On the angular variation of thermal infrared emissivity of inorganic soils



[1] Land surface temperature (LST), a key parameter for many environmental studies, can be most readily estimated by using thermal infrared (TIR) sensors onboard satellites. Accurate LST are contingent upon simultaneously accurate estimates of land surface emissivity (ε), which depend on sensor viewing angle and the anisotropy of optical and structural properties of surfaces. In the case of inorganic bare soils (IBS), there are still few data that quantify emissivity angular effects. The present work deals with the angular variation of TIR emissivity for twelve IBS types, representative of nine of the twelve soil textures found on Earth according to United States Department of Agriculture classification. Emissivity was measured with a maximum error of ±0.01, in several spectral ranges within the atmospheric window 7.7–14.3 μm, at different zenithal (θ) and azimuthal (φ) angles. Results showed that ε of all IBS studied is almost azimuthally isotropic, and also zenithally up to θ = 40°, from which ε values decrease with the increase of θ. This decrease is most pronounced in sandy IBS which is rich in quartz reaching a maximum difference from nadir of +0.101 at θ = 70°. On the other hand, clayey IBS did not show a significant decrease of ε up to θ= 60°. A parameterization of the relative-to-nadir emissivity in terms ofθ and sand and clay percentage was established. Finally, the impact of ignoring εangular effects on the retrievals of LST, using split-window-type algorithms, and of outgoing longwave radiation, was analyzed. Results showed systematic errors ranging between ±0.4 K to ±1.3 K for atmospheres with water vapor values lower than 4 cm in the case of LST, and errors between 2%–8%, in the estimation of different terms of the surface energy balance.

1. Introduction

[2] Land surface temperature (LST) is a key parameter, essential for numerous studies related to terrestrial surface processes such as the atmosphere-surface energy budget [Sánchez et al., 2008], wildfire risk studies [Yi et al., 2009], weather and climate predictions, or soil moisture measurements [Wen et al., 2003]. An accurate LST measurement from satellite radiometry critically depends upon corrections for atmospheric and land surface emissivity (ε) effects. Emissivity and LST are coupled in a remote sensing radiance measurement in the thermal infrared (TIR) spectral domain, so the knowledge of the emissivity behavior with respect to factors such as soil composition and texture [Salisbury and D'Aria, 1992], soil moisture [Mira et al., 2007, 2010; Ogawa et al., 2006,] or viewing geometry [Takashima and Masuda, 1987; Labed and Stoll, 1991; Sobrino and Cuenca, 1999] are important when analyzing satellite TIR data.

[3] In the last two decades different satellite-based sensors have taken terrestrial measurements from different viewing angles. Sensors such as Moderate Resolution Imaging Spectroradiometer (MODIS), onboard Terra and Aqua satellites [Barnes et al., 1998], and Advanced Very High Resolution Radiometer (AVHRR), onboard National Oceanic and Atmospheric Administration 17/18 (NOAA) [Goodrum et al., 2001] collect observations with at-sensor view up to 55° (actually 65° at the surface due to Earth's curvature) from nadir because of their field-of-view (FOV) scanning. Other instruments with large observation angles are Advanced Along-Track Scanning Radiometer (AATSR) onboard the Environmental Satellite (ENVISAT) [Llewellyn-Jones et al., 2001] that collects biangular observations at two zenithal angles in the forward direction (close to nadir and 55°), or the Spinning Enhanced Visible and Infrared Imager (SEVIRI) on board Meteosat Second Generation (MSG) [Aminou et al., 1997] that can reach viewing angles of ±50°. The knowledge of the angular effects on surface thermal infrared emission can be important to evaluate different geophysical parameters. For instance, Lagouarde et al. [2000, 2004] during a flight campaign found a hot spot effect in angular measurements of LST over a forest and in an urban area, in which a significant increase in temperature was observed at certain observation angles. This hot spot was dependent on tree height, LAI and size of leaves, in the case of forest, and on sunlit and shaded faces due to the structure of buildings, in the case of the urban area, concluding that this effect plays an important role when retrieving LST from satellite at different view angles; moreover, this effect can be important for understanding the relationship between LST distributions and the surface energy budget. Niclòs et al. [2007]showed that sea surface temperature (SST) can be more accurately measured when the emissivity angular variation is taken into account. They obtained an emissivity-dependent split-window equation for MODIS Terra/Aqua sensors, which takes into account the decrease of sea surface emissivity with viewing angle. This algorithm was validated with in situ SST measurements with an accuracy of ±0.3 K.Chehbouni et al. [2001]showed that, under clear sky and constant vegetation conditions, difference between nadir and off-nadir temperature is well correlated with surface soil moisture. Finally,Ball and Pinkerton [2006] showed the benefit of angular measurements of basalt temperature in volcanology studies to establish the location of the most active parts of the lava domes and lava flows. These applications, among others, show that accurate angular temperature measurements are needed to have access to different biophysical and geophysical quantities.

[4] Closely related to angular variations of LST are angular variations in thermal emissivity, denoted as ε(θ, φ), where θ represents zenith angle, and φ represents azimuth angle. Previous works have analyzed these variations for water [Rees and James, 1992; Niclòs et al., 2005] showing that it is important to select the suitable emissivity for the accurate retrieval of SST; snow [Dozier and Warren, 1982; Hori et al., 2006] for which emissivity is also important for the nighttime cloud detection over cold snow/ice surfaces needed for radiation budget studies; and vegetation [McAtee et al., 2003; Cuenca and Sobrino, 2004] in which brightness temperature (Tb) is evidently affected by a relationship between solar illumination and viewing angle through differential heating and shading. The present study is focused on a specific type of surface, inorganic bare soils (IBS), which are mineralogical soils with low organic matter (OM) content (less than 9%). There exist few studies about the angular variation of thermal emissivity for IBS. Table 1 summarizes the most important conclusions drawn from these works. Barton and Takashima [1986] used a single channel radiometer to measure the radiation from the sand for zenith angles between 30° and 70°. Takashima and Masuda [1987] took measurements of ε(θ, φ) for a sandy soil with high quartz content from Sahara desert on the spectral range 7–17 μm evaluating the effect of particle size on emissivities. Becker et al. [1985] investigated experimentally the reflectance of various soils at different zenithal angles, expanding the number of samples to a lehm agricultural soil and Al3O2 powders. Labed and Stoll [1991]dealt with the study of the relative-to-nadir value ofε(θ, φ), measured under laboratory conditions for both sandy and silty soils, plus three agricultural soils with different texture and organic content. In addition to these soils Snyder et al. [1997] measured a relative value of ε(θ, φ) between θ = 10° and θ = 53°, with a Fourier transform spectrometer in the 3–14 μm range for an organic soil plus another one vegetated and gravel. Sobrino and Cuenca [1999] added results of clay and grass, expanding their results from the broadband 8–14 μm to narrower spectral bands [Cuenca and Sobrino, 2004].

