Propagation mechanisms for the Madden-Julian Oscillation

The Madden-Julian Oscillation (MJO) is examined using 20 years of outgoing longwave radiation and NCEP-NCAR reanalysis data. Two mechanisms for the eastward propagation and regeneration of the convective anomalies are suggested. The first is a local mechanism operating over the warm pool region. At the phase of the MJO with a dipole structure to the convection anomalies, there is enhanced tropical convection over the eastern Indian Ocean and reduced convection over the western Pacific. Over the equatorial western Indian Ocean, the equatorial Rossby wave response to the west of the enhanced convection includes a region of anomalous surface divergence associated with the anomalous surface westerlies and pressure ridge. This tends to suppress ascent in the boundary layer and shuts off the deep convection, eventually leading to a convective anomaly of the opposite sign. Over the Indonesian sector, the equatorial Kelvin wave response to the east of the enhanced convection includes a region of anomalous surface convergence into the anomalous equatorial surface easterlies and pressure trough, which will tend to favour convection in this region. The Indonesian sector is also influenced by an equatorial Rossby wave response (of opposite sign) to the west of the reduced convection over the western Pacific, which also has a region of anomalous surface convergence associated with its anomalous equatorial surface easterlies and pressure trough. Hence, convective anomalies of either sign tend to erode themselves from the west and initiate a convective anomaly of opposite sign via their equatorial Rossby wave response, and expand to the east via their equatorial Kelvin wave response. The second is a global mechanism involving an anomaly completing a circuit of the equator. Enhanced convection over the tropical western Pacific excites a negative sea level pressure (SLP) anomaly which radiates rapidly eastward as a dry equatorial Kelvin wave at approximately 35 m s-1 over the eastern Pacific. It is blocked by the orographic barrier of the Andes and Central America for several days before propagating through the gap at Panama. After rapidly propagating as a dry equatorial Kelvin wave over the Atlantic, the SLP anomaly is delayed further by the East African Highlands before it reaches the Indian Ocean and coincides with the development of enhanced convection at the start of the next MJO cycle

Nonlinear metastability for a parabolic system of reaction-diffusion equations

We consider a system of reaction-diffusion equations in a bounded interval of the real line, with emphasis on the metastable dynamics, whereby the time-dependent solution approaches its steady state in an asymptotically exponentially long time interval as the viscosity coefficient $\varepsilon>0$ goes to zero. To rigorous describe such behavior, we analyze the dynamics of solutions in a neighborhood of a one-parameter family of approximate steady states, and we derive an ODE for the position of the internal interfaces.Comment: This paper has been withdrawn by the author due to an error in Theorem 1.1. Please refer to the paper "Slow dynamics in reaction-diffusion systems

Fast and slow Kelvin waves in the Madden-Julian Oscillation of a GCM

The structure of the Madden-Julian Oscillation (MJO) in an 1800-day integration of the Hadley Centre Unified Model was analysed, and interpreted within a Kelvin wave framework. The model was forced with constant equinoctial (March) boundary conditions so that a ``clean'' MJO signal could be separated from the effects of the seasonal cycle and forced interannual variability. The simulated MJO was fairly realistic in terms of its large-scale spatial structure and propagation characteristics, although its period of 30 days (corresponding to an average phase speed of 15 \mps) was shorter than that observed. The signal in deep convection was less coherent than in observations, and appeared to move eastward as a sequence of discrete convective anomalies, rather than by a smooth eastward propagation. Both ``fast'' and ``slow'' equatorial Kelvin waves appeared to play an important role in the eastward propagation of the simulated MJO. Enhanced convection over the Indian Ocean was associated with a ``fast'' equatorial Kelvin wave that propagated eastward at 55 m s-1 over the Pacific. On reaching the west coast of South America, a component of this Kelvin wave propagated northward and southward as a trapped wave along the mountain ranges of Central America and the Andes, in agreement with observations. The anomalous surface easterlies over the tropical eastern Pacific associated with this fast Kelvin wave enhanced the climatological mean easterlies and led to positive convective anomalies over the eastern Pacific consistent with the WISHE mechanism. However, WISHE was not able to account for the eastward development of the convective anomalies over the Indian Ocean/western Pacific region. By splitting the equatorial divergence anomalies of the simulated MJO into their du/dx and dv/dy components, the role of Kelvin wave dynamics in the ``slow'' (15 m s-1) average eastward propagation of the simulated MJO was examined. Although the two components were of comparable magnitude, the \dudx\ component exhibited a pronounced eastward propagation which tended to be disrupted by the \dvdy\ component, thus supporting the paradigm of an underlying, but strongly modified, Kelvin wave mechanism

