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A model for the remote sensing of snow water equivalent (SWE) using coherent detection of reflected communication satellite “signals of opportunity” is described in this paper. We modeled the snowpack by a layered medium and compute the phase of specularly reflected signals from the snowpack. Phase change of the reflected signal is predicted to be strongly dependent on SWE for dry snow and on snow depth for wet snow. Phase sensitivity to SWE increases with frequency. Reflected signals with frequencies above S-band, however, will experience rapid phase wrapping (360° change) and become more susceptible to fringe washing due to spatial variability of SWE across the footprint. We also examined the impact of snow grain size, snow density, snow layering, ground surface scattering, and incoherent scattering from ice grains embedded in the snowpack, concluding that these factors do not have a substantial impact on the phase-SWE relationship. However, the snow wetness of more than a few percent can make the reflection from air–snow interface dominant, leading to a correlation between phase change and snow depth. To address the path delay due to the ionosphere, dual-frequency observations would have to be considered. Modeling analysis indicates that the coherent change detection is a promising technique for remote sensing of SWE.

We propose a single galaxy gravitational lensing model with a mass density that has a spiral structure. Namely, we extend the arcsine gravitational lens (a truncated singular isothermal elliptical model), adding an additional parameter that controls the amount of spiraling in the structure of the mass density. An important feature of our model is that, even though the mass density is sophisticated, we succeed in integrating the deflection term in closed form using a Gauss hypergeometric function. When the spiraling parameter is set to zero, this reduces to the arcsine lens.