Oceanic surface currents reconstruction with the Direct Sampling method: a test case on the high frequency radar data set of the Gulf of Naples

Measurements of the oceanic surface collected by coastal high frequency (HF) radars can have a crucial role in the study of coastal areas. For example, data collected by these instrument can be very useful for the study of wind induced currents, wave properties and tidal currents, or Lagrangian transport models. Unfortunately, measurement collected by these instruments are sometimes affected by large errors due to a number of reasons, including for example unfavorable weather conditions. Due to these large errors, for some time steps and at some locations, the grid of these measurements contains gaps. In some situation, these gaps can cover and important portion of the area measured by the HF radar. To fill these gaps, diverse techniques can be used. Previous studies explored the possibility to reconstruct the missing velocity values with Self Organizing Maps (SOM), Open Boundary Model Analysis (OMA) and Data Interpolating Empirical Orthogonal Functions (DINEOF). In particular, some of these studies focused on a data set collected by the University Parthenope with a HF radar system located in the Gulf of Naples, operating since 2004. In this new study, a multiple-point statistics (MPS) based algorithm is applied for the reconstruction of the aforementioned data set and its results are compared against the results obtained with the previously mentioned methods. In particular, the Direct Sampling (DS) algorithm is used for the reconstruction of missing measurements of velocity due to its flexibility in handling multi-variate data. In fact, current data, with their two components, represent a multi-variate reconstruction problem that can be easily handled with the DS algorithm by considering a multi-variate training image. To test the reconstruction performance of the DS, artificial gaps are created in some (complete) maps for some reference time steps, to compare the reconstructed current values against the measured ones. Diverse gap configurations are tested, both with different spatial distribution (randomly scattered or with structured gaps) and different data coverage (from the original data set a fraction of measurements ranging from 10% to 40% is removed). The results show that the DS method allows to better reconstruct the incomplete velocity maps when the number of missing data remains below the 20%. For higher portions of missing data, other methods, like for example DINEOF, provide better reconstruction, although they require a more complex preliminary setup.