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Recent observational analysis reveals the central role of three multicloud 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. A systematic model convective parameterization highlighting the dynamic role of… (More)

- Andrew J. Majda, Samuel N. Stechmann
- Proceedings of the National Academy of Sciences…
- 2009

The Madden-Julian oscillation (MJO) is the dominant mode of variability in the tropical atmosphere on intraseasonal timescales and planetary spatial scales. Despite the primary importance of the MJO and the decades of research progress since its original discovery, a generally accepted theory for its essential mechanisms has remained elusive. Here, we… (More)

A multiscale model of the MJO is developed here that accounts, in a simplified fashion, for both the upscale transfer from synoptic to planetary scales of momentum and temperature from wave trains of thermally driven equatorial synoptic-scale circulations in a moving convective envelope as well as direct mean heating on planetary scales. This model involves… (More)

Systematic multiscale perturbation theory is utilized to develop self-consistent simplified model equations for the interaction across multiple spatial and/or temporal scales in the Tropics. One of these models involves simplified equations for intraseasonal planetary equatorial synoptic-scale dynamics (IPESD). This model includes the self-consistent… (More)

Several simple mathematical models for the turbulent di!usion of a passive scalar "eld are developed here with an emphasis on the symbiotic interaction between rigorous mathematical theory (including exact solutions), physical intuition, and numerical simulations. The homogenization theory for periodic velocity "elds and random velocity "elds with… (More)

- Peter Constantint, Andrew J. Majda, Esteban Tab
- 2002

The formation of smng and potentially singular fronts in a two-dimensional quasigeostrophic active scalar is studied here through the symbiotic interaction of mathematical theory and numerical experiments. This active scalar represents the temperature evolving on the two dimensional boundary of a rapidly rotating half space with small Rosshy and Ekman… (More)

A family of one-dimensional nonlinear dispersive wave equations is introduced as a model for assessing the validity of weak turbulence theory for random waves in an unambiguous and transparent fashion. These models have an explicitly solvable weak turbulence theory which is developed here, with Kolmogorov-type wave number spectra exhibiting interesting… (More)

- Andrew J. Majda, Ilya Timofeyev
- Proceedings of the National Academy of Sciences…
- 2000

A simplified one-dimensional model system is introduced and studied here that exhibits intrinsic chaos with many degrees of freedom as well as increased predictability and slower decay of correlations for the large-scale features of the system. These are important features in common with vastly more complex problems involving climate modeling or molecular… (More)

A minimal, nonlinear oscillator model is analyzed for the Madden–Julian oscillation (MJO) ‘‘skeleton’’ (i.e., its fundamental features on intraseasonal/planetary scales), which includes the following: (i) a slow eastward phase speed of roughly 5 m s, (ii) a peculiar dispersion relation with dv/dk ’ 0, and (iii) a horizontal quadrupole vortex structure.… (More)

- Andrew J. Majda, Boris Gershgorin
- Proceedings of the National Academy of Sciences…
- 2010

Quantifying the uncertainty for the present climate and the predictions of climate change in the suite of imperfect Atmosphere Ocean Science (AOS) computer models is a central issue in climate change science. Here, a systematic approach to these issues with firm mathematical underpinning is developed through empirical information theory. An information… (More)