Table 1. List of Previous Studies on the Angular Variation of TIR Emissivity of IBS, Which Are Referenced in the Main Texta
 IBS Number and TypesMain Findings
  • a

    The second column presents the number and soil types analyzed in each case, and the third column summarizes the main conclusions obtained.

Barton and Takashima [1986]1 sample beach sandEmissivity of a sand sample decreases by 3% with the increase of zenith angle from nadir to θ = 70°.
Takashima and Masuda [1987]2 samples quartz and Sahara dust powdersDifference between temperatures of channels 4 and 5 of NOAA-AVHRR are significant at different zenithal angles. This difference is attributed to angular variation of the emissivity
Becker et al. [1985]3 samples quartz sand lehm Al2O3 powdersSand and loam showed a decrease of 3% and 2%, respectively. Evidence of strong spectral effects, and important and specific roles of the surface roughness and nature medium on the emissivity change
Labed and Stoll [1991]4 samples SiO2 sand Loam soil Loess (silty) AN (silty)Sand does not present angular dependence up to θ = 50°. For larger viewing angles emissivity decrease does not exceed 4.5%. Loam soil exhibits the largest angular variation (a decrease of 9% at θ = 70°) and the effect is appreciable at θ = 20°. Silty soils exhibit a maximum decrease from θ = 0° of 3% at θ = 70°.
Snyder et al. [1997]2 samples Sand Silt-loamSand shows a decrease around 4% at spectral range 8–9 μm. This decrease is less than 2% at 10–12 μm. Silt-loam soil presents a decrease less than 1%.
Sobrino and Cuenca [1999]3 samples Clay, sand and siltClay and silt show a decrease of 0.5% and 0.9%, respectively at θ = 70°. Sand shows a decrease of 2% at θ = 70°.
Cuenca and Sobrino [2004]3 samples Clay, sand and siltSand presents decrease around 2% at spectral ranges: 8–14 μm, 11.5–12.5 μm and 10.3–11.3 μm, but presents a pronounced decrease (around 5%) at spectral range 8.2–9.2 μm. Clay and silt present a decrease in emissivity of 1 and 2%, respectively at four spectral channels. The pattern of the curve corresponding to a specific sample is conserved if we are operating at different wavelengths.
Present study12 samples Comprise 9 of the 12 textural classes defined by USDA texture triangleEmissivity decreases with the increase of zenith angle and is azimuthally isotropic, depending on soil texture and composition. A parameterization of the emissivity variation with view angle is proposed for different spectral channels. The impact of this variation on LST and outgoing longwave radiation assessment is provided.

[5] The present work extends these results limited to specific types of textural IBS to a wider range, retrieving ε(θ, φ) for twelve soils classified in nine of the twelve textural classes defined by the United States Department of Agriculture (USDA) texture triangle. With this aim, experimental measurements were carried out through the ensemble of a goniometer together with two multispectral thermal radiometers which allowed taking simultaneous angular measurements of radiance from IBS in two different angular configurations.

[6] In section 2 we discuss the theory followed to obtain ε(θ, φ) for the studied IBS. Section 3 presents the methodological details implemented to obtain the angular measurements. Section 4 presents results of ε(θ, φ) for each IBS, discussing the results obtained, as well as regression analyses to retrieve the relative-to-nadir emissivity for any IBS.Section 5presents the impact of ignoring angular effects of IBS emissivity on the retrieval of LST using the split-window algorithm, and on the estimation of the outgoing longwave radiation. Finally, conclusions are presented insection 6.

2. Theory

[7] For a thermal sensor spanning the 8–14 μm atmospheric window the radiative transfer can be modeled with three terms: direct surface emission, surface reflected environmental radiation (hemispheric downwelling radiance), and atmospheric absorption and emission effects. However, for this study, where sensor-surface distances are short, atmospheric effects can be reduced to the reflected term of hemispheric downwelling radiance. The spectral radiance can be modeled afterNorman and Becker [1995]:

display math

where Li(θ, φ) is the band radiance measured directly by the sensor from surface at θ and φ; Bi is the Planck function for blackbody radiance at temperature T; Li is the hemispheric downwelling radiance made up from atmosphere and surrounding elements contribution, ρ(θ, φ) is the hemispherical-directional band reflectance [Nicodemus et al., 1977], and εi(θ, φ) is absolute band emissivity of the surface. Subscript i stands for the spectral band where measurements have been taken.

[8] A relationship between surface emissivity and hemispherical-directional reflectance for a surface opaque to radiation in thermal equilibrium can be established by means of Kirchhoff's law [Nicodemus, 1965] as:

display math

This relation can be applied in two cases, either for anisotropic radiation over a Lambertian surface or for the inverse situation, with a non-Lambertian surface receiving isotropic radiation from its surroundings [Nicodemus et al., 1977].

[9] From equations (1) and (2) emissivity is retrieved as:

display math

However, emissivities from equation (3) are often inaccurate because of the difficulties in obtaining accurate measurements of the surface temperature T from which the Planck's radiance, B(T), is calculated as this radiative temperature corresponds to a thin superficial layer on the order of a few micrometers.

[10] A way to avoid this problem is to calculate relative-to-nadir values ofε(θ, φ) [Labed and Stoll, 1991], by taking two or more measurements, one of them at nadir and the rest at an arbitrary angular configuration, simultaneously or in a time period short enough to avoid significant changes of T or Liduring the measurement process. It is possible to obtain relative-to-nadir emissivity measurements by dividingequation (3) considered at a given angle (θ, φ) and at nadir viewing (0, 0):

display math

where εri(θ, φ) is the relative-to-nadir emissivity and Li(0, 0) is the radiance measured by the sensor at nadir viewing.

