Efficient 3D real-time adaptive AUV sampling of a river plume front

Abstract

The coastal environment faces multiple challenges due to climate change and human activities. Sustainable marine resource management necessitates knowledge, and development of efficient ocean sampling approaches is increasingly important for understanding the ocean processes. Currents, winds, and freshwater runoff make ocean variables such as salinity very heterogeneous, and standard statistical models can be unreasonable for describing such complex environments. We employ a class of Gaussian Markov random fields that learns complex spatial dependencies and variability from numerical ocean model data. The suggested model further benefits from fast computations using sparse matrices, and this facilitates real-time model updating and adaptive sampling routines on an autonomous underwater vehicle. To justify our approach, we compare its performance in a simulation experiment with a similar approach using a more standard statistical model. We show that our suggested modeling framework outperforms the current state of the art for modeling such spatial fields. Then, the approach is tested in a field experiment using two autonomous underwater vehicles for characterizing the three-dimensional fresh-/saltwater front in the sea outside Trondheim, Norway. One vehicle is running an adaptive path planning algorithm while the other runs a preprogrammed path. The objective of adaptive sampling is to reduce the variance of the excursion set to classify freshwater and more saline fjord water masses. Results show that the adaptive strategy conducts effective sampling of the frontal region of the river plume.

Fractional Stochastic Partial Differential Equations: Numerical Advances and Practical Applications—A State of the Art Review

“…At its essence, SPDEs elegantly merge the unpredictability of stochastic processes with the foundational principles of partial differential equations (PDEs), providing a robust framework for the mathematical modeling of physical phenomena with randomness, alongside the spatial and temporal dynamics inherent in them. The versatility and depth of SPDEs have led to their application in a diverse range of fields, from the intricate patterns of physics to the innovative designs of engineering [1][2][3][4][5], the fluctuating dynamics of financial markets [6][7][8][9][10], and the complex processes within biological sciences [11][12][13][14][15][16]. This cross-disciplinary enthusiasm highlights the crucial importance of SPDEs in deepening our understanding of the world, connecting theoretical exploration with pragmatic resolutions to complex problems.…”