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Effect of Water Saturation on Radiative Transfer

^a Soil Physic, Institute of Terrestrial Ecology ETH Zürich, Switzerland
^b Institut für Computeranwendungen im Bauingenieurwesen, TU Braunschweig

View larger version (48K): [in a new window]   Fig. 1. Definition of the light source used in the beam tracing model. L, width of the light source; , half opening angle of light source; yshift, distance between sample and light source; D, edge length of the sample.

View larger version (18K): [in a new window]   Fig. 2. Schematic of the beam tracing approach for a four particle medium. The incident beam I hits the surface of a solid particle and is forked into a reflected and transmitted beam. Thus, the number of light beams increases quickly. The letter s denotes the scattered light beams leaving the medium, and the letter a the absorbed light beams. The gray intensities of the lines characterize the number of preceding scattering events.

View larger version (10K): [in a new window]   Fig. 3. Real part of the refractive index of water (solid line) and ice (dashed line). Data were taken from Segelstein (1981) for water and from Warren (1984) for ice.

View larger version (11K): [in a new window]   Fig. 4. Imaginary part of the refractive index of water (solid line) and ice (dashed line). Data were taken from Segelstein (1981) for water and from Warren (1984) for ice.

View larger version (72K): [in a new window]   Fig. 5. Examples of the four methods used for arranging the water phase in the two-dimensional particulate structure: (a) added-water-film, (b) two-dimensional pore network, (c) three-dimensional pore network, (d) Lattice–Boltzmann.

View larger version (17K): [in a new window]   Fig. 6. Spectral characteristic of a dry and wet soil sample in the vicinity of an absorption band of water. Symbols are defined in the text.

View larger version (31K): [in a new window]   Fig. 7. Setup for measuring reflectance and transmittance of wet soil samples. The right-hand side depicts a cross- section through the plane of the optical path. Due to the distance of the sample from the opening of the light source, the incident light on the sample is partially diffuse, as indicated by the dashed lines.

View larger version (11K): [in a new window]   Fig. 8. Sample holder to measure a wet soil.

View larger version (13K): [in a new window]   Fig. 9. Measured spectra of the ferric soil material (Bs horizon) illustrating the influence of water saturation on reflectance and transmittance. The particle size was 63 to 71 µm; the sample thickness was 0.5 mm. Reflectance was measured by placing the samples on a white support.

View larger version (14K): [in a new window]   Fig. 10. Dependence of reflectance on water content for the particle size fraction 142 to 224 µm of different soil materials. The reflectance was measured at 1000 nm. Gr refers to the strongly reduced clayey material, Bs to the yellow-reddish sand coated by oxidized Fe hydroxides, and Ae to the bleached quartz sand.

View larger version (17K): [in a new window]   Fig. 11. Measured dependence of reflectance and transmittance on water saturation degree. Data are taken from Fig. 9. The particle size fraction was 224 to 250 µm and the wavelength 900 nm.

View larger version (17K): [in a new window]   Fig. 12. Comparison of our measured data with those published by Weidong et al. (2002) and Whiting et al. (2003). They reported gravimetric and volumetric water contents that we converted to water saturation.

View larger version (15K): [in a new window]   Fig. 13. Computed dependence of reflectance and transmittance on water saturation. The water distribution was calculated with the added water film method.

View larger version (15K): [in a new window]   Fig. 14. Computed dependence of reflectance and transmittance on water saturation. The water distribution was calculated with the pore network model.

View larger version (16K): [in a new window]   Fig. 15. Computed reflectance and transmittance of the cross-section sample at a depth of 52.5 µm from the top of the tomographed sand cube. The cross section had a size of 0.35 by 0.35 mm. For this particular simulation we used collimate light incidence. The wavelength was set to = 900 nm, the refractive index for water to w = 1.33 + i1.06 x 10–6 and for solid to s = 1.8 + i5 x 10–5.

View larger version (14K): [in a new window]   Fig. 16. Reflectance and transmittance computed for seven cross sections of the tomographed sand cube. The cross sections were taken at depths of 140, 210, 280, 350, 420, 490, and 560 µm, respectively.

View larger version (14K): [in a new window]   Fig. 17. Reflectance and transmittance computed for samples with and without bound water. The refractive index of water is w = 1.33 + i4 x 10–8, of ice i = 1.305 + i2 x 10–8, and of soil s = 1.8 + i5 x 10–5. The image size was 6.3 by 1.8 mm. The incident light was collimated.

View larger version (13K): [in a new window]   Fig. 18. Computed dependence of water saturation degree vs. depth of the absorption band a. To calculate the water distribution in the sample we used the two-dimensional pore network model. The refractive index for water at = 500 nm was set to w = 1.33 + i1 x 10–9, and at = 1400 nm to w = 1.32 + i1.38 x 10–4. The refractive index of the soil was set to s = 1.8 + i1 x 10–4. The incident light was collimated.