- Email: [email protected]
Bidirectional-reflectance measurements for various snow crystal morphologies
Cold Regions Science and Technology 124 (2016) 110–117
Contents lists available at ScienceDirect
Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions
Bidirectional-reflectance measurements for various snow crystal morphologies Brad Stanton a,⁎, Daniel Miller b, Edward Adams a, Joseph A. Shaw c a b c
Department of Civil Engineering, Montana State University, 205 Cobleigh Hall, Bozeman, MT 59717-3900, United States Mechanical and Industrial Engineering, Montana State University, 220 Roberts Hall, Bozeman, MT 59717-3800, United States Electrical and Computer Engineering, Montana State University, 610 Cobleigh Hall, Bozeman, MT 59717-3780, United States
a r t i c l e
i n f o
Article history: Received 6 November 2014 Received in revised form 2 December 2015 Accepted 31 December 2015 Available online 21 January 2016 Keywords: Surface hoar Rounded grains Snow reflectance BRDF Albedo BRF
a b s t r a c t An understanding of snow optical properties is vital to accurately quantifying the effect of snow cover on the Earth's radiative energy balance. Central to these models is the need for accurate bidirectional reflectance data for various snow surface types. However, few studies in this area exist and none focus specifically on surface hoar—a well-known surface crystal type often responsible for avalanches. In this study, it is postulated that the bidirectional reflectance distribution of the snow's surface before and after surface hoar growth will be predictably and quantifiably different when viewed in the visible wavelengths. To test this hypothesis, a methodology for reliably growing surface hoar in a lab setting was developed. Temporal changes in crystal habit were documented using computed tomography and visible microscopic imaging. A spectrometer was used to measure bidirectional-reflectance factors (BRF) both before and after surface hoar growth. Analysis of the results revealed three primary conclusions: 1) Surface hoar growth is accompanied by a departure from Lambertian scattering. The effect is more apparent the larger the surface hoar grains. 2) The incident lighting and viewing geometries at which maximum and minimum BRF values occur are difficult to discern. 3) In the transition from rounded grains to surface hoar, spectral albedo (as calculated by averaging the BRF over a hemispheric solid angle at 510 nm) decreases slightly. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Advances in satellite remote sensing capabilities have introduced the need for accurate multi-angle reflectance studies at a high temporal and spatial resolution for the plethora of snow crystal morphologies in existence (Bruegge et al., 2000). To address this need, this study focuses on the bidirectional reflectance of two distinct snow surface types: rounded grains and surface hoar. Multi-angle studies focused on capturing crystal habit effects often report results in terms of a bidirectional reflection distribution function (BRDF) or a bidirectional-reflectance factor (BRF). As the name implies, a BRDF “describes the scattering of a parallel beam of incident light from one direction in the hemisphere into another direction in the hemisphere” (Bruegge et al., 2000; Nicodemus et al., 1977). BRDF is the ratio of radiance L (W m−2 sr−1) exiting the surface in a single direction to the incident irradiance E (W m−2) from a single direction, BRDF ¼
dLr ðθi ; ϕi ; θr ; ϕr Þ −1 sr : dEi ðθi ; ϕi Þ
⁎ Corresponding author. E-mail address: [email protected] (B. Stanton).
http://dx.doi.org/10.1016/j.coldregions.2015.12.011 0165-232X/© 2016 Elsevier B.V. All rights reserved.
ð1Þ
This ratio is a function of reflectance azimuth (θr) and zenith (ϕr) angles, as well as incident zenith (θi) and azimuth (ϕi) angles and, finally, wavelength (λ) (Fig. 1). Note that, in this study, the azimuth is defined relative to the incident light such that ϕi = 180°. Hemispherically integrating the BRDF across all azimuth and zenith angles yields the albedo (α), Z α ðθi Þ ¼
2π Z 0
2 π
0
f r ðθi ; ϕi ; θr ; ϕr Þ cos θr sinθr dθr dϕr ;
ð2Þ
the ratio of all exiting light to all incident light across the entire hemisphere and across all wavelengths. Spectral albedo is albedo at a particular wavelength. Because it is a ratio of infinitesimal properties, the BRDF cannot be measured directly (Schaepman-Strub et al., 2006). In studies where reflection is measured directly, results are reported in terms of a BRF value, a unitless ratio of power Φr,snow reflected from the snow surface to the power Φr,ideal reflected from a commercially available Lambertian reference standard such as Spectralon,
BRF ¼
Φr;snow ðθi ; ϕi ; θr ; ϕr Þ : Φr;ideal ðθi ; ϕi Þ
ð3Þ
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117
Fig. 1. Reflectance azimuth (θ_r) and zenith (ϕ_r) angle as well as incident zenith (θ_i) and azimuth (ϕ_i) angle. In this study, 0 azimuth is defined relative to the incident light such that ϕ_i = 180°.
Like BRDF, averaging the BRF over a hemispheric solid angle produces the albedo, which expresses a ratio of the reflected and incident irradiances. After field observations made by eye suggested a difference in the reflective properties of rounded grains and surface hoar, it was hypothesized that microstructural changes due to the deposition of faceted surface hoar crystals at the snow's surface will alter the visible bidirectional reflectance as compared to rounded grains. Specifically, it was postulated that the BRF of the snow's surface before and after surface hoar growth would be predictably and quantifiably different. To test this hypothesis, a methodology for growing surface hoar in a lab setting was developed. Both microscopic and computed tomography (CT) images were used to document snow grain habit before and after surface hoar growth. Once various surface hoar morphologies were predictably and reliably grown in the lab, protocols for optical testing were developed and carried out on two distinct crystal morphologies: rounded grains and plate-like surface hoar—i.e. surface hoar dominate by crystallographic a-axis growth (Nakaya, 1954). The resulting CT and microscopic images as well as BRF values for both grain types are presented. 2. Background In practice, field studies using the sun as the illumination source have both a direct component and a diffuse component that arises from atmospheric scattering. These studies often report a hemispherical–directional reflectance factor (HDRF) to indicate that the result
111
includes incident light scattered by the atmosphere. HDRF values, which depend on daily atmospheric conditions, are of limited use in comparison to BRDF. Leroux et al. (1998) performed ground HDRF (later converted to BRDF) measurements in the near and short-wave infrared, out to 1650 nm, for clustered rounded grains, faceted and fine particles, and faceted crystal/surface hoar. Though not specified in the discussion of their measured results, observation of their reflectance data suggests that, at 1650 nm, the BRDF of rounded grains varies significantly less than the BRDF of surface hoar. Similarly, Aoki et al. (2000) measured HDRF data in the 350 to 2500 nm range for new snow, granular snow, and faceted crystals but does not indicate whether the faceted crystals were surface hoar. The study concludes that BRDF showed significant anisotropy in the NIR, but was generally insensitive to grain shape in the visible range. Painter and Dozier (2004) measured HDRF values for fine-grained, decomposed dendritic forms and medium sized clustered grains after a melt–freeze cycle. They noticed the fine-grain faceted snow “exhibited a local backscattering peak at the view zenith near the solar zenith angle, whereas (the HDRF) for medium grain, clustered snow did not have a local backscattering peak.” Further, an increase in grain radius from 80 μm to 280 μm was accompanied by a decrease in the HDRF for all wavelengths. Li and Zhou (2004), performed HDRF measurements (and later translated the results into BRF values) in the 350–1050 nm range on rounded, sintered, composite coarse grains overlain by broken fine particles and solid, faceted, coarse particles overlain by fine grains. They looked at large solar zenith angles (65° and 85°). The results showed that these snow types had a strong forward-scattering peak under large solar incidence angles. Similarly, Bourgeois et al. (2006) performed HDRF (350–1050 nm) studies in Greenland on wind-broken small grained snow and a surface covered with rime causing a higher surface roughness. They found a wide range of HDRF values (from 0.6 to 13) depending on the solar zenith angle. It varied from nearly isotropic at nadir illumination angles to highly forward-scattering at solar zenith angle of 85°. Additionally, surfaces covered with rime exhibited less forward-scattering than smooth surfaces. Dumont et al. (2010), using a methodology similar to the one used here, looked at the directional dependence of 4 different grains (dendritic fragments, clustered rounded grains, melt freeze crusted grains, new wet snow) over a wide range of lighting and viewing geometries. They concluded that both grain size and shape have an effect on the reflectance distribution (primarily in the NIR and longer wavelengths) but that it is difficult to predict. Further, they were able to distinguish a recognizable reflectance pattern for elongated or faceted shapes. Specifically, they noted darkening at viewer grazing angles in situations of near
Fig. 2. Left: Goniometer and spectrometer configuration. Right: Sun angle θi was varied by tilting the snow surface with respect to the fixed light source.
