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Statistical Field Estimation for Complex Coastal Regions and Archipelagos (PREPRINT)

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Journal article preprint

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A fundamental requirement in realistic ocean simulations and dynamical studies is the optimal estimation of gridded fields from the spatially irregular and multivariate data sets that are collected by varied platforms. In this work, we derive and utilize new schemes for the mapping and dynamical inference of ocean fields in complex multiply-connected domains and study the computational properties of these schemes. Specifically, we extend a multiscale Objective Analysis OA approach to complex coastal regions and archipelagos. Bayesian-based OAs using covariances as inputs commonly require an estimate of the distances between data and model points, without going across complex landforms. New OA schemes based on estimating the length of shortest sea paths using the Level Set Method LSM and Fast Marching Method FMM are thus derived, implemented and utilized in idealized and realistic ocean cases. An FMM-based methodology for the estimation of total velocity under geostrophic balance in complex domains is also presented. Comparisons with other OA approaches are provided, including those using stochastically forced partial differential equations SPDEs. We find that the FMM-based OA scheme is the most efficient and accurate. We also show that the FMM-based field maps do not require postprocessing smoothing. Mathematical and computational properties of our new OA schemes are studied in detail using fundamental theorems and illustrations. We find that higher-order FMMs schemes improve accuracy and that a multi-order scheme is efficient. We also provide solutions that ensure the use of positive-definite covariances, even in complex multiply-connected domains.

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  • Cartography and Aerial Photography
  • Physical and Dynamic Oceanography
  • Numerical Mathematics
  • Computer Programming and Software

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