Remote Sensing of Environment 99 (2005) 304 – 314 www.elsevier.com/locate/rse
Canopy directional emissivity: Comparison between models Jose´ A. Sobrino a,*, Juan C. Jime´nez-Mun˜oz a, Wout Verhoef a
b
Global Change Unit, Department of Thermodynamics, Faculty of Physics, University of Valencia, Burjassot, Spain b National Aerospace Laboratory (NLR), Emmeloord, The Netherlands Received 22 February 2005; received in revised form 5 September 2005; accepted 10 September 2005
Abstract Land surface temperature plays an important role in many environmental studies, as for example the estimation of heat fluxes and evapotranspiration. In order to obtain accurate values of land surface temperature, atmospheric, emissivity and angular effects should be corrected. This paper focuses on the analysis of the angular variation of canopy emissivity, which is an important variable that has to be known to correct surface radiances and obtain surface temperatures. Emissivity is also involved in the atmospheric corrections since it appears in the reflected downwelling atmospheric term. For this purpose, five different methods for simulating directional canopy emissivity have been analyzed and compared. The five methods are composed of two geometrical models, developed by Sobrino et al. [J. A. Sobrino, V. Caselles, & F. Becker (1990). Significance of the remotely sensed thermal infrared measurements obtained over a citrus orchard. ISPRS Photogrammetric Engineering and Remote Sensing 44, 343 – 354] and Snyder and Wan [W. C. Snyder & Z. Wan, (1998). BRDF models to predict spectral reflectance and emissivity in the thermal infrared. IEEE Transactions on Geoscience and Remote Sensing 36, 214 – 225], in which the vegetation is considered as an opaque medium, and three are based on radiative transfer models, developed by Franc¸ois et al. [C. Franc¸ois, C. Ottle´, & L. Pre´vot (1997). Analytical parametrisation of canopy emissivity and directional radiance in the thermal infrared: Application on the retrieval of soil and foliage temperatures using two directional measurements. International Journal of Remote Sensing 12, 2587 – 2621], Snyder and Wan [W. C. Snyder & Z. Wan (1998). BRDF models to predict spectral reflectance and emissivity in the thermal infrared. IEEE Transactions on Geoscience and Remote Sensing 36, 214 – 225.] and Verhoef et al. [W. Verhoef, Q. Xiao, L. Jia, & Z. Su (submitted for publication). Extension of SAIL to a 4-component optical – thermal radiative transfer model simulating thermodynamically heterogenous canopies. IEEE Transactions on Geoscience and Remote Sensing], in which the vegetation is considered as a turbid medium. Over surfaces with sparse and low vegetation cover, high angular variations of canopy emissivity are obtained, with differences between at-nadir view and 80- of 0.03. Over fully vegetated surfaces angular effects on emissivity are negligible when radiative transfer models are applied, so in these situations the angular variations on emissivity are not critical on the retrieved land surface temperature from remote sensing data. Angular variations on emissivity are lower when the emissivity of the soil and the emissivity of the vegetation are closer. All the models considered assume Lambertian behaviour for the soil and the leaves. This assumption is also discussed, showing a different behaviour of directional canopy emissivity when a non-Lambertian soil is considered. D 2005 Elsevier Inc. All rights reserved. Keywords: Radiative transfer; Emissivity; Geometrical model; Angular variations
1. Introduction Land surface temperature (LST) is a key variable for environmental studies, as for example the estimation of the fluxes at the surface/atmosphere interface. Moreover, many other applications rely on the knowledge of LST (geology, hydrology, vegetation monitoring, global circulation models—GCMs, etc.). In order to retrieve accurate LST values from remote sensing or satellite data, atmospheric and emissivity effects * Corresponding author. Tel./fax: +34 96 354 31 15. E-mail address:
[email protected] (J.A. Sobrino). 0034-4257/$ - see front matter D 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2005.09.005
