A satellite altimetry data assimilation approach to optimise sea state estimates from vessel motion

This article was published on 31 January 2023.

👤 Filippo Nelli, Marzieh H. Derkani, Alberto Alberello, Alessandro Toffoli


Estimates of directional wave spectra and related parameters can be obtained from ship motion data through the wave-buoy analogy approach. The fundamental input is the response amplitude operator (RAO), which translates ship response into a wave energy spectrum. While ship motion is routinely measured on ocean going vessels, the RAO is not directly available and it is approximated using ship hydrodynamic models. The lack of publicly available details of hull geometry and loading conditions can results in significant inaccuracy of this operator. Considering the reliability of remotely sensed wave height, here we propose an assimilation technique that uses satellite altimeter observations to calibrate the RAO and minimise its uncertainties. The method is applied to estimate sea state conditions during the Antarctic Circumnavigation Expedition by converting motion response of the icebreaker Akademik Tryoshnikov as recorded by the on-board inertial measurement unit. Comparison against concurrent sea state observations obtained from a marine radar device shows a good agreement for a variety of parameters including significant wave height, wave periods and mean wave direction.


Vessels across the world have surveyed the sea state through the voluntary observing ships (VOS) scheme for centuries, reporting visual estimates of wave height, period and mean direction for wind sea
and swell systems (e.g. Gulev and Grigorieva, 2004; Grigorieva et al., 2017). Nowadays, satellite borne sensors scan the Earth surface twice a day, providing records of significant wave height (i.e. four times
the standard deviation of the surface elevation; Holthuijsen, 2010) from altimeter sensors (Ribal and Young, 2019), and directional wave spectra from synthetic aperture radar (SAR; Collard et al., 2009) and
surface waves investigation and monitoring (SWIM; Aouf et al., 2021) sensors. Despite the global coverage, a low observation density and contamination of sea ice in the satellite footprints at high latitudes result in significant under-sampling and high uncertainties of measured wave properties in polar regions (Takbash and Young, 2019). Following the opening of new shipping routes in the Arctic ocean (e.g. Smith and Stephenson, 2013) and a renewed interest in the marginal ice zone for its contribution to the global climate, there has been a growing demand for reliable sea state measurements at high latitudes to enhance performance of Earth system models. To complement satellite data, ice-tethered and drift buoys have been deployed during recent campaigns (e.g. Kohout et al., 2014; Thomson et al., 2018; Vichi et al., 2019; Alberello et al., 2020a), but these devices only endure the harsh polar environment for a short period of time (usually few weeks). Considering the numerous expeditions taking place every year (Schmale et al., 2019), ship based observations, whether through visual or technological means, still remain a key source of wave data at high latitudes (e.g. Derkani et al., 2021; Alberello et al., 2022; Løken et al., 2021).

Remote sensing techniques using the vessel’s marine radars are extensively employed to measure the directional wave spectrum in the open ocean with good accuracy (see comparison against buoy data in e.g. Hessner et al., 2002; Borge et al., 2004). However, the strong back-scatter from sea ice is a significant source of uncertainty in the marginal ice zone (Derkani et al., 2021). Stereo imaging has recently been applied effectively to detect wave properties from moving vessels (Alberello et al., 2022), but the technique is limited to daylight hours. A promising approach based on bow-mounted altimeter sensors has recently been proposed by Løken et al. (2021), but no directional properties can be extrapolated. An alternative and inexpensive method that uses standard ship sensors consists in converting the vessel six-degree-of-freedom motion response from the on-board inertial measurement units (IMU) into an incident directional wave spectrum through the response amplitude operator(RAO; Newman, 2018), i.e. a transfer function that determines the behaviour of the vessel at sea. The method is referred to as the wave-buoy analogy (WBA) and it has been demonstrated to produce reliable measurements of integrated wave parameters such as significant wave height and mean periods (e.g.
Nielsen, 2007; Nielsen and Stredulinsky, 2012; Nielsen, 2017; Nielsen and Dietz, 2020). Nevertheless, the reconstruction of the full wave spectrum remains challenging. A relevant cause is the low-pass filtering effect of the vessel itself. This prevents accuracy in the upper tail of the reconstructed wave spectrum and hampers applications related to nonlinear wave dynamics (e.g. estimates of wave height distributions and probability of occurrence of large waves) and wave-structure interaction (Fadaeiazar et al., 2018, 2020; Decorte et al., 2021). Other reasons relate to inaccuracies of various sources in the estimates of the RAO.

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