A non-oscillatory balanced scheme for an idealized tropical climate model

We use the non-oscillatory balanced numerical scheme developed in Part I to track the dynamics of a dry highly nonlinear barotropic/baroclinic coupled solitary wave, as introduced by Biello and Majda (2004), and of the moisture fronts of Frierson et al. (2004) in the presence of dry gravity waves, a barotropic trade wind, and the beta effect. It is demonstrated that, for the barotropic/baroclinic solitary wave, except for a little numerical dissipation, the scheme utilized here preserves total energy despite the strong interactions and exchange of energy between the baroclinic and barotropic components of the flow. After a short transient period where the numerical solution stays close to the asymptotic predictions, the flow develops small scale eddies and ultimately becomes highly turbulent. It is found here that the interaction of a dry gravity wave with a moisture front can either result in a reflection of a fast moistening front or the pure extinction of the precipitation. The barotropic trade wind stretches the precipitation patches and increases the lifetime of the moisture fronts which decay naturally by the effects of dissipation through precipitation while the Coriolis effect makes the moving precipitation patches disappear and appear at other times and places.     

Simulation of convectively coupled waves using WRF: a framework for assessing the effects of mesoscales on synoptic scales

The atmospheric variability in the tropics is primarily driven by convective heating. Observations revealed that convection in the tropics is organized into a hierarchy of multiscale convective systems ranging from the individual cloud cells to planetary scale disturbances that are nested within each other like Russian dolls. Current global climate models simulate very poorly these convectively coupled waves due in part to inadequate treatment of organized convection by the underlying cumulus parameterizations. Here, we present idealized simulations of convectively coupled equatorial waves (CCWs) using the weather research and forecast model in a horizontally limited domain consisting of a 4,500 km-wide square centered at the equator at moderate horizontal resolution of 10 km. We attempted and compared various configuration options, including switching on and off the cumulus parameterization (CP) and nesting a fine resolution 3.33 km domain, a 2,000 km-wide square, in the middle of the domain. It turns out that the results without a CP are much superior than those using a CP. While the cases without a CP resulted in a coherent eastward propagating CCW, which has many common features with observed convectively coupled Kelvin waves, the cumulus parameterization tends to destroy both the coherence of the propagating waves, even in the case with a nested domain, and reduces dramatically the variability. A primary demonstration on how such results could be used to show evidence of energy exchange, through momentum transport, between small-scale circulation due to mesoscale convection and the propagating synoptic scale wave will be reported is also presented.     

Simple models for the diurnal cycle and convectively coupled waves

This paper presents a study of the diurnal cycle of tropical precipitation and its interaction with convectively coupled waves in the context of simple models with crude vertical resolution. One and two baroclinic mode models are tested in both the context of a one-column model and the context of a full spatial dependency that permits waves to propagate and interact with the diurnal cycle. It is found that a one baroclinic mode model is capable of reproducing a realistic diurnal cycle of tropical precipitation both over land and over the ocean provided an adequate switch function is used to mimic the congestus preconditioning mechanism that operates in the multicloud model of Khouider and Majda. However, a full two baroclinic mode multicloud model is needed to capture the interaction of convectively coupled tropical waves with the diurnal cycle. In a more conventional mass flux parameterization framework, both one and two baroclinic mode models fail to capture the diurnal cycle of tropical precipitation.     

A zonally symmetric model for the monsoon-Hadley circulation with stochastic convective forcing

Idealized models of reduced complexity are important tools to understand key processes underlying a complex system. In climate science in particular, they are important for helping the community improve our ability to predict the effect of climate change on the earth system. Climate models are large computer codes based on the discretization of the fluid dynamics equations on grids of horizontal resolution in the order of 100 km, whereas unresolved processes are handled by subgrid models. For instance, simple models are routinely used to help understand the interactions between small-scale processes due to atmospheric moist convection and large-scale circulation patterns. Here, a zonally symmetric model for the monsoon circulation is presented and solved numerically. The model is based on the Galerkin projection of the primitive equations of atmospheric synoptic dynamics onto the first modes of vertical structure to represent free tropospheric circulation and is coupled to a bulk atmospheric boundary layer (ABL) model. The model carries bulk equations for water vapor in both the free troposphere and the ABL, while the processes of convection and precipitation are represented through a stochastic model for clouds. The model equations are coupled through advective nonlinearities, and the resulting system is not conservative and not necessarily hyperbolic. This makes the design of a numerical method for the solution of this system particularly difficult. Here, we develop a numerical scheme based on the operator time-splitting strategy, which decomposes the system into three pieces: a conservative part and two purely advective parts, each of which is solved iteratively using an appropriate method. The conservative system is solved via a central scheme, which does not require hyperbolicity since it avoids the Riemann problem by design. One of the advective parts is a hyperbolic diagonal matrix, which is easily handled by classical methods for hyperbolic equations, while the other advective part is a nilpotent matrix, which is solved via the method of lines. Validation tests using a synthetic exact solution are presented, and formal second-order convergence under grid refinement is demonstrated. Moreover, the model is tested under realistic monsoon conditions, and the ability of the model to simulate key features of the monsoon circulation is illustrated in two distinct parameter regimes.     

Further on Set-Valued Equilibrium Problems and Applications to Browder Variational Inclusions

In this paper, we introduce some concepts of convexity and semicontinuity for real set-valued mappings similar to those of real single-valued mappings. Then, we obtain different results on the existence of solutions of set-valued equilibrium problems generalizing in a common way several old ones for both single-valued and set-valued equilibrium problems. Applications to Browder variational inclusions, with weakened conditions on the involved set-valued operator, are given.     