must be corrected. Several techniques have been published since the 1970s for performing this correction. Most of them applied to thermal data acquired in the atmospheric window located in the region between 8 and 14 Am. The existence of different techniques for retrieving LST and emissivity has triggered the publication of some review papers, which can be consulted by the reader interested in this topic: Becker and Li (1995), Dash et al. (2002), Kerr et al. (2004), Sobrino (2000), Sobrino et al. (2002), among others. Jointly with atmospheric and emissivity corrections, angular effects must also be corrected. This last effect is important for satellite sensors with a large swath angle, like MODIS (Moderate Resolution
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Imaging Spectroradiometer) and the NOAA (National Oceanic and Atmospheric Administration) series (with a swath angle higher than 50-), or for sensors with off-nadir view observation angles, like the ATSR (Along Track Scanning Radiometer) or AATSR (Advanced ATSR), with a forward view of 55-. In fact, the problem of the angular effects on atmospheric parameters is to a large extent solved, since radiative transfer codes like MODTRAN (Abreu & Anderson, 1996; Berk et al., 1999) allow the estimation of these parameters depending on the observation angle. However, the angular variation of land surface emissivity (LSE) is not a well-known problem, especially for bare surfaces like soil or rocks. The LSE angular dependence has been studied from field and also laboratory measurements (Cuenca & Sobrino, 2004; Labed & Stoll, 1991; Rees & James, 1992; Sobrino & Cuenca, 1999; etc.). The results obtained show lower emissivity values with increasing view angle for bare soil surfaces, whereas for dense vegetated canopies the angular dependence is minimal, in agreement with the usual assumption of Lambertian behaviour for vegetation. Some attempts have been carried out in order to parameterize in a simple way the angular variation on LSE, as the one proposed by Prata (1993), in which directional emissivity is given by ((h) = ((0) cos(h/2), where h is the view angle and ((0) the at-nadir emissivity. However, this expression, despite its easy application, is not appropriate for all surfaces and does not always provides good results. For sea or water surfaces, different models have been successfully developed for directional emissivity (see for example Masuda et al., 1988). In recent years different models have also been developed in order to analyze the angular variation over vegetation canopies, using among others the soil and vegetation emissivities as input data and the assumption of Lambertian behaviour for these components. This study addresses the simulation of the directional angular variation of emissivity. LSE is an important variable that has to be known to correct surface radiances and obtain surface temperatures. LSE is also involved in the atmospheric corrections since it appears in the reflected downwelling atmospheric term. An analysis of how important the knowledge of LSE in the LST retrieval is can be found in Jime´nez-Mun˜oz and Sobrino (in press). As a general result, an uncertainty on the LSE of 0.01 leads to an error on the LST of around 0.5 K. Emissivities are also important per se, so they may be diagnostic of composition, especially for the silicate minerals. LSE is thus important for studies of soil development and erosion and for estimation amounts and changes in sparse vegetation cover, in addition to bedrock mapping and resource exploration (Gillespie et al., 1998). The following sections provide a description of the models used in order to analyze the angular variation of canopy emissivity, classified as geometrical or radiative transfer models, as well as the results obtained when these models are applied to mixed surfaces composed by bare soil and vegetation with different vegetation covers and different values of soil and vegetation emissivities. Despite that a detailed comparison between different models can also be found in Franc¸ois (2002), in this paper we include results
