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1
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A Suite of Skeleton Models for the MJO with Refined Vertical Structure

100%
Thual S., Majda A. J.
Mathematics of Climate and Weather Forecasting
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2015
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tom 1
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nr 1
EN
The Madden-Julian oscillation (MJO) is the dominant mode of variability in the tropical atmosphere on intraseasonal timescales and planetary spatial scales. The skeleton model is a minimal dynamical model that recovers robustly the most fundamental MJO features of (I) a slow eastward speed of roughly 5 ms−1, (II) a peculiar dispersion relation with dw/dk ≈ 0, and (III) a horizontal quadrupole vortex structure. This model depicts the MJO as a neutrally-stable atmosphericwave that involves a simple multiscale interaction between planetary dry dynamics, planetary lower-tropospheric moisture and the planetary envelope of synoptic-scale activity. Here we propose and analyze a suite of skeleton models that qualitatively reproduce the refined vertical structure of the MJO in nature. This vertical structure consists of a planetary envelope of convective activity transitioning from the congestus to the deep to the stratiform type, in addition to a front-to-rear (i.e. tilted) structure of heating, moisture, winds and temperature. A first example of skeleton model achieving this goal has been considered recently in work by the authors. The construction of such a model satisfies an energy conservation principle, such that its solutions at the intraseasonal-planetary scale remain neutrally stable. Here, additional classes of skeleton models are constructed based on the same principle. In particular, those new models are more realistic then the former one as they consider fully coupled interactions between the planetary dry dynamics of the first and second baroclinic mode and the details of the vertical structure of moisture and convective activity. All models reproduce qualitatively the refined vertical structure of the MJO. In addition,when considered with a simple stochastic parametrization for the unresolved details of synopticscale activity, all models show intermittent initiation, propagation and shut down of MJO wave trains, as in previous studies.
2
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Predicting the Cloud Patterns for the Boreal Summer Intraseasonal Oscillation Through a Low-Order Stochastic Model

100%
Chen N., Majda A. J.
Mathematics of Climate and Weather Forecasting
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2015
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tom 1
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nr 1
EN
We assess the predictability limits of the large-scale cloud patterns in the boreal summer intraseasonal variability (BSISO), which are measured by the infrared brightness temperature, a proxy for convective activity. A recent developed nonlinear data analysis technique, nonlinear Laplacian spectrum analysis (NLSA), is applied to the brightness temperature data, defining two spatial modes with high intermittency associated with the BSISO time series. Then a recent developed data-driven physics-constrained low-ordermodeling strategy is applied to these time series. The result is a four dimensional system with two observed BSISO variables and two hidden variables involving correlated multiplicative noise through the nonlinear energyconserving interaction. With the optimal parameters calibrated by information theory, the non-Gaussian fat tailed probability distribution functions (PDFs), the autocorrelations and the power spectrum of the model signals almost perfectly match those of the observed data. An ensemble prediction scheme incorporating an effective on-line data assimilation algorithm for determining the initial ensemble of the hidden variables shows the useful prediction skill in the non-El Niño years is at least 30 days and even reaches 55 days in those years with regular oscillations and the skillful prediction lasts for 18 days in the strong El Niño year (year 1998). Furthermore, the ensemble spread succeeds in indicating the forecast uncertainty. Although the reduced linear model with time-periodic stable-unstable damping is able to capture the non-Gaussian fat tailed PDFs, it is less skillful in forecasting the BSISO in the years with irregular oscillations. The failure of the ensemble spread to include the truth also indicates failure in quantification of the uncertainty. In addition, without the energy-conserving nonlinear interactions, the linear model is sensitive with parameter variations. mcwfnally, the twin experiment with nonlinear stochastic model has comparable skill as the observed data, suggesting the nonlinear stochastic model has significant skill for determining the predictability limits of the large-scale cloud patterns of the BSISO.
3
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Initiation and termination of intraseasonal oscillations in nonlinear Laplacian spectral analysis-based indices

81%
Székely E., Giannakis D., Majda A. J.
Mathematics of Climate and Weather Forecasting
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2016
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tom 2
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nr 1
1-25
EN
We present a statistical analysis of the initiation and termination of boreal winter and boreal summer intraseasonal oscillations (ISOs). This study uses purely convection (infrared brightness temperature) data over a 23-year time interval from 1984–2006. The indices are constructed via the nonlinear Laplacian spectral analysis (NLSA) method and display high intermittency and non-Gaussian statistