Thomas Dubos

Using nudging to improve global-regional dynamic consistency in limited-area climate modeling: What should we nudge?

Regional climate modelling sometimes requires that the regional model be nudged towards the large-scale driving data to avoid the development of inconsistencies between them. These inconsistencies are known to produce large surface temperature and rainfall artefacts. Therefore, it is essential to maintain the synoptic circulation within the simulation domain consistent with the synoptic circulation at the domain boundaries. Nudging techniques, initially developed for data assimilation purposes, are increasingly used in regional climate modeling and offer a workaround to this issue. In this context, several questions on the “optimal” use of nudging are still open. In this study we focus on a specific question which is: What variable should we nudge? in order to maintain the consistencies between the regional model and the driving fields as much as possible. For that, a “Big Brother Experiment”, where a reference atmospheric state is known, is conducted using the weather research and forecasting (WRF) model over the Euro–Mediterranean region. A set of 22 3-month simulations is performed with different sets of nudged variables and nudging options (no nudging, indiscriminate nudging, spectral nudging) for summer and winter. The results show that nudging clearly improves the model capacity to reproduce the reference fields. However the skill scores depend on the set of variables used to nudge the regional climate simulations. Nudging the tropospheric horizontal wind is by far the key variable to nudge to simulate correctly surface temperature and wind, and rainfall. To a lesser extent, nudging tropospheric temperature also contributes to significantly improve the simulations. Indeed, nudging tropospheric wind or temperature directly impacts the simulation of the tropospheric geopotential height and thus the synoptic scale atmospheric circulation. Nudging moisture improves the precipitation but the impact on the other fields (wind and temperature) is not significant. As an immediate consequence, nudging tropospheric wind, temperature and moisture in WRF gives by far the best results with respect to the Big-Brother simulation. However, we noticed that a residual bias of the geopotential height persists due to a negative surface pressure anomaly which suggests that surface pressure is the missing quantity to nudge. Nudging the geopotential has no discernible effect. Finally, it should be noted that the proposed strategy ensures a dynamical consistency between the driving field and the simulated small-scale field but it does not ensure the best “observed” fine scale field because of the possible impact of incorrect driving large-scale field.

How Large-Scale and Cyclogeostrophic Barotropic Instabilities Favor the Formation of Anticyclonic Vortices in the Ocean

Large-scale vortices, that is, eddies whose characteristic length scale is larger than the local Rossby radius of deformation Rd, are ubiquitous in the oceans, with anticyclonic vortices more prevalent than cyclonic ones. Stability or robustness properties of already formed shallow-water vortices have been investigated to explain this cyclone-anticyclone asymmetry. Here the focus is on possible asymmetries during the generation of vortices through barotropic instability of a parallel flow. The initial stage and the nonlinear stage of the instability are studied by means of linear stability analysis and direct numerical simulations of the one-layer rotating shallow-water equations, respectively. A wide variety of parallel flows are studied: isolated shears, the Bickley jet, and a family of wakes obtained by combining two shears of opposite signs. The results show that, when the flow is characterized by finite relative isopycnal deviation, the barotropic instability favors the formation of large-scale anticyclonic eddies. The authors emphasize here that the cyclone- anticyclone asymmetry of parallel flowsmay appear at the linear stage of the instability. This asymmetry finds its origin in the linear stability property of localized shear flows. Indeed, for both the cyclogeostrophic regime (finite Rossby number) and the frontal geostrophic regime (smallBurger number), an anticyclonic shear flowhas higher linear growth rates than an equivalent cyclonic shear flow. The nonlinear saturation then leads to the formation of almost axisymmetric anticyclones, while the cyclones tend to be more elongated in the shear direction. However, although some unstable parallel flows exhibit the asymmetry at the linear stage, others exhibit such asymmetry at the nonlinear stage only. If the distance separating two shear regions is large enough, the barotropic instability develops independently in each shear, leading in the frontal and the cyclogeostrophic regime to a significant cyclone-anticyclone asymmetry at the linear stage. Conversely, if the two shear regions are close to each other, the shears tend to be coupled at the linear stage. The most unstable perturbation then resembles the sinuous mode of the Bickley jet, making no distinction between regions of cyclonic or anticyclonic vorticity. Nevertheless, when the nonlinear saturation occurs, large-scale anticyclones tend to be axisymmetric while the cyclonic structures are highly distorted and elongated along the jet meander.