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obtained with geometrical models as well as a discussion regarding to the assumption the of Lambertian behaviour for soils, which is not included in the reference cited. 2. Description of models Models are interesting tools because they make it possible to set up relationships between the thermal infrared (TIR) observations and surface biophysical parameters, as for example relationships between emissivity and vegetation index (Olioso, 1995). Models simulate the radiance measured by a radiometer, provided that the surface, atmosphere and sensor characteristics are known (Guillevic et al., 2003). In the TIR, two major types of models can be considered: geometrical models (GM) and radiative transfer models (RTM). GM (Jackson et al., 1979; Kimes & Kirchner, 1983; Norman & Welles, 1983; Sobrino et al., 1990; Sutherland & Bartholic, 1977; etc.) estimate the TIR radiance of a cover with the help of geometric considerations to describe the canopy structure. First, they calculate the proportions of projected surface area of the different surface components, which are directly observed in a particular view direction. Thus, the TIR radiance at the sensor is a weighting of these proportions by the TIR radiance from the respective components. GM represent the vegetation as an opaque medium and do not simulate radiative transfer with the cover. RTM (Franc¸ois et al., 1997; Kimes, 1980; Kimes et al., 1980; Luquet, 2002; Luquet et al., 2001; McGuire et al., 1989; Olioso, 1995; Olioso et al., 1999; Pre´vot, 1985; Smith et al., 1981; etc.) estimate the cover radiance as a function of sensor viewing direction, temperature distribution, and leaf angle distribution within the canopy. They simulate the propagation and the interactions within the cover of TIR radiation emitted by the cover components or incoming from the atmosphere. The canopy is represented as a set of plane elements (leaves) statistically distributed into homogeneous horizontal layers. The upward and downward radiative contributions of each layer are based upon the concept of directional gap frequency through the vegetation. The directional radiance of the cover is calculated by summing the radiative contributions of all layers. Iterations are sometimes performed to account for multiple scattering within the cover. The aforementioned models do not account for the canopy three-dimensional (3D) architecture, so they are one-dimensional (1D) models. In this respect and since it has not been used in this paper, the DART (Discrete Anisotropic Radiative Transfer) model developed by Guillevic et al. (2003) deserves special mention, which is a 3D model and simulates the TIR radiance of vegetation covers with incomplete canopy. Moreover, other models not belonging to geometrical or radiative transfer models have been developed, like for example models based on the estimation of the BRDF (Bidirectional Reflectance Distribution Function) (Snyder & Wan, 1998) or hybrid models (Pinheiro, 2003). In this paper five models have been considered for analyzing and comparing the results obtained from them: the GM for row distributed crops developed by Sobrino et al.
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(1990), the GM based on the estimation of the BRDF (Snyder & Wan, 1998), the volumetric model (VM) based on the estimation of the BRDF (Snyder & Wan, 1998), an analytical parameterization using the gap function based on the model of Pre´vot (1985) and described in Franc¸ois et al. (1997), and the extension of SAIL (Scattering by Arbitrarily Inclined Leaves) to the thermal infrared region and four components, called 4SAIL and developed by Verhoef et al. (submitted for publication). In order to simplify the notation, these models will be referred in the paper as SOBGM, S&WGM, S&WVM, FRARTM and VERRTM, respectively. Previously to the analysis of the results obtained, we give a brief explanation of each model in the next sections. 2.1. SOBGM: geometrical model for row distributed crops (Sobrino et al., 1990) Land surface emissivity can be obtained for a row distributed crop (see Fig. 1) by the following expression (Sobrino et al., 1990): e ¼ et Pt þ es þ ð1 es Þep FV Ps þ ep þ 1 ep es GV þ 1 ep ep Fµ Pp ð1Þ where P t is the proportion of the top, P s is the proportion of soil and P p is the proportion of the wall. These magnitudes can be calculated from geometrical considerations and the altitude and instantaneous field of view of the sensor (Sobrino, 1989). FV, GV and Fµ are shape factors given by: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi H H ð2Þ FV ¼ 1 þ 1þ S S sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi S S Fµ ¼ 1 þ H H s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi S S GV ¼ 0:5 1 þ 1þ H H
