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

Learning Parameterized Skills

We introduce a method for constructing skills capable of solving tasks drawn from a distribution of parameterized reinforcement learning problems. The method draws example tasks from a distribution of interest and uses the corresponding learned policies to estimate the topology of the lower-dimensional piecewise-smooth manifold on which the skill policies lie. This manifold models how policy parameters change as task parameters vary. The method identifies the number of charts that compose the manifold and then applies non-linear regression in each chart to construct a parameterized skill by predicting policy parameters from task parameters. We evaluate our method on an underactuated simulated robotic arm tasked with learning to accurately throw darts at a parameterized target location.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

A Short Proof of Gamas's Theorem

If \chi^\lambda is the irreducible character of the symmetric group S_n corresponding to the partition \lambda of n then we may symmetrize a tensor v_1 \otimes ... \otimes v_n by \chi^\lambda. Gamas's theorem states that the result is not zero if and only if we can partition the set {v_i} into linearly independent sets whose sizes are the parts of the transpose of \lambda. We give a short and self-contained proof of this fact

Equality of symmetrized tensors and the coordinate ring of the flag variety

In this note we give a transparent proof of a result of da Cruz and Dias da Silva on the equality of symmetrized decomposable tensors. This will be done by explaining that their result follows from the fact that the coordinate ring of a flag variety is a unique factorization domain.Comment: 5 page

Triggered Convection, Gravity Waves, and the MJO: A Shallow-Water Model

The Madden–Julian oscillation (MJO) is the dominant mode of intraseasonal variability in the tropics. Despite its primary importance, a generally accepted theory that accounts for fundamental features of the MJO, including its propagation speed, planetary horizontal scale, multiscale features, and quadrupole structures, remains elusive. In this study, the authors use a shallow-water model to simulate the MJO. In this model, convection is parameterized as a short-duration localized mass source and is triggered when the layer thickness falls below a critical value. Radiation is parameterized as a steady uniform mass sink. The following MJO-like signals are observed in the simulations: 1) slow eastward-propagating large-scale disturbances, which show up as low-frequency, low-wavenumber features with eastward propagation in the spectral domain, 2) multiscale structures in the time–longitude (Hovmöller) domain, and 3) quadrupole vortex structures in the longitude–latitude (map view) domain. The authors propose that the simulated MJO signal is an interference pattern of westward and eastward inertia–gravity (WIG and EIG) waves. Its propagation speed is half of the speed difference between the WIG and EIG waves. The horizontal scale of its large-scale envelope is determined by the bandwidth of the excited waves, and the bandwidth is controlled by the number density of convection events. In this model, convection events trigger other convection events, thereby aggregating into large-scale structures, but there is no feedback of the large-scale structures onto the convection events. The results suggest that the MJO is not so much a low-frequency wave, in which convection acts as a quasi-equilibrium adjustment, but is more a pattern of high-frequency waves that interact directly with the convection

A theory of the MJO horizontal scale

Here we ask, what controls the horizontal scale of the Madden-Julian Oscillation, i.e., what controls its zonal wave number k? We present a new one-dimensional (1D) β-plane model that successfully simulates the MJO with the same governing mechanism as the 2D shallow water model of Yang and Ingersoll (2013). Convection is parameterized as a short-duration localized mass source that is triggered when the layer thickness falls below a critical value. Radiation is parameterized as a steady uniform mass sink. Both models tend toward a statistically steady state—a state of radiative-convective equilibrium, not just on a global scale but also on the scale of each MJO event. This gives k ~ (S_(c)/c)^(1/2), where S_c is the spatial-temporal frequency of convection events and c is the Kelvin wave speed. We offer this scaling as a prediction of how the MJO would respond to climate change