## 1 Introduction  
The oceans are of major importance for the global climate and life on Earth. In addition to their ecological impact, they play an important role in civil and economic life. Besides knowledge of global and local sea level changes, sea state information is used to gain insights into ocean-atmosphere interaction and is also essential for the planning of coastal protection and shipping safety. The significant wave height (SWH) is a substantial parameter for describing the sea state in a specific region. This statistical value is defined as the mean value of the highest one-third of wave heights observed over a period of time [1]. A standard technique for doing in situ SWH observations is moored wave buoys where the SWH is calculated from vertical acceleration measurements [1]. Such observations can be used to generate SWH time series for a specific location, which are important for calibration and validation of remote sensing techniques like satellite altimetry [2], marine radar [3], or SAR satellites [4]. Another remote sensing technique is GNSS reflectometry with which a surface is probed using the reflected signal. The SWH can be observed with satellite-based [5] and airborne [6] systems, which make use of the characteristics of delay Doppler maps. For more than a decade, the reflections of GNSS signals have been used for the estimation of sea surface parameters from terrestrial receivers [7]. In particular, during the last few years, the interference of the direct and the reflected signal that creates a characteristic oscillation in the signal-to-noise ratio (SNR), which is observed by the majority of GNSS receivers, has been shown to be a useful tool for observing the distance between a GNSS antenna and the reflecting water surface [8]. Other surface properties like snow coverage [9] or soil moisture [10] can be studied with this method as well. The SNR observations also provide the opportunity to make SWH measurements [11]. While a GNSS satellite moves along its orbit, the specular point moves over the water surface, yielding an interference variation with the direct signal, which results in an oscillation of the GNSS SNR observables. The oscillation is attenuated with increasing elevation angles mainly due to the gain pattern of the receiving antenna. Additionally, the attenuation depends on the roughness of the reflecting surface. In Figure 1, SNR observations and the fitted SNR model of two satellites gathered under different wave conditions are presented. The signal gathered at SWH of 1.5 m is more attenuated and more noisy than the one gathered at SWH of 0.3 m. For lower elevation angles, the attenuation due to the antenna gain pattern is commonly low, while an attenuation increase is clearly noticeable when the sea surface is rough. [PERSON] et al. used a short-time Fourier transform of the attenuated SNR oscillation to calculate the cutoff angle, at which the signal coherence is lost [11]. They found a non-linear relation between the cutoff angle and the SWH that was observed in parallel by a radar-based instrument. The estimation of higher SWH using this approach is somewhat problematic since the decrease of the cutoff angle is enhanced due to the non-linear structure of the relation. Especially because the influence of tropospheric refraction and shadowing effects grows with low elevation angles, the quality of the SWH could become low. In this work, we suggest a different approach using the damping coefficient of the attenuated SNR oscillation. Since the attenuation depends exponentially on the damping coefficient, the direct relation between the damping coefficient and the SWH is assumed to show a linear or quasi-linear behavior. We investigated this assumption and its usability using data from two experiments. If the accuracy of the estimated SWH is similar to the accuracy of the wave buoys, these data could be useful for validation purposes. Existing GNSS stations near the coast, on offshore structures, or on ships could be used for such measurements.