Usual Approximations to the Equations of Atmospheric Motion: A Variational Perspective

AbstractThe usual geophysical approximations are reframed within a variational framework. Starting from the Lagrangian of the fully compressible Euler equations expressed in a general curvilinear coordinates system, Hamilton’s principle of least action yields Euler–Lagrange equations of motion. Instead of directly making approximations in these equations, the approach followed is that of Hamilton’s principle asymptotics; that is, all approximations are performed in the Lagrangian. Using a coordinate system where the geopotential is the third coordinate, diverse approximations are considered. The assumptions and approximations covered are 1) particular shapes of the geopotential; 2) shallowness of the atmosphere, which allows for the approximation of the relative and planetary kinetic energy; 3) small vertical velocities, implying quasi-hydrostatic systems; and 4) pseudoincompressibility, enforced by introducing a Lagangian multiplier.This variational approach greatly facilitates the derivation of the equa...

A Semihydrostatic Theory of Gravity-Dominated Compressible Flow

AbstractFrom Hamilton’s least-action principle, compressible equations of motion with density diagnosed from potential temperature through hydrostatic balance are derived. Slaving density to potential temperature suppresses the degrees of freedom supporting the propagation of acoustic waves and results in a soundproof system. The linear normal modes and dispersion relationship for an isothermal state of rest on f and β planes are accurate from hydrostatic to nonhydrostatic scales, except for deep internal gravity waves. Specifically, the Lamb wave and long Rossby waves are not distorted, unlike with anelastic or pseudoincompressible systems.Compared to similar equations derived by A. Arakawa and C. S. Konor, the semihydrostatic system derived here possesses an additional term in the horizontal momentum budget. This term is an apparent force resulting from the vertical coordinate not being the actual height of an air parcel but its hydrostatic height (the hypothetical height it would have after the atmosph...

Stability of parallel wake flows in quasigeostrophic and frontal regimes

Recent laboratory experiments [G. Perret, A. Stegner, M. Farge, and T. Pichon, Phys. Fluids 18, 036603 (2006)] have shown that the vortex-street formed in the wake of a towed cylinder in a rotating shallow-water layer could present a strong cyclone-anticyclone asymmetry. In extreme cases, only large-scale anticyclones were observed in the far wake. This asymmetry occurs in the so-called frontal regime when the Rossby number is small and the surface deviation is large. This asymmetry may have various origins and in particular may be attributed to the asymmetry of the flow around the cylinder, to the linear stability property of the wake, or to its nonlinear evolution. To discriminate between these mechanisms, we study the stability of two idealized parallel flows in the quasigeostrophic and in the frontal regimes. These parallel flows correspond to two velocity profiles measured just behind the cylinder in a region where the perturbations are negligible. According to our linear stability analysis, the most...

Equations of Atmospheric Motion in Non-Eulerian Vertical Coordinates: Vector-Invariant Form and Quasi-Hamiltonian Formulation

AbstractThe curl form of equations of inviscid atmospheric motion in general non-Eulerian coordinates is obtained. Narrowing down to a general vertical coordinate, a quasi-Hamiltonian form is then obtained in a Lagrangian, isentropic, mass-based or z-based vertical coordinate. In non-Lagrangian vertical coordinates, the conservation of energy by the vertical transport terms results from the invariance of energy under the vertical relabeling of fluid parcels. A complete or partial separation between the horizontal and vertical dynamics is achieved, except in the Eulerian case. The horizontal–vertical separation is especially helpful for (quasi-)hydrostatic systems characterized by vanishing vertical momentum. Indeed for such systems vertical momentum balance reduces to a simple statement: total energy is stationary with respect to adiabatic vertical displacements of fluid parcels. From this point of view the purpose of (quasi-)hydrostatic balance is to determine the vertical positions of fluid parcels, for...

