than the critical angle∠jgq, the whole surface of Awill be illuminated. Then the openness ofthe whole surface of A (KA) is the mean of the maximum andminimum openness of surface A
KA =kj + kg
2=
0:5 + arctan½ðd−bÞ= h�2
ðB1Þ
When solar inclination angle (α) is larger than the critical angle∠ jgq, the sunlight intersects surface A at point o for example inFig. A1. So the openness of point o equals ∠ joq /π=α /π. Then theopenness of the illuminated part of surface A (KA
α) is
KαA =
0:5 + α= π2
ðB2Þ
The computation of the openness of the whole surface B or part ofit is similar to A's. However, in this case, 180°<φs<360°, α is negative(by Eq. (1)). To remain physically meaningful, the absolute value of αshould be used:
KB =0:5 + arctan½ðd−bÞ= h�
2; Kα
B =0:5 + jα j = π
2:
When α is less than the critical angle∠jgq, part or all of the surfaceC can be illuminated. With the same principle and approximationmethod, we can get the openness of the whole surface C (KC) and partof it (KC
The effective reflectance of a single isolated row is determined bythe openness of the row wall. Approximately, the openness of themid-height point on the cross-row wall is used, and computed by theintegration of gap probability of the isolated row (Li et al, 1995):
kopenh2
� �=
2π∫π = 20 P
h2; θ
� �sin 2θdθ ðB4Þ
Then the effective reflectance reff is given by
reff = 1−kh2
� �� �⋅rl ðB5Þ
Where rl is leaf hemispherical reflectance, and θ is zenith angle inthe plane perpendicular to the rows taken as a variable. Gapprobability P (θ) is computed by Eq. (6). Note here P (θ) is verticalwall's gap probability, different from that of horizontal background. Sowhen computing attenuation coefficient, leaf inclination angle ratherthan leaf normal angle is used.
The scattering process in the U-shaped area.When α is larger than or equal to the critical angle arctan[(d−b) /
h], part of surface A will be illuminated. Then we think about thescattering process of a photon.
It may be directly reflected out of U-shaped area, and theprobability the photon escapes from it is the openness of this partof the surface A: KA
α. Then the part of energy reflected out of U-shapedarea equals KA
αreff. This part contributes to first-order scattering, whichhas been calculated by rso. Otherwise, it may be scattered to surface Bor C, and the probability to B is m1, n1 to C. m1 and n1 are determined
by the angles the point faces B and C. m1 and n1 are given below. Andwe can see m1+n1=1.
Then when the photon is scattered to surface B, the energy will be(1−KA
α)×reff×m1. If the photon is scattered from surface B out of theU-shaped area, the energy will be (1−KA
α)×reff×m1×KB×reff. Whenthe photon is scattered to surface C, the energy will be (1−KA
α)×reff×n1. If the photon is scattered from surface C out of the U-shapedarea, the energy will be (1−KA
α)×reff×n1×KC×reff. To make theprocess clearer to us, we divide into two cases: photons are scatteredbetween two walls (A and B), and photons are scattered among threesurfaces (A, B and C). During those processes, there are always thechances of photons escaping from theU-shaped area.Whatwe need todo is to calculate the energy scattered out of the U-shaped area fromevery process and sum up all of the energy to get the reflected energy.
Here we analyze the first case: photons are scattered between twowalls.
AðBÞ→1 BðAÞ→2 AðBÞ→3 BðAÞ→4 AðBÞ→5 BðAÞ⋯ ð1Þ
The energy escaped from the U-shaped area from each step is:
1 .KαA reff ; 2 . ð1−Kα
A Þreffm1KBreff ; 3 . ð1−KαA Þreffm1ð1−KBÞreffm2KAreff ;
Wherem2 is the probability of photon scattering from A (or B) to B(or A) and n2 is the probability of photon scattering from A (or B) to C.The computation of m2 and n2 is similar to that of m1 and n1. m2 andn2 are given by
m2 =2arctanfh= ½2ðd−bÞ�g
2 arctanfh= ½2ðd−bÞ�g + arctan½2ðd−bÞ= h� ;
n2 =arctan½2ðd−bÞ= h�
2 arctanfh= ½2ðd−bÞ�g + arctan½2ðd−bÞ= h� :
Excluding the first term, which is first-order scattering, the remainingconsists of a geometric series. The summation of this geometric series(fA−B) is
fA−B =ð1−Kα
A Þreffm1KBreff1−ð1−KAÞreffm2
ðB6Þ
For case 2 (photons scattered among A, B and C), the same analysisprocess gives the total fraction of diffuse flux as follows:
A Þreff ð1−KCÞrsKBreff ½n1 + m1ð1−KBÞreffn2�1−ð1−KBÞreffm2
ðB7Þ
Therefore, when α≥arctan[(d−b)/h], the summation of Eqs. (B6)and (B7) gives the total contribution of diffuse fluxes from U-shapedarea rsd.
