# Shipborne GNSS-Determined Sea Surface Heights Using Geoid Model and Realistic Dynamic Topography
## 1 Introduction  
Sea surface height (SSH), an imperative parameter for understanding the marine environment, sees an increasing demand for accurate and reliable estimates from coastal and marine applications (e.g., engineering, navigation, research). Historically, tide gauge (TG) stations, some as old as a few centuries, have provided continuous sea level information, which is now essential, for instance, to climate studies [1; 2; 3]. Although modern TGs also allow a high accuracy (centimeter-level) and sampling rate (up to seconds), the distribution of TG stations is generally sparse and restricted to land-bound coastal locations. Since the TG-determined sea level information represents only a limited spatial domain, complementary data from space geodetic techniques are invaluable. Satellite altimetry (SA) records now span over three decades, densely covering most of the Earth's marine areas with a reasonable quantification of SSH [4; 5; 6]. However, the SA method is often limited by its spatial and temporal resolution characteristics and reliability, which tend to diminish in the coastal zone due to approximations in atmospheric, sea state, and geophysical corrections and waveform distortions caused by coastal inhomogeneities [7; 8; 9]. Approaches based on GNSS (global navigation satellite system) positioning have, thus, become favored for bridging the gap between TG and SA measurements in the coastal zone and complementing SA data offshore. These methods are also appropriate for the validation and calibration of SA-based SSH, in addition to commonly used TG-based methods. It has been demonstrated that relatively accurate SSH can be acquired by shipborne GNSS measurements [10; 11; 12], airborne laser scanning surveys [13; 14; 15], and other alternatives, such as GNSS-equipped buoys [16; 17] and uncrewed sea vessels [18; 19]. While airborne laser scanning surveys currently require expensive equipment and a survey aircraft, and buoys or uncrewed vessels may first demand watercraft development, the shipborne GNSS approach appears most convenient. Some studies have used transit vessels (e.g., ferries) and their routes for research purposes [20; 21; 22], demonstrating that dedicated survey vessels and routes are not necessarily required either. In the spring and summer of 2021, six marine survey campaigns were conducted with the primary focus on marine condition monitoring of the Baltic Sea. Concurrently, four GNSS devices installed on the research vessel collected SSH data autonomously. In [23] are provided a comprehensive review of the six marine survey campaigns, discussions concerning the problems occurring during autonomous data collection, and a description of the GNSS data post-processing. Following lessons learned in our previous studies [11; 24], this paper presents improved data processing approaches and a complete exploration of the methodology for deriving accurate SSH from initial post-processed GNSS measurements (i.e., instantaneous SSH), which, unless further treated, are impractical for use in data applications. Accurate derivation of shipborne GNSS-based SSH requires consideration of a vessel's high-frequency attitude changes (e.g., pitch and roll motions) [11] and sea state conditions (i.e., waves) [24], which contaminate the instantaneous SSH, but also need vessel sailing-related corrections [11]. These corrections account for the squat effect, which causes a moving vessel to sail deeper than its nominal draft, and gradual changes in the static draft (e.g., continuous fuel consumption causes a vessel to float higher). Aside from deriving SSH, the developed methodology involves a joint validation of the results, demanding comparable data from an independent source. It will be demonstrated that such a joint approach can enhance data accuracy by processing residual values instead of the instantaneous SSH. Thus, the emphasis of the study is also on the structuring of validation datasets.