Abstract
Lagrangian tracers are drifters and floaters that collect real-time information of fluid flows. This paper studies the model error in filtering multiscale random rotating compressible flow fields utilizing noisy Lagrangian tracers. The random flow fields are defined through random amplitudes of Fourier eigenmodes of the rotating shallow-water equations that contain both incompressible geostrophically balanced (GB) flows and rotating compressible gravity waves, where filtering the slow-varying GB flows is of primary concern. Despite the inherent nonlinearity in the observations with mixed GB and gravity modes, there are closed analytical formulas for filtering the underlying flows. Besides the full optimal filter, two practical imperfect filters are proposed. An information-theoretic framework is developed for assessing the model error in the imperfect filters, which can apply to a single realization of the observations. All the filters are comparably skillful in a fast rotation regime (Rossby number
Denotes Open Access content.