ð3Þ
ð4Þ
where H is the height of the row and S the separation between rows (see Fig. 1). The SOBGM has been validated by Sobrino and Caselles (1990), and is the basis of the NDVITHM (NDVI THreshold Method) developed by Sobrino and Raissouni (2000) in order to retrieve LSE from satellite data. The model
has been extended also to sunlit and shadowed components (Caselles et al., 1992) and n-components with different emissivities and other geometries (Jime´nez-Mun˜oz, 2005), but these modifications have not been validated yet. 2.2. S&WGM: geometrical model based on the BRDF estimation (Snyder & Wan, 1998) The model is based on the geometrical model of Li and Strahler (1992) for a sparse canopy composed by soil and spheres, extended to the thermal infrared region by Snyder and Wan (1998). The BRDF is calculated using a linear kernel approximation. Then, the BRDF is integrated over the hemisphere in order to obtain hemispherical reflectivity. Emissivity is obtained by applying Kirchhoff’s law. In the S&WGM the BRDF (referred as f geo) is estimated using the following approximation: g c fgeo ¼ c1 kgeo þ c2 kgeo þ c3
ð5Þ
g c where k geo and k geo are the kernels, given by:
g kgeo ¼
1 ðsechi þ sechr Þðt costsint Þ sechr sechi þ 1 p ð6Þ
c ¼ sechr sechi cos2 ðn=2Þ 1 kgeo
ð7Þ
and c 1, c 2, c 3 are the kernel coefficients given by: c1 ¼ nr2 qg
ð8Þ
2 2 nr qc 3 2 c3 ¼ 1=p nr2 qg þ nr2 qc : 3 c2 ¼
ð9Þ ð10Þ
In the previous expressions, h i is the incident angle, h r is the reflected angle, n is the spheres density, r is the radius of the spheres, q g is the ground reflectivity, q c is the canopy reflectivity, n is the scattering angle given by n ¼ arcosðcoshi coshr þ sinhi sinhr cos/Þ
ð11Þ
where / is the relative azimuth and t is a parameter given by
cost ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D2 þ ðtanhi tanhr sin/Þ2 sechi þ sechr
ð12Þ
and D2 ¼ tan2 hi þ tan2 hr 2tanhi tanhr cos/:
ð13Þ
2.3. S&WVM: volumetric model based on the BRDF estimation (Snyder & Wan, 1998)
Fig. 1. Geometry based on Lambertian boxes for describing a rough surface.
The model is based on the volumetric model of Roujean et al. (1992) for a vegetation canopy composed by facet leaves with transmissivity s and reflectivity q above a soil
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surface with reflectivity q 0. Similarly to the previous model, the BRDF is given by: q s fvol ¼ c1 kvol þ c2 kvol þ c3
s ¼ kvol
where F is a structural constant, which is related to LAI (Leaf Area Index), and b is given by 1 ð20Þ b ¼ ðcoshi þ coshr Þ: 2 The application of the BRDF models developed by Snyder and Wan (1998) can be found in Snyder et al. (1998), in which the BRDF approach is used in order to generate emissivities for land cover classes.
ð14Þ
the kernels by ðp nÞcosn þ sinn p q kvol ¼ coshi þ coshr 2
ð15Þ
ncosn þ sinn coshi þ coshr
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ð16Þ 2.4. FRARTM: analytical parameterization based on the gap function (Franc¸ois et al., 1997)
and the coefficients by c1 ¼
2q ½1 expð bF Þ 3p2
ð17Þ
c2 ¼
2s ½1 expð bF Þ 3p2
ð18Þ
c3 ¼
q q ½1 expð bF Þ þ 0 ½1 expð bF Þ 3p p
ð19Þ
Based on the radiative transfer model of Pre´vot (1985), Franc¸ois et al. (1997) proposed the following analytical parameterization for emissivity: eðhÞ ¼ 1 bðhÞM ð1 es Þ a½1 bðhÞM ð1 ev Þ
ð21Þ
where h is the view angle, ( s is the emissivity of the soil, ( v is the emissivity of the vegetation, a is a parameter related to the
(a) 0.995 0.990
directional emissivity
0.985 0.980 0.975 0.970 0.965 0.960 Pv = 13% Pv = 48% Pv = 83%
0.955 0.950 0
10
20
30
40
50
60
70
80
90
view angle (°)
(b) 0.995 0.990
directional emissivity
0.985 0.980 0.975 0.970 0.965 0.960 Pv = 13% Pv = 48% Pv = 83%
0.955 0.950 0
10
20
30
40
50
60
70
80
90
view angle (°)
Fig. 2. Directional emissivity obtained with the geometrical model proposed by Sobrino et al. (1990) for a) soil emissivity 0.94 and vegetation emissivity 0.98 and b) soil emissivity 0.97 and vegetation emissivity 0.99, and for different proportion of vegetation ( P v) at nadir view (13%, 48% and 83%).
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J.A. Sobrino et al. / Remote Sensing of Environment 99 (2005) 304 – 314 0.995 soil = 0.94 vegetation = 0.98 soil = 0.97 vegetation = 0.99
directional emissivity
0.990 0.985 0.980 0.975 0.970 0.965 0.960 0
10
20
30
40
50
60
70
80
view angle (°)
Fig. 3. Directional emissivity obtained with the geometrical model proposed by Snyder and Wan (1998) and based on the BRDF estimation by means of kernel models. The two lines correspond to soil and vegetation emissivity of 0.94 and 0.98, and 0.97 and 0.99, respectively.
(a) LAI = 0.5 LAI = 1 LAI = 2.5 LAI = 4 LAI = 6
1.000
directional emissivity
0.995 0.990 0.985 0.980 0.975 0.970 0.965 0
10
20
30
40
50
60
70
80
90
view angle (°)
(b) 1.000
directional emissivity
0.995 0.990 0.985 0.980 LAI = 0.5 LAI = 1 LAI = 2.5 LAI = 4 LAI = 6
0.975 0.970 0.965 0
10
20
30
40
50
60
70
80
90
view angle (°)
Fig. 4. Directional emissivity obtained according to the parameterization proposed by Franc¸ois et al. (1997) for a) soil and vegetation emissivity of 0.94 and 0.98 and b) soil and vegetation emissivity of 0.97 and 0.99, as a function of different LAI values (0.5, 1, 2.5, 4 and 6).
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cavity effect which values are given in Franc¸ois (2002), b is the directional gap frequency given for spherical LIDF (Leaf Inclination Distribution Function) and random dispersion by 0:5 bðhÞ ¼ exp LAI ð22Þ cosh
Verhoef (1984, 1985). The SAIL model is based on a four-stream approximation of the radiative transfer equation, in which case one distinguishes two direct fluxes (incident solar flux and radiance in the viewing direction) and two diffuse fluxes (upward and downward hemispherical flux). The interactions of these fluxes with the canopy are described by a system of four linear differential equations that can be analytically solved. Incorporation of the hot spot effect in SAIL was accomplished in 1989 and resulted in the model called SAILH (Verhoef, 1998). In SAILH the single scattering contribution to the bi-directional reflectance was modified according to the theory of Kuusk (1985), while all other terms remained the same. The new 4SAIL model differs from its predecessors by improvements in numerica robustness and computational efficiency. Moreover, it provides additional facilities to support the calculation of internal flux profiles and some extra quantities related to its application in the thermal infrared domain. In this way, from hemispherical – directional reflectivity values and by applying Kirchhoff’s law, it is possible to obtain the directional
and M is the hemispheric gap frequency given by M¼
1 p
Z
p 2
bðhÞdh:
309
ð23Þ
p2
2.5. VERRTM: 4SAIL radiative transfer model (Verhoef et al., submitted for publication) The 4SAIL model is a modern version of the SAIL (Scattering by Arbitrarily Inclined Leaves) model, first published by Verhoef and Bunnik (1981) in the early eighties in order to obtain canopy reflectance, and described in detail in
(a) LAI = 0.5 LAI = 1 LAI = 2.5 LAI = 4 LAI = 6
1.000
directional emissivity
0.995 0.990 0.985 0.980 0.975 0.970 0.965 0
10
20
30
40
50
60
70
80
90
view angle (°)
(b) LAI = 0.5 LAI = 1 LAI = 2.5 LAI = 4 LAI = 6
0.998 0.996
directional emissivity
0.994 0.992 0.990 0.988 0.986 0.984 0.982 0
10
20
30
40
50
60
70
80
90
view angle (°)
Fig. 5. Directional emissivity obtained from the volumetric BRDF model proposed by Snyder and Wan (1998) for a) soil and vegetation emissivity of 0.94 and 0.98 and b) soil and vegetation emissivity of 0.97 and 0.99, as a function of different LAI values (0.5, 1, 2.5, 4 and 6).
