Two recent events are showing the relevance of choosing good routes for maritime navigation. On the one hand, the crisis in the Red Sea is forcing many shipping companies to operate the route around Africa instead of the Suez Canal. Is it possible to choose a new route that consumes less fuel or is covered in the minimum time? On the other hand, the recent loss of containers full of pellets plastic freighter Toconao near the coast of Galicia, caused by a wave strike, is having a considerable environmental impact. Could routes be designed that make navigation safer in adverse weather conditions, to avoid accidents of this type? The so-called mathematical optimization techniques can help us answer these questions.
These tools, whose study was initiated by great mathematicians such as Euler, Lagrange and the Bernoulli brothers, allow us to theoretically describe the route that must be followed to get from one point to another in the fastest, cheapest or safest way, depending on what we are looking for. optimize. The shortest route in distance is not always the ideal route. For example, if you want to choose the fastest road trip, it is better to go on a highway, even if the distance is greater.
In maritime navigation we must consider marine currents, areas with different waves and wind, which are constantly changing. The first to formulate and theoretically analyze this problem was the German mathematician Ernst Zermelo (1871-1953). He was able to find, for a boat moving at a constant speed, the fastest trajectory between two fixed points, considering that the wind or currents could vary in space and time.
For your solution to be of practical use in real navigation, it is necessary to have reliable predictions of navigation conditions. The main American (NOAA) and European (Copernicus) prediction centers make detailed 10-day forecasts available with a spatial resolution of less than 10 kilometers. They use modern meteorological models, whose progress in recent decades has been spectacular: the five-day forecast today is more reliable than the one-day forecast in 1980. This is thanks, mainly, to the greater density of observations of the state of the atmosphere at the current moment. But other mathematical disciplines are also fundamental, such as statistics – specifically, the so-called Kalman filters for the assimilation of observation data –, partial differential equations – to model atmospheric dynamics – and numerical methods – to calculate the evolution of these models. These disciplines have recently been joined by artificial intelligence, which promises to improve results even further, as Google DeepMind researchers are already demonstrating.
In addition, it is possible to make a more detailed description of the movement of the ship – which allows obtaining better solutions –, modeling the movement and consumption per unit of time of each specific ship, depending on the navigation conditions, currents, wave height. , angle of incidence, direction and intensity of the wind, etc. To do this, knowledge of naval engineering and data science is used.
With this information, mathematical optimization algorithms of a very different nature have been developed: the so-called variational methods, graph optimization and evolutionary algorithms. All of them are used today to find favorable sea routes.
On the other hand, any prediction entails uncertainty that must also be quantified and taken into consideration when optimizing navigation routes. For this reason, new optimization algorithms – dynamic and stochastic – must be developed to achieve robust results under any possible atmospheric evolution scenario. This becomes especially important in a global warming scenario in which the atmosphere is more unstable and extreme events are increasingly frequent.
Recently, all of these mathematical techniques mentioned above have been integrated to optimize maritime routes in real time, based on meteorological and oceanographic predictions, with consumption models adapted to each vessel. This tool, which aims to be a Google Maps of the ocean, is being developed by a multidisciplinary team, with a majority presence of Spanish researchers. With it you can save 5-10% on fuel on each trip, improve navigation safety by avoiding areas with adverse conditions and reduce CO2 emissions. All of this is of crucial importance since, today, more than 80% of trade is transported by sea, which accounts for close to 3% of global carbon dioxide emissions. Annual spending on fuel amounts to 250,000 million euros and accounts for more than 60% of the operating costs of maritime transport.
David Gómez-Ullate He is a professor of Applied Mathematics at IE University and director of the Green Navigation project.
David Martin De Diego He is a scientific researcher at the CSIC at the Institute of Mathematical Sciences.
Coffee and Theorems is a section dedicated to mathematics and the environment in which it is created, coordinated by the Institute of Mathematical Sciences (ICMAT), in which researchers and members of the center describe the latest advances in this discipline, share meeting points between mathematics and other social and cultural expressions and remember those who marked their development and knew how to transform coffee into theorems. The name evokes the definition of the Hungarian mathematician Alfred Rényi: “A mathematician is a machine that transforms coffee into theorems.”
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