When α<arctan[(d−b)/h], the whole surface A and part of C willbe illuminated. The two fractions of impinged photons are:
rc =ðd−b−h tanαÞ cosα
ðd−b−h tanαÞ cosα + h sinα;
ra =h sinα
ðd−b−h tanαÞ cosα + h sinα
ðB8Þ
284 F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
The problem of photons impinging on surface A has been resolvedabove, and what's different is that the whole surface A is illuminated,instead of part of it. So we just need to replace the openness KA
α withKA in the final result.
For the part of photons impinging on surface C, similarly we candivide into following two processes and get the total fraction of diffuseflux.
a. C→1AðBÞ→2 C→
3AðBÞ→4 C→
5AðBÞ⋯
b. C→1AðBÞ→2 BðAÞ→3 AðBÞ→4 BðAÞ→5 AðBÞ⋯
The above results are derived when surface A is directlyilluminated. However because of symmetry of sun azimuth anglewith respect to the row orientation, the results also apply to all sunazimuth angles. But when surface B is directly illuminated(180°<φs<360°), we should take the absolute value of α where itis used to compute the openness of the row wall. Finally, we can getgeneral formulas:
C Þreff rs½KA + ð1−KAÞn2KCrs�1−ð1−KCÞrsð1−KAÞreffn2
+ð1−Kα
C ÞrsKAreff1−ð1−KBÞreffm2
gðB10Þ
References
Annandale, J. G., Jovanovic, N. Z., Campbell, G. S., Du Sautoy, N., & Lobit, P. (2004). Two-dimensional solar radiation interception model for hedgerow fruit trees. Agricul-tural and Forest Meteorology, 121, 207−225.
Bégué, A., Roujean, J. L., Hanan, N. P., Prince, S. D., Thawley, M., Huete, A., et al. (1994).Shortwave radiation budget of Sahelian vegetation 1. Techniques of measurementand results during HAPEX-Sahel. Agricultural and Forest Meteorology, 79, 79−96.
Borel, C. C., Gerstl, S., & Powers, B. (1991). The radiosity method in optical remotesensing of structured 3-D surfaces. Remote Sensing Environment, 36, 13−44.
Caselles, V., Sobrino, J. A., & Coll, C. (1992). A physical model for interpreting the landsurface temperature obtained by remote sensors over incomplete canopies. RemoteSensing Environment, 39, 203−211.
Chen, Liangfu, Liu, Qinhuo, Fan, Wenjie, Li, Xiaowen, Xiao, Qing, Yan, Guangjian, et al.(2002). A bi-directional gap model for simulating the directional thermal radianceof row crops. Science in China, 45, 1087−1098 Series D.
Chen, J. M., & Leblanc, S. G. (2001). Multiple-scattering scheme useful for hyperspectralgeometrical optical modeling. IEEE Transactions on Geoscience and Remote Sensing,39, 1061−1071.
Cohen, S., Fuchs, M., Moreshet, S., & Cohen, Y. (1987). The distribution of leaf area,radiation, photosynthesis, and transpiration in a Shamouti orange hedgeroworchard: Part II. Photosynthesis, transpiration, and the effect of row shape anddirection. Agricultural and Forest Meteorology, 40, 145−162.
Ganis, A. (1997). Radiation transfer estimate in a row canopy: A simple procedure.Agricultural and Forest Meteorology, 88, 67−76.
Gijzen, H., & Goudriaan, J. (1989). A flexible and explanatory model of light distributionand photosynthesis in row crops. Agricultural and Forest Meteorology, 48, 1−20.
Gobron, N., Pinty, B., Verstraete, M. M., & Govaerts, Y. (1997). A semidiscrete model for thescattering of light by vegetation. Journal of Geophysical Research, 102, 9431−9446.
Goel, N. S., & Grier, T. (1986). Estimation of canopy parameters for inhomogeneousvegetation canopies from reflectance data I. Two-dimensional row canopy. Inter-national Journal of Remote Sensing, 7, 665−681.
Goel, N., Rozehnal, I., & Thompson, R. (1991). A computer graphics based model forscattering from objects of arbitrary shapes in the optical region. Remote Sensing ofEnvironment, 36, 73−104.
Huang, W., Niu, Z., Wang, J., Liu, L., Zhao, C., & Liu, Q. (2006). Identifying crop leaf angledistribution based on two-temporal and bidirectional canopy reflectance. IEEETransaction on Geoscience and Remote Sensing, 44, 3601−3609.