Held‐Suarez simulations with the Community Atmosphere Model Spectral Element (CAM‐SE) dynamical core: A global axial angular momentum analysis using Eulerian and floating Lagrangian vertical coordinates

In this paper, an analysis of the global AAM conservation properties of NCAR’s Community Atmosphere Model Spectral Element (CAM-SE) dynamical core under Held-Suarez forcing is presented. It is shown that the spurious sources/sinks of AAM in CAM-SE are 3 orders of magnitude smaller than the parameterized (physical) sources/sinks. The effect on AAM conservation by changing various numerical aspects of the dynamical core (e.g., different vertical coordinates, reduced formal order of accuracy, increased dissipation, and decreased divergence damping) is investigated. In particular, it is noted that changing from Eulerian (hybrid-sigma) to floating Lagrangian vertical coordinates does not alter the global AAM conservation properties of CAM-SE.

Emergence and Secondary Instability of Ekman Layer Rolls

Abstract The authors revisit the idealized scenario by which long-lived rolls are believed to emerge in the neutral planetary boundary layer, that is, through the saturation of the shear instability of the neutrally stratified Ekman flow. First, the nonlinear stages of the primary instability are studied, using a constant turbulent viscosity with Reynolds numbers up to 1000. Two-dimensional equilibrated rolls are found to exist, as predicted earlier based on a weakly nonlinear expansion. However, the flow may not saturate into those equilibrated rolls if the turbulent Reynolds number is too high. Second, a linear stability analysis of these equilibrated rolls is performed, which finds that they are subject to a three-dimensional instability. The growth rate of the most unstable mode is comparable to the growth rate of the primary instability; the selected horizontal length scale is about 4 times shorter. The unstable mode draws its energy by interacting with both across-roll and along-roll shear, the latt...

Comparing the two-dimensional cascades of vorticity and a passive scalar

We compare two-dimensional vorticity and passive scalar cascades seen as a gradient enhancement process. Our criteria are based on conditional averages of the first and second Lagrangian derivatives of vorticity and passive scalar gradients in relation to the local flow geometry. In order to interpret these criteria, transient properties are derived for random vorticity and scalar fields, showing that the second-order Lagrangian derivatives of vorticity and passive scalar gradients may behave differently. Cascades obtained in numerical simulations of decaying and forced incompressible turbulence are analysed. First-order analysis reveals that the direct cascade in elliptic domains is more efficient than previously suspected. While several first-order diagnostics collapse to a single curve for vorticity and passive scalars, second-order diagnostics consistently show that the vorticity gradient exhibits faster temporal fluctuations than the passive scalar gradient, a property which we anticipate qualitatively in the study of random fields.

A conservative adaptive wavelet method for the shallow-water equations on the sphere

We introduce an innovative wavelet-based approach to adjust local grid resolution dynamically to maintain a uniform specified error tolerance. Extending the work of Dubos and Kevlahan, a wavelet multiscale approximation is used to make the Thuburn-RinglerSkamarock-Klemp (TRiSK) model dynamically adaptive for the rotating shallow-water equationsonthesphere.Thisarticlefocusesonthechallengesencounteredwhenextending theadaptivewaveletmethodtothesphereandensuringanefficientparallelimplementation using message passing interface (MPI). The wavelet method is implemented in Fortran 95 with an emphasis on computational efficiency and scales well up to O(10 2 ) processors for load-unbalanced scenarios and up to at least O(10 3 ) processors for load-balanced scenarios. The method is verified using standard smooth test cases and a nonlinear test case proposed by Galewsky et al. The dynamical grid adaption provides compression ratios of up to 50 times in a challenging homogenous turbulence test case. The adaptive code is aboutthreetimesslowerperactivegridpointthantheequivalentnon-adaptiveTRiSKcode and about four times slower per active grid point than an equivalent spectral code. This computationally efficient adaptive dynamical core could serve as the foundation on which to build a complete climate or weather model.