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We present a framework for forecasting significant wave height on the Southwestern Atlantic Ocean using the long short-term memory algorithm (LSTM), trained with the ERA5 database available through Copernicus Climate Data Store (CDS) implemented by ECMWF (European Center for Medium Range Forecast) and also with buoy data. The predictions are made for seven different locations in the Brazilian coast, where buoy data are available, ranging from shallow to deep water. Experiments are conducted using exclusively historical series at the selected locations and the influence of other variables as inputs for training is investigated. The results shows that a data-driven methodology can be used as a surrogate to the computational expensive physical models, with the best accuracy near $95\%$, compared to reanalysis, Comment: 30 pages, 17 figures

An algorithm for representing irregular satellite data obtained from advanced synthetic aperture radar (ASAR) uniformly in space and time is introduced and comparison with WAVEWATCH III model (WW3) data is carried out. Swell global data for 2007 are analysed using statistical parameters such as bias and scattering index. Satellite data showed a great spatial uniformity compared with WW3 model. Results show underestimation of swell height by the model in the tropics and at specific higher latitude regions.

This paper is concerned mainly with the deceptively simple integral equation \[ u(x) - \frac{1}{\pi}\int_{-1}^{1} \frac{\alpha\, u(y)}{\alpha^2+(x-y)^2} \, \rd y = 1, \quad -1 \leq x \leq 1, \] where $\alpha$ is a real non-zero parameter and $u$ is the unknown function. This equation is classified as a Fredholm integral equation of the second kind with a continuous kernel. As such, it falls into a class of equations for which there is a well developed theory. The theory shows that there is exactly one continuous real solution $u$. Although this solution is not known in closed form, it can be computed numerically, using a variety of methods. All this would be a curiosity were it not for the fact that the integral equation arises in several contexts in classical and quantum physics. We review the literature on these applications, survey the main analytical and numerical tools available, and investigate methods for constructing approximate solutions. We also consider the same integral equation when the constant on the right-hand side is replaced by a given function.