Numerical representation of internal waves propagation

Similar to surface waves propagating at the interface of two fluid of different densities (like air and water), internal waves in the oceanic interior travel along surfaces separating waters of different densities (e.g. at the thermocline). Due to their key role in the global distribution of (physical) diapycnal mixing and mass transport, proper representation of internal wave dynamics in numerical models should be considered a priority since global climate models are now configured with increasingly higher horizontal/vertical resolution. However, in most state-of-the-art oceanic models, important terms involved in the propagation of internal waves (namely the horizontal pressure gradient and horizontal divergence in the continuity equation) are generally discretized using very basic numerics (i.e. second-order approximations) in space and time. In this paper, we investigate the benefits of higher-order approximations in terms of the discrete dispersion relation (in the linear theory) on staggered and nonstaggered computational grids. A fourth-order scheme discretized on a C-grid to approximate both pressure gradient and horizontal divergence terms provides clear improvements but, unlike nonstaggered grids, prevents the use of monotonic or non- oscillatory schemes. Since our study suggests that better numerics is required, second and fourth order direct space-time algorithms are designed, thus paving the way toward the use of efficient high-order discretizations of internal gravity waves in oceanic models, while maintaining good sta- bility properties (those schemes are stable for Courant numbers smaller than 1). Finally, important results obtained at a theoretical level are illustrated at a discrete level using two-dimensional (x,z) idealized experiments

A reduced-order strategy for 4D-Var data assimilation

This paper presents a reduced-order approach for four-dimensional variational data assimilation, based on a prior EO F analysis of a model trajectory. This method implies two main advantages: a natural model-based definition of a mul tivariate background error covariance matrix $\textbf{B}_r$, and an important decrease of the computational burden o f the method, due to the drastic reduction of the dimension of the control space. % An illustration of the feasibility and the effectiveness of this method is given in the academic framework of twin experiments for a model of the equatorial Pacific ocean. It is shown that the multivariate aspect of $\textbf{B}_r$ brings additional information which substantially improves the identification procedure. Moreover the computational cost can be decreased by one order of magnitude with regard to the full-space 4D-Var method

Cork suberin as an additive in offset lithographic printing inks

Suberin oligomers, isolated from cork (Quercus suber L.), were used as additives in ‘Waterless’ and vegetable-oil ink formulations, in the range of 2–10% w/w. The rheological behaviour of the suberin oligomers as well as of the inks, with and without suberin, were investigated as a function of temperature. It was shown that the addition of suberin induces a decrease of viscosity of both inks. The tack of pristine inks, suberin oligomers and their mixtures were determined at different temperatures: the variation of this parameter as a function of time provided information about the drying kinetics of these formulations. The tack of the ‘Waterless’ ink was found to increase with the introduction of suberin, whereas that of vegetable-oil based counterparts decreased. All the trends observed were interpreted in terms of the differences in composition between the two types of inks. Preliminary printing tests were carried out with the various suberin-containing inks.info:eu-repo/semantics/publishedVersio

Physics–Dynamics Coupling in weather, climate and Earth system models: Challenges and recent progress

This is the final version. Available from American Meteorological Society via the DOI in this record.Numerical weather, climate, or Earth system models involve the coupling of components. At a broad level, these components can be classified as the resolved fluid dynamics, unresolved fluid dynamical aspects (i.e., those represented by physical parameterizations such as subgrid-scale mixing), and nonfluid dynamical aspects such as radiation and microphysical processes. Typically, each component is developed, at least initially, independently. Once development is mature, the components are coupled to deliver a model of the required complexity. The implementation of the coupling can have a significant impact on the model. As the error associated with each component decreases, the errors introduced by the coupling will eventually dominate. Hence, any improvement in one of the components is unlikely to improve the performance of the overall system. The challenges associated with combining the components to create a coherent model are here termed physics–dynamics coupling. The issue goes beyond the coupling between the parameterizations and the resolved fluid dynamics. This paper highlights recent progress and some of the current challenges. It focuses on three objectives: to illustrate the phenomenology of the coupling problem with references to examples in the literature, to show how the problem can be analyzed, and to create awareness of the issue across the disciplines and specializations. The topics addressed are different ways of advancing full models in time, approaches to understanding the role of the coupling and evaluation of approaches, coupling ocean and atmosphere models, thermodynamic compatibility between model components, and emerging issues such as those that arise as model resolutions increase and/or models use variable resolutions.Natural Environment Research Council (NERC)National Science FoundationDepartment of Energy Office of Biological and Environmental ResearchPacific Northwest National Laboratory (PNNL)DOE Office of Scienc

Piston-driven numerical wave tank based on WENO solver of well-balanced shallow water equations

A numerical wave tank equipped with a piston type wave-maker is presented for long-duration simulations of long waves in shallow water. Both wave maker and tank are modelled using the nonlinear shallow water equations, with motions of the numerical piston paddle accomplished via a linear mapping technique. Three approaches are used to increase computational efficiency and accuracy. First, the model satisfies the exact conservation property (C-property), a stepping stone towards properly balancing each term in the governing equation. Second, a high-order weighted essentially non-oscillatory (WENO) method is used to reduce accumulation of truncation error. Third, a cut-off algorithm is implemented to handle contaminated digits arising from round-off error. If not treated, such errors could prevent a numerical scheme from satisfying the exact C-property in long-duration simulations. Extensive numerical tests are performed to examine the well-balanced property, high order accuracy, and shock-capturing ability of the present scheme. Correct implementation of the wave paddle generator is verified by comparing numerical predictions against analytical solutions of sinusoidal, solitary, and cnoidal waves. In all cases, the model gives satisfactory results for small-amplitude, low frequency waves. Error analysis is used to investigate model limitations and derive a user criterion for long wave generation by the model

Sensitivity of ocean-atmosphere coupled models to the coupling method : example of tropical cyclone Erica

In this paper, the sensitivity of Atmospheric and Oceanic Coupled Models (AOCMs) to the coupling method is investigated. We propose the adaptation of a Schwarz-like domain decomposition method to AOCMs. We show that the iterative process of the method ensures consistency of the coupled solution across the air-sea interface, contrarily to usual \textit{ad-hoc} algorithmic approaches. The latter are equivalent to only one iteration of a Schwarz-like iterative method, which does not provide a converged state. It is generally assumed that this lack of consistency does not affect significantly the physical properties of the solution. The relevancy of this statement is first assessed in a simplified problem, then in the realistic application of a mesoscale atmospheric model (WRF) coupled with a regional oceanic model (ROMS) to simulate the genesis and propagation of tropical cyclone Erica. Sensitivity tests to the coupling method are carried out in an ensemble approach.We show that with a mathematically consistent coupling the spread of the ensemble is reduced,suggesting that there is room for further improvements in the formulation of AOCMs at a mathematicaland numerical level

Advanced Data Assimilation for Geosciences : Lecture Notes of the Les Houches School of Physics

This book gathers notes from lectures and seminars given during a three-week school on theoretical and applied data assimilation held in Les Houches in 2012. Data assimilation aims at determining as accurately as possible the state of a dynamical system by combining heterogeneous sources of information in an optimal way. Generally speaking, the mathematical methods of data assimilation describe algorithms for forming optimal combinations of observations of a system, a numerical model that describes its evolution, and appropriate prior information. Data assimilation has a long history of application to high-dimensional geophysical systems dating back to the 1960s, with application to the estimation of initial conditions for weather forecasts. It has become a major component of numerical forecasting systems in geophysics, and an intensive field of research, with numerous additional applications in oceanography and atmospheric chemistry, with extensions to other geophysical sciences. The physical complexity and the high dimensionality of geophysical systems have led the community of geophysics to make significant contributions to the fundamental theory of data assimilation. This book is composed of a series of main lectures, presenting the fundamentals of four-dimensional variational data assimilation, the Kalman filter, smoothers, and the information theory background required to understand and evaluate the role of observations; a series of specialized lectures, addressing various aspects of data assimilation in detail, from the most recent developments in the theory to the specificities of various thematic applications