Modeling angular-dependent spectral emissivity of snow and ice in the thermal infrared atmospheric window Masahiro Hori,1,* Teruo Aoki,2 Tomonori Tanikawa,1 Akihiro Hachikubo,3 Konosuke Sugiura,4 Katsuyuki Kuchiki,2 and Masashi Niwano2 1
Earth Observation Research Center, Japan Aerospace Exploration Agency, 2-1-1, Sengen, Tsukuba, Ibaraki 305-8505, Japan
2
Meteorological Research Institute, 1-1 Nagamine, Tsukuba, Ibaraki 305-0052, Japan
3
Environmental and Energy Resources Research Center, Kitami Institute of Technology, 165 Koen-cho, Kitami 090-8507, Japan
4
Center for Far Eastern Studies, University of Toyama, 3190, Gofuku, Toyama-shi, Toyama 930-8555, Japan *Corresponding author: [email protected] Received 20 May 2013; revised 7 August 2013; accepted 16 September 2013; posted 17 September 2013 (Doc. ID 190829); published 15 October 2013
A model of angular-dependent emissivity spectra of snow and ice in the 8–14 μm atmospheric window is constructed. Past field research revealed that snow emissivity varies depending on snow grain size and the exitance angle. Thermography images acquired in this study further revealed that not only welded snow particles such as sun crust, but also disaggregated particles such as granular snow and dendrite crystals exhibit high reflectivity on their crystal facets, even when the bulk snow surface exhibits blackbody-like behavior as a whole. The observed thermal emissive behaviors of snow particles suggest that emissivity of the bulk snow surface can be expressed by a weighted sum of two emissivity components: those of the specular and blackbody surfaces. Based on this assumption, a semi-empirical emissivity model was constructed; it is expressed by a linear combination of specular and blackbody surfaces’ emissivities with a weighting parameter characterizing the specularity of the bulk surface. Emissivity spectra calculated using the model succeeded in reproducing the past in situ measured directional spectra of various snow types by employing a specific weighting parameter for each snow type. © 2013 Optical Society of America OCIS codes: (280.0280) Remote sensing and sensors; (280.6780) Temperature; (290.0290) Scattering; (290.6815) Thermal emission. http://dx.doi.org/10.1364/AO.52.007243
1. Introduction
Directional emissivity spectra of snow cover at thermal infrared (TIR) wavelengths are essential properties for remote sensing of the earth’s thermal properties, such as snow surface temperature [1–5], cloud discrimination from space [6,7], and for estimating 1559-128X/13/307243-13$15.00/0 © 2013 Optical Society of America
Earth’s long-wave radiation budget on the Greenland and Antarctic ice sheets by broadband radiometer such as the clouds and the Earth’s radiant energy system (CeRES) [8]. The spectra may also be potentially utilized for sensing remote planets in astronomical applications [9]. The spectral emissivities of snow in TIR had been investigated based on theoretical radiative transfer (RT) calculation approaches in addition to laboratory or field measurements. Berger [10] indicated that 20 October 2013 / Vol. 52, No. 30 / APPLIED OPTICS
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snow emissivity exhibits weak dependence on snow density by adapting a simple geometric optics approximation to the theoretical scattering calculation. Dozier and Warren [11] simulated the directional-hemispherical reflectance (DHR) of snow, which can be equalized to 1 − ε using Kirchhoff’s law (where ε is the directional emissivity at an exitance angle), based on a more rigorous treatment: Mie scattering for single scattering and the deltaEddington approximation for multiple scattering. This indicated significant angular dependence of the DHR, but little dependence on grain size and density. Most of the algorithms for retrieving snow surface temperatures from space (e.g., [1,12,13]) have been developed based on the simulated emissivity by Dozier and Warren [11]. Rees and James [14] investigated angular variation of the infrared emissivity of an ice surface using a simple TIR sensor for the measurement of brightness temperature averaged between 8 and 14 μm, together with a thermocouple thermometer for measuring the physical temperature of the surface. They found that the broadband emissivity of ice surfaces is in agreement with the Fresnel formula for a plane interface. Subsequently, Rees [15,16] attempted to measure the emissivity of various snow covers including fresh snow, employing the same measurement approach, yet the resulted emissivity seems to vary widely between 0.70 and 0.92, even in the same snow type (fresh snow). This is possibly due to a failure in making accurate physical temperature measurements at the feathery low-density surface of the fresh snow cover. Salisbury et al. [17] conducted laboratory measurements of DHR and found that snow emissivity varies depending on snow types, including frost, fine