**1. Introduction**

The last few years have seen the increase of human settlement in the coastal areas, for social, touristic or economic reasons. This phenomenon leads to a consequent increase in human occupation of coastal areas (e.g. [1]). All these factors, combined with the attention paid to the sea level rise scenarios (e.g. [2]) and with the problem of coastal erosion (e.g. [3–5]), justify the increasing attention paid to storm surge events and related coastal flooding.

As it is well known, the tide level is the superposition of a harmonic component related to the mutual influence of the earth, sun and moon and a meteorological one. The first is purely deterministic and has been studied since the last years of the nineteenth century. Indeed, since the observation of the phenomenon started before Christ, only after Newton's theory [6] researchers as George Darwin [7] provided the first mathematical description of the tides. However, the first model of the tides is the "harmonic theory" developed in 1927 by Doodson [8]. It considers the tides as a superposition of sinusoidal constituents, whose frequencies are referred to as those evaluated on the basis of astronomical forces. The amplitude, instead, is influenced by the shallow water conditions, the coastal effects and morphological phenomena due to the interaction between waves and bottom [9].

For a more comprehensive description of the "harmonic theory", the reader may refer to Godin, McCully, and Pugh [9–11].

The difference between the deterministic component and the total measured level oscillation can be related to meteorological phenomena and may be defined as *storm surge*. It is also referred to as *meteorological component* or *residual*. In European literature, the term storm surge is commonly used [12].

Generally speaking, the generation of storm surges is (mainly) due to pressure gradients and wind set-up. The effect of the wind is to push the water in the principal direction of the wind causing an increase in sea level. The other factor that induces variation in sea level is the barotropic field (e.g. pressure anomalies) causing the physical phenomenon of the "inverse barometric effect" that is the increase of mean sea level as the pressure decreases (e.g. 1 cm for each hPa).

Talking about small and semi-enclosed basins (e.g. Adriatic Sea, Black Sea, Caspian Sea, Great Lakes, etc.), there is another effect contributing to the level increase. This effect may be attributed to the case in which meteorological perturbations persist for a long time over the basin (e.g. until several days). In those situations, there are two main consequences: The first is that it could be difficult to forecast the storm surge (e.g. [13]), and the second is related to the dynamic of the basin. Indeed, if the basin is semi-enclosed, its natural modes, i.e. seiches, may be excited, and level oscillations may persist for several days in the whole basin area (e.g. [14–16]).

While the astronomical component can be estimated and reconstructed by means of standard techniques (based on the theory of harmonic analysis) (e.g. [11, 17, 18]) performed by using measured level time series, the reconstruction of storm surge events, with both forecast and hindcast purposes, is not deterministic and requires more effort in its evaluation.

The topic of storm surge and their forecast has been investigated in the past by many researchers (e.g. [19–22]), and the importance of the topic is also highlighted observing that there are countries that are being equipped with early warning systems (e.g. [23]).

From a practical point of view, there are three ways to study storm surges: pure numerical approaches (i.e. circulation models), statistical approaches (i.e. artificial neural networks) and mixed approaches.

In the case of a pure numerical approach, the aim is to focus the attention on the ability of the model to reproduce the physical processes (e.g. [24]). These methods are physics-based and are often referred to as "dynamical method" (e.g. [25]). They numerically solve the classical mathematical set of equations composed by the continuity equation and the equation of motion where the initial and boundary conditions are given by a meteorological model (e.g. [25]). As pointed out by Vilibić et al. (e.g. [25]), the first examples of dynamical methods, at least for the Adriatic Sea, are [26, 27], for the only Adriatic area and for the entire Mediterranean Sea, respectively. An improvement in terms of forecast reliability (also in terms of forecast window) is the use of ensemble-based prediction systems (e.g. [28]) that allow having a more consistent forecast than that obtained with a single deterministic one.

Statistical approaches, instead, are based on the use of regression models to estimate a series of predictors and weights to forecast the desired variable (i.e. water level). The database is usually composed by observed or forecast and/or hindcast data given by a meteorological model (e.g. [29–33]).

Numerical models are accurate, with great reliability, as they are physics-based. However they involve high computational costs compared to the statistical ones. These are fast, show an acceptable reliability, but have no physics inside.

A possible way to overcome these problems is the use of the last category of approaches, the "mixed" ones. They statistically correct the results coming from *Simplified Methods for Storm Surge Forecast and Hindcast in Semi-Enclosed Basins: A Review DOI: http://dx.doi.org/10.5772/intechopen.92171*

numerical models with the aim to reduce the computational costs. The idea is to use numerical models accepting low reliability using meshes with lower resolution (i.e. lower computational costs) and correcting the obtained results by means of statistical tools (e.g. [34–36]).

In all the three cases (dynamical, statistical and mixed approaches), meteorological data provided by global general circulation models (e.g. European Centre for Medium-Range Weather Forecasts (ECMWF), the Meteorological Research Institute model (MRI-AGCM3.2) [37, 38]) have to be used, so the final reliability is often related to those of the GCMs.

This chapter aims to propose a review of two simplified methods [36, 39] finalized to forecast and hindcast storm surge levels. Both approaches are mixed, so they have a first physics-based approach where the water level due to the wind is evaluated (once at all) and a separate step in which the obtained results are corrected (i.e. the barotropic effects are considered) by means of statistical techniques. The chapter is structured as follows. Section 2 describes the general outline of the two methods, Section 2.2 illustrates the forecast method, while Section 2.3 details the hindcast one. The applications of the two approaches are described in Section 3. Concluding remarks close the chapter.