Irons, J. R., Campbell, G. S., Norman, J. M., Graham, D. W., & Kovalick, W. M. (1992).Prediction and measurement of soil bidirectional reflectance. IEEE Transaction onGeoscience and Remote Sensing, 30, 249−260.
Jackson, J. E., & Palmer, J. W. (1972). Interception of light by model hedgerow orchardsin relation to latitude, time of year and hedgerow configuration and orientation.Journal of Applied Ecology, 9, 341−357.
Jackson, R. D., Reginato, R. J., Pinter, P. J., & Idso, S. B. (1979). Plant canopy informationextraction from composite scene reflectance of row crops. Applied Optics, 18,3775−3782.
Jupp, D. L. B., & Strahler, A. H. (1991). A hotspot model for leaf canopies. Remote Sensingof Environment, 38, 193−210.
Kimes, D. S. (1983). Remote sensing of row crop structure and component temperatureusing directional radiometric temperatures and inversion techniques. RemoteSensing of Environment, 13, 33−55.
Kimes, D. S., & Kirchner, J. A. (1982). Directional radiometric measurements of row-croptemperatures. International Journal of Remote Sensing, 4, 299−311.
Kuusk, A. (1991). The hot spot effect in plant canopy reflectance. In R. B. Myneni & J.Ross (Eds.), Photon–vegetation interactions. Applications in optical remote sensingand plant ecology (pp. 139−159). Berlin: Springer-Verlag.
Kuusk, A. (1995). A fast, invertible canopy reflectance model. Remote Sensing ofEnvironment, 51, 250−342.
Kuusk, A. (2001). A two-layer canopy reflectance model. Journal of QuantitativeSpectroscopy & Radiative Transfer, 71, 1−9.
Li, X.W., & Strahler, A. H. (1988). Modeling the gap probability of a discontinuous vegetationcanopy. IEEE Transactions on Geoscience and Remote Sensing, 26, 161−170.
Li, X. W., Strahler, A. H., & Woodcock, C. E. (1995). A hybrid geometric optical-radiativetransfer approach for modeling albedo and directional reflectance of discontinuouscanopies. IEEE Transactions on Geoscience and Remote Sensing, 33, 466−480.
Liang, S., & Strahler, A. H. (1993). Analytic BRDF model of canopy radiative transfer andits inversion. IEEE Transactions on Geoscience and Remote Sensing, 31, 1081−1092.
Marshak, A. L. (1989). The effect of the hot spot on the transport equation in plantcanopies. Journal of Quantitative Spectroscopy & Radiative Transfer, 42, 615−630.
Milton, E. J., Schaepman, M. E., Anderson, K., Kneubühler, M., & Fox, N. (2009). Progressin field spectroscopy. Remote Sensing of Environment, 113, S92−S109.
Moran, M. S., Inoue, Y., & Barnes, E. M. (1997). Opportunities and limitations for image-based remote sensing in precision crop management. Remote Sensing ofEnvironment, 61, 319−346.
Nicodemus, F. F., Richmond, J. C., Hsia, J. J., Ginsberg, I.W., & Limperis, T. L. (1977).Geometricalconsiderations and nomenclature for reflectance. National Bureau of Standards Monograph,Vol. 160 (pp. 20402). Washington D.C: U.S. Govt. Printing Office.
Nilson, T., & Kuusk, A. (1989). A reflectance model for the homogeneous plant canopyand its inversion. Remote Sensing of Environment, 27, 157−167.
Nilson, T. (1991). Approximate analytic methods for calculating the reflectancefunctions of leaf canopies in remote sensing applications. In R. B. Myneni & J.Ross (Eds.), Photon–vegetation interactions: Applications in optical remote sensingand plant ecology (pp. 162−190). New York: Springer-Verlag.
Norman, J. M., & Welles, J. M. (1983). Radiative transfer in an array of canopies. Agr-onomy Journal, 75, 481−488.
Pinty, B., Gobron, N., Widlowski, J. L., et al. (2001). The Radiation transfer ModelIntercomparison (RAMI) exercise. Journal of Geophysical Research, 106, 11937−11956.
Pinty, B., Widlowski, J. -L., Taberner, M., et al. (2004). Radiation Transfer ModelIntercomparison (RAMI) exercise: Results from the second phase. Journal ofGeophysical Research, 109(D6) D06210 10.1029/ 2003JD004252 25.
Qin, W., & Jupp, D. L. B. (1993). An analytical and computationally efficient reflectancemodel for leaf canopies. Agricultural and Forest Meteorology, 66, 31−64.
