The temporal evolution of snowpacks is important for avalanche forecasts and flood predictions. Especially in complex alpine terrain, such as avalanche starting zones, it is until now difficult to derive continuous and non-destructive information on snow parameters. In our previous work, we already demonstrated the feasibility to quantitatively derive snowpack properties and monitor their evolution in time using an upward-looking ground penetrating radar (upGPR) that was buried underneath the snow. To determine some properties, we still needed additional information such as independently measured snow height. To overcome these limitations, we present two promising methods: (1) We combined the upGPR travel-time information with tomographic GPS signal strength losses. This combination allowed determining liquid water content, snow height and snow water equivalent from beneath the snow cover without using external information. The snow parameters derived by combining upGPR and GPS data are in good agreement with conventional sensors as e.g. laser distance gauges or snow pillows. As the GPS sensors are cheap, they can easily be installed in parallel with upGPR systems. (2) To fully exploit the information content of upGPR data, and thus to at least partially compensate for the lack of information, we applied full-waveform inversion (FWI) techniques. We refined the model of the snowpack by repeated forward modeling the waveforms and updating the model parameters to match it with recorded data. This allowed us to determine the density and the liquid water content for each layer in the snowpack. Both approaches show a high potential for alpine management tasks.