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The physically-based module simulates soil temperature in different soil layers as a result of energy transfer between the atmosphere and soil (or snow) interface.
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Reflected signals from the air-snow interface arrive at the GPS receiver both coherently and incoherently.
This translates to an antenna height of approximately 48.6 cm above the air-snow interface.
This probe was placed at approximately 1 cm below the air-snow interface at the site location.
The radial distance of the reflection point is the antenna height above the air-snow interface divided by the tangent of the elevation angle.
The tilt angle (θt) at the air-snow interface (X′ axis) is along the axis of the receiving antenna's main beam center.
The receiving antenna's height above the tilted air-snow interface (shown in green) is given by h - (t1 + t2), where h is the height of antenna above the frozen-soil surface (m), t1 is the snow layer thickness (m), and t2 is the prairie grass layer thickness (m) as given in [17].
Figure 1 illustrates the total field (the sum of the direct and specularly reflected signals) at the GPS receiving antenna in the local (primed coordinates shown in red) and reference (unprimed coordinates shown in black) frames; the tilt angle (θt) is along the axis of the receiving antenna's main beam center, and the X' axis represents the tilted air-snow interface.
With an antenna height of 48.6 cm above the air-snow interface and an elevation angle of 5°, the first Fresnel zone is calculated to have a major axis length of approximately 26 m and a minor axis length of approximately 2.3 m [10].
We used the permittivities of the dry-snow densities given in Section 2.1 and calculated the reflection coefficients r i for the snow-to-air interface by Eq. (1).
Therefore, the phase of the ith reflection coefficient δ1 approximates either 0° (reflection from interface between more dense and less dense snow or snow to air) or 180° (interface between less dense and more dense snow).
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