**5. Preliminary Information and Modeling Phases**

The modeling approach has to be feasible both from the controlling authorities point of view, that need reliable results to avoid, or at least to minimize, detrimental effects on the environment, and from the contractors point of view that have to pay attention to the economic and technical feasibility of the work.

Within the framework of the preliminary information phase, the preliminary analysis should be devoted to identifying the need of more detailed studies to prevent and/or mitigate the expected environmental effects.

The first and more basic preliminary studies are based on the retrieval and analyses of known data about environmental forcing (i.e., mainly related to hydrodynamics) along with the physical features of handled sediments (i.e., fine fraction). This approach allows gaining insight into the big picture of the phenomena at hand by identifying potential environmental effects. Environmental issues have to be identified within the frame of a holistic approach, hence by engaging scientists with different expertise (e.g., [38]). Of course, this phase has strong limitations and needs a more detailed analysis if significant environmental effects are expected to occur. In this way, the probability of detrimental environmental effects identified within the preliminary information phase may be confirmed. If this is the case, a second (and deeper) level of modeling to ge<sup>t</sup> reliable expectation in terms of turbidity plume evolution and deposition rate distribution at and around the work site should be then performed.

When preliminary modeling phase is concerned, the synthetic scenarios approach is considered the proper candidate to provide fast results. Despite their limitations, analytical models can be used to provide modeling results taking into account the main features of the phenomenon with low computational costs. The solutions of the (simplified) governing equations are typically given in closed-form (they require simple arithmetic operations) or integral-form (they require standard numerical integration techniques). Simplified models for sediment transport and deposition rate estimates often rely on the solution of the two-dimensional advection and diffusion equation of the re-suspended sediments that reads as follow (e.g., [39]):

$$\frac{\partial \mathbf{C}}{\partial t} + \mathrm{II} \frac{\partial \mathbf{C}}{\partial \mathbf{x}} + V \frac{\partial \mathbf{C}}{\partial y} + \frac{\partial}{\partial \mathbf{x}} \left( D\_x \frac{\partial \mathbf{C}}{\partial \mathbf{x}} \right) + \frac{\partial}{\partial y} \left( D\_y \frac{\partial \mathbf{C}}{\partial y} \right) = q - \frac{w\_s}{h} \mathbf{C}, \tag{4}$$

where *x* and *y* are the horizontal coordinates; *t* is the elapsed time; *C* is the depth-averaged sediments concentration (intimately related to the SSC); *U* and *V* are the *x*- and *y*-component of the ambient current respectively; *Dx* and *Dy* are the diffusion coefficients; *ws* is the settling velocity; *h* is the water depth; *q* is the source term, often referred to as re-suspension source strength (e.g., [6]). The latter is intended to describe the sediments actually available to the far-field passive transport (see Section 4). Equation (4) neglects the vertical variability of SSC. These models also consider homogeneous environmental currents (i.e., not variable in space), even if variable over time, homogeneous and constant diffusion coefficients (albeit with the possibility of simulating anisotropy of the medium and of the flow), constant depth and constant settling velocity. It is therefore clear that these models can only be used within the preliminary modeling phase, in which simplified models can in any case describe salient features of the spatial and temporal evolution of the plume, and thus highlight when environmental critical issues can potentially occur.

As far as the source term is concerned, analytical models are usually able to evaluate the evolution of the turbidity plume with a constant production of sediments over time located in a fixed area (often referred to as continuous source, e.g., [40,41]). Nevertheless, analytical models can take into account the variation, in both time and space, of location and strength of the re-suspension source during the work progression (e.g., [39]). Thus, it is possible to provide the temporal and spatial picture of the resulting plume evolution. Figure 5 shows a typical example obtained by using the analytical approach proposed by Di Risio et al. ([39]) in the case of dredging activities performed with a hydraulic dredge and a mechanical dredge. In the former case (left panel), the re-suspension is modeled as a moving and continuous source with varying intensity. In the latter (right panel), the re-suspension is modeled as a moving and intermittent source.

Even with their strong limitations, analytical models were demonstrated to be able for describing the big picture of the phenomenon at hand [39] and for the comparison of the effects for different scenarios. Therefore, they can be used to address the general environmental questions, allowing a first rough estimation of the maximum impacted area. Indeed, this is useful to guide more detailed numerical analysis and to select the more appropriate simulation scenarios in terms of both environmental forcing and operational techniques.