Qin, W., & Xiang, Y. (1994). On the hotspot effect of leaf canopies: Modeling study andinfluence of leaf shape. Remote Sensing of Environment, 50, 95−106.
Qin, W., & Goel, N. S. (1995). An evaluation of hotspot models for vegetation canopies.Remote Sens. Rev., 13, 121−159.
Qin, W., Goel, N. S., & Wang, B. (1996). The hotspot effect in heterogeneous vegetationcanopies and performances of various hotspot models. Remote Sensing Reviews, 14,283−332.
Qin, W., & Gerstl, S. A. W. (2000). 3-D scene modeling of semidesert vegetation coverand its radiation regime. Remote Sensing of Environment, 74, 145−162.
Ranson, K. J., Irons, J. R., & Daughtry, C. S. T. (1991). Surface albedo from bidirectionalreflectance. Remote Sensing of Environment, 35, 201−211.
Sandmeier, St, Müller, Ch., Hosgood, B., & Andreoli, G. (1998). Sensitivity analysis andquality assessment of laboratory BRDF data. Remote Sensing of Environment, 64,176−191.
285F. Zhao et al. / Remote Sensing of Environment 114 (2010) 265–285
Schaepman-Strub, G., Schaepman, M. E., Painter, T. H., Dangel, S., & Martonchik, J. V.(2006). Reflectance quantities in optical remote sensing—Definitions and casestudies. Remote Sensing of Environment, 103, 27−42.
Sobrino, J. A., Caselles, V., & Becker, F. (1990). Significance of the remotely sensedthermal infrared measurements obtained over a citrus orchard. ISPRS Photogram-metric Engineering and Remote Sensing, 44, 343−354.
Su, Lihong (2000). Study on land surface directional thermal emission and scale effects.Ph.D. Dissertation, Institute of Remote Sensing Applications. Beijing, China: ChineseAcademy of Sciences.
Su, Lihong, Li, X., Liang, S., & Strahler, A. H. (2003). Simulation of scaling effects ofthermal emission from non-isothermal pixels with the typical three-dimensionalstructure. International Journal of Remote Sensing, 24, 3743−3753.
Suits, G. H. (1972). The calculation of the directional reflectance of a vegetative canopy.Remote Sensing of Environment, 2, 117−125.
Suits, G. H. (1983). Extension of a uniform canopy reflectance model to include roweffects. Remote Sensing of Environment, 13, 113−129.
Verhoef, W., & Bunnik, N. J. J. (1976). The spectral directional reflectance of row cropsDelft, Netherlands: NIWARS Publ., No. 35.
Verhoef, W. (1984). Light scattering by leaf layers with application to canopyreflectance modeling: the SAIL model. Remote Sensing of Environment, 6, 125−184.
Verhoef, W. (1985). Earth observation modeling based on layer scattering matrices.Remote Sensing of Environment, 17, 165−178.
Verhoef,W. (1998), Theory of radiative transfermodels applied in optical remote sensing ofvegetation canopies, Ph.D. thesis,WageningenAgriculturalUniversity, TheNetherlands.
Verhoef, W., Jia, L. and Su, Z. (2006), Optical–thermal canopy radiance directionalitymodel by unified 4SAIL model. In: Second recent advances in quantitative remotesensing: Proceedings of the 2nd international symposium on recent advances inquantitative remote sensing RAQRS'II, 25–29 September 2006, Valencia, Spain./ed.by J.A. Sobrino, Valencia: Universitat de Valencia, pp.1–6.
Wang, W. -M., Li, Z. -L., & Su, H. -B. (2007). Comparison of leaf angle distributionfunctions: Effects on extinction coefficient and fraction of sunlit foliage. Agriculturaland Forest Meteorology, 143, 106−122.
Widlowski, J-L., Taberner, M., Pinty, B., et al. (2007). The third RAdiation transfer ModelIntercomparison (RAMI) exercise: Documenting progress in canopy reflectancemodelling. Journal of Geophysical Resources, 112. doi:10.1029/2006JD007821, 2007.
Yan, Guangjian, Jiang, Lingmei, Wang, Jindi, Chen, Liangfu, & Li, Xiaowen (2003).Thermal bi-directional gap probability model for row crop canopies and validation.Science in China, 46, 1241−1249 Series D.
Yang, Hua (2001). Modeling and inversion of multi-angular vegetation remote sensing.Beijing, China: Postdoctoral Research Report in Beijing Normal University.
Yu, T., Gu, X., Tian, G., Legrand, M., Baret, F., Hanocq, J., et al. (2004). Modelingdirectional brightness temperature over a maize canopy in row structure. IEEETransactions on Geoscience and Remote Sensing, 42, 2290−2304.