new snow, and medium- and coarse-granular snow, and the resultant emissivity spectra deviate notably from the simulated ones based on the Mie theory. These measured emissivity spectra are the first practical emissivity spectra of snow and are archived in the ASTER spectral library [18], although obtained only for a near nadir exitance angle (10° from the normal) owing to limitations in the instrument design [17]. The snow emissivity spectra have been used for developing a recent remote-sensing algorithm to retrieve snow surface temperature from data of the moderate resolution imaging spectroradiometer (MODIS) [4]. Wald [19] proposed several theoretical approaches to simulating grain-size-dependent emissivity spectra and succeeded in modeling the spectral DHR (at the near nadir angle) of the disaggregated coarse-granular snow and welded snow obtained by Salisbury et al. [17]. The DHR of disaggregated snow was modeled by employing the diffraction subtraction method in which the diffracted components of the scattered light were subtracted in the RT simulation for a close-packed snow media, while the DHR of the welded snow was expressed as the weighted sum of the RT reflectance and Fresnel reflectance. 7244
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Wald [19] also pointed out that the angular dependence determined with any RT approach is only applicable for disaggregated snow samples, and the emissivity of welded samples should be partly accounted for using the Fresnel reflectance theory, which itself has a strong angular dependence. Therefore, not only grain size but also cementation effects—thus whether the snow is welded or disaggregated—are considered important factors that determine the directionality of snow emissivity [in general, snow particles are expressed as “an aggregate of ice crystals.” However, in this paper, we use the term “disaggregated snow (or particles)” for expressing snow conditions consisting of fineto coarse-grained snow particles according to the usage in [19] to discriminate them from those consisted of welded film-like ice particles such as in the case of sun crust snow]. Hori et al. [20] conducted in situ measurements of the spectral directional emissivity of snow and ice and revealed that snow emissivity actually varies depending both on snow surface grain size and exitance angle. Their in situ measured emissivities clearly indicated that angular emissivity of snow in TIR is near isotropic for fine disaggregated snow but approaches an anisotropic nature, exhibiting specular reflectance, as snow particles become larger and more welded. Thus the results of [20] further demonstrated the importance of understanding whether snow grains are welded or not when determining the directional emissivity of snow. Hori et al. [20] also showed the close correlation between TIR emissivity and shortwave infrared reflectance measured for various snow types (fine, medium, coarse, and sun crust), which again indicates that TIR emissivity varies depending on the snow grain shape on the upper skin surface. They also discussed the applicability of the spectral contrast in TIR snow emissivity around the wavelengths 11–12 μm in an attempt to discriminate among snow types from space. The applicability of TIR spectral contrast to the monitoring of snow and ice from space was also examined by Tonooka and Watanabe [21] based on nadir angle spectra from the ASTER spectral library. Cheng et al. [22] recently compared several RT models in order to examine their capability in simulating the in situ measured snow TIR emissivity acquired by [20]. They investigated RT models based on the Mie scattering theory, both with and without corrections for the packing effect, which violates the independent scattering approximation assumed in the theory. Their results indicated that several RT models based on the Mie theory with the diffraction subtraction correction proposed by [19] were able to simulate the emissivity only at the nadir angle. However, none of the models succeeded in simulating snow emissivities at off-nadir angles. The snow surface is generally densely packed, but at the same time is sometimes porous and sometimes a specular medium and therefore has complex surface structures from the point of views of the light
