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Reflectance Modeling for Real Snow Structures Using a Beam Tracing Model

View Article: PubMed Central

ABSTRACT

It is important to understand reflective properties of snow, for example for remote sensing applications and for modeling of energy balances in snow packs. We present a method with which we can compare reflectance measurements and calculations for the same snow sample structures. Therefore, we first tomograph snow samples to acquire snow structure images (6 × 2 mm). Second, we calculated the sample reflectance by modeling the radiative transfer, using a beam tracing model. This model calculates the biconical reflectance (BR) derived from an arbitrary number of incident beams. The incident beams represent a diffuse light source. We applied our method to four different snow samples: Fresh snow, metamorphosed snow, depth hoar, and wet snow. The results show that (i) the calculated and measured reflectances agree well and (ii) the model produces different biconical reflectances for different snow types. The ratio of the structure to the wavelength is large. We estimated that the size parameter is larger than 50 in all cases we analyzed. Specific surface area of the snow samples explains most of the difference in radiance, but not the different biconical reflectance distributions. The presented method overcomes the limitations of common radiative transfer models which use idealized grain shapes such as spheres, plates, needles and hexagonal particles. With this method we could improve our understanding for changes in biconical reflectance distribution associated with changes in specific surface area.

No MeSH data available.


Calculating the reflectance seen by the sensors fore optic. The half opening angle of our fore optic was ω = 1.5°. The angle of 90°-α corresponds to the viewing angle which is in our setup equal to 68°. The little sketch in the upper right corner illustrates which range of the BR is seen by the fore optic when being far away from the snow sample.
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f3-sensors-08-03482: Calculating the reflectance seen by the sensors fore optic. The half opening angle of our fore optic was ω = 1.5°. The angle of 90°-α corresponds to the viewing angle which is in our setup equal to 68°. The little sketch in the upper right corner illustrates which range of the BR is seen by the fore optic when being far away from the snow sample.

Mentions: The reflected light seen by the sensor is defined by the field-of-view given by the sensors fore-optic. The reflectance is computed from the BR as outlined in Figure 3 [30]. In case the field of view of the sensor is small, the recorded radiance depends strongly on the sensors position and on the shape of the BR. Since we can compute only a small, finite number of incident beams we get a noisy BR which is disadvantageous for a sensor with small field of view. This problem can be reduced when having a smoother BR. To get a smoother BR we simultaneously apply three different approaches: (i) For each sample we run the model several times and calculate the mean BR of the single model runs. Repeatedly running the model with a given number of incident beams (with a randomized distribution) is equivalent with running the model once with a multiple number of incident beams. (ii) For each angle of the BR we calculate the mean value from the reflectance at the angles with the same negative and positive angle. We are allowed to do this because the incidence of the axial symmetric Ulbricht sphere is normal, thus the BR is axial symmetric with respect to the normal of the sample surface. (iii) For further smoothing of the BR we applied a moving average.


Reflectance Modeling for Real Snow Structures Using a Beam Tracing Model
Calculating the reflectance seen by the sensors fore optic. The half opening angle of our fore optic was ω = 1.5°. The angle of 90°-α corresponds to the viewing angle which is in our setup equal to 68°. The little sketch in the upper right corner illustrates which range of the BR is seen by the fore optic when being far away from the snow sample.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3675556&req=5

f3-sensors-08-03482: Calculating the reflectance seen by the sensors fore optic. The half opening angle of our fore optic was ω = 1.5°. The angle of 90°-α corresponds to the viewing angle which is in our setup equal to 68°. The little sketch in the upper right corner illustrates which range of the BR is seen by the fore optic when being far away from the snow sample.
Mentions: The reflected light seen by the sensor is defined by the field-of-view given by the sensors fore-optic. The reflectance is computed from the BR as outlined in Figure 3 [30]. In case the field of view of the sensor is small, the recorded radiance depends strongly on the sensors position and on the shape of the BR. Since we can compute only a small, finite number of incident beams we get a noisy BR which is disadvantageous for a sensor with small field of view. This problem can be reduced when having a smoother BR. To get a smoother BR we simultaneously apply three different approaches: (i) For each sample we run the model several times and calculate the mean BR of the single model runs. Repeatedly running the model with a given number of incident beams (with a randomized distribution) is equivalent with running the model once with a multiple number of incident beams. (ii) For each angle of the BR we calculate the mean value from the reflectance at the angles with the same negative and positive angle. We are allowed to do this because the incidence of the axial symmetric Ulbricht sphere is normal, thus the BR is axial symmetric with respect to the normal of the sample surface. (iii) For further smoothing of the BR we applied a moving average.

View Article: PubMed Central

ABSTRACT

It is important to understand reflective properties of snow, for example for remote sensing applications and for modeling of energy balances in snow packs. We present a method with which we can compare reflectance measurements and calculations for the same snow sample structures. Therefore, we first tomograph snow samples to acquire snow structure images (6 × 2 mm). Second, we calculated the sample reflectance by modeling the radiative transfer, using a beam tracing model. This model calculates the biconical reflectance (BR) derived from an arbitrary number of incident beams. The incident beams represent a diffuse light source. We applied our method to four different snow samples: Fresh snow, metamorphosed snow, depth hoar, and wet snow. The results show that (i) the calculated and measured reflectances agree well and (ii) the model produces different biconical reflectances for different snow types. The ratio of the structure to the wavelength is large. We estimated that the size parameter is larger than 50 in all cases we analyzed. Specific surface area of the snow samples explains most of the difference in radiance, but not the different biconical reflectance distributions. The presented method overcomes the limitations of common radiative transfer models which use idealized grain shapes such as spheres, plates, needles and hexagonal particles. With this method we could improve our understanding for changes in biconical reflectance distribution associated with changes in specific surface area.

No MeSH data available.