112
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117
nadir illumination, as well as strong forward-scatter peak in the NIR wavelengths for all grain types. However, Dumont's study did not specifically address surface hoar. Several distinct themes can be seen in these studies: 1) snow in the UV/VIS appears far more Lambertian than snow observed at longer wavelengths; 2) albedo decreases with increasing grain size; 3) snow tends to demonstrate a strong forward-scatter peak at large incident light angles; 4) grain habit plays a role but is not well understood. Vollmer and Shaw (2013) as well as several prominent works by S. G. Warren provide theoretical rationale for these observations (Warren, 1982, 1984; Warren and Wiscombe, 1980a, 1980b). In addition to
new findings, the above well-known, effects are confirmed in the data presented here and will be discussed briefly in a subsequent section. 3. Methodology To assure the necessary control of the meteorological conditions affecting both the surface hoar crystal habit as well as the lighting conditions, all experiments in this study were conducted in a walk-in environmental chamber at Montana State University's Subzero Science and Engineering Research Facility (SSERF). This chamber allowed control of meteorological conditions such that surface hoar could be
Fig. 3. From top to bottom respectively: Select CT and microscopic images for tests 1, 2, and 3. The sampled images were taken from within ~15 cm of the optically tested snow. Optical testing was performed on the initial rounded grains and the final, fully developed, surface hoar. CT scan images are ~400 mm2. All microscopic images are taken on a 2 mm grid. Note: in test 1, a fan malfunction resulted in minimal surface hoar growth in the location of the CT sample container. The microscopic images in test 1 are representative of the optically tested surface hoar.
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117
grown on a 30 × 30-cm snow surface. In addition, a built-in solar simulator located near the snow surface eliminated excess atmospheric scatter, allowing the reporting of directional (as opposed to hemispherical– directional) characteristics. A single test consisted of recording BRF values from 42 different lighting/viewing geometries (21 forward scatter and 21 backscatter), both before and after surface hoar growth. In addition, optical microscopic images and CT scans were used to document crystal type before and after surface hoar growth. In total, three of these tests were conducted to verify repeatability, resulting in three sets of optical data on
rounded grains and three sets of optical data on plate-like (a-axis dominant) surface hoar (Nakaya, 1954). 3.1. Optics procedure In the SSERF cold chamber, a metal-halide solar simulation lamp provided a spectral distribution comparable to the sun for wavelengths in the range of 280–2480 nm. Since the light source was built into the ceiling and could not be moved, sun geometry was controlled by tilting the snow surface with respect to the light (Fig. 2). This study used
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
BRF
BRF
Test 1 Rounded Grains 1
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1 500
600
700
800
900
1000
1100
1200
1300
0 400
1400
Test 1 Surface Hoar
0.5
0.4
0 400
500
600
700
Wavelength (nm)
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6 BRF
BRF
1
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1 700
800
900
1000
1100
1200
1300
0 400
1400
500
600
700
Wavelength (nm)
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
700
800
900
1000
Wavelength (nm)
1300
1400
800
900
1000
1100
1200
1300
1400
1200
1300
1400
0.5
0.4
600
1200
Test 3 Surface Hoar 1
BRF
BRF
Test 3 Rounded Grains
500
1100
Wavelength (nm)
1
0 400
1000
0.5
0.4
600
900
Test 2 Surface Hoar
Test 2 Rounded Grains
500
800
Wavelength (nm)
1
0 400
113
1100
1200
1300
1400
0 400
500
600
700
800
900
1000
1100
Wavelength (nm)
Fig. 4. Test 1 top; test 2 middle; test 3 bottom. BRF as a function of wavelength. Each line represents a different lighting and viewing geometry. Initial rounded form (left) and surface hoar (right). Subsequent discussion focuses on BRF values at 510 nm. Note the spreading of the BRF values along the ordinate axis in the visible range when comparing the rounded grains to the surface hoar.
114
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117
incident zenith angles of 0° , 15°, 30°, and 45° as well as the common convention of defining a solar incident plane such that the sun was always at an incident azimuth angle of 180°. A Stellarnet Inc. Black Comet-HR spectrometer with a holographic concave grating (200– 1100 nm) supported by a custom, hemispherical gantry was used to capture forward reflectance data from viewer zenith (θr) angles of 30° , 45° , 60°, and 63° and viewer azimuth (ϕr) angles of 0° , 45°, and 315° respectively; the same, symmetrical, viewer geometries were used in the back scatter direction. The accompanying supplemental online data set provides both the geometries and the resulting BRF values. Finally, in order to average out local surface variability (Nicodemus et al., 1977), the probe was positioned to capture reflected light from a minimum snow surface area of 11.5 cm2. At each geometry, spectral data were collected from the snow surface and then normalized with spectral data collected from a Labsphere™ Spectralon reference standard (https://www.labsphere.com/products/ reflectance-targets/calibrated-diffuse-reflectance-targets/). According to Labsphere, at 510 nm and observer zenith angles less than 8°, the Spectralon has reflectance values within ~ 99.5% of an idealized Lambertian surface in the visible wavelengths. All snow radiance values were normalized by Spectralon radiance values from the same lighting Φ
ðθ ;ϕ ;θ ;ϕ Þ
i i r r Þ. and viewing geometries, that is ð Φr;snow r;ideal ðθi ;ϕ ;θr ;ϕ Þ i
r
3.2. Documenting crystal habit To ensure accurate, high quality documentation of surface crystal type, as well as to document changes in microstructural parameters that might affect optical results, computed tomography (CT) images were taken at various times during growth as well as before and after each optical test. To facilitate in-situ CT scans of growing surface hoar, a cylindrical sample holder with a cross-sectional area of 706 mm2 and a height of 51 mm was buried with its top edge flush with the snow surface. An ASTM #8 soil sieve (mesh size: 2.36 mm) was used to both fill the sample container and sift a uniform, level layer of rounded grains onto the snow surface. Before, during, and after each experiment, the sample holder was carefully removed, scanned using a SkyScan 1173 CT scanner at a resolution of 14.8 μm, and then returned to its original position and orientation. The CT sample container represents only a small portion of the total surface area on which the surface hoar was grown. In order to account for variability of crystal habit across the entire 30 × 30-cm snow surface, microscopic still photographs of disaggregate grains were taken at locations away from the CT sample. Images were taken at magnifications ranging from 6 × to 50 × to document general grain shape across many grains and to provide a detailed view of individual grains. 4. Results and discussion The following section presents CT and microscopic images of the snow surface before and after surface hoar growth, summary plots of BRF vs wavelength for all 42 viewing and lighting geometries, BRF range data, and BRF standard deviation data. The analysis primarily reveals surface hoar to be less Lambertian than rounded grains, but suggests that there is no discernable pattern to the angular distribution of the reflected light. Please refer to CRST supplemental online materials for the raw data collected from the optical test—namely BRF values as a function of lighting and viewing angle for 510 nm as well as polar plots. 4.1. Computed tomography and microscopic images Fig. 3 provides the three-dimensional CT scans and photographic imaging used in all three tests to document crystal morphology. All CT scans were taken at a resolution of 14.8 μm and all microscopic images are taken on a 2 mm grid. The development of surface hoar is evident in
the sequence of images. The initial image (left side) and final image (right side) are representative of the rounded grains and final surface hoar on which optical tests were performed. Note that in test 1, the sample container for the CT scans experienced less growth than the optically tested snow surface a ~15 cm away, due to a frozen fan. In this case, microscopic images are more representative of the snow that was optically tested.
4.2. Plots of BRF vs wavelength Fig. 4 depicts representative BRF values for all 42 sampled geometries for each of the three tests (each line represents a different lighting and viewing configuration). No legend is provided, as it would be impractical for 42 values; instead these data are meant to reveal general trends. Note that perfect Lambertian scatter would be represented on the plots as BRF value of 1 across all wavelengths. In subsequent discussion, BRF values at 510 nm (green light) are used as a representative value for the scattering behavior of light in the visible wavelengths. Future study will examine additional wavelengths. Polar plots showing BRF as a function of azimuth and zenith scatter angles are presented in the Cold Regions Science and Technology online supplemental material. The plots in Fig. 4 reveal surface hoar to be a less Lambertian scattering surface than rounded grains. From the initial form (left plots) to the surface hoar form (right plots), there is a distinct spreading of the data along the ordinate axis (particularly pronounced in tests 2 and 3). That is, when the data set is looked at as a whole, a greater range of BRF values are seen for surface hoar than for rounded grains. Quantitatively, at 510 nm, there is a 10%, 70%, and 170% increase in the range (max minus min) of BRF values in the transition between rounded grains and surface hoar in each of the three tests respectively (Table 1). This indicates that surface hoar reflectance is significantly less Lambertian than rounded grains. Table 2 further quantifies this effect, providing the percent change in standard deviation between the rounded grains and surface hoar for each test. Again, one can see evidence that the surface hoar is less Lambertian in the increase in standard deviation of the BRF between the two snow habits. Two questions arise: is it possible to distinguish the effects of grain shape and grain size in this data and is there a discernible pattern in the geometry of surface hoar scatter? The former question is addressed in the following discussion. Subsequent sections address the geometric variation in BRF. Both grain size and shape changed from the initial rounded form to the final surface hoar. Current theory suggests that grain size plays a primary role in single scattering albedo, while crystal habit has little effect in this area but greatly impacts the phase function (Xie et al., 2006). In this light, BRF changes in the data are first driven by grain size changes and second by crystal habit. It is difficult to tease apart these two effects with the above data set. However, the effects of grain size should be less pronounced in the visible than in the NIR suggesting that changes in
Table 1 The range (max minus min) of BRF values (at 510 nm) for each test and the percent change in range between rounded grains and surface hoar. Note that surface hoar tends to have a wider range of BRF values than rounded grains, suggesting a departure from Lambertian scatter with surface hoar development. Test#
BRF range
% Increase in BRF range
1 (Rounded grains) 1 (Surface hoar) 2 (Rounded grains) 2 (Surface hoar) 3 (Rounded grains) 3 (Surface hoar)
0.064 0.072 0.070 0.116 0.052 0.142
10% 70% 170%
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117 Table 2 Percent change in standard deviation of BRF values at 510 nm from rounded grains to surface hoar in each of the three tests. Test # 1 RG 1 SH 2 RG 2 SH 3 RG 3 SH
Std. dev. 0.013 0.019 0.018 0.031 0.014 0.028
% Change 50% 70% 100%
surface roughness due to the development of surface hoar are likely responsible for part of the BRF changes seen in the data. With each subsequent test, the surface hoar appears to be less and less Lambertian. That is, the spreading along the ordinate axis becomes progressively more obvious from tests 1 to 3. Likewise, this is apparent in the sharp contrast between percent change values in both Table 1 (10% in test 1 and 170% in test 3), and in Table 2 (50% in test 1 and 100% in test 3). Observation of microscopic images in Fig. 3 reveal that the optically tested surface hoar in test 1 was significantly smaller (~2 mm) than in tests 2 (~5 mm) and 3 (~6–7 mm). This suggests another important result: as surface hoar grain size increases, the scatter becomes less and less Lambertian. In addition, optical grain size plays a role in predicting the spectral albedo. Consistent with the idea that optically large grains absorb more light than smaller grains, the data shows a slight decrease (≤2.9%) in spectral albedo (as calculated by averaging all 42 BRF values at 510 nm) between rounded grains and surface hoar (Table 3). This effect is quite small compared to the considerable change in the BRF range values. To be consistent with the observed increase in surface hoar size between each of the three tests, it is expected in Table 3 that test 1 would have the smallest change in spectral albedo in the transition between rounded grains and surface hoar, test three the largest, and test 2 somewhere in between. However, this trend is not apparent. It is speculated that averaging more than 42 BRF values, from even more observer geometries would help bring these numbers into alignment with known theory. Nevertheless, the trend toward lower spectral albedo with surface hoar growth is apparent. In summary, the spectral albedo is relatively unchanged by the growth of surface hoar demonstrating a slight decrease due to increase in grain size. This change in grain size does not account for the general increase in the range and standard deviation that occurs in the transition from rounded grains to surface hoar. More likely this is due to grain shape and indicates that the bright points get brighter and the dark areas get darker when viewing surface hoar as compared to rounded grains. That is, as surface hoar develops, the reflected light departs from Lambertian scatter. Further, this distinction is more pronounced the larger the surface hoar grains. Having distinguished the role of grain size in this effect, the question now becomes: do these bright points and dark points correspond to predictable viewing/incident geometry?
Table 3 Spectral albedo (as calculated by averaging all 42 BRF values) for tests 1, 2, and 3 and percent change from rounded grains to surface hoar at 510 nm. Note that the data indicates a slight decrease in albedo. Test # 1 RG 1 SH 2 RG 2 SH 3 RG 3 SH
Albedo 0.892 0.867 0.873 0.872 0.884 0.870
Table 4 Maximum BRF for each test as well as corresponding BRF value and percent change between initial form and final form. A positive sign on the % change indicates an increase in BRF. A sun azimuth angle of 180° was used in all tests. Test # 1 RG 1 SH 2 RG 2 SH 3 RG 3 SH
Obs azm
Sun zen
Sun azm
BRF
% Change
30 60 60 30 45 60
0 0 180 135 225 45
0 45 30 0 15 15
180 180 180 180 180 180
0.927 0.892 0.907 0.933 0.911 0.949
−3.9% 2.8% 4.0%
Tables 4 and 5 provide insight into the directional nature of the snow's reflectance at 510 nm. Most importantly, it reveals no discernible geometric pattern in BRF values. With the notable exception of test 1 in Table 4, which demonstrates a decrease in maximum BRF (negative percent change) between rounded grains and surface hoar, the effect of increased BRF spread can be seen in the percent change values. That is, after surface hoar growth the bright points (maximum BRF values) are brighter and the dark points (minimum BRF values) are darker. The expectation in test 1 has no ready explanation, except to again note that the surface hoar grain size in test 1 was smaller than in tests 2 and 3. Predicting the geometry of the maximum and minimum BRF values is difficult with the above data. Established theory suggests, for both surface hoar and rounded grains, one should find the maximum and minimum BRF in the forward and backward scatter directions respectively (Warren, 1982). Additionally, one should find a darkening trend at grazing observation angles when the light source is directly overhead (Dumont et al., 2010). The back/forward scatter trend is not readily apparent in Table 4 where only the surface hoar in test 1 demonstrates a maximum value in the forward scatter direction. In Table 5, three of the six minimum BRF values are in the backscatter direction. However, it should be noted that, due to the limitations of the gantry supporting the spectrometer, it was not possible to measure all angles. It is likely that the true maximum and minimum values were not captured in the 42 geometries tested with each snow sample. The trend toward darkening at grazing observation angle is more apparent. As observed in Table 6, at nadir sun angle, BRF values are lower for observation zenith angles near the horizon (θr = 60°) than for observation angles near nadir (θr = 30°). Concisely, with increasing observer zenith angle, there is a general trend toward darkening at grazing observation angles when the light source is straight overhead. In short, while it seems clear from Table 4 that surface hour's maximum and minimum BRF values will be pronouncedly larger/smaller respectively for surface hoar than for rounded grains, it is difficult to predict where the angular distribution of the maximum or minimum BRF values will occur from the data. In other words, an observer inspecting a field of surface hoar will likely find it brighter or darker at certain viewing angles as compared to rounded snow (which appears
Table 5 Minimum BRF for each test as well as corresponding BRF value and percent change between initial form and final form. A negative sign on the % change indicates a decrease in BRF. A sun azimuth angle of 180° was used in all tests. Test #
−2.9%
1 RG 1 SH 2 RG 2 SH 3 RG 3 SH
−1.6%
Obs zen
4.3. Distribution of scattered light geometry
% Change
−0.1%
115
Obs zen
Obs azm
Sun zen
Sun azm
BRF
% Change
60 60 60 60 63 60
180 0 0 0 225 225
45 0 45 30 45 0
180 180 180 180 180 180
0.863 0.820 0.837 0.817 0.858 0.807
−5.2% −2.4% −6.4%
Light ↓ Dark
Light ↓ Dark
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117 Light ↓ Dark
116
more Lambertian), predicting the geometry of the bright and dark points is not possible with the above data.
BRF
0.890 0.880 0.840
θr
0.905 0.904 0.871
30 45 60
BRF θr
30 45 60
BRF
0.885 0.875 0.839
θr
30 45 60
Three primary conclusions suggest an optical signature unique to surface hoar. As surface hoar develops, albedo decreases. This is consistent with theory, which suggests that albedo decreases with increasing optical grain size. In addition, as surface hoar develops, the reflectance from the snow surface becomes less and less Lambertian. Further, as surface hoar grain size (as measured by the longest axis) increases, the departure from Lambertian scatter becomes more pronounced. However, the data suggests that the viewer/incident geometry at which point the BRF value is maximum or minimum is difficult to predict. That is, while an observer of a field of surface hoar will notice locations at which the snow appears brighter and other locations at which the snow appears darker, the exact positioning of those light and dark points cannot be predicted. Further, for every dark point observed there will be a corresponding light point somewhere else in the hemisphere; therefore, albedo changes very little.
θi
0 0 0
Test 3: Surface hoar
θi
0 0 0
Test 2: Surface hoar
θi
0 0 0
Test 1: Surface hoar
Acknowledgments This work was supported by The Department of Civil Engineering at Montana State University, National Aeronautics and Space Administration (NASA) through the Montana Space Grant Consortium (NASA Grant Number M254-10-W1749), and the Murdock Charitable Trust (2010158:JVZ:5/19/2011). Reviewing a paper can be a thankless task, but the excellent feedback and guidance provided on this paper should not be overlooked. On behalf of all the authors, I would like to extend my gratitude to the reviewers for the extensive and thoughtful comments that helped mold this work. Thank you.
No pattern
Light ↓ Dark
No pattern
Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.coldregions.2015.12.011.
0.886 0.889 0.880 30 45 60 0 0 0
BRF θr θi
Test 3: Rounded grains
BRF
0.876 0.881 0.877
θr
30 45 60
θi
0 0 0
Test 2: Rounded grains
BRF θr
30 45 60
θi
0 0 0
0.904 0.898 0.886
References
Test 1: Rounded grains
Table 6 BRF values for nadir illumination angle θi showing darking at grazing observation angles (i.e larger values of θr). Initial forms (rounded grains) are shown on the left while finial forms (surface hoar) is shown on the right.
5. Conclusion
Aoki, T., Aoki, T., Fukabori, M., Hachikubo, A., Tachibana, Y., Nishio, F., 2000. Effects of snow physical parameters an spectral albedo and bidirectional reflectance of snow surface. J. Geophys. Res. 105, 10219–10236. Bourgeois, C.S., Calanca, P., Ohmura, A., 2006. A field study of the hemispherical directional reflectance factor and spectral albedo of dry snow. J. Geophys. Res. 111, 1–13. Bruegge, C.J., Martonchik, J.V., Strahler, A.H., 2000. A review of reflectance nomenclature used in remote sensing. Remote Sens. Rev. 19, 9–20. Dumont, M., Brissaud, O., Picard, G., Schmitt, B., Gallet, J.C., Arnaud, Y., 2010. Highaccuracy measurements of snow bidirectional reflectance distribution function at visible and NIR wavelengths—comparison with modeling results. Atmos. Chem. Phys. 10, 2507–2520. Labsphere | A Halma Company. (n.d.). Retrieved June 26, 2015, from https://www. labsphere.com/ Leroux, C., Deuze, j.L., Goloub, P., Sergent, C., Fily, M., 1998. Ground measurements of the polarized bidirectional reflectance of snow in the near-infrared spectrum domain: comparison with model results. J. Geophys. Res. 103, 19721–19731. Li, S., Zhou, X., 2004. Modeling and measuring the spectral bidirectional-reflectance factor of snow-covered sea ice: An intercomparison study. Hydrol. Process. 18, 3559–3581. Nakaya, U., 1954. Snow Crystals: Natural and Artificial. Harvard University Press, Cambridge, Mass. Nicodemus, F.E., Richmond, J.C., Hsia, J.J., Ginsberg, I.W., Limperis, T., 1977. Geometrical considerations and nomenclature for reflectance. NBS Monograph 160. National Bureau of Standards, US Department of Commerce, Washington, D.C. Painter, T.H., Dozier, J., 2004. Measurements of the hemispherical–directional reflectance of snow at fine spectral and angular resolution. J. Geophys. Res. 109 (D18), D18115. http://dx.doi.org/10.1029/2003JD004458. Schaepman-Strub, G., Schaepman, M.E., Painter, T.H., Dangel, S., Martonchik, J.V., 2006. Reflectance quantities in optical remote sensing—definitions and case studies. Remote Sens. Environ. 103, 27–42. Vollmer, M., Shaw, J.A., 2013. Brilliant colours from a white snow cover. Phys. Educ. 48, 322–331. http://dx.doi.org/10.1088/0031-9120/48/3/322.
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117 Warren, S.G., Wiscombe, W.J., 1980a. A model for the spectral albedo of snow I, snow containing atmospheric aerosols. J. Atmos. Sci. 37, 2712–2733. Warren, S.G., Wiscombe, W.J., 1980b. A model for the spectral albedo of snow II, snow containing atmospheric aerosols. J. Atmos. Sci. 37, 111–144. Warren, S.G., 1982. Optical properties of snow. Rev. Geophys. Space Phys. 20, 67–89.
117
Warren, S.G., 1984. Optical constants of ice from the ultraviolet to the microwave. Appl. Opt. 23, 1206–1225. Xie, Y., Yang, B.-C., Gao, G.W. Kattawar, Mishchenko, M.I., 2006. Effect of ice crystal shape and effective size on snow bidirectional reflectance. J. Quant. Spectrosc. 100, 457–469. http://dx.doi.org/10.1016/j.jqsrt.2005.11.056.
Contents lists available at ScienceDirect
Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions
Bidirectional-reflectance measurements for various snow crystal morphologies Brad Stanton a,⁎, Daniel Miller b, Edward Adams a, Joseph A. Shaw c a b c
Department of Civil Engineering, Montana State University, 205 Cobleigh Hall, Bozeman, MT 59717-3900, United States Mechanical and Industrial Engineering, Montana State University, 220 Roberts Hall, Bozeman, MT 59717-3800, United States Electrical and Computer Engineering, Montana State University, 610 Cobleigh Hall, Bozeman, MT 59717-3780, United States
a r t i c l e
i n f o
Article history: Received 6 November 2014 Received in revised form 2 December 2015 Accepted 31 December 2015 Available online 21 January 2016 Keywords: Surface hoar Rounded grains Snow reflectance BRDF Albedo BRF
a b s t r a c t An understanding of snow optical properties is vital to accurately quantifying the effect of snow cover on the Earth's radiative energy balance. Central to these models is the need for accurate bidirectional reflectance data for various snow surface types. However, few studies in this area exist and none focus specifically on surface hoar—a well-known surface crystal type often responsible for avalanches. In this study, it is postulated that the bidirectional reflectance distribution of the snow's surface before and after surface hoar growth will be predictably and quantifiably different when viewed in the visible wavelengths. To test this hypothesis, a methodology for reliably growing surface hoar in a lab setting was developed. Temporal changes in crystal habit were documented using computed tomography and visible microscopic imaging. A spectrometer was used to measure bidirectional-reflectance factors (BRF) both before and after surface hoar growth. Analysis of the results revealed three primary conclusions: 1) Surface hoar growth is accompanied by a departure from Lambertian scattering. The effect is more apparent the larger the surface hoar grains. 2) The incident lighting and viewing geometries at which maximum and minimum BRF values occur are difficult to discern. 3) In the transition from rounded grains to surface hoar, spectral albedo (as calculated by averaging the BRF over a hemispheric solid angle at 510 nm) decreases slightly. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Advances in satellite remote sensing capabilities have introduced the need for accurate multi-angle reflectance studies at a high temporal and spatial resolution for the plethora of snow crystal morphologies in existence (Bruegge et al., 2000). To address this need, this study focuses on the bidirectional reflectance of two distinct snow surface types: rounded grains and surface hoar. Multi-angle studies focused on capturing crystal habit effects often report results in terms of a bidirectional reflection distribution function (BRDF) or a bidirectional-reflectance factor (BRF). As the name implies, a BRDF “describes the scattering of a parallel beam of incident light from one direction in the hemisphere into another direction in the hemisphere” (Bruegge et al., 2000; Nicodemus et al., 1977). BRDF is the ratio of radiance L (W m−2 sr−1) exiting the surface in a single direction to the incident irradiance E (W m−2) from a single direction, BRDF ¼
dLr ðθi ; ϕi ; θr ; ϕr Þ −1 sr : dEi ðθi ; ϕi Þ
⁎ Corresponding author. E-mail address: [email protected] (B. Stanton).
http://dx.doi.org/10.1016/j.coldregions.2015.12.011 0165-232X/© 2016 Elsevier B.V. All rights reserved.
ð1Þ
This ratio is a function of reflectance azimuth (θr) and zenith (ϕr) angles, as well as incident zenith (θi) and azimuth (ϕi) angles and, finally, wavelength (λ) (Fig. 1). Note that, in this study, the azimuth is defined relative to the incident light such that ϕi = 180°. Hemispherically integrating the BRDF across all azimuth and zenith angles yields the albedo (α), Z α ðθi Þ ¼
2π Z 0
2 π
0
f r ðθi ; ϕi ; θr ; ϕr Þ cos θr sinθr dθr dϕr ;
ð2Þ
the ratio of all exiting light to all incident light across the entire hemisphere and across all wavelengths. Spectral albedo is albedo at a particular wavelength. Because it is a ratio of infinitesimal properties, the BRDF cannot be measured directly (Schaepman-Strub et al., 2006). In studies where reflection is measured directly, results are reported in terms of a BRF value, a unitless ratio of power Φr,snow reflected from the snow surface to the power Φr,ideal reflected from a commercially available Lambertian reference standard such as Spectralon,
BRF ¼
Φr;snow ðθi ; ϕi ; θr ; ϕr Þ : Φr;ideal ðθi ; ϕi Þ
ð3Þ
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117
Fig. 1. Reflectance azimuth (θ_r) and zenith (ϕ_r) angle as well as incident zenith (θ_i) and azimuth (ϕ_i) angle. In this study, 0 azimuth is defined relative to the incident light such that ϕ_i = 180°.
Like BRDF, averaging the BRF over a hemispheric solid angle produces the albedo, which expresses a ratio of the reflected and incident irradiances. After field observations made by eye suggested a difference in the reflective properties of rounded grains and surface hoar, it was hypothesized that microstructural changes due to the deposition of faceted surface hoar crystals at the snow's surface will alter the visible bidirectional reflectance as compared to rounded grains. Specifically, it was postulated that the BRF of the snow's surface before and after surface hoar growth would be predictably and quantifiably different. To test this hypothesis, a methodology for growing surface hoar in a lab setting was developed. Both microscopic and computed tomography (CT) images were used to document snow grain habit before and after surface hoar growth. Once various surface hoar morphologies were predictably and reliably grown in the lab, protocols for optical testing were developed and carried out on two distinct crystal morphologies: rounded grains and plate-like surface hoar—i.e. surface hoar dominate by crystallographic a-axis growth (Nakaya, 1954). The resulting CT and microscopic images as well as BRF values for both grain types are presented. 2. Background In practice, field studies using the sun as the illumination source have both a direct component and a diffuse component that arises from atmospheric scattering. These studies often report a hemispherical–directional reflectance factor (HDRF) to indicate that the result
111
includes incident light scattered by the atmosphere. HDRF values, which depend on daily atmospheric conditions, are of limited use in comparison to BRDF. Leroux et al. (1998) performed ground HDRF (later converted to BRDF) measurements in the near and short-wave infrared, out to 1650 nm, for clustered rounded grains, faceted and fine particles, and faceted crystal/surface hoar. Though not specified in the discussion of their measured results, observation of their reflectance data suggests that, at 1650 nm, the BRDF of rounded grains varies significantly less than the BRDF of surface hoar. Similarly, Aoki et al. (2000) measured HDRF data in the 350 to 2500 nm range for new snow, granular snow, and faceted crystals but does not indicate whether the faceted crystals were surface hoar. The study concludes that BRDF showed significant anisotropy in the NIR, but was generally insensitive to grain shape in the visible range. Painter and Dozier (2004) measured HDRF values for fine-grained, decomposed dendritic forms and medium sized clustered grains after a melt–freeze cycle. They noticed the fine-grain faceted snow “exhibited a local backscattering peak at the view zenith near the solar zenith angle, whereas (the HDRF) for medium grain, clustered snow did not have a local backscattering peak.” Further, an increase in grain radius from 80 μm to 280 μm was accompanied by a decrease in the HDRF for all wavelengths. Li and Zhou (2004), performed HDRF measurements (and later translated the results into BRF values) in the 350–1050 nm range on rounded, sintered, composite coarse grains overlain by broken fine particles and solid, faceted, coarse particles overlain by fine grains. They looked at large solar zenith angles (65° and 85°). The results showed that these snow types had a strong forward-scattering peak under large solar incidence angles. Similarly, Bourgeois et al. (2006) performed HDRF (350–1050 nm) studies in Greenland on wind-broken small grained snow and a surface covered with rime causing a higher surface roughness. They found a wide range of HDRF values (from 0.6 to 13) depending on the solar zenith angle. It varied from nearly isotropic at nadir illumination angles to highly forward-scattering at solar zenith angle of 85°. Additionally, surfaces covered with rime exhibited less forward-scattering than smooth surfaces. Dumont et al. (2010), using a methodology similar to the one used here, looked at the directional dependence of 4 different grains (dendritic fragments, clustered rounded grains, melt freeze crusted grains, new wet snow) over a wide range of lighting and viewing geometries. They concluded that both grain size and shape have an effect on the reflectance distribution (primarily in the NIR and longer wavelengths) but that it is difficult to predict. Further, they were able to distinguish a recognizable reflectance pattern for elongated or faceted shapes. Specifically, they noted darkening at viewer grazing angles in situations of near
Fig. 2. Left: Goniometer and spectrometer configuration. Right: Sun angle θi was varied by tilting the snow surface with respect to the fixed light source.
112
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117
nadir illumination, as well as strong forward-scatter peak in the NIR wavelengths for all grain types. However, Dumont's study did not specifically address surface hoar. Several distinct themes can be seen in these studies: 1) snow in the UV/VIS appears far more Lambertian than snow observed at longer wavelengths; 2) albedo decreases with increasing grain size; 3) snow tends to demonstrate a strong forward-scatter peak at large incident light angles; 4) grain habit plays a role but is not well understood. Vollmer and Shaw (2013) as well as several prominent works by S. G. Warren provide theoretical rationale for these observations (Warren, 1982, 1984; Warren and Wiscombe, 1980a, 1980b). In addition to
new findings, the above well-known, effects are confirmed in the data presented here and will be discussed briefly in a subsequent section. 3. Methodology To assure the necessary control of the meteorological conditions affecting both the surface hoar crystal habit as well as the lighting conditions, all experiments in this study were conducted in a walk-in environmental chamber at Montana State University's Subzero Science and Engineering Research Facility (SSERF). This chamber allowed control of meteorological conditions such that surface hoar could be
Fig. 3. From top to bottom respectively: Select CT and microscopic images for tests 1, 2, and 3. The sampled images were taken from within ~15 cm of the optically tested snow. Optical testing was performed on the initial rounded grains and the final, fully developed, surface hoar. CT scan images are ~400 mm2. All microscopic images are taken on a 2 mm grid. Note: in test 1, a fan malfunction resulted in minimal surface hoar growth in the location of the CT sample container. The microscopic images in test 1 are representative of the optically tested surface hoar.
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117
grown on a 30 × 30-cm snow surface. In addition, a built-in solar simulator located near the snow surface eliminated excess atmospheric scatter, allowing the reporting of directional (as opposed to hemispherical– directional) characteristics. A single test consisted of recording BRF values from 42 different lighting/viewing geometries (21 forward scatter and 21 backscatter), both before and after surface hoar growth. In addition, optical microscopic images and CT scans were used to document crystal type before and after surface hoar growth. In total, three of these tests were conducted to verify repeatability, resulting in three sets of optical data on
rounded grains and three sets of optical data on plate-like (a-axis dominant) surface hoar (Nakaya, 1954). 3.1. Optics procedure In the SSERF cold chamber, a metal-halide solar simulation lamp provided a spectral distribution comparable to the sun for wavelengths in the range of 280–2480 nm. Since the light source was built into the ceiling and could not be moved, sun geometry was controlled by tilting the snow surface with respect to the light (Fig. 2). This study used
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
BRF
BRF
Test 1 Rounded Grains 1
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1 500
600
700
800
900
1000
1100
1200
1300
0 400
1400
Test 1 Surface Hoar
0.5
0.4
0 400
500
600
700
Wavelength (nm)
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6 BRF
BRF
1
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1 700
800
900
1000
1100
1200
1300
0 400
1400
500
600
700
Wavelength (nm)
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
700
800
900
1000
Wavelength (nm)
1300
1400
800
900
1000
1100
1200
1300
1400
1200
1300
1400
0.5
0.4
600
1200
Test 3 Surface Hoar 1
BRF
BRF
Test 3 Rounded Grains
500
1100
Wavelength (nm)
1
0 400
1000
0.5
0.4
600
900
Test 2 Surface Hoar
Test 2 Rounded Grains
500
800
Wavelength (nm)
1
0 400
113
1100
1200
1300
1400
0 400
500
600
700
800
900
1000
1100
Wavelength (nm)
Fig. 4. Test 1 top; test 2 middle; test 3 bottom. BRF as a function of wavelength. Each line represents a different lighting and viewing geometry. Initial rounded form (left) and surface hoar (right). Subsequent discussion focuses on BRF values at 510 nm. Note the spreading of the BRF values along the ordinate axis in the visible range when comparing the rounded grains to the surface hoar.
114
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117
incident zenith angles of 0° , 15°, 30°, and 45° as well as the common convention of defining a solar incident plane such that the sun was always at an incident azimuth angle of 180°. A Stellarnet Inc. Black Comet-HR spectrometer with a holographic concave grating (200– 1100 nm) supported by a custom, hemispherical gantry was used to capture forward reflectance data from viewer zenith (θr) angles of 30° , 45° , 60°, and 63° and viewer azimuth (ϕr) angles of 0° , 45°, and 315° respectively; the same, symmetrical, viewer geometries were used in the back scatter direction. The accompanying supplemental online data set provides both the geometries and the resulting BRF values. Finally, in order to average out local surface variability (Nicodemus et al., 1977), the probe was positioned to capture reflected light from a minimum snow surface area of 11.5 cm2. At each geometry, spectral data were collected from the snow surface and then normalized with spectral data collected from a Labsphere™ Spectralon reference standard (https://www.labsphere.com/products/ reflectance-targets/calibrated-diffuse-reflectance-targets/). According to Labsphere, at 510 nm and observer zenith angles less than 8°, the Spectralon has reflectance values within ~ 99.5% of an idealized Lambertian surface in the visible wavelengths. All snow radiance values were normalized by Spectralon radiance values from the same lighting Φ
ðθ ;ϕ ;θ ;ϕ Þ
i i r r Þ. and viewing geometries, that is ð Φr;snow r;ideal ðθi ;ϕ ;θr ;ϕ Þ i
r
3.2. Documenting crystal habit To ensure accurate, high quality documentation of surface crystal type, as well as to document changes in microstructural parameters that might affect optical results, computed tomography (CT) images were taken at various times during growth as well as before and after each optical test. To facilitate in-situ CT scans of growing surface hoar, a cylindrical sample holder with a cross-sectional area of 706 mm2 and a height of 51 mm was buried with its top edge flush with the snow surface. An ASTM #8 soil sieve (mesh size: 2.36 mm) was used to both fill the sample container and sift a uniform, level layer of rounded grains onto the snow surface. Before, during, and after each experiment, the sample holder was carefully removed, scanned using a SkyScan 1173 CT scanner at a resolution of 14.8 μm, and then returned to its original position and orientation. The CT sample container represents only a small portion of the total surface area on which the surface hoar was grown. In order to account for variability of crystal habit across the entire 30 × 30-cm snow surface, microscopic still photographs of disaggregate grains were taken at locations away from the CT sample. Images were taken at magnifications ranging from 6 × to 50 × to document general grain shape across many grains and to provide a detailed view of individual grains. 4. Results and discussion The following section presents CT and microscopic images of the snow surface before and after surface hoar growth, summary plots of BRF vs wavelength for all 42 viewing and lighting geometries, BRF range data, and BRF standard deviation data. The analysis primarily reveals surface hoar to be less Lambertian than rounded grains, but suggests that there is no discernable pattern to the angular distribution of the reflected light. Please refer to CRST supplemental online materials for the raw data collected from the optical test—namely BRF values as a function of lighting and viewing angle for 510 nm as well as polar plots. 4.1. Computed tomography and microscopic images Fig. 3 provides the three-dimensional CT scans and photographic imaging used in all three tests to document crystal morphology. All CT scans were taken at a resolution of 14.8 μm and all microscopic images are taken on a 2 mm grid. The development of surface hoar is evident in
the sequence of images. The initial image (left side) and final image (right side) are representative of the rounded grains and final surface hoar on which optical tests were performed. Note that in test 1, the sample container for the CT scans experienced less growth than the optically tested snow surface a ~15 cm away, due to a frozen fan. In this case, microscopic images are more representative of the snow that was optically tested.
4.2. Plots of BRF vs wavelength Fig. 4 depicts representative BRF values for all 42 sampled geometries for each of the three tests (each line represents a different lighting and viewing configuration). No legend is provided, as it would be impractical for 42 values; instead these data are meant to reveal general trends. Note that perfect Lambertian scatter would be represented on the plots as BRF value of 1 across all wavelengths. In subsequent discussion, BRF values at 510 nm (green light) are used as a representative value for the scattering behavior of light in the visible wavelengths. Future study will examine additional wavelengths. Polar plots showing BRF as a function of azimuth and zenith scatter angles are presented in the Cold Regions Science and Technology online supplemental material. The plots in Fig. 4 reveal surface hoar to be a less Lambertian scattering surface than rounded grains. From the initial form (left plots) to the surface hoar form (right plots), there is a distinct spreading of the data along the ordinate axis (particularly pronounced in tests 2 and 3). That is, when the data set is looked at as a whole, a greater range of BRF values are seen for surface hoar than for rounded grains. Quantitatively, at 510 nm, there is a 10%, 70%, and 170% increase in the range (max minus min) of BRF values in the transition between rounded grains and surface hoar in each of the three tests respectively (Table 1). This indicates that surface hoar reflectance is significantly less Lambertian than rounded grains. Table 2 further quantifies this effect, providing the percent change in standard deviation between the rounded grains and surface hoar for each test. Again, one can see evidence that the surface hoar is less Lambertian in the increase in standard deviation of the BRF between the two snow habits. Two questions arise: is it possible to distinguish the effects of grain shape and grain size in this data and is there a discernible pattern in the geometry of surface hoar scatter? The former question is addressed in the following discussion. Subsequent sections address the geometric variation in BRF. Both grain size and shape changed from the initial rounded form to the final surface hoar. Current theory suggests that grain size plays a primary role in single scattering albedo, while crystal habit has little effect in this area but greatly impacts the phase function (Xie et al., 2006). In this light, BRF changes in the data are first driven by grain size changes and second by crystal habit. It is difficult to tease apart these two effects with the above data set. However, the effects of grain size should be less pronounced in the visible than in the NIR suggesting that changes in
Table 1 The range (max minus min) of BRF values (at 510 nm) for each test and the percent change in range between rounded grains and surface hoar. Note that surface hoar tends to have a wider range of BRF values than rounded grains, suggesting a departure from Lambertian scatter with surface hoar development. Test#
BRF range
% Increase in BRF range
1 (Rounded grains) 1 (Surface hoar) 2 (Rounded grains) 2 (Surface hoar) 3 (Rounded grains) 3 (Surface hoar)
0.064 0.072 0.070 0.116 0.052 0.142
10% 70% 170%
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117 Table 2 Percent change in standard deviation of BRF values at 510 nm from rounded grains to surface hoar in each of the three tests. Test # 1 RG 1 SH 2 RG 2 SH 3 RG 3 SH
Std. dev. 0.013 0.019 0.018 0.031 0.014 0.028
% Change 50% 70% 100%
surface roughness due to the development of surface hoar are likely responsible for part of the BRF changes seen in the data. With each subsequent test, the surface hoar appears to be less and less Lambertian. That is, the spreading along the ordinate axis becomes progressively more obvious from tests 1 to 3. Likewise, this is apparent in the sharp contrast between percent change values in both Table 1 (10% in test 1 and 170% in test 3), and in Table 2 (50% in test 1 and 100% in test 3). Observation of microscopic images in Fig. 3 reveal that the optically tested surface hoar in test 1 was significantly smaller (~2 mm) than in tests 2 (~5 mm) and 3 (~6–7 mm). This suggests another important result: as surface hoar grain size increases, the scatter becomes less and less Lambertian. In addition, optical grain size plays a role in predicting the spectral albedo. Consistent with the idea that optically large grains absorb more light than smaller grains, the data shows a slight decrease (≤2.9%) in spectral albedo (as calculated by averaging all 42 BRF values at 510 nm) between rounded grains and surface hoar (Table 3). This effect is quite small compared to the considerable change in the BRF range values. To be consistent with the observed increase in surface hoar size between each of the three tests, it is expected in Table 3 that test 1 would have the smallest change in spectral albedo in the transition between rounded grains and surface hoar, test three the largest, and test 2 somewhere in between. However, this trend is not apparent. It is speculated that averaging more than 42 BRF values, from even more observer geometries would help bring these numbers into alignment with known theory. Nevertheless, the trend toward lower spectral albedo with surface hoar growth is apparent. In summary, the spectral albedo is relatively unchanged by the growth of surface hoar demonstrating a slight decrease due to increase in grain size. This change in grain size does not account for the general increase in the range and standard deviation that occurs in the transition from rounded grains to surface hoar. More likely this is due to grain shape and indicates that the bright points get brighter and the dark areas get darker when viewing surface hoar as compared to rounded grains. That is, as surface hoar develops, the reflected light departs from Lambertian scatter. Further, this distinction is more pronounced the larger the surface hoar grains. Having distinguished the role of grain size in this effect, the question now becomes: do these bright points and dark points correspond to predictable viewing/incident geometry?
Table 3 Spectral albedo (as calculated by averaging all 42 BRF values) for tests 1, 2, and 3 and percent change from rounded grains to surface hoar at 510 nm. Note that the data indicates a slight decrease in albedo. Test # 1 RG 1 SH 2 RG 2 SH 3 RG 3 SH
Albedo 0.892 0.867 0.873 0.872 0.884 0.870
Table 4 Maximum BRF for each test as well as corresponding BRF value and percent change between initial form and final form. A positive sign on the % change indicates an increase in BRF. A sun azimuth angle of 180° was used in all tests. Test # 1 RG 1 SH 2 RG 2 SH 3 RG 3 SH
Obs azm
Sun zen
Sun azm
BRF
% Change
30 60 60 30 45 60
0 0 180 135 225 45
0 45 30 0 15 15
180 180 180 180 180 180
0.927 0.892 0.907 0.933 0.911 0.949
−3.9% 2.8% 4.0%
Tables 4 and 5 provide insight into the directional nature of the snow's reflectance at 510 nm. Most importantly, it reveals no discernible geometric pattern in BRF values. With the notable exception of test 1 in Table 4, which demonstrates a decrease in maximum BRF (negative percent change) between rounded grains and surface hoar, the effect of increased BRF spread can be seen in the percent change values. That is, after surface hoar growth the bright points (maximum BRF values) are brighter and the dark points (minimum BRF values) are darker. The expectation in test 1 has no ready explanation, except to again note that the surface hoar grain size in test 1 was smaller than in tests 2 and 3. Predicting the geometry of the maximum and minimum BRF values is difficult with the above data. Established theory suggests, for both surface hoar and rounded grains, one should find the maximum and minimum BRF in the forward and backward scatter directions respectively (Warren, 1982). Additionally, one should find a darkening trend at grazing observation angles when the light source is directly overhead (Dumont et al., 2010). The back/forward scatter trend is not readily apparent in Table 4 where only the surface hoar in test 1 demonstrates a maximum value in the forward scatter direction. In Table 5, three of the six minimum BRF values are in the backscatter direction. However, it should be noted that, due to the limitations of the gantry supporting the spectrometer, it was not possible to measure all angles. It is likely that the true maximum and minimum values were not captured in the 42 geometries tested with each snow sample. The trend toward darkening at grazing observation angle is more apparent. As observed in Table 6, at nadir sun angle, BRF values are lower for observation zenith angles near the horizon (θr = 60°) than for observation angles near nadir (θr = 30°). Concisely, with increasing observer zenith angle, there is a general trend toward darkening at grazing observation angles when the light source is straight overhead. In short, while it seems clear from Table 4 that surface hour's maximum and minimum BRF values will be pronouncedly larger/smaller respectively for surface hoar than for rounded grains, it is difficult to predict where the angular distribution of the maximum or minimum BRF values will occur from the data. In other words, an observer inspecting a field of surface hoar will likely find it brighter or darker at certain viewing angles as compared to rounded snow (which appears
Table 5 Minimum BRF for each test as well as corresponding BRF value and percent change between initial form and final form. A negative sign on the % change indicates a decrease in BRF. A sun azimuth angle of 180° was used in all tests. Test #
−2.9%
1 RG 1 SH 2 RG 2 SH 3 RG 3 SH
−1.6%
Obs zen
4.3. Distribution of scattered light geometry
% Change
−0.1%
115
Obs zen
Obs azm
Sun zen
Sun azm
BRF
% Change
60 60 60 60 63 60
180 0 0 0 225 225
45 0 45 30 45 0
180 180 180 180 180 180
0.863 0.820 0.837 0.817 0.858 0.807
−5.2% −2.4% −6.4%
Light ↓ Dark
Light ↓ Dark
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117 Light ↓ Dark
116
more Lambertian), predicting the geometry of the bright and dark points is not possible with the above data.
BRF
0.890 0.880 0.840
θr
0.905 0.904 0.871
30 45 60
BRF θr
30 45 60
BRF
0.885 0.875 0.839
θr
30 45 60
Three primary conclusions suggest an optical signature unique to surface hoar. As surface hoar develops, albedo decreases. This is consistent with theory, which suggests that albedo decreases with increasing optical grain size. In addition, as surface hoar develops, the reflectance from the snow surface becomes less and less Lambertian. Further, as surface hoar grain size (as measured by the longest axis) increases, the departure from Lambertian scatter becomes more pronounced. However, the data suggests that the viewer/incident geometry at which point the BRF value is maximum or minimum is difficult to predict. That is, while an observer of a field of surface hoar will notice locations at which the snow appears brighter and other locations at which the snow appears darker, the exact positioning of those light and dark points cannot be predicted. Further, for every dark point observed there will be a corresponding light point somewhere else in the hemisphere; therefore, albedo changes very little.
θi
0 0 0
Test 3: Surface hoar
θi
0 0 0
Test 2: Surface hoar
θi
0 0 0
Test 1: Surface hoar
Acknowledgments This work was supported by The Department of Civil Engineering at Montana State University, National Aeronautics and Space Administration (NASA) through the Montana Space Grant Consortium (NASA Grant Number M254-10-W1749), and the Murdock Charitable Trust (2010158:JVZ:5/19/2011). Reviewing a paper can be a thankless task, but the excellent feedback and guidance provided on this paper should not be overlooked. On behalf of all the authors, I would like to extend my gratitude to the reviewers for the extensive and thoughtful comments that helped mold this work. Thank you.
No pattern
Light ↓ Dark
No pattern
Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.coldregions.2015.12.011.
0.886 0.889 0.880 30 45 60 0 0 0
BRF θr θi
Test 3: Rounded grains
BRF
0.876 0.881 0.877
θr
30 45 60
θi
0 0 0
Test 2: Rounded grains
BRF θr
30 45 60
θi
0 0 0
0.904 0.898 0.886
References
Test 1: Rounded grains
Table 6 BRF values for nadir illumination angle θi showing darking at grazing observation angles (i.e larger values of θr). Initial forms (rounded grains) are shown on the left while finial forms (surface hoar) is shown on the right.
5. Conclusion
Aoki, T., Aoki, T., Fukabori, M., Hachikubo, A., Tachibana, Y., Nishio, F., 2000. Effects of snow physical parameters an spectral albedo and bidirectional reflectance of snow surface. J. Geophys. Res. 105, 10219–10236. Bourgeois, C.S., Calanca, P., Ohmura, A., 2006. A field study of the hemispherical directional reflectance factor and spectral albedo of dry snow. J. Geophys. Res. 111, 1–13. Bruegge, C.J., Martonchik, J.V., Strahler, A.H., 2000. A review of reflectance nomenclature used in remote sensing. Remote Sens. Rev. 19, 9–20. Dumont, M., Brissaud, O., Picard, G., Schmitt, B., Gallet, J.C., Arnaud, Y., 2010. Highaccuracy measurements of snow bidirectional reflectance distribution function at visible and NIR wavelengths—comparison with modeling results. Atmos. Chem. Phys. 10, 2507–2520. Labsphere | A Halma Company. (n.d.). Retrieved June 26, 2015, from https://www. labsphere.com/ Leroux, C., Deuze, j.L., Goloub, P., Sergent, C., Fily, M., 1998. Ground measurements of the polarized bidirectional reflectance of snow in the near-infrared spectrum domain: comparison with model results. J. Geophys. Res. 103, 19721–19731. Li, S., Zhou, X., 2004. Modeling and measuring the spectral bidirectional-reflectance factor of snow-covered sea ice: An intercomparison study. Hydrol. Process. 18, 3559–3581. Nakaya, U., 1954. Snow Crystals: Natural and Artificial. Harvard University Press, Cambridge, Mass. Nicodemus, F.E., Richmond, J.C., Hsia, J.J., Ginsberg, I.W., Limperis, T., 1977. Geometrical considerations and nomenclature for reflectance. NBS Monograph 160. National Bureau of Standards, US Department of Commerce, Washington, D.C. Painter, T.H., Dozier, J., 2004. Measurements of the hemispherical–directional reflectance of snow at fine spectral and angular resolution. J. Geophys. Res. 109 (D18), D18115. http://dx.doi.org/10.1029/2003JD004458. Schaepman-Strub, G., Schaepman, M.E., Painter, T.H., Dangel, S., Martonchik, J.V., 2006. Reflectance quantities in optical remote sensing—definitions and case studies. Remote Sens. Environ. 103, 27–42. Vollmer, M., Shaw, J.A., 2013. Brilliant colours from a white snow cover. Phys. Educ. 48, 322–331. http://dx.doi.org/10.1088/0031-9120/48/3/322.
B. Stanton et al. / Cold Regions Science and Technology 124 (2016) 110–117 Warren, S.G., Wiscombe, W.J., 1980a. A model for the spectral albedo of snow I, snow containing atmospheric aerosols. J. Atmos. Sci. 37, 2712–2733. Warren, S.G., Wiscombe, W.J., 1980b. A model for the spectral albedo of snow II, snow containing atmospheric aerosols. J. Atmos. Sci. 37, 111–144. Warren, S.G., 1982. Optical properties of snow. Rev. Geophys. Space Phys. 20, 67–89.
117
Warren, S.G., 1984. Optical constants of ice from the ultraviolet to the microwave. Appl. Opt. 23, 1206–1225. Xie, Y., Yang, B.-C., Gao, G.W. Kattawar, Mishchenko, M.I., 2006. Effect of ice crystal shape and effective size on snow bidirectional reflectance. J. Quant. Spectrosc. 100, 457–469. http://dx.doi.org/10.1016/j.jqsrt.2005.11.056.