Fast and flexible spatial sampling methods based on the Quadtree algorithm for ocean monitoring

Abstract

Although existing in situ oceanographic data are sparse, such data still play an important role in submarine monitoring and forecasting. Considering budget limitations, an efficient spatial sampling scheme is critical to obtain data with much information from as few sampling stations as possible. This study improved existing sampling methods based on the Quadtree (QT) algorithm. In the first-phase sampling, the gradient-based QT (GQT) algorithm is recommended since it avoids the repeated calculation of variance in the Variance QT (VQT) algorithm. In addition, based on the GQT algorithm, we also propose the algorithm considering the change in variation (the GGQT algorithm) to alleviate excessive attention to the area with large changes. In second-phase sampling, QT decomposition and the greedy algorithm are combined (the BG algorithm). QT decomposition is used to divide the region into small blocks first, and then within the small blocks, the greedy algorithm is applied to sampling simultaneously. In terms of sampling efficiency, both the GQT (GGQT) algorithm and the BG algorithm are close to the constant time complexity, which is much lower than the time consumption of the VQT algorithm and the dynamic greedy (DG) algorithm and conducive to large-scale sampling tasks. At the same time, the algorithms recommend above share similar qualities with the VQT algorithm and the dynamic greedy algorithm.