Amorphous carbon nitride as an alternative electrode material in electroanalysis: Simultaneous determination of dopamine and ascorbic acid

Boron-doped diamond (BDD) films are excellent electrode materials, whose electrochemical activity for some analytes can be tuned by controlling their surface termination, most commonly either to predominantly hydrogen or oxygen. This tuning can be accomplished by e.g. suitable cathodic or anodic electrochemical pretreatments. Recently, it has been shown that amorphous carbon nitride (a-CN_x) films may present electrochemical characteristics similar to those of BDD, including the influence of surface termination on their electrochemical activity toward some analytes. In this work, we report for the first time a complete electroanalytical method using an a-CN_x electrode. Thus, an a-CN_x film deposited on a stainless steel foil by DC magnetron sputtering is proposed as an alternative electrode for the simultaneous determination of dopamine (DA) and ascorbic acid (AA) in synthetic biological samples by square-wave voltammetry. The obtained results are compared with those attained using a BDD electrode. For both electrodes, a same anodic pretreatment in 0.1 mol L⁻¹ KOH was necessary to attain an adequate and equivalent separation of the DA and AA oxidation potential peaks of about 330 mV. The detection limits obtained for the simultaneous determination of these analytes using the a-CN_x electrode were 0.0656 μmol L⁻¹ for DA and 1.05 μmol L⁻¹ for AA, whereas with the BDD electrode these values were 0.283 μmol L⁻¹ and 0.968 μmol L⁻¹, respectively. Furthermore, the results obtained in the analysis of the analytes in synthetic biological samples were satisfactory, attesting the potential application of the a-CN_x electrode in electroanalysis.     

Stochastic viscosity solutions for SPDEs with continuous coefficients

In this note, nonlinear stochastic partial differential equations (SPDEs) with continuous coefficients are studied. Via the solutions of backward doubly stochastic differential equations (BDSDEs) with continuous coefficients, we provide an existence result of stochastic viscosity sub- and super-solutions to this class of SPDEs. Under some stronger conditions, we prove the existence of stochastic viscosity solutions.     

Multicloud Convective Parametrizations with Crude Vertical Structure

Recent observational analysis reveals the central role of three multi-cloud types, congestus, stratiform, and deep convective cumulus clouds, in the dynamics of large scale convectively coupled Kelvin waves, westward propagating two-day waves, and the Madden–Julian oscillation. The authors have recently developed a systematic model convective parametrization highlighting the dynamic role of the three cloud types through two baroclinic modes of vertical structure: a deep convective heating mode and a second mode with low level heating and cooling corresponding respectively to congestus and stratiform clouds. The model includes a systematic moisture equation where the lower troposphere moisture increases through detrainment of shallow cumulus clouds, evaporation of stratiform rain, and moisture convergence and decreases through deep convective precipitation and a nonlinear switch which favors either deep or congestus convection depending on whether the troposphere is moist or dry. Here several new facets of these multi-cloud models are discussed including all the relevant time scales in the models and the links with simpler parametrizations involving only a single baroclinic mode in various limiting regimes. One of the new phenomena in the multi-cloud models is the existence of suitable unstable radiative convective equilibria (RCE) involving a larger fraction of congestus clouds and a smaller fraction of deep convective clouds. Novel aspects of the linear and nonlinear stability of such unstable RCE’s are studied here. They include new modes of linear instability including mesoscale second baroclinic moist gravity waves, slow moving mesoscale modes resembling squall lines, and large scale standing modes. The nonlinear instability of unstable RCE’s to homogeneous perturbations is studied with three different types of nonlinear dynamics occurring which involve adjustment to a steady deep convective RCE, periodic oscillation, and even heteroclinic chaos in suitable parameter regimes.     

Les Sels de Bismuth (III) Comme Catalyseurs Dans la Reaction D'ouverture Des Epoxydes Par Les Amines

BiCl 3 and Bi (OTf) 3 catalyze the opening of epoxides ( 1-7 ) by amines ( 8-12 ). High regioselectivities are observed. BiCl 3 et Bi (OTf) 3 catalysent la réaction d'ouverture des époxydes ( 1-7 ) par les amines ( 8-12 ). La réaction est fortement régiosélective.     

The interaction of equatorial waves with a barotropic shear: a potential test case for climate model dynamical cores

We compare the performances of two different numerical methods to solve the equatorial shallow water equations in a background meridional shear: A coarse-resolution Galerkin-truncation-based method and a finite-volume method, for the case of an equatorial Rossby wave. In the presence of the barotropic shear, the Rossby wave quickly loses its energy through shear interaction and excites other equatorially trapped waves despite the fact that the PDE system is linear. The two methods handle this sudden energy exchange across scales very differently. While the finite volume converges statistically to a coherent large-scale solution, the Galerkin truncation method results in large-scale and slow oscillations where energy is bumped back and forth within the resolved-scale spectrum, involving higher-order equatorial wave modes heavily depending on numerical resolution, that is, the number of Galerkin basis functions. The addition of an artificial viscosity for the coarse-resolution Galerkin method heavily damps the energy oscillations without significantly changing its transient dynamics. This provides an example of interaction across scales where the resolution of scales that are apparently not representative of the statistical solution are important for the transient dynamics. Therefore, non-linear interactions of equatorially trapped waves may provide an interesting test bed for the validation of climate model dynamical cores.