Interaction between tide and surge : modelling the time evolution of the residual surge

Dit onderzoek geeft een advies over de relatie (het fase verschil) tussen getij en opzet.

This study is a follow up to Schematization of storm surges. Analysis based on simulated KNMI-data. [HKV-rapport PR3874.10]. Chris Geerse, Guus Rongen en Bart Strijker. HKV lijn in water. In that study patterns of storm surges were derived, based on 6500 years of water levels simulated by the KNMI along the Dutch coast. The new storm surge patterns, representing average time evolutions of the surges, are significantly different from the surge patterns used in the WBI2017. Based on the 6500 years of simulated water levels, it was also investigated what the probability distribution for the (tidal) phase looks like; here the phase equals the difference in time of the moments the maximum surge occurs and the moment the astronomical high tide occurs. What is remarkable is that phases near zero are almost absent in the (simulated) data: the maximum of the surge almost never coincides with astronomical high tide. That fact looks surprising. And one might expect that the new patterns can lead to wrong superpositions of surge and tide, yielding an underestimation of extreme water levels (note that high surges occurring only during low tide result in lower water levels). In addition to the observation that phases near zero are virtually absent, it was found in [Geerse et al, 2019] that the probability distribution for the phase is strongly non-uniform, and that the maximum surge has a tendency to occur shortly after astronomical low tide.

The most important conclusion from this study is that many aspects of the storm surge, such as derived from 6500 years of KNMI simulations, can be reproduced with a relatively simple model. That model gives a time-dependent description of the (residual) surge S(t) and contains the following components/assumptions:
• • Astronomical tide of a specific location As input, the astronomical tide (one repeating tidal cycle) of a considered location is used.

• • Modelling the sea-surge The sea-surge SZ(t) is modelled with a cosine-squared function, with the maximum of the sea-surge, occurring at t = tZ, can occur with equal probability at any time during the tide (tZ follows a uniform distribution).
• • Modelling the tidal advancement During a storm across the North Sea, the tidal wave propagates faster due to larger water depths, implying that during a storm the tide at a location arrives sooner than without a storm. The difference between the arrival times is called the tidal advancement. The model contains a tidal advancement ?(t) that is proportional to the height of the sea-surge SZ(t). The motivation of this assumption follows from a (pragmatic) formula relating the depth of the water to the speed of the tidal wave.
• • Modelling the depth effect The model also contains a term taking into account that during low tide, with smaller water depth, the surge (or wind set-up) develops better than during high tide. This depth effect is taken to be proportional to the surge height.