Inverse Modeling of GPS Multipath for Snow Depth Estimation—Part I: Formulation and Simulations

Snowpacks provide reservoirs of freshwater. The amount stored and how fast it is released by melting are vital information for both scientists and water supply managers. GPS multipath reflectometry (GPS-MR) is a new technique that can be used to measure snow depth. Signal-to-noise ratio data collected by GPS instruments exhibit peaks and troughs as coherent direct and reflected signals go in and out of phase. These interference fringes are used to retrieve the unknown land surface characteristics. In this two-part contribution, a forward/inverse approach is offered for GPS-MR of snow depth. Part I starts with the physically based forward model utilized to simulate the coupling of the surface and antenna responses. A statistically rigorous inverse model is presented and employed to retrieve parameter corrections responsible for observation residuals. The unknown snow characteristics are parameterized, the observation/parameter sensitivity is illustrated, the inversion performance is assessed in terms of its precision and its accuracy, and the dependence of model results on the satellite direction is quantified. The latter serves to indicate the sensing footprint of the reflection.