High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: O(1)\mathcal{O}(1) Sampling Cost via Incident-Field Windowing and Recentering

This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains. Relying on Fourier Transformation in time, the method utilizes a fixed (time-independent) number of frequency-domain integral-equation solutions to evaluate, with superalgebraically-small errors, time domain solutions for arbitrarily long times. The approach relies on two main elements, namely, 1) A smooth time-windowing methodology that enables accurate band-limited representations for arbitrarily-long time signals, and 2) A novel Fourier transform approach which, in a time-parallel manner and without causing spurious periodicity effects, delivers numerically dispersionless spectrally-accurate solutions. A similar hybrid technique can be obtained on the basis of Laplace transforms instead of Fourier transforms, but we do not consider the Laplace-based method in the present contribution. The algorithm can handle dispersive media, it can tackle complex physical structures, it enables parallelization in time in a straightforward manner, and it allows for time leaping---that is, solution sampling at any given time $T$ at $\mathcal{O}(1)$-bounded sampling cost, for arbitrarily large values of $T$, and without requirement of evaluation of the solution at intermediate times. The proposed frequency-time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including e.g. the time-domain Maxwell equations), and which is applicable in a wide range of scientific and engineering contexts, provides significant advantages over other available alternatives such as volumetric discretization, time-domain integral equations, and convolution-quadrature approaches.Comment: 33 pages, 8 figures, revised and extended manuscript (and now including direct comparisons to existing CQ and TDIE solver implementations) (Part I of II

An application of interpolating scaling functions to wave packet propagation

Wave packet propagation in the basis of interpolating scaling functions (ISF) is studied. The ISF are well known in the multiresolution analysis based on spline biorthogonal wavelets. The ISF form a cardinal basis set corresponding to an equidistantly spaced grid. They have compact support of the size determined by the underlying interpolating polynomial that is used to generate ISF. In this basis the potential energy matrix is diagonal and the kinetic energy matrix is sparse and, in the 1D case, has a band-diagonal structure. An important feature of the basis is that matrix elements of a Hamiltonian are exactly computed by means of simple algebraic transformations efficiently implemented numerically. Therefore the number of grid points and the order of the underlying interpolating polynomial can easily be varied allowing one to approach the accuracy of pseudospectral methods in a regular manner, similar to high order finite difference methods. The results of numerical simulations of an H+H_2 collinear collision show that the ISF provide one with an accurate and efficient representation for use in the wave packet propagation method.Comment: plain Latex, 11 pages, 4 figures attached in the JPEG forma

Testing the Hypothesis that the MJO is a Mixed Rossby-Gravity Wave Packet

The Madden Julian oscillation (MJO), also known as the intraseasonal oscillation (ISO), is a planetary-scale mode of variation in the tropical Indian and western Pacific Oceans. Basic questions about the MJO are why it propagates eastward at ~5 m s^(-1), why it lasts for intraseasonal time scales, and how it interacts with the fine structure that is embedded in it. This study will test the hypothesis that the MJO is not a wave but a wave packet-the interference pattern produced by a narrow frequency band of mixed Rossby gravity (MRG) waves. As such, the MJO would propagate with the MRG group velocity, which is eastward at ~5 m s^(-1) Simulation with a 3D model shows that MRG waves can be forced independently by relatively short-lived, eastward- and westward-moving disturbances, and the MRG wave packet can last long enough to form the intraseasonal variability. This hypothesis is consistent with the view that the MJO is episodic, with an irregular time interval between events rather than a periodic oscillation. The packet is defined as the horizontally smoothed variance of the MRG wave-the rectified MRG wave, which has features in common with the MJO. The two-dimensional Fourier analysis of the NOAA outgoing longwave radiation (OLR) dataset herein indicates that there is a statistically significant correlation between the MJO amplitude and wave packets of MRG waves but not equatorial Rossby waves or Kelvin waves, which are derived from the Matsuno shallow water theory. However, the biggest absolute value of the correlation coefficient is only 0.21, indicating that the wave packet hypothesis explains only a small fraction of the variance of the MJO in the OLR data