Simulations of the Marine Environment: parameters, equations, and data
Data and equations: a never-ending story!
Our time is characterised by the ongoing demand for reaching fast and accurate simulations in environmental sciences. The reason relies on a shared goal: forecasting. Indeed, a marine ecosystem is related to other important social factors such as, for example, natural resources preservation, monitoring plans, economic growth… Moreover, it is very complicated to be studied and understood since natural phenomena and anthropic consequences coexist in such a context. A parametric framework is needed to better analyse the marine environment. A parameter might represent several physical and geometrical configurations of the system: say the shape of a harbour or how fast the currents are moving (from small to large scales)…
However, parameterised equations do not suffice in environmental sciences, characterised by a large gap between mathematical models and real data is usually present. Indeed, mathematical models are too simple: the results may be inaccurate and not reliable. Why do you need mathematics then? Data are scattered, noisy, complicated to interpret, and, besides, costly to collect. Mathematics combined with computer science provides numerical simulations that avoid direct interaction with unreliable data. The point now is to add data information into the mathematical model.
Optimal Control: a terrific tool!
Mathematics usually scares people, I know, but indisputably is a necessary tool to better represent the world around us. I am going to introduce a complicated model, the optimal control in a data assimilation fashion. Optimal control changes the behaviour of an equation acting with external variables to achieve a goal: in our case, the collected data. It is quite boring, isn’t it? Let me use some drawings! Let us suppose to run a factory that transforms the raw material (our external variable), resulting in money. However, the factory produces a large pollutant loss, way over the threshold (our goal) dictated by law. Optimal control answers the following question: is it possible to act on the system to stay within the legal limits?
Indeed, optimal control can change the system at hand thanks to the data information. I do not want to be too specific… This mathematical technique changes the raw material, the external variable, to reach a lower pollutant release.
Optimal control for the marine environment: keep calm and stay safer!
Thanks to its capability of changing a system, Optimal Control has high potential in environmental sciences. Among all the possible applications in this sector, let us focus on their growing employment for coastal marine environment safeguard. The latter is related to economic growth, natural resources preservation, monitoring plans, and limitation of anthropic consequences. Below you see the Shallow Waters simulation is a square tub representing the physical phenomenon that arises along the coastlines and bays. The main features of the model are superficial waves. They might result in dangerous oscillations for harbour and touristic activities, for example.
Optimal control may help in this context. Indeed, the strategy relies on adding data information on the safest setting for marine activities we are dealing with. This reduces the potential effects of the waves on a portion of the considered geographical domain. Below, for example, we were able to understand the wind stress needed to globally lower the height at the center of a square basin.
I now present another application in the fashion of marine environment safeguard and protection. It deals with the control of a pollutant release in the Gulf of Trieste. The city is one with its coastline environment characterised by very peculiar flora and fauna (Miramare). Furthermore, the Trieste Gulf is a very windy region: the effects of a pollutant loss may vary. We imagined the accident happening in front of the city coastlines. We aim at studying how Bora wind influences the system, showing the controlled loss that guarantees the safeguard of the Miramare area.
The image represents a maximum uncontrolled loss of the pollutant compared with a controlled version of the same problem, with a lowered quantity of pollutants, to keep Miramare safe.
Conclusions: data and control, this is the way!
It is clear now that, indisputably, adding data information and control the systems to achieve a goal gives more realistic simulations and predictions. This is of utmost importance for marine phenomena. Indeed, even if the focus is the seaside and the preservation of the coastline, the marine environment is related to many aspects of social life, economic activities, natural care, safeguard… Mathematics combined with natural sciences is a tool that can help the whole community: it is the way of better analysis of the world that surrounds us.
