## 2 Methods and Observations  
High-altitude GPS measurements made at the Haleakala Summit on Maui, Hawaii, have revealed the spectral characteristics of the direct signal and the ocean reflected signal. The altitude of the observation site at 3040 m gave a long line-of-sight view over the ocean to the horizon with multiple paths primarily due to the ocean surface roughness. The chosen high altitude gives a signal only impacted by the ocean wave structures in the reflection zone at several hundred kilometers from the coast. The receiving part of the instrument comprises separate L1 and L2 antennas both oriented with the main gain lobe toward the horizon. The two receiving antennas were directionally centered on the horizon toward south-southwest having an antenna opening angle of 50\({}^{\circ}\). In this way, all ocean reflected measurements only sensed multiple paths due to ocean reflections since no other obstacles were in the field of view of the antennas. The use of directive antennas pointed toward the horizon enabled signal recordings down to the lowest layers of the atmosphere. The instrumentation consisted of a prototype high-precision GNSS receiver, equivalent to the GNSS receiver flying on the EUMETSAT MetOp satellites, linked to an ultra-stable atomic clock [17; 18]. The rubidium reference oscillator gave an improved temporal stability with an Allen deviation of 2 \(\times\) 10\({}^{-12}\). This way timing errors were minimized to only the thermal noise of the instrument. One of the key features of the instrument is the open-loop tracking mode. Since carrier tracking is not reliable, when turbulent conditions drive the measurements, code phase measurements are chosen to capture the signal at a prescribed frequency, named the Doppler model [17; 19]. The open-loop tracking mode combined with high sampling rates of 100-1000 Hz identifies the navigation and atmosphere modulation, clock frequency errors, and errors caused by the Doppler model. It turns out that the Doppler model is independent of atmosphere conditions and the position of the observations on Earth (independent of polar, mid-latitudinal, and equatorial conditions) [17]. However, the Doppler model is a function of the straight-line tangent altitude between the GNSS satellite and the receiver, which in the spectral domain defines the center of the power spectrum. The lowest altitude between this straight-line and the ocean defines the straight-line tangent altitude for the applied time window used in the spectral analysis. The straight-line tangent altitude can be down to \(-\)35 km during grazing angle measurements. The acquisition of rising occultations is much more demanding than acquiring setting occultations measurements because the autonomous search for the GNSS signal is started before it exists in the receiver. Calculations based on the known GNSS satellite orbits, positions, and the applied Doppler model, leads to sets of code phase delays, which continuously are tested against the measured signal power. The code phase delay with the largest signal energy is then chosen and verified. This tracking strategy has a success rate of 97% once the signal-to-noise power density C/N\({}_{0}\) is high enough. Figure 2 shows the measured \(C/N_{0}\) for a rising GNSS satellite. The instrument acquires the signal at 30 dBHz and keeps tracking L1 and L2 phase and code as long as the signal is larger than this value. The receiver normally tracks the L1 (C/A)-code from below the surface defined by the measured signal-to-noise level and straight-line tangent altitude. This continues until the GNSS satellite disappears from within the opening angle of the receiving antenna. Measurements of the L1/L2 P(Y)-code signals are activated above the atmosphere boundary layer. The receiver tracks in parallel both L1 and L2 phase signals using semi-codeless tracking and L1 signals in open-loop mode. In open loop tracking, the signal is down-converted using a numerically controlled oscillator, which generates a frequency given by the onboard Doppler model.