A multiscale model for tropical intraseasonal oscillations

Abstract

The tropical intraseasonal 40-to 50-day oscillation (TIO) is the dominant component of variability in the tropical atmosphere with remarkable planetary-scale circulation generated as envelopes of complex multiscale processes. A new multiscale model is developed here that clearly demonstrates the fashion in which planetary-scale circulations sharing many features in common with the observational record for the TIO are generated on intraseasonal time scales through the upscale transfer of kinetic and thermal energy generated by wave trains of organized synoptic-scale circulations having features in common with observed superclusters. The appeal of the multiscale models developed below is their firm mathematical underpinnings, simplicity, and analytic tractability while remaining self-consistent with key features of the observational record. The results below demonstrate, in a transparent fashion, the central role of organized vertically tilted synoptic-scale circulations in generating a planetary circulation resembling the TIO.T he dominant component of intraseasonal variability in the tropics is the 40-to 50-day tropical intraseasonal oscillation (TIO), often called the Madden-Julian oscillation (MJO) after its discoverers (1). In the troposphere, the MJO is an equatorial planetary-scale wave envelope of complex multiscale convective processes that begins as a standing wave in the Indian Ocean and propagates across the Western Pacific at a speed of Ϸ5 ms Ϫ1 (2-5). The planetary-scale circulation anomalies associated with the MJO significantly affect monsoon development and intraseasonal predictability in mid-latitudes and impact the development of the El Niño southern oscillation (ENSO) in the Pacific Ocean, which is one of the most important components of seasonal prediction (6-8). Present-day computer general circulation models (GCMs) typically poorly represent the MJO (9). One conjecture for the reason for this poor performance of GCMs is the inadequate treatment across multiple spatial scales of the interaction of the hierarchy of organized structures that generate the MJO as their envelope.There have been a large number of theories attempting to explain the MJO through a specific linearized mechanism such as evaporation wind feedback (10, 11), boundary layer frictional convective instability (12), stochastic linearized convection (13), radiation instability (14), and the planetary-scale linear response to moving heat sources (15). Moncrieff (16) recently developed an interesting phenomenological nonlinear theory for the upscale transport of momentum from equatorial mesoscales [O (300 km)] to planetary scales and applied this theory to explain the ''MJO-like'' structure in recent ''super-parametrization'' computer simulations (17) with a scale gap (no resolution at all) on scales between 200 and 1,200 km. Despite all of these interesting contributions, the problem of explaining the MJO has recently been called the search for the Holy Grail of tropical atmospheric dynamics (14). Here we contribute to this sear...

A general theoretical framework for understanding essential dynamics of Madden–Julian oscillation

“…; the moisture mode theory (Raymond and Fuchs 2009;Maloney 2012, 2013;Benedict et al 2014;Adames and Kim 2015); the MJO skeleton driven by synoptic wave activity (Majda and Biello 2004;Majda and Stechmann 2009); the MJO modified by interactive upscale transfer of eddy momentum, heat and moisture (Wang and Liu 2011;Wang 2012a, b, 2013); the multi-cloud model of MJO Majda 2006, 2007); the MJO wave packet driven by the interference pattern of a narrow frequency band of mixed Rossby-gravity waves (Yang and Ingersoll 2011) or westward and eastward inertia-gravity waves (Yang and Ingersoll 2013); and the air-sea interaction theory (Flatau et al 1997;Wang and Xie 1998;Wang and Zhang 2002;Fu and Wang 2004).…”

Multiple spatial scales in engineering and atmospheric low Mach number flows

“…Biello and Majda [3,21], demonstrate how such multi-scale interactions can trigger long-wave phenomena that do not resemble any of the classical long wave solutions represented by the homogeneous version of (74), but that have striking similarity with the thus far unexplained Madden-Julian-Oscillation [20].…”

“…We have neglected additional source terms in the two momentum equations (68) 3,4 , here. These were included in the original derivations in [22], but were found not to be important in a detailed study of solution structures related to the so-called "MaddenJulian-Oscillation" in [3,21]. Thus we assume the momentum sources to appear only at the next order in the expansions (see below).…”

A Review of the Nonlinear Dynamics of Intraseasonal Oscillations

“…The MJO is generated on intraseasonal time scales through the upscale transfer of kinetic and thermal energy generated by wave trains of organized synoptic-scale circulations that have features in common with observed convective superclusters. As shown by Majda and Klein (2003), Majda and Biello (2004), and Biello and Majda (2005), the IPESD models have firm mathematical underpinnings, conceptual simplicity, and analytic tractability while representing some of the crucial multiscale interactions for the planetary scale response, and they provide a better theoretical understanding of the multiscale aspects of the MJO.…”

“…Recently, a multi-scale theory of the MJO was developed by Majda and Biello (2004), Majda (2005, 2006), and Biello et al (2007) in which the structure of the planetary scale MJO is determined by upscale momentum and temperature fluxes from the synoptic scales in addition to direct heating on the planetary scale.…”