[11] Given that equation (4) is the quotient between absolute emissivity from an angular configuration and nadir, a previous knowledge of absolute emissivity at nadir allows estimation of the absolute value of emissivity in that specific angular configuration by:

display math

Equation (5) was used in the present study to retrieve the angular value of absolute emissivity.

3. Methodology

3.1. IBS Samples

[12] In this study we used twelve IBS samples, all with OM content lower than 9%, and spanning a wide range of textural compositions. Table 2 lists the textural and mineralogical features for the twelve IBS selected to carry out the study, all of them with a low roughness, after sieving particles size is between 0.2 cm and 1 cm, and almost completely dry with volumetric soil moisture values lower than 0.02 m3⋅m−3 [Mira et al., 2007, 2010]. Figure 1 shows the distribution of the twelve IBS in the different subclasses given by the texture triangle defined by the USDA, and according to the International Organization for Standardization [2002]. Samples studied here present a wide percentage of sand content (14–99%), the most common constituent of this sand is silica in the form of quartz, which also spans a wide range (19–100%); the other textures, silt and clay, present a percentage range from 0% to 54%. Additional details about these IBS can be found in the works of Mira et al. [2007, 2010].

Table 2. Organic Matter (OM) Content, and Textural and Mineralogical Features of the Twelve IBS Selected for the Analysisa
Soil CodeUSDA Texture TypeOM (%)Textural Classification (%)Mineral Classification (%)
LW03loamy sand0.737718553.746.3----
BR2sandy loam1.4769151682.316.80.8---
Esandy loam1.506720137221.43.2---
LW52sandy clay loam1.7162152358.432.29.4---
LW45Silty loam1.1529541772.423.44.2---
Cclay loam8.9020433729.45.59-56.1-
DSilty clay loam4.5014503519.33.568.962.3-
Figure 1.

Distribution of the IBS analyzed in the texture triangle defined by USDA.

[13] According to Lagouarde et al. [1995], for samples whose texture implies particles size less than 4–5 cm, the effects associated with angular measurements of Tb are caused by the emissivity of the IBS. On the other hand, in soils with coarse granularity and presence of particles which size is greater than 5 cm, angular effects in retrieving Tb are caused additionally by measuring shadowed or sunlit parts. Present work tries to study the angular emissivity of IBS with a roughness almost constant (particles size ranging between 0.2 and 1 cm). The objective is to evaluate the behavior of angular emissivity for each textural class defined in the text.

3.2. Instrumentation

[14] Angular radiance measurements over the IBS samples described in Table 2 were carried out on the roof of the Physics Faculty of the University of Valencia, Spain (13°30′25″N, 0°25′13″W) to determine the angular behavior of thermal emissivity by means of equation (5). Radiances were taken with two multispectral thermal radiometers CIMEL Electronique model CE312-2 [Brogniez et al., 2003]. This radiometer works in six different spectral bands, one of them operating in the broad range 7.7–14.3 μm (channel 1) and the other five channels working in narrow bands allocated within the previous broadband: 8.2–8.7 μm (channel 6), 8.4–8.9 μm (channel 5), 8.9–9.4 μm (channel 4), 10.1–11.1 μm (channel 3) and 10.9–11.9 μm (channel 2).

3.2.1. Calibration

[15] Two CE312-2 radiometers used in the experiment were calibrated with a thermal source with near blackbody behavior, LandCal Blackbody Source model P80P (http://www.landinst.com/infrared/products/p80p), for a range temperature from 0°C to 30°C, to check the accuracy and precision of this radiometer. The P80P blackbody source in turn was calibrated in the National Physics Laboratory (NPL, London) during a comparison of TIR instruments, organized by the Committee on Earth Observation Satellites in April 2009 [Theocharous and Fox, 2010]. Results show that P80P agreed with the NPL reference radiometer with an accuracy of ±0.19°C at the three different reference temperatures of 10°C, 20°C and 30°C.

[16] Temperature measurements of CE312-2 against the P80P blackbody source were made at temperature values of 5°C, 10°C, 20°C and 30°C. Results showed that the accuracy of channels 1 to 6 of CE 312-2 with regard to the blackbody temperature is: ±0.03°C, ±0.02°C, ±0.03°C, ±0.018°C, ±0.03°C and ±0.02°C, respectively. Therefore, the absolute accuracy of CE 312-2 channels is within ±0.19°C.

[17] Measurements of Li in equation (4)were carried out by means of a panel with high diffuse reflectivity in the TIR, Infragold Reflectance Target (IRT-94-100) made by Labsphere. It is a squared panel with dimensions 25.4 × 25.4 cm2 with a golden rough surface characterized by a high reflectance. The reflectance signature filtered for the six channels of the radiometer gives values of 0.926 (channel 1), 0.927 (channel 2), 0.926 (channel 3), 0.920 (channel 4), 0.917 (channel 5) and 0.918 (channel 6) (http://www.pro-lite.co.uk/File/Tech_Guide_-_Coatings_&_Materials.pdf), which imply small emissivities in all bands by virtue of Kirchhoff law. Nevertheless, direct measurements of radiance from the panel must be corrected by the radiative effect of this small emissivity, to get accurate values of Li, using the following relationship:

display math

where Lpanel,i is the direct measurement of radiance from panel, εpanel,i is the emissivity of the panel and Tpanel is the kinetic temperature of the golden surface which is measured by means of a contact thermometer, with an accuracy of ±1°C. This accuracy caused an error in Li, of ±0.09 Wm−2 sr−1 μm−1 (or ±0.3 K in terms of environmental effective temperature) when Li is calculated in each of the six radiometer channels. It was decided to use a gold diffusive panel to retrieve the Li over other methods, such as direct sky measurements through using the diffusive approximation [Kondratyev, 1969; Rubio et al., 1997], or the simulation of Li values obtained by introducing atmospheric profiles into radiative transfer codes, because in a previous study [García-Santos et al., 2012] it was observed that all these methods agreed under clear sky conditions, but with the presence of clouds or surrounding elements (trees, buildings, instrumentation, etc.) only the gold panel took into account these radiative contributions that could lead to significant systematic errors in retrieving emissivity or LST [García-Santos et al., 2012].