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(a) 1.000
directional emissivity
0.995 0.990 0.985 0.980 LAI = 0.5 LAI = 1 LAI = 2.5 LAI = 4 LAI = 6
0.975 0.970 0.965 0
10
20
30
40
50
60
70
80
90
view angle (°)
(b) 1.000
directional emissivity
0.995 0.990 0.985 0.980 LAI = 0.5 LAI = 1 LAI = 2.5 LAI = 4 LAI = 6
0.975 0.970 0.965 0
10
20
30
40
50
60
70
80
90
view angle (°)
Fig. 6. Directional emissivity obtained from the 4-SAIL model developed by Verhoef et al. (submitted for publication) for a) soil and vegetation emissivity of 0.94 and 0.98 and b) soil and vegetation emissivity of 0.97 and 0.99, as a function of different LAI values (0.5, 1, 2.5, 4 and 6).
emissivity of the canopy –soil ensemble in the thermal infrared from the emissivities of leaves and soil background. The 4SAIL model can be executed for 4 distinct components, i.e. by taking into account sunlit soil temperature, shaded soil temperature, sunlit vegetation temperature and shaded vegetation temperature, but for emissivity calculations this feature is not required. For uniform leaf temperatures, the model is based on the resolution of the following system of 4 linear equations: d Es ¼ kEs Ldx d E ¼ sVEs þ aE rEþ Ps Hh ð1 Ps ÞHc Ldx d þ E ¼ sEs þ rE aEþ þ Ps Hh þ ð1 Ps ÞHc Ldx d E0 ¼ wEs þ vE þ vVEþ KE0 þ KPs Hh þ K ð1 Ps ÞHc Ldx ð24Þ
where E s, E , E + and E 0 are respectively the direct solar irradiance on a horizontal plane, the diffuse downward irradiance, the diffuse upward irradiance and the fluxequivalent radiance in the direction of observation, L is the LAI, x is the relative optical height coordinate, which runs from 1 at bottom of the canopy to 0 at the top, the coefficients k and K are the extinction coefficients for direct flux in the directions of the sun and the observer, respectively and the other coefficients describe the scattering of incident fluxes and the extinction of diffuse incident flux. The hemispherical flux H is the result of thermal emission by leaves, expressed in terms of leaf emissivities and Planck’s law. The soil temperature is incorporated after solution of Eq. (24) and application of the adding method (Verhoef, 1985) to the combination canopy – soil. In the adding method one combines the optical/thermal properties of the isolated canopy layer with those of the background soil in order to compute the optical/thermal properties of the combination canopy –soil.
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311
covers, i.e., almost Lambertian behaviour, whereas for low vegetation cover canopy emissivity increases with increasing view angle due to the greater vegetation cover observed. In Fig. 2a angular variations for the lowest vegetation cover (13%) are within 0.01 when the view angle changes from nadir to 50-. The difference between 80- and nadir view reach a value of 0.03. In Fig. 2b similar behaviour can be found, but differences on angular emissivity are lower, within 0.01 between 0- and 70-, with a difference of 0.015 between 80- and nadir view. Fig. 2 also shows the cavity effect, since emissivity values for the vegetation canopy are greater than the simple averaged values. Fig. 3 shows the results obtained with the S&WGM. The comparison between this model and the SOBGM is not trivial because S&WGM assumes spheres in order to characterize the vegetation and SOBGM considers boxes and rows. In order to apply the model a value of nr 2 = 0.1 has been considered. The relation between this value and the vegetation cover is not clear, since it depends on the radius of the spheres. Values of ( s = 0.94
3. Results The physics involved in GM, in which vegetation is considered as an opaque medium, and RTM, in which vegetation is considered as a turbid medium, is quite different, since the comparison between GM and RTM is not an easy task and is difficult to interpret. For this reason, on the one hand a comparison between SOBGM and S&WGM has been carried out, whereas in the other hand S&WVM, FRARTM and VERRTM have been compared. Fig. 2 shows the results obtained with SOBGM. Values of H (height of the crop) and S (separation between rows) have been arbitrarily chosen in order to simulate low (13%), medium (48%) and high (83%) vegetated cover surfaces. In Fig. 2a values of ( s = 0.94 and ( v = 0.98 have been considered for soil and vegetation emissivities, respectively, whereas in Fig. 2b values of ( s = 0.97 and ( v = 0.99 have been considered. The results obtained show low angular variation for high vegetation
(a) 0.0025
0.0015
0.0005
VM
- S&W
RTM
FRA
LAI = 0.5 LAI = 1 LAI = 2.5 LAI = 4 LAI = 6
-0.0005
0
10
20
30
40
50
60
70
-0.0015
-0.0025
-0.0035 view angle (°)
(b) LAI = 0.5 LAI = 1 LAI =2.5 LAI = 4 LAI = 6
0.0025
FRA
RTM
- VER
RTM
0.0015
0.0005
-0.0005
0
10
20
30
40
50
60
70
-0.0015
-0.0025
-0.0035 view angle (°)
Fig. 7. Differences between the emissivity obtained according to the parameterization proposed by Franc¸ois et al. (1997) and the emissivity obtained with a) the BRDF volumetric model proposed by Snyder and Wan (1998) and b) the 4SAIL model developed by Verhoef et al. (submitted for publication). A soil emissivity of 0.94 and a vegetation emissivity of 0.98 have been considered.
