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<p>The Gauss–Listing geopotential value <i>W</i><sub>0</sub> defines the fundamental equipotential surface used as the global vertical reference datum in modern height systems. In this study, the methodology of Dayoub et al. (J Geod 86:681–694, 2012) is revisited using contemporary global datasets and models. The analysis employs the latest mean sea surface (MSS) models DTU25 and CLS22, the mean dynamic topography (MDT) from the ECCO4 ocean state estimate, and the high-resolution global gravity field model XGM2019e_2159, all consistently reduced to the mean-tide system. Compared to earlier realisations, these datasets provide improved spatial coverage and accuracy, particularly in high-latitude and coastal regions, enabling a more robust global determination of <i>W</i><sub>0</sub>. This update is timely given the availability of improved global MSS models and ocean state estimates, which enable a more consistent and comprehensive reassessment of <i>W</i><sub>0</sub>. A global least‐squares adjustment of geopotential values computed from these datasets yields <i>W</i><sub>0</sub> = 62636853.8 m<sup>2</sup>s<sup>−2</sup> at epoch 2003.0. An alternative computation using the normal gravity field formulation provides the same value of <i>W</i><sub>0</sub> and produces a new best-fitting reference ellipsoid with semi-major axis <i>a</i><sub>0</sub> = 6,378,136.886 m and semi-minor axis <i>b</i><sub>0</sub> = 6,356,751.887 m. Sensitivity analyses indicate that the estimated <i>W</i><sub>0</sub> is robust with respect to model selection and resolution, and that the use of the ECCO4 MDT yields results that agree with the MDT-independent formulation at the centimetre level. Random errors are negligible due to global, multi-year averaging and the large number of data points, while a realistic systematic uncertainty of ± 0.3 m<sup>2</sup> s<sup>−2</sup> (≈ 3 cm in height) is attributed mainly to altimeter calibration and the input models’ biases. The resulting ellipsoid, satisfying <i>U</i><sub>0</sub> = <i>W</i><sub>0</sub> provides a self-consistent surface for gravity field modelling and geoid computation, eliminating the need for a degree-zero correction. The updated <i>W</i><sub>0</sub> value lies between that of Dayoub et al. (J Geod 86:681–694, 2012) and the IAG conventional value. The result represents a physically consistent modern realisation of <i>W</i><sub>0</sub> and a refined reference ellipsoid suitable for contemporary geodetic applications.</p>

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Updated determination of the Gauss–Listing geopotential value W0 and a best-fitting global reference ellipsoid

  • 期刊论文

  • 发表日期：

    2026年7月17日

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  • Nadim Dayoub

摘要

The Gauss–Listing geopotential value W0 defines the fundamental equipotential surface used as the global vertical reference datum in modern height systems. In this study, the methodology of Dayoub et al. (J Geod 86:681–694, 2012) is revisited using contemporary global datasets and models. The analysis employs the latest mean sea surface (MSS) models DTU25 and CLS22, the mean dynamic topography (MDT) from the ECCO4 ocean state estimate, and the high-resolution global gravity field model XGM2019e_2159, all consistently reduced to the mean-tide system. Compared to earlier realisations, these datasets provide improved spatial coverage and accuracy, particularly in high-latitude and coastal regions, enabling a more robust global determination of W0. This update is timely given the availability of improved global MSS models and ocean state estimates, which enable a more consistent and comprehensive reassessment of W0. A global least‐squares adjustment of geopotential values computed from these datasets yields W0 = 62636853.8 m2s−2 at epoch 2003.0. An alternative computation using the normal gravity field formulation provides the same value of W0 and produces a new best-fitting reference ellipsoid with semi-major axis a0 = 6,378,136.886 m and semi-minor axis b0 = 6,356,751.887 m. Sensitivity analyses indicate that the estimated W0 is robust with respect to model selection and resolution, and that the use of the ECCO4 MDT yields results that agree with the MDT-independent formulation at the centimetre level. Random errors are negligible due to global, multi-year averaging and the large number of data points, while a realistic systematic uncertainty of ± 0.3 m2 s−2 (≈ 3 cm in height) is attributed mainly to altimeter calibration and the input models’ biases. The resulting ellipsoid, satisfying U0 = W0 provides a self-consistent surface for gravity field modelling and geoid computation, eliminating the need for a degree-zero correction. The updated W0 value lies between that of Dayoub et al. (J Geod 86:681–694, 2012) and the IAG conventional value. The result represents a physically consistent modern realisation of W0 and a refined reference ellipsoid suitable for contemporary geodetic applications.