scattering. Although, as described above, the emissivity of snow has been modeled by rigorous application of Mie scattering and RT theories, currently no theoretically unified model can simulate the angular dependence of emissivity spectra for different snow and ice types. There remain discrepancies between the simulated and in situ measured emissivities, particularly at wavelengths longer than 10.5 μm, where typical split-window channels of satelliteborne optical sensors are located. These instruments are commonly used for the remote sensing of surface temperatures from space. Approaches involving the Mie scattering and RT models therefore fail to accurately simulate TIR emissive properties of snow particles with wide ranges of sphericity and size. This problem has also been discussed in [17]. For practical applications, such as the remote sensing of snow surface temperature from space, a simple model that is capable of simulating angular and grain-size-dependent TIR emissivity spectra is desired. As Wald [19] proposed, a weighted summation of a RT model (using the diffraction subtraction method) and the Fresnel reflectance could be one potential approach to such a goal, although no such model has yet been presented. Recent advances in handheld thermographic imaging technology has enabled and facilitated observation of in situ TIR emissive behaviors of snow surfaces with high spatial resolution (e.g., [23,24]). We recently carried out thermography measurements coincident with snow pit works in snowfields and gained physical insights into the TIR emissive behaviors of several different snow types. Based on these thermography measurement results in addition to the experimental knowledge obtained in the past studies, we propose, in this study, a semiempirical model of snow surface emissivity to reproduce the in situ measured directional snow emissivity spectra [20]. The model introduces a
weighting parameter that characterizes the specularity of the bulk snow surface and bridges the gap between the specular and blackbody-like behaviors of snow. This approach provides an alternative to inappropriate RT calculations for the densely packed snow medium. Section 2 briefly reviews and summarizes past experimental knowledge from the literature. The thermography images of various snow types acquired in situ are also discussed; these images give insight into the thermal radiative behaviors of snow covers. Section 3 describes our modeling of snow emissivity, including the concept for constructing a snow emissivity model and the introduction of emissivity equations. Comparison of the model with past in situ measured spectra and an example of the application of the emissivity model to an analysis of thermography images are also presented. Section 4 comprises a brief discussion on the validity and applicability of the emissivity model to other uses such as remote sensing from space. A summary and conclusion of this paper is included in the Section 5. 2. Experimental Knowledge A. Typical Emissivity Spectra Obtained in Past Experimental Studies
As described above, there is still a conflict between snow emissivity simulated by RT calculations and that measured by laboratory and in situ experiments. In this study, we employ the angulardependent spectral emissivity of snow and ice measured by Hori et al. [20] to construct a practical model for simulating the emissive behavior of the snow surface. Figure 1 indicates the in situ measured spectral emissivity of five different snow types: fine dendrite, medium-granular, coarse-grained, sun crust, and bare ice with a smooth specular surface. Each is
Fig. 1. In situ measured spectral directional emissivity of five different snow types (fine dendrite, medium-granular snow, coarse-grained snow, sun crust, and smooth bare ice) at six exitance angles (θ): (a) 0°, (b) 15°, (c) 30°, (d) 45°, (e) 60°, and (f) 75° measured from the surface normal toward the sensor [20] reproduced from the JAXA in situ data archive for GCOM mission [25]. 20 October 2013 / Vol. 52, No. 30 / APPLIED OPTICS
7245
shown for five different exitance angles. Typical snow emissivity spectra have a reststrahlen band (emissivity trough) centered at 13 μm, which occur at surface-scattering maxima typically associated with fundamental molecular vibration bands [26,19]. Spectra also have an emissivity peak at 10.5 μm, at which the single scattering albedo of ice particles reaches a minimum in the 8–14 μm window. As the angle of exitance increases, the emissivity at the surface-scattering maximum decreases. This angular behavior is qualitatively explained by the fact that the fraction of emission that undergoes multiple scattering inside the snow layer decreases toward the surface because of leakage from the surface, and as the exitance angle increases, the field of view at off-nadir angles incorporates a greater contribution from the smaller flux closer to the surface [26]. As snow particles age and become welded and therefore flat, the surface scattering component becomes dominant; therefore the spectra become more similar to the spectrum of a smooth ice surface (the extreme lower limit of ice emissivity), which can be completely simulated with the Fresnel reflectance theory using the complex refractive indices of ice [27]. As indicated in Fig. 1, the increase in exitance angle from 0° to 75° further enhances specular reflectances. These in situ measurements by [20] verified that the expected angular and snow-type dependences of snow emissivity predicted by [19] do in fact exist. B.
