A Combined Modeling and Measurement Approach to Assess the Nodal Tide Modulation in the North Sea

Abstract

The scientific assessment of past and future mean sea level (MSL) trends requires reliable predictions of natural cyclic behavior on short and long time scales, with the current rate of sea-level rise (SLR) being estimated at 2 mm/year in the North Sea (Dangendorf et al., 2015). On a global scale, rates around 1.5 mm/ year between 1900 and 2012 are detected (Oppenheimer et al., 2019) as well as recent accelerations of up to 3 mm/year (Dangendorf et al., 2019). Typical cycles concerning sea level are tides, which are a result of the gravitational potential of sun and moon, centrifugal force of the earth and meteorological forcing. Tides are distinguished by their frequency, which is predominantly diurnal or semidiurnal, even though monthly, interannual, annual, and perennial frequencies exist as well. The nodal tide (Bradley, 1728) is a harmonic signal with a period of 18.61 years, caused by the precession of the lunar ascending node (Pugh, 1987). It is the most important low frequency tidal constituent apart from the lunar perigee and has shown to have an amplitude of up to 30 cm (Peng et al., 2019). In order to consider the nodal tide in MSL analysis, the theoretical equilibrium tide concept is applied (Godin, 1986; Proudman, 1960; Woodworth, 2012). Nonresolved low frequency cyclic behavior of water levels may lead to an erroneous estimation of SLR. The influence

Secular Trends in Global Tides Derived From Satellite Radar Altimetry

“…The time span of 4 years was chosen primarily because this allows the separation of M 2 , S 2 , and O 1 from other signals (this requires at least 3 years). On the other hand, there is in some instances (mainly coastal) a discrepancy between the actual nodal modulation of lunar tides (18.6 years cycle) and the theoretical value (Hagen et al, 2021). Hence, although amplitude/phase estimates are corrected for the nodal modulation during tidal analysis, there may be a residual modulation left.…”

A review on advanced numerical methods for free-surface hydrodynamics

“…Moreover, an extension of this algorithm that includes saturated as well as variable saturated flows in a groundwater environment was recently documented in [12,[16][17][18]. A large numbers of applications worldwide have demonstrated the capability of the proposed methods to simulate environmental free-surface flows (see, e.g., [19][20][21][22][23][24][25]). Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.…”

“…At every time step, system (25) can be solved iteratively by a Newton type method in order to determine the new free-surface elevations η n+1 i . To this purpose note that the Jacobian matrix associated to system (25) is D(ζ ) + T where D(ζ ) is a diagonal matrix whose diagonal entries are…”

Robust validation of trends and cycles in sea level and tidal amplitude in the Dutch North Sea

“…Doodson & Lamb (1924) investigated long-term changes in amplitudes and phase of the lunar semidiurnal tide, in the North Sea the dominant component of the tide. More recently the shape of the tide, sometimes combined with mean sea level, was investigated in several studies (Amin, 1985;Arns et al, 2015;Führböter, 1989;Führböter & Jensen, 1985;Hagen et al, 2021). Haigh et al (2020) identify six possible causes of long-term changes in tides, recognizing that the most dramatic changes of the tides are observed in estuaries.…”