## 4 Results and Discussion  
Figure 3 shows the time series of air and soil temperature recorded at different depths over the nine-day measurement period. Air temperature was mostly below \(0\,^{\circ}\mathrm{C}\) and reached a minimum level of \(-10\,^{\circ}\mathrm{C}\) on Day 8 of the measurement campaign. The vertical dynamics of the soil temperature recorded at six depths indicate five freeze-thaw events during the measurement period, which are identified by soil temperatures below \(0\,^{\circ}\mathrm{C}\), as indicated by arrows in Figure 3b. The snow cover fluctuated over the period  
Figure 2: Decagon EC-TM capacitance probes were installed near the footprint of the ground-penetrating radar (GPR) antenna in a trench to monitor the vertical and lateral dynamics of soil temperature and dielectric permittivity (**a**), and the fully-automated off-ground GPR setup with an antenna fixed at 110 cm above the ground (**b**) (after [42]). from 3-10 cm due to precipitation, ablation, sublimation, but also wind drift. Ambient temperature fluctuates around \(0\,^{\circ}\mathrm{C}\). Seasonal snow cover has a cooling effect on the soil surface when the snow cover is comparatively thin and with a high albedo. This phenomena can be observed in the second freeze-thaw event, where soil temperature drops rapidly to \(-1.7\,^{\circ}\mathrm{C}\) in the top 3 cm (Figure 3b). In Figure 3a, the air temperature dropped below \(-5\,^{\circ}\mathrm{C}\) during Days 335-338 of the year, and the snow thickness increased, causing an insulating effect of the snow cover. This insulation effect resulted in a warmer soil surface. As a consequence, soil temperature in the top 3 cm rarely drops to below \(-0.5\,^{\circ}\mathrm{C}\) (Figure 3b). Irrespective of the low air temperatures over the entire course of the experiment, the soil freeze-thaw cycles were most prevalent in the top 4 cm of the soil. In the cold regions, the snowpack persists for a longer time with a thickness in meters and can undergo compaction due to frozen water layer accumulation. Complexities related to the accumulation of frozen water layers in the snow were not observed during measurements. Figure 4a,b presents the raw and processed GPR signal for the measurements carried out with the antenna placed at different heights over a perfect electrical conductor (copper sheet). In total, 17 GPR measurements were performed by lifting the antenna to different heights, with the antenna aperture elevation ranging from 0.08 m-1.2 m. The frequency-dependent GPR measurements were selected from 200-800 MHz, as higher frequencies (>800 MHz) were affected by noise arising due to soil roughness scattering [45]. Furthermore, the signal-to-noise ratio in the higher frequency range is lower due to a higher return loss and lower gain [46]. For convenience, an inverse discrete fast Fourier transform was used to convert the measured frequency domain measurements to time domain signals. In the raw b-scan \(S_{11}(t)\) of Figure 4a, we observe the wave reflections occurring at the antenna feed point and within the antenna between 0 and 8 ns, with reflection from the aperture taking place at the time interval between 10 and 15 ns. In the raw signal b-scan, the second order reflection at the copper sheet occurs between 15 and 20 ns due to the feedback loss of the antenna. In the processed GPR signal \(g_{xx}^{\uparrow}(t)\), the noise in the form of feedback losses and the reflections occurring within the antenna and at the antenna feed point  
Figure 3: (**a**) Time series of air temperature and (**b**) soil temperature recorded at shallow depths (2, 3, 4, 5, 7, 8 cm) over a nine-day period. Arrows indicate the freeze-thaw cycles as the soil temperature dynamics is below 0 \({}^{\circ}\mathrm{C}\). are removed quantitatively by the antenna transfer functions, and only the response of the copper sheet is visible between 5 and 12 ns (Figure 4b).