3.2.2. Angular Measurements

[18] A goniometer was used to perform the measurements on each sample at different viewing directions, together with two identical CE 312-2 radiometers (seeFigure 2). In order to take relative-to-nadir emissivity measurements at different viewing angles usingequation (4), radiance measurements were performed simultaneously setting one of the radiometers in the goniometer at nadir, and the second one in a viewing direction (θ, φ) (this last radiometer can be moved along the arc of the goniometer varying the viewing angle). With this configuration simultaneous measurements were readily achieved ensuring the stability of sample temperature. The experimental design of the ensemble can be seen in Figure 2, where the two radiometers are deployed to collect simultaneous measurements at nadir (CE1) and at a different angle (CE2).

Figure 2.

Experimental ensemble used in the study during two simultaneous measurements at nadir (CE1) and at zenithal angle (CE2).

[19] Angular measurements were taken at different combinations of zenith and azimuth angles. Zenith angles were considered from θ = 10° to θ= 70° at intervals of 10°. For each zenith angle, the IBS emissivity was measured at four different azimuthal orientations turning the samples 90° each time, instead of turning the goniometer-radiometer system. This process was repeated three times for each zenith angle. Azimuthal rotation of the sample, instead of the goniometer framework, was done to speed data collection and to ensure that observations were made using the same surrounding conditions (i.e., solar elevation, atmosphere contribution, etc.). In this way any difference in retrieving emissivity byequation (4) at different azimuthal angles, can be attributed exclusively to the sample.

[20] Li was measured before the CE1(0°)–CE2(10°) and after the CE1(0°)–CE2(70°) measurement configurations, placing the gold panel inside the FOV of CE1(0°). The period of time between both panel measurements was 30 min, which implied an average fluctuation of Li of ±7%; this relative value was obtained from the quotient of the difference between the Li values measured before and after the 30 min interval, and the average value of both measurements, given in percentage. This fluctuation, considered as an error of Li measurement, results in an equivalent emissivity error of ±0.0003, i.e., around ±0.03%. This error is much lower than the current accuracies in field emissivity measurements, and thus it was deemed appropriate to take the average value of Li for application to equation (4).

[21] Once the relative-to-nadir emissivity for each sample was measured, it is easy to obtain its absolute value by means ofequation (5), provided that the absolute emissivity value at nadir is measured using one of the existing methodologies. In the present study the absolute emissivity at nadir was obtained by means of temperature-emissivity separation (TES) method originally developed for the ASTER instrument [Gillespie et al., 1998], which was adapted to the field instrumentation taking into account that the radiometers have five bands that essentially fit those of ASTER [Mira et al., 2009].

[22] Errors associated with εi(θ, φ) were obtained through error propagation in equation (5) by means of expression:

display math

The term δεi(0, 0) is the precision for emissivity values at nadir derived as the standard deviation of ten individual emissivity measurements for each IBS sample, made with the TES method; these errors showed an average value of ±0.005 at all spectral channels of CE 312-2 and for all the samples analyzed. On the other hand, the termδεri(θ, φ) is the error of relative-to-nadir values of emissivity that are obtained as the maximum value of: (i) the values resulting from error propagation inequation (4), in which errors of each radiance measurement are given by the accuracy of the radiometer (see section 3.2.1), except in case of Li which is given by the standard deviation of the Li measurements made according to the methodology (see section 3.2.2); or (ii) the standard deviation of the three measurements made over a sample in each angular viewing direction. Results showed that the propagation error in equation (4), associated to accuracy of radiometers, was most of the time higher than the standard deviation of the three measurements; in addition, the maximum of these two errors, at a zenithal angle for all the azimuths measured, was very similar in all the spectral channels. As a result these values were averaged, taking all azimuth and channel error values in a specific zenithal angle obtaining, together with the standard deviation, the root-mean square deviation (RMSD) associated toεri(θ, φ) for each IBS. As can be seen, results given in Table 3 show that values of RMSD are mostly lower than ±0.01, except in the case of sample B at 30°, and sample LW03 from 50° to 70°. Average error associated to εri(θ, φ) is ±0.006. Therefore we considered that only variations of εri(θ, φ) larger than ±0.01 imply significant changes of emissivity with viewing angle.

Table 3. RMSD Obtained From the Average and Standard Deviation of δεri(θ, φ) for All the Azimuthal Angles and Spectral Channels in a Specific Zenith Angle, for Each One of the IBS Studied

4. Results and Discussion

4.1. Azimuthal Variation of IBS Emissivity

[23] The azimuthal dependence of the IBS relative-to-nadir emissivity was first analyzed.εri(θ, φ) for the twelve samples was retrieved, at each zenith angle, at four different azimuthal orientations, turning the sample 90° each time. Figure 3 shows εri(θ, φ) for the sample E at the four azimuths along the zenithal variation. Results show emissivity almost azimuthally isotropic compared to the zenithal decrease. Given the results of Figure 3, it was calculated the standard deviation of the four εri(θ, φ) values retrieved in each azimuth, for a specific zenithal angle and spectral channel. Then, this standard deviation value was averaged at all six spectral channels, since it presented a very similar value in all cases, and their standard deviations were also calculated; with these two values it was obtained finally the RMSD for each one of the zenith angles studied here. Table 4 shows this last RMSD for the twelve IBS.

Figure 3.

εri(θ, φ) for the E sample at the four azimuth angles, obtained turning azimuthally 90 degrees each time the sample for a specific zenith angle. Results are presented along the zenithal variation.

Table 4. RMSD Obtained From the Average of the Standard Deviation Calculated for the Four Azimuth Angles and for All the Spectral Channels in a Specific Zenith Anglea
  • a

    Results are presented for the twelve IBS.


[24] Results of Table 4 show that the azimuthal variation of εri(θ, φ) (RMSD less than ±0.01) is in general lower than the measurement error associated (given in Table 3) with the exception of samples BR3, from θ = 50° to θ = 70°, and LW45 at θ = 50°. According to this result, azimuthal variation of εri(θ, φ) for a IBS (with a roughness lower than 5 mm) could be ignored, assuming an uncertainty in the measurement lower than ±0.01.

