Search for: All records

Abstract. In sequential estimation methods often used in oceanic and general climatecalculations of the state and of forecasts, observations act mathematicallyand statistically as source or sink terms in conservation equations for heat, salt, mass, and momentum.These artificial terms obscure the inference of the system's variability or secular changes.Furthermore, for the purposes of calculating changes inimportant functions of state variables such as total mass and energy orvolumetric current transports, results of both filter and smoother-based estimates are sensitive to misrepresentationof a large variety of parameters, including initial conditions, prioruncertainty covariances, and systematic and random errors in observations.Here, toy models of a coupled mass–spring oscillator system and of a barotropic Rossby wave system are used todemonstrate many of the issues that arise from such misrepresentations.Results from Kalman filter estimates and those from finite intervalsmoothing are analyzed.In the filter (and prediction) problem, entry of data leads to violation ofconservation and other invariant rules.A finite interval smoothing method restores the conservation rules, butuncertainties in all such estimation results remain. Convincing trend andother time-dependent determinations in “reanalysis-like” estimates require a full understanding of models, observations, and underlying error structures. Application of smoother-type methods that are designed for optimal reconstruction purposes alleviate some of the issues. 

Maas ( J. Fluid Mech. , vol. 684, 2011, pp. 5–24) showed that, for an oscillating two-dimensional barotropic tide flowing over sub-critical topography of compact support, some topographic forms existed that produced non-radiating baroclinic disturbances. The problem is related to ‘stealth’ and ‘cloaking’ problems. Here Maas's result is derived using a simpler approach, not involving complicated mappings, but formally restricted to perturbation topography. Wider results come from the discussion of nearly compact support topographic disturbances provided by Schwartz functions with weak high-wavenumber radiation and by exploiting both a known functional equation formulation and Fourier methods. The problem is extended to disturbances on uniform slopes. A variety of non-radiating topographies can be found, although they are mathematically delicate and unlikely to be found in nature. Topography with weak radiation at high wavenumber is a much wider class of structures. Application of these solutions would lie with the ability to estimate dissipation over and near the topography from motions observed at a distance.