Insights from Thermography Images of Snow Surfaces
1. Advantages of the Thermography for Snow Observations The past studies reviewed above have revealed that snow TIR emissivity is dependent on snow particle morphology and the angle of exitance. It should be noted here, however, that past in situ or laboratorymeasured emissive properties were in all cases derived not from individual snow particles such as fine dendrite crystals or crusts, but rather for bulk snow surfaces (i.e., a mixture of ice facets and cavities between ice particles) within the field of view of the spectrometer (e.g., approx. 3–4 cm square at the nadir and over 10 cm square at off-nadir angles for measurements in [20]). Thus, the average snow emissivity for several tens of square centimeters has been evaluated, and as yet no study has captured the emissive properties of individual snow particles. Recent technological advances in developing handheld thermography equipment have enabled us to take thermography images in a real snowfield, so the thermal emissive behavior of individual snow particles can be easily visualized in situ. The typical spectral range of the thermography camera is broad, around the wavelengths 7–13 μm, and thus the sensitivity to variation in snow-type-dependent emission is less than that for a high spectral resolution spectrometer such as FT-IR. However, the thermography is capable of visualizing emissive behaviors of individual ice particles, which is a significant 7246
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advantage of this technology. In addition, the thermography measurements have the potential to rapidly assess the spatial uniformity of snow types in the snow cover. We performed in situ thermography measurements at snowfields in Hokkaido, Japan, in Feb. of 2011, 2012, and 2013 using a portable IR camera [FLIR, SC660, detector: focal plane array (uncooled microbolometer), spectral range: 7.5– 13 μm, IR image resolution: 640 × 480 pixels, weight: 1.7 kg, dimensions: 299 × 144 × 147 mm, temperature range: −40 to 120°C, accuracy of absolute temperature: 2°C, temperature resolution:
Earth Observation Research Center, Japan Aerospace Exploration Agency, 2-1-1, Sengen, Tsukuba, Ibaraki 305-8505, Japan
2
Meteorological Research Institute, 1-1 Nagamine, Tsukuba, Ibaraki 305-0052, Japan
3
Environmental and Energy Resources Research Center, Kitami Institute of Technology, 165 Koen-cho, Kitami 090-8507, Japan
4
Center for Far Eastern Studies, University of Toyama, 3190, Gofuku, Toyama-shi, Toyama 930-8555, Japan *Corresponding author: [email protected] Received 20 May 2013; revised 7 August 2013; accepted 16 September 2013; posted 17 September 2013 (Doc. ID 190829); published 15 October 2013
A model of angular-dependent emissivity spectra of snow and ice in the 8–14 μm atmospheric window is constructed. Past field research revealed that snow emissivity varies depending on snow grain size and the exitance angle. Thermography images acquired in this study further revealed that not only welded snow particles such as sun crust, but also disaggregated particles such as granular snow and dendrite crystals exhibit high reflectivity on their crystal facets, even when the bulk snow surface exhibits blackbody-like behavior as a whole. The observed thermal emissive behaviors of snow particles suggest that emissivity of the bulk snow surface can be expressed by a weighted sum of two emissivity components: those of the specular and blackbody surfaces. Based on this assumption, a semi-empirical emissivity model was constructed; it is expressed by a linear combination of specular and blackbody surfaces’ emissivities with a weighting parameter characterizing the specularity of the bulk surface. Emissivity spectra calculated using the model succeeded in reproducing the past in situ measured directional spectra of various snow types by employing a specific weighting parameter for each snow type. © 2013 Optical Society of America OCIS codes: (280.0280) Remote sensing and sensors; (280.6780) Temperature; (290.0290) Scattering; (290.6815) Thermal emission. http://dx.doi.org/10.1364/AO.52.007243
1. Introduction
Directional emissivity spectra of snow cover at thermal infrared (TIR) wavelengths are essential properties for remote sensing of the earth’s thermal properties, such as snow surface temperature [1–5], cloud discrimination from space [6,7], and for estimating 1559-128X/13/307243-13$15.00/0 © 2013 Optical Society of America
Earth’s long-wave radiation budget on the Greenland and Antarctic ice sheets by broadband radiometer such as the clouds and the Earth’s radiant energy system (CeRES) [8]. The spectra may also be potentially utilized for sensing remote planets in astronomical applications [9]. The spectral emissivities of snow in TIR had been investigated based on theoretical radiative transfer (RT) calculation approaches in addition to laboratory or field measurements. Berger [10] indicated that 20 October 2013 / Vol. 52, No. 30 / APPLIED OPTICS
7243
snow emissivity exhibits weak dependence on snow density by adapting a simple geometric optics approximation to the theoretical scattering calculation. Dozier and Warren [11] simulated the directional-hemispherical reflectance (DHR) of snow, which can be equalized to 1 − ε using Kirchhoff’s law (where ε is the directional emissivity at an exitance angle), based on a more rigorous treatment: Mie scattering for single scattering and the deltaEddington approximation for multiple scattering. This indicated significant angular dependence of the DHR, but little dependence on grain size and density. Most of the algorithms for retrieving snow surface temperatures from space (e.g., [1,12,13]) have been developed based on the simulated emissivity by Dozier and Warren [11]. Rees and James [14] investigated angular variation of the infrared emissivity of an ice surface using a simple TIR sensor for the measurement of brightness temperature averaged between 8 and 14 μm, together with a thermocouple thermometer for measuring the physical temperature of the surface. They found that the broadband emissivity of ice surfaces is in agreement with the Fresnel formula for a plane interface. Subsequently, Rees [15,16] attempted to measure the emissivity of various snow covers including fresh snow, employing the same measurement approach, yet the resulted emissivity seems to vary widely between 0.70 and 0.92, even in the same snow type (fresh snow). This is possibly due to a failure in making accurate physical temperature measurements at the feathery low-density surface of the fresh snow cover. Salisbury et al. [17] conducted laboratory measurements of DHR and found that snow emissivity varies depending on snow types, including frost, fine new snow, and medium- and coarse-granular snow, and the resultant emissivity spectra deviate notably from the simulated ones based on the Mie theory. These measured emissivity spectra are the first practical emissivity spectra of snow and are archived in the ASTER spectral library [18], although obtained only for a near nadir exitance angle (10° from the normal) owing to limitations in the instrument design [17]. The snow emissivity spectra have been used for developing a recent remote-sensing algorithm to retrieve snow surface temperature from data of the moderate resolution imaging spectroradiometer (MODIS) [4]. Wald [19] proposed several theoretical approaches to simulating grain-size-dependent emissivity spectra and succeeded in modeling the spectral DHR (at the near nadir angle) of the disaggregated coarse-granular snow and welded snow obtained by Salisbury et al. [17]. The DHR of disaggregated snow was modeled by employing the diffraction subtraction method in which the diffracted components of the scattered light were subtracted in the RT simulation for a close-packed snow media, while the DHR of the welded snow was expressed as the weighted sum of the RT reflectance and Fresnel reflectance. 7244
APPLIED OPTICS / Vol. 52, No. 30 / 20 October 2013
Wald [19] also pointed out that the angular dependence determined with any RT approach is only applicable for disaggregated snow samples, and the emissivity of welded samples should be partly accounted for using the Fresnel reflectance theory, which itself has a strong angular dependence. Therefore, not only grain size but also cementation effects—thus whether the snow is welded or disaggregated—are considered important factors that determine the directionality of snow emissivity [in general, snow particles are expressed as “an aggregate of ice crystals.” However, in this paper, we use the term “disaggregated snow (or particles)” for expressing snow conditions consisting of fineto coarse-grained snow particles according to the usage in [19] to discriminate them from those consisted of welded film-like ice particles such as in the case of sun crust snow]. Hori et al. [20] conducted in situ measurements of the spectral directional emissivity of snow and ice and revealed that snow emissivity actually varies depending both on snow surface grain size and exitance angle. Their in situ measured emissivities clearly indicated that angular emissivity of snow in TIR is near isotropic for fine disaggregated snow but approaches an anisotropic nature, exhibiting specular reflectance, as snow particles become larger and more welded. Thus the results of [20] further demonstrated the importance of understanding whether snow grains are welded or not when determining the directional emissivity of snow. Hori et al. [20] also showed the close correlation between TIR emissivity and shortwave infrared reflectance measured for various snow types (fine, medium, coarse, and sun crust), which again indicates that TIR emissivity varies depending on the snow grain shape on the upper skin surface. They also discussed the applicability of the spectral contrast in TIR snow emissivity around the wavelengths 11–12 μm in an attempt to discriminate among snow types from space. The applicability of TIR spectral contrast to the monitoring of snow and ice from space was also examined by Tonooka and Watanabe [21] based on nadir angle spectra from the ASTER spectral library. Cheng et al. [22] recently compared several RT models in order to examine their capability in simulating the in situ measured snow TIR emissivity acquired by [20]. They investigated RT models based on the Mie scattering theory, both with and without corrections for the packing effect, which violates the independent scattering approximation assumed in the theory. Their results indicated that several RT models based on the Mie theory with the diffraction subtraction correction proposed by [19] were able to simulate the emissivity only at the nadir angle. However, none of the models succeeded in simulating snow emissivities at off-nadir angles. The snow surface is generally densely packed, but at the same time is sometimes porous and sometimes a specular medium and therefore has complex surface structures from the point of views of the light
scattering. Although, as described above, the emissivity of snow has been modeled by rigorous application of Mie scattering and RT theories, currently no theoretically unified model can simulate the angular dependence of emissivity spectra for different snow and ice types. There remain discrepancies between the simulated and in situ measured emissivities, particularly at wavelengths longer than 10.5 μm, where typical split-window channels of satelliteborne optical sensors are located. These instruments are commonly used for the remote sensing of surface temperatures from space. Approaches involving the Mie scattering and RT models therefore fail to accurately simulate TIR emissive properties of snow particles with wide ranges of sphericity and size. This problem has also been discussed in [17]. For practical applications, such as the remote sensing of snow surface temperature from space, a simple model that is capable of simulating angular and grain-size-dependent TIR emissivity spectra is desired. As Wald [19] proposed, a weighted summation of a RT model (using the diffraction subtraction method) and the Fresnel reflectance could be one potential approach to such a goal, although no such model has yet been presented. Recent advances in handheld thermographic imaging technology has enabled and facilitated observation of in situ TIR emissive behaviors of snow surfaces with high spatial resolution (e.g., [23,24]). We recently carried out thermography measurements coincident with snow pit works in snowfields and gained physical insights into the TIR emissive behaviors of several different snow types. Based on these thermography measurement results in addition to the experimental knowledge obtained in the past studies, we propose, in this study, a semiempirical model of snow surface emissivity to reproduce the in situ measured directional snow emissivity spectra [20]. The model introduces a
weighting parameter that characterizes the specularity of the bulk snow surface and bridges the gap between the specular and blackbody-like behaviors of snow. This approach provides an alternative to inappropriate RT calculations for the densely packed snow medium. Section 2 briefly reviews and summarizes past experimental knowledge from the literature. The thermography images of various snow types acquired in situ are also discussed; these images give insight into the thermal radiative behaviors of snow covers. Section 3 describes our modeling of snow emissivity, including the concept for constructing a snow emissivity model and the introduction of emissivity equations. Comparison of the model with past in situ measured spectra and an example of the application of the emissivity model to an analysis of thermography images are also presented. Section 4 comprises a brief discussion on the validity and applicability of the emissivity model to other uses such as remote sensing from space. A summary and conclusion of this paper is included in the Section 5. 2. Experimental Knowledge A. Typical Emissivity Spectra Obtained in Past Experimental Studies