4.2. Zenithal Variation of IBS Emissivity

[25] Considering the relatively low azimuthal variation of IBS emissivity in comparison to the zenithal variation, the relative-to-nadir emissivities at each zenith angle were calculated as the average of the values measured at all azimuthal angles. This finalεri value was multiplied by an absolute nadir emissivity value calculated from TES method [Gillespie et al., 1998] to retrieve the absolute value at a specific θ according to equation (5). Figures 4a4d present the zenithal variation of absolute emissivity, for each of the twelve IBS samples, in all six channels of the radiometer. The errors have been calculated according to equation (7). The uncertainties obtained for all zenith angles, IBS samples and spectral channels were lower than ±0.015 in 98% of cases and lower than ±0.01 in 71% of cases. So, the average value of this error for all the channels and zenith angles for all samples was ±0.009 with a standard deviation of ±0.003, being the RMSD ±0.01. This value was established as a threshold to determine if the absolute emissivity of an IBS changes significantly with the zenith angle with respect to its nadir value.

Figure 4a.

Absolute angular emissivity values obtained for the IBS samples B, BR3 and LW03, and for the six spectral channels of the radiometer. First column of graphs shows results for channel 1 (black dots) that extends over 7.7–14.3 m, and for channels 2 (blue dots) and 3 (red dots) that are placed within the 10–12 m region. Second column of graphs shows the results for channels 4 (green dots), 5 (purple dots) and 6 (orange dots) that are allocated in the 8–9.5 m interval. The errors shown have been calculated using equation (7).

Figure 4b.

Absolute angular emissivity values obtained for the IBS samples BR2, E and LW52, and for the six spectral channels of the radiometer. First column of graphs shows results for channel 1 (black dots) that extends over 7.7–14.3 m, and for channels 2 (blue dots) and 3 (red dots) that are placed within the 10–12 m region. Second column of graphs shows the results for channels 4 (green dots), 5 (purple dots) and 6 (orange dots) that are allocated in the 8–9.5 m interval. The errors shown have been calculated using equation (7).

Figure 4c.

Absolute angular emissivity values obtained for the IBS samples F, LW13 and LW45, and for the six spectral channels of the radiometer. First column of graphs shows results for channel 1 (black dots) that extends over 7.7–14.3 m, and for channels 2 (blue dots) and 3 (red dots) that are placed within the 10–12 m region. Second column of graphs shows the results for channels 4 (green dots), 5 (purple dots) and 6 (orange dots) that are allocated in the 8–9.5 m interval. The errors shown have been calculated using equation (7).

Figure 4d.

Absolute angular emissivity values obtained for the IBS samples BR1, C and D, and for the six spectral channels of the radiometer. First column of graphs shows results for channel 1 (black dots) that extends over 7.7–14.3 m, and for channels 2 (blue dots) and 3 (red dots) that are placed within the 10–12 m region. Second column of graphs shows the results for channels 4 (green dots), 5 (purple dots) and 6 (orange dots) that are allocated in the 8–9.5 m interval. The errors shown have been calculated using equation (7).

4.3. Spectral Features of εi(θ, φ)

[26] Results of Figures 4a4d show that for all the IBS, the absolute emissivity decreases with increasing viewing angle. The magnitude of the decrease depends on IBS texture and composition. Analyzing the difference between the value of εi(θ, φ), hereafter referred as εi(θ), at nadir and other zenith angles, shows that no significant angular variation is observed for zenith angles lower than 40°, independently of IBS composition.

[27] In the broad interval 7.7–14.3μm (channel 1), Figures 4a4d show that difference εi(0°) − εi(θ) becomes significant for IBS with sand and quartz content greater than 80% and 90%, respectively (samples B and BR3, Table 2) even for zenith angles lower than 50°. Angular effects in emissivity must be taken into account for zenithal angles above 60° for all IBS, independently of its textural or mineralogical composition. In this broad spectral range the maximum angular variation of emissivity from nadir appears at θ = 70°, for the sandy soil B being the emissivity difference εi(0°)–εi(70°) of +0.047. However, the minimum variation obtained is +0.012 (sample C), and therefore still significant. At θ = 60°, just IBS with high percentage of sand and quartz (samples B, BR3, LW03 and BR2, see Table 2) show significant differences from nadir, ranging between +0.014 and +0.028.

[28] The angular effects in the range 10–12 μm (channels 2 and 3) are negligible for zenith angles up to 60°. For IBS with sand and quartz contents above 80% (B, BR2 and BR3), the emissivity angular variation becomes relevant at a zenith angle of 60°, ranging from +0.013 to +0.018. For zenith angles of 70°, the angular effects are important for all IBS, and are more pronounced for sandy soils with high quartz content; at this specific zenith angle, differences range from +0.011 to +0.036.

[29] Results for channels 4, 5 and 6, show that angular decrease of emissivity are strongly affected by sand composition and quartz content of the IBS, being significantly large for sandy soils with high quartz content (B and BR3), for zenith angles above 40°. If sand and quartz contents are higher than 50% (all samples except most clayey samples: BR1, C and D), the angular effects become important from 50°, whose differences from nadir range between +0.01 and +0.035. At θ = 60° these differences increase, ranging between +0.014 and +0.051. Maximum angular variation is reached at θ = 70°, for sandy soils with a high quartz content (sample B). This difference is of +0.091.

[30] In order to quantify the zenithal dependence of emissivity on textural and mineralogical composition, we first calculated an average value of εri(θ) for all IBS sample data analyzed at each specific zenith angle (12 values per angle), with the purpose of checking possible dependences on soil composition. Errors associated to these average values were calculated as the root mean square of (i) the average error of εri(θ) at the specific zenithal angle derived from Table 3 values (Av(δεri)), and (ii) the standard deviation of the 12 εri(θ) values (δεσ):

display math

[31] Results are presented in Table 5. For spectral ranges 7.7–14.3 μm (CE312-2 channel 1) and 10–12μm (CE312-2 channels 2 and 3),εri(θ) shows a decrease with the increase of θ, that can be considered independent of any IBS composition, since the observed uncertainties are lower, or of the same order than ±0.01, except for 70° at the broad channel 1. Therefore, specific values can be established to assess the angular variation of εri(θ) for every IBS. For the spectral range 8–9.4 μm (CE312-2 channels 4, 5 and 6), averaged values ofεri(θ) show uncertainties lower than ±0.01 for zenith angles lower than 30°. Nevertheless, for θ ≥ 40° the dispersion of results gave uncertainties larger than ±0.01, reaching values greater than ±0.03 for θ = 70°. These large errors showed that the emissivity zenith variation has a strong dependence with soil composition, which is addressed in the next section.

Table 5. Averaged Relative-to-Nadir Emissivity Values at Each Zenith Angle (θ) for the Six Spectral Channels of CE312-2, for All the IBSa
θ(°)εr ch1(θ)εr ch2(θ)εr ch3(θ)εr ch4(θ)εr ch5(θ)εr ch6(θ)
7.7–14.3 μm10.9–11.9 μm10.1–11.1 μm8.9–9.4 μm8.4–8.9 μm8.2–8.7 μm
  • a

    Errors obtained with equation (8) are included in parentheses. From θ≥ 40° and for channels 4, 5 and 6 of CE 312-2, the relative emissivity presents errors greater than ±0.01.

± (0.006)± (0.005)± (0.006)± (0.006)± (0.006)± (0.006)
± (0.006)± (0.006)± (0.006)± (0.006)± (0.007)± (0.007)
± (0.006)± (0.006)± (0.006)± (0.008)± (0.009)± (0.010)
± (0.007)± (0.006)± (0.006)± (0.012)± (0.012)± (0.013)
± (0.008)± (0.007)± (0.007)± (0.017)± (0.017)± (0.019)
± (0.010)± (0.008)± (0.008)± (0.02)± (0.02)± (0.03)
± (0.014)± (0.010)± (0.010)± (0.04)± (0.04)± (0.04)

4.4. Parameterization of εri(θ)

[32] A parameterization of the angular variation of emissivity was addressed from the results shown in Table 5. First, considering that the relative emissivity values are very similar for the spectral ranges 7.7–14.3 μm and 10–12 μm, a single relationship was derived for these spectral ranges that define the relative emissivity as a function of observation angle θ (in degrees):

display math

The regression presents a determination coefficient of R2 = 0.993 and a RMSE = ±0.001. Taking into account also the uncertainties in those channels given by equation (8), the final error using the parameterization of equation (9) ranges from ±0.002 (at θ = 10°–20°) to ±0.009 (at θ = 70°), with an average value of ±0.004.

[33] As mentioned previously, in the spectral range 8–9.4 μm εri(θ) shows great discrepancies for θ ≥ 40° considering the different types of IBS (see Figures 4a4d and Table 5). Consequently, a parameterization that includes the IBS textural and mineralogical composition was set up. In a first step, the relevant parameters for the relative emissivity variation with viewing angle were assessed, by using a principal component analysis [Field, 2009] for all data available in Table 1 about IBS samples (except mineralogical data, excluding quartz and feldspar, since there was no complete information for all the samples), plus the measured values of εri. The most interesting statistical results are summarized in Figure 5.

Figure 5.

(a) Scree Plot of components that shows the number of components needed to explain most of the variance. (b) Plot of components in rotated space, which shows the correlation of the relevant components to relative-to-nadir emissivity. (See main text for details.)

[34] Figure 5a shows the Scree Plot, which according to Field [2009] shows how many factors are necessary to represent the total variance of data introduced. This quantity of factors is given by the number of components at which the slope becomes almost horizontal. Scree Plot presented here (see Figure 5a) shows that only four factors are enough. Results of the Total Variance Explained matrix (Field [2009], not included here) show that the first four factors represent a 90% of the variance.

[35] Once fixed how many factors are necessary, it is needed to know which ones are the most relevant, since during the PCA it was applied an extraction of those factors whose Eigenvalues were greater than 1, according to Kaiser's recommendation [Field, 2009]. PCA found only two factors to be extracted, εr and θ, both represented in axes of rotated space, Figure 5b. The reason of this extraction is because εr explains the 60.5% of the total variance, being the most significant factor and θ is the second most significant, explaining a 16% of the total variance, different from that explained by εr. To select the two other factors, the plot of components in rotated space (Figure 5b) is used. This plot represents the correlation degree of each component to relative-to-nadir emissivity. According toField [2009], values lower than ±0.5 are not well correlated with the component of interest, and all factors greater than ±0.5 could be taken into account. In Figure 5b, the factors to take under consideration for the relative-to-nadir emissivity are sand and quartz (negatively correlated), which would be expected because the common constituent of sand of our IBS samples is silica in the form of quartz, and silt, clay and OM (positively correlated).Sand is the most correlated factor withεr followed by OM, Clay and Quartz, it is obvious that sand should be the first factor selected. Deciding to select which one will be the last factor is difficult because OM and Clay present similar correlation with εr, for this reason the parameterization was made including first OM and finally substituting OM by clay. Comparison between observed εri(θ) values and those parameterized at the three considered spectral ranges showed that including clay results are slightly better than choose OM. Results showed a correlation coefficient (R2) ranging between 0.97 and 0.98 and a RMSE ranging between ±0.003–±0.005 for the case of clay and a R2ranging between 0.95 and 0.96 and a RMSE ranging between ±0.005–±0.006 for the case of OM. Finally, sand and clay were the two factors chosen, the model to calculate the relative-to-nadir emissivity obtained considering these parameters is:

display math

where i represents the spectral range (8.9–9.4 μm, 8.4–8.9 μm or 8.2–8.7 μm), S and C are sand and clay percentage, respectively and parameters a(θ) to f(θ) are quadratic zenith angle-dependent polynomials:

display math

Coefficients of polynomials in (11) are given in Table 6 for each spectral range, together with the determination coefficients and RMSE of the regressions.

Table 6. Coefficients for the Quadratic Zenith-Dependent Polynomials a(θ) to f(θ) Included in Equation (10), Together With R2 and RMSE Regression Parameters
Channel 4 8.9–9.4 μm      
Channel 5 8.4–8.9 μm      
Channel 6 8.2–8.7 μm      

[36] Values of S and C contents could be estimated remotely using radar data. As shown in Singh and Kathpalia [2007], applying a Genetic Algorithm technique to radar data retrieved from Synthetic Aperture Radar onboard European Remote Sensing 2, percentages of S and C are obtained with an standard error ranging between 0.07%–0.18%. Another possibility is to have a previous knowledge of S and C content from ancillary data. In these cases the parameterizations given above (equations (9) to (11), depending on the channel) could be applied to classification-based emissivity mapping, such as the one used in MODIS [Snyder et al., 1998], SEVIRI [Trigo et al., 2008], or more recently AATSR data [Caselles et al., 2012], in order to refine their algorithms.

[37] Figure 6 shows the comparison between the observed εri(θ) values and those modeled using equation (10) at the three considered spectral ranges. Results show an average correlation of 0.98 and an average RMSE of ±0.004. Considering also error propagation in equation (10), the final uncertainty showed an average value for all three spectral ranges of ±0.009 for θ = 10° to 50°, at θ = 60° the average error was ±0.011, and at θ = 70° it was ±0.013. The average error for all spectral channels and zenith angles was ±0.01, so this error could be considered as final error for results retrieved with equation (10).

Figure 6.

Self-validation of model represented byequation (10), comparing εrivalues measured with those calculated from the model. The plots represent self-validation made at the three spectral channels: (top) Ch4 (8.9–9.4μm), (middle) Ch5 (8.4–8.9 μm) and (bottom) Ch6 (8.2–8.7 μm), respectively. RMSE and R2 values of the regression are also included in each plot.

5. Implications for LST and Longwave Radiation Retrieval Accuracy

5.1. Implications for LST Accuracy

[38] The impact of ignoring angular effects on emissivity when measuring LST from space were addressed using one of the available split-window algorithms that present explicit dependence on emissivity. To this end, the algorithm proposed byGalve et al. [2008]for the MODIS spectral bands 31 and 32 were used, these bands are similar to CE312-2 channels 2 (10.9–11.9μm) and 3 (10.1–11.1 μm) in this study, although the results may be similar for other comparable algorithms and instruments. This algorithm gives LST corrected for emissivity and atmospheric effects as:

display math

where T31 and T32 are brightness temperatures measured in MODIS bands 31 and 32, respectively; a0, a1 and a2 are regression coefficients that can be found in Galve et al. [2008]; coefficients α and β determine the weight of the emissivity correction and are dependent on atmospheric water vapor content or precipitable water (W in cm); and inline image and Δ inline image are the average and emissivity difference in MODIS at bands 31 and 32, respectively.

[39] Since relative-to-nadir emissivities in CE312-2 channels 2 and 3 show almost the same angular variation (seeTable 4), the emissivity difference Δ inline image will remain almost constant at any angle, and thus the impact in this term should be negligible. However, this is not the case for the average emissivity term inline image, for which error propagation gives:

display math

where Δ inline imageis the difference between the average emissivity values of CE312-2 spectral channels 2 and 3 at nadir and at a zenith angleθ. As mentioned above, αis a W-dependent parameter following a quadratic relationship [Galve et al., 2008]:

display math

[40] Table 7 shows the variation of absolute emissivity between nadir values and the values at θ = 40° and θ= 65°, respectively, for all the analyzed samples, and for CE312-2 channels 2 and 3. The emissivity differences between 0° and 40° are generally small, but this is not the case for viewing angles of 65°. The emissivity differences in this last case were used inequation (13)to assess the possible impact of ignoring the angular variation of emissivity on LST, at large observation angles, if emissivity values at nadir are used instead of the correct off-nadir value. The results are shown inFigure 7, in which error values are represented for different W (i.e., for different values of α), ranging from 0 to 7 cm at intervals of 0.1 cm. For sandy soil BR3, LST errors reaches values up to +1.3 K for drier atmospheres, and sample LW52 presents LST errors lower than +0.5 K independently of W. Overall results show that retrieving LST for pixels of a IBS at θ = 65°, implies to make a systematic error between +0.4 and +1.3 K for an atmosphere with W values lower than 4 cm. For wet atmospheres (W ≥ 6 cm), errors in LST are lower than +0.5 K for each IBS studied here, and for extremely wet atmospheres (W ≥ 7 cm), errors can be considered not significant, taking values lower than +0.1 K for each IBS. In summary, drier atmospheres have the largest effect in LST retrieval accuracy, for a pixel observed at a large zenith angle, if it is ignored the angular effect of IBS emissivity.

Table 7. Averaged Emissivity Values of CE312-2 Channels 2 and 3 for the Twelve IBS Samples at Zenith Angles 0°, 40° and 65°a
Soil Codeθ = 0°θ = 40°θ = 65°Δε(40°)Δε(65°)
  • a

    The right column of each averaged emissivity is the averaged emissivity error associated at both channels for a given θ. The last two columns are the difference of averaged emissivity at nadir and at zenith angles 40° and 65°, respectively.

LW 130.9580.0020.9530.0040.9410.0060.0050.017
LW 520.9550.0020.9510.0040.9470.0060.0040.009
Figure 7.

LST errors obtained applying split-window algorithm (equation (11)) for the twelve IBS if angular emissivity effect at θ = 65° is ignored. δLST(65°) values, calculated through equation (12), are represented for W values ranging from 0 to 7 cm at intervals of 0.1 cm.

5.2. Implications for Longwave Radiation Accuracy

[41] Another parameter that could be affected by the angular variation of the emissivity is the outgoing longwave radiation (F), which can be calculated as follows:

display math

where ε is the hemispherical emissivity value for the whole TIR range, σis the Stefan-Boltzmann constant and T is the thermodynamic surface temperature. Usuallyε is considered Lambertian and its value at nadir is taken as the hemispherical one, but the present work has shown that this value varies with the zenith angle. Ignoring this effect could lead to errors in retrieving F. For this reason we have evaluated this error studying the relative sensitivity of F to the emissivity angular variation image following Zhan et al. [1996]:

display math

where Δε is the difference of 7.7–14.3 μm emissivity between θ = 0° and θ = 65°, F0 is the outgoing longwave radiation when the 7.7–14.3 μm emissivity value at nadir is introduced in (15), and F and F+ are the outgoing longwave radiation values when emissivity in (15) is decreased and increased by Δε, respectively. Table 8 shows the values used to retrieve image in each IBS sample. A fixed temperature value of 320 K was chosen in (15) for this sensitivity analysis.

Table 8. Sensitivity of F to the Emissivity Angular Variation image Retrieved From Equation (16) for the Twelve IBS Studieda
  • a

    The table presents the values of nadir absolute emissivity in the spectral range 7.7–14.3 μm (first row), the difference of 7.7–14.3 μm emissivity between θ = 0° and θ = 65° (second row), and the relative sensitivity values of F (third row).

ε7.7–14.3μm (0°)0.8780.9450.9580.9170.9620.9370.9540.9340.9480.9740.9380.907
SF↑ε) (%)833734253248

[42] Results from Table 8 show that accuracy of Fcan suffer variation between 2%–8%, depending on the type of IBS, which may lead to significant errors in the estimation of the different terms of the surface energy balance, as shown in the sensitivity analysis of the two-source models carried out bySánchez et al. [2008]. Measurements of radiation made over surfaces at high viewing angles by TIR sensors onboard satellites, could probably be more affected by atmospheric attenuation or nonlinear effects in radiative transfer modeling, especially retrieving LST. But the present study has shown that ignoring angular effects of surface emissivity may lead also to significant errors in retrieving parameters such as LST or F, even if this parameter has a secondary role in the radiative transfer budget.

6. Conclusions

[43] Angular effects in TIR radiance measurements may have consequences for the retrieval of accurate LSTs or the outgoing longwave radiation, F, for instance. In the case of IBS, with organic matter content less than 9% and low roughness with a particle size between 0.2 and 1 cm, angular effects are mainly associated with the IBS emissivity. The present study measured the TIR emissivity of twelve different IBS samples, completely dry, and representative of a wide range of surface textures. Uncertainties associated to the methodology were lower than ±0.015 in the 98% of the cases and lower than ±0.01 in the 71% of cases, being the average value of ±0.009 and the standard deviation of ±0.003. So a threshold of ±0.01 was established to consider that the absolute emissivity of an IBS changes significantly with the observation angle respect to its nadir value.

[44] The emissivity of the analyzed samples presents a low azimuthal variation, and the zenithal emissivity change is also small for viewing angles lower than 40°, from which emissivity decreases significantly. The most influential factors in the decrease of emissivity are sand and quartz content. For all sensors operating within the spectral range 7.7–14.3 μm, emissivity of IBS with sand and quartz content larger than 80% change significantly at zenith angles larger than 60°, showing differences from the nadir value ranging from +0.011 to +0.101. In the specific spectral range 8–9.4 μm, this angular decrease of emissivity must be considered from zenith angles larger than 40°. On the other hand, clayey samples do not show significant decrease in emissivity with the increase of the zenith angle, in fact samples with a clay content ranging from 35% to 54%, and a sand content lower than 40%, present a negligible decrease in emissivity for zenith angles lower than 70°.

[45] Results also showed that the decrease of emissivity with increasing viewing angles can be considered independent of textural and mineralogical IBS composition at the broadband 7.7–14.3 μm, and at the spectral channels within 10–12 μm. This work established a single zenith-dependent relationship for these spectral ranges between relative-to-nadir emissivity and zenith viewing angle with a maximum uncertainty of ±0.009. However, in the spectral domain 8–9.4μm, the decrease of emissivity is also dependent on IBS textural composition. A principal component analysis showed that sand and clay are the most influential factors, explaining a 90% of the variance. Sand is the main factor responsible to make the IBS emissivity decreases with the increase of θ, on the other hand emissivity of clayey soils remains almost constant with zenithal variation. It was possible to establish a relationship of relative-to-nadir emissivity as function of sand and clay percentage for an IBS, in which coefficients are zenithal-dependent quadratic polynomials. This relationship allows retrieving a relative-to-nadir emissivity value with a maximum error of ±0.01. The absolute emissivity value can be obtained later by multiplying the relative-to-nadir value by the absolute emissivity value at nadir, which can be retrieved using different methods.

[46] Finally, the impact of ignoring angular effects of emissivity on parameters such as LST or Ffrom satellite data was assessed. LST retrievals using an emissivity-dependent split-window algorithm applied to MODIS thermal bands 31 and 32, showed that for pixels measured at zenith angles larger than 65°, ignoring the angular dependence of emissivity could produce systematic errors on LST ranging from +0.4 K to +1.3 K, depending on the type of soil and for atmospheres with a water vapor content lower than 4 cm. Accuracy of F retrieved from satellite can suffer variation between ±2%–±8%, depending on the type of IBS if the zenithal decrease of the TIR emissivity is not taken into account in the final hemispherical value of the emissivity. These inaccuracies in F may lead to significant errors in the estimation of the different terms of the surface energy balance. TIR radiance measurements made over surfaces at high viewing angles could probably be more affected by atmospheric attenuation or nonlinear effects in radiative transfer modeling. But ignoring angular effects of surface emissivity may lead to inaccuracies retrieving parameters such as LST or F, even if this parameter has a secondary role in the radiative transfer budget.

[47] Although most current moderate-resolution operational TIR instruments have at-satellite view angles up to 55 degrees, the view angle relative to the vertical at surface level (that is what actually is being measured in this study) might be larger depending on surface orientation and considering Earth's curvature, and in that case the emissivity angular effect could be significant as shown by the obtained measurements. It will be even more critical to account for this effect in future TIR instruments as long as their spatial resolutions are improved (for instance the HyspIRI mission will have a spatial resolution of 60 m [Roberts et al., 2012]). The angular effects on soil emissivity may also be important for high spatial resolution instruments onboard airplanes, or also for field radiometers deployed viewing the surface with large observation angles. The results obtained in the present work will contribute to improve the accuracy and understanding of the measurements carried out by these range of instruments.


[48] This work was possible with the finance of the Spanish Ministerio de Ciencia e Innovación(grant of V. García-Santos associated to project CGL2007-64666/CLI) and projects CGL2007-29819-E/CLI and CGL2010-17577/CL, cofinanced by FEDER funds, and the financial support of theConselleria d'Educació de la Generalitat Valenciana (project PROMETEO/2009/086). The authors want to thank Juan Manuel Sánchez at the University of Castilla La Mancha for his comments and suggestions made in the present work on the effect of angular emissivity in the accuracy retrieving the outgoing longwave radiation. Useful comments and suggestions made by three anonymous reviewers are also acknowledged.