Measurement of long waves at the harbor of Marina di Carrara, Italy

Abstract

"\"This paper presents the analysis of measurements. of long waves at the harbor of Marina di Carrara, Italy. Nine pressure gauges (eight in the inner harbor and one outside the harbor) were used to. record continuously the water surface elevation, for. about 3 years; incoming short waves were measured using a directional buoy at about 500 m offshore the breakwaters. The analysis is carried out splitting the energy of the long waves into two bands, i.e., very long waves (VLW; f < 0.003 Hz) and long waves (LW; 0.003 < f < 0.030 Hz); it is found that LW energy is. strongly correlated with the energy of the incoming short waves while no correlation (or very poor) is found for VLW. During energetic sea states, surface elevation spectra of VLW and LW, normalized against the wave energy of each frequency band, appear to be autosimilar; this suggests that the spectra of the incoming long waves have a mostly constant shape. Simple numerical computations of harbor resonance, carried out using a mild-slope equation linearized model, indicate that the amplification of the height of the incoming LW. generated by short waves (calculated using empirical. formulae from previous researches by Melito et al.. 2007) inside the harbor can be reasonably predicted using such simple approach, assuming that the LW spectra are rectangular. The shape of the amplification diagram calculated by the numerical model shows reasonable (but not perfect) agreement with the shape of the normalized measured spectra inside the harbor.\"

Hindcasting Long Waves in a Port: An ANN Approach

“…The significant wave-height of a given frequency band X: H X , is a parameter widely used to characterize the wave energy within the band of the spectrum [e.g. Bellotti and Franco, 2011;González-Marco et al, 2008] and can be obtained as:…”

“…As for the analytical modeling, laboratory tests substantiate this alternative, but the validation through field study cases has not been discussed yet [Stiassnie and Drimer, 2006]. On the other hand, the traditional empirical formulae require simpler procedures at the expense of the accuracy; in fact, only a small sample of observational data is needed to adjust their parameters [Bellotti and Franco, 2011;Bowers, 1992;López et al, 2012]. Finally, artificial intelligence implies low computational and data costs in comparison with the numerical modelling, but provides significantly better results than the empirical formulae [López and Iglesias, 2013].…”

“…For this purpose, we used ANNs to calculate the characteristic wave-height of the Low Frequency (LF) band -related to the infragravity waves [Bellotti and Franco, 2011;López et al, 2012] -and the characteristic wave-height of the swell (SW) band, both inside a port basin. As a novelty, we incorporate as an input to the model the wave directionality of swell, in order to improve the results obtained by López and Iglesias [2013], who calculated the infragravity wave energy based on scalar parameters.…”

Long Waves and Artificial Neural Networks

“…The energy of the long waves was characterized, by analogy with short waves, using the 'significant long wave height' (e.g. Bellotti and Franco, 2011;Bowers, 1992;González-Marco et al, 2008;Melito et al, 2007). This parameter, H x , represents the energy of a given frequency band of the spectrum and is calculated by replacing in Eq.…”

Statistical properties of coastal long waves analysed through sea-level time-gradient functions: exemplary analysis of the Siracusa, Italy, tide-gauge data

“…Despite the recognised importance of longwave studies and coastal resonances, direct measurements of long waves are not common, and they have been carried out especially for research purposes (Okihiro et al, 1993;Okihiro and Guza, 1996;Lara et al, 2004;Bellotti and Franco, 2011;Guerrini et al, 2014). In recent years, the upgrade of the traditional coastal tide gauge networks, that usually recorded data every 10 or 15 min, to faster sampling and recording rates (1-10 s) has allowed the use of sea-level data to study waves in the longwave range, which are however usually analysed only for extreme events such as tsunamis (Rabi-novich and Thomson, 2007;Bressan and Tinti, 2011;Rabinovich et al, 2013).…”