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and ( v = 0.98 or ( s = 0.97 and ( v = 0.99 have been also considered. The curves obtained in Fig. 3 have difficult interpretation because a parabola is obtained, whereas one expects to obtain a decay curve with increasing angle, as in the previous case. It should be noted that emissivity retrieval from BRDF data shows an important problem: the kernel model diverges at high view angles. Snyder and Wan (1998) point out that the hemispheric integration can only be done from 0- to 75-. We have observed that the model diverges even before than 75-. In order to obtain the results with the RTM, different emissivity values, ( s = 0.94 and ( v = 0.98 and also ( s = 0.97 and ( v = 0.99, and LAI values, 0.5, 1, 2.5, 4 and 6, have been considered. Fig. 4 shows the results obtained with the FRARTM. Two different tendences can be found in this figure. Hence, for LAI 1 canopy emissivity increases with increasing view angle due to a similar reason that the one explained in the SOBGM. However, for LAI > 1 a decreasing tendency for canopy emissivity with increasing view angle is observed. The proportion of leaves is higher than the proportion of soil for surfaces with LAI > 1, and the at-nadir emissivity is higher than the vegetation emissivity due to the cavity effect. At 90-, canopy emissivity recovers the vegetation emissivity value, so the cavity effect seems to disappear at this view angle. The comparison between Fig. 4a (( s = 0.94 and ( v = 0.98) and Fig. 4b (( s = 0.97 and ( v = 0.99) shows that lower angular variations are obtained when ( s and ( v are closer. Fig. 5 shows the results obtained with the S&WVM. In order to compare this model with the FRARTM, the term exp( bF) involved in Eqs. (17) – (19) has been chosen to be equal to the term Mb(h) involved in Eq. (21). View angles up to 70- have not been represented in order to avoid the divergence problems related to the hemispherical integration of the BRDF. The results obtained are similar to the ones obtained with the FRARTM, with differences between both models lower than 0.0015 in most cases. Fig. 6 shows the results obtained with the VERRTM. Despite similar behaviour than in the previous cases is obtained, a significant difference when comparing with
the FRARTM at high view angles can be found. In VERRTM the cavity effect still remains at 90-. These differences are illustrated in Fig. 7, in which the differences between the S&WVM and the FRARTM and also between the VERRTM and the FRARTM as a function of the view angle are represented. The comparison between the S&WVM and the FRARTM (Fig. 7a) shows differences are lower than 0.015 in most cases, whereas the comparison between the VERRTM and the FRARTM (Fig. 7b) shows differences higher than 0.015, the maximum difference found at 90-, higher than 0.025. Finally, in order to analyze the assumption of Lambertian behaviour for soil surfaces, the SOBGM has been applied again assuming the angular variations for soil proposed by Cuenca and Sobrino (2004) from in situ measurements. The results are shown in Fig. 8, in which at-nadir values for vegetation cover of 13%, ( s = 0.97 and ( v = 0.99 have been considered. The canopy emissivity considering a Lambertian soil has been also represented for comparison. Despite the fact that differences between the Lambertian case and non-Lambertian case are lower than 0.005, the behaviour is quite different, so errors on directional canopy emissivity could be significant when assuming Lambertian behaviour. 4. Conclusions In this paper two GM (SOBGM, S&WGM) and three RTM (FRARTM, S&WRTM and VERRTM) have been analyzed and compared. GM consider a sparse vegetation canopy as an opaque medium, whereas RTM consider a uniform vegetation cover as a turbid medium. Models based on the BRDF estimation show divergence problems for view angles up to 75- or even lower, so the analysis has been mainly focussed on SOBGM, FRARTM and VERRTM. SOBGM shows an increasing canopy emissivity with increasing view angle, due to the greater proportion of vegetation observed at off-nadir view angles. RTM show different trends depending on the LAI values. For LAI 1, when the proportion of leaves is lower
