Extreme levels

When designing port infrastructure projects, coastal constructions or oil rigs, it is important to know the minimum and maximum sea level over long periods (up to a century). While maximum tide heights are known, it is vital to examine the likelihood of positive and negative surges. Such studies require long series of good quality measurements.

Observation, Prediction et Surcote à St-Nazaire du 7 au 13 mars 2008


Definition of positive and negative storm surge - extreme levels

Storm surge

Instantaneous storm surge is the difference at time t between the observed water level and the predicted water level. A surge is positive if the water level is higher than the expected tide, and negative if lower. Storm surge is mainly meteorological in origin: it is generated during the passage of low pressure systems or anticyclones, by changes in atmospheric pressure and winds. It may also have other origins: waves, seiches, tsunamis, etc.

High tide surge is the difference between the height of the sea observed and the predicted high tide (astronomical tide); this does not necessarily occur at the same time. Similarly, low tide surge is the difference between the low tide observed and the low tide predicted.

Illustration de la surcote de pleine mer et de la décote de basse mer


Extreme levels

To study extreme surges, the appropriate variables are high tide surge and low tide surge, not the instantaneous storm surge. By definition these values are free from the effects of the phase difference between observation and prediction. Thus, if only one phase difference exists between the predicted height and observed height either for physical reasons or because the harmonic constants are poorly determined (eg, short-term and poor quality records), the instantaneous storm surge will be even more significant, which is not the case for high tide and low tide surges.


Return period

As a result, the highest high water level, a component of which is random, is a concept that makes sense only if it is estimated in terms of probability. We must determine the mean interval of time, called the return period, between two rare events with sea levels above a certain threshold.


Determining the return period

Expressed in this way, the return period would seem to be determined simply by calculating the mean. However, for the mean to be significant, the observation periods must be much longer than the return periods being calculated. Given the available observations, we can hardly estimate return periods longer than two or three years in most cases.

However, it is possible to effectively address this problem for ports, where more than 10 years of tidal observations are available, based on the fact that storm surges and tide are largely independent. If there are many tide observations available, it is easy to calculate the probability distributions governing rare but not exceptional events like high spring tides or major storm surges. But the two types of events may never have been observed simultaneously. However, the return period for this type of very rare event can be calculated with a good degree of confidence by combining the probability distributions for the tide and for surges. The figures show the results for Brest and present the probability for a predicted high tide to be equal to a given value within 1 cm.

Exemple de graphique de probabilité des hauteurs de pleines mer à Brest


Gumbel Distribution

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