Agarwal, A. and P.F.J. Lermusiaux, 2011. Statistical Field Estimation for Complex Coastal Regions and Archipelagos. Ocean Modeling, 40(2), 164-189, doi: 10.1016/j.ocemod.2011.08.001.
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 Bayesian-based multiscale Objective
Analysis (OA) approach to complex coastal regions and archipelagos. Such OAs
commonly require an estimate of the distances between data and model points,
without going across complex landforms. New OA schemes that estimate 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. 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 FMM’s 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.