0.985
directional emissivity
lambertian non-lambertian
0.980
0.975
0.970 0
10
20
30
40
50
60
70
view angle (°)
Fig. 8. Comparison between the directional emissivity obtained from the geometrical model proposed by Sobrino et al. (1990) assuming a Lambertain behaviour for soil or considering the angular variations measured in situ by Cuenca and Sobrino (2004). An initial value for soil emissivity of 0.97 and for vegetation emissivity of 0.99 have been considered.
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than the proportion of soil, canopy emissivity grows with increasing view angle, as in geometrical models, but decreases for LAI > 1, due to the greater proportion of leaves than proportion of soil and the cavity effect. Differences between FRARTM and VERRTM have been also found for high view angles. In particular, for view angles of 90- the cavity effect disappears in the FRARTM, whereas in the VERRTM it still remains. An additional comparison between the Pre´vot (1985) model, the FRARTM and the VERRTM can be also found in Franc¸ois (2002), from which similar conclusions can be extracted. Actually land surface emissivity is retrieved with an accuracy between 0.01 and 0.02 (see for example Gillespie et al., 1998; Sobrino et al., 2001, 2002), which leads to errors lower than 1 K for surface temperature. Most of the angular differences obtained with RTM are lower than these values, so the impact of angular effects on emissivity are not critical on the retrieved land surface temperature over fully covered surfaces, but not over sparse vegetation. The models shown in the paper are difficult to validate, since angular measurement of emissivity is not an easy task. Some attempts of validation can be found in Pre´vot (1985) and Snyder et al. (1997). It should be noted that these models assume a Lambertian behaviour for soil and vegetation surfaces. Under this assumption, angular variation on emissivity is due to changes in the observed geometry. Despite the fact that vegetation surfaces show a near Lambertian behaviour, bare soil surfaces do not show this behaviour, and the angular variation on emissivity can not be neglected. However, this angular dependence is difficult to know, so it depends mainly on the scattering mechanism, grain size and porosity (Labed & Stoll, 1991). The models analyzed in the paper provide the emissivity angular variation over vegetation canopies and a better understanding of the geometrical effects and the role of the canopy parameters on radiative transfer processes in the thermal part of the spectrum, but the assumption of Lambertian behaviour should be revised, at least for the bare soil component. For this purpose, further research on the angular variation of emissivity for natural surfaces is needed. Acknowledgments We wish to thank to the European Union (EAGLE, project SST3-CT-2003-502057) and the Ministerio de Ciencia y Tecnologı´a (project REN2001-3105/CLI) for the financial support. This work has been carried out while Juan C. Jime´nez-Mun˜oz was having a contract ‘‘V segles’’ from the University of Valencia. References Abreu, L. W. & Anderson, G. P. (Eds.) (1996). The MODTRAN 2/3 Report and LOWTRAN 7 MODEL, Modtran Report, Contract F19628-91-C-0132. Becker, F., & Li, Z. -L. (1995). Surface temperature and emissivity at various scales: Definition, measurement and related problems. Remote Sensing Reviews, 12, 225 – 253. Berk, A., Anderson, G. P, Acharya P. K., Chetwynd, J. H., Bernstein, L. S., et al. (1999). MODTRAN4 User’s Manual, Air Force Research Laboratory, Hanscom AFB, MA 01731-3010.
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