As described above, there is still a conflict between snow emissivity simulated by RT calculations and that measured by laboratory and in situ experiments. In this study, we employ the angulardependent spectral emissivity of snow and ice measured by Hori et al. [20] to construct a practical model for simulating the emissive behavior of the snow surface. Figure 1 indicates the in situ measured spectral emissivity of five different snow types: fine dendrite, medium-granular, coarse-grained, sun crust, and bare ice with a smooth specular surface. Each is
Fig. 1. In situ measured spectral directional emissivity of five different snow types (fine dendrite, medium-granular snow, coarse-grained snow, sun crust, and smooth bare ice) at six exitance angles (θ): (a) 0°, (b) 15°, (c) 30°, (d) 45°, (e) 60°, and (f) 75° measured from the surface normal toward the sensor [20] reproduced from the JAXA in situ data archive for GCOM mission [25]. 20 October 2013 / Vol. 52, No. 30 / APPLIED OPTICS
7245
shown for five different exitance angles. Typical snow emissivity spectra have a reststrahlen band (emissivity trough) centered at 13 μm, which occur at surface-scattering maxima typically associated with fundamental molecular vibration bands [26,19]. Spectra also have an emissivity peak at 10.5 μm, at which the single scattering albedo of ice particles reaches a minimum in the 8–14 μm window. As the angle of exitance increases, the emissivity at the surface-scattering maximum decreases. This angular behavior is qualitatively explained by the fact that the fraction of emission that undergoes multiple scattering inside the snow layer decreases toward the surface because of leakage from the surface, and as the exitance angle increases, the field of view at off-nadir angles incorporates a greater contribution from the smaller flux closer to the surface [26]. As snow particles age and become welded and therefore flat, the surface scattering component becomes dominant; therefore the spectra become more similar to the spectrum of a smooth ice surface (the extreme lower limit of ice emissivity), which can be completely simulated with the Fresnel reflectance theory using the complex refractive indices of ice [27]. As indicated in Fig. 1, the increase in exitance angle from 0° to 75° further enhances specular reflectances. These in situ measurements by [20] verified that the expected angular and snow-type dependences of snow emissivity predicted by [19] do in fact exist. B.
Insights from Thermography Images of Snow Surfaces
1. Advantages of the Thermography for Snow Observations The past studies reviewed above have revealed that snow TIR emissivity is dependent on snow particle morphology and the angle of exitance. It should be noted here, however, that past in situ or laboratorymeasured emissive properties were in all cases derived not from individual snow particles such as fine dendrite crystals or crusts, but rather for bulk snow surfaces (i.e., a mixture of ice facets and cavities between ice particles) within the field of view of the spectrometer (e.g., approx. 3–4 cm square at the nadir and over 10 cm square at off-nadir angles for measurements in [20]). Thus, the average snow emissivity for several tens of square centimeters has been evaluated, and as yet no study has captured the emissive properties of individual snow particles. Recent technological advances in developing handheld thermography equipment have enabled us to take thermography images in a real snowfield, so the thermal emissive behavior of individual snow particles can be easily visualized in situ. The typical spectral range of the thermography camera is broad, around the wavelengths 7–13 μm, and thus the sensitivity to variation in snow-type-dependent emission is less than that for a high spectral resolution spectrometer such as FT-IR. However, the thermography is capable of visualizing emissive behaviors of individual ice particles, which is a significant 7246
APPLIED OPTICS / Vol. 52, No. 30 / 20 October 2013
advantage of this technology. In addition, the thermography measurements have the potential to rapidly assess the spatial uniformity of snow types in the snow cover. We performed in situ thermography measurements at snowfields in Hokkaido, Japan, in Feb. of 2011, 2012, and 2013 using a portable IR camera [FLIR, SC660, detector: focal plane array (uncooled microbolometer), spectral range: 7.5– 13 μm, IR image resolution: 640 × 480 pixels, weight: 1.7 kg, dimensions: 299 × 144 × 147 mm, temperature range: −40 to 120°C, accuracy of absolute temperature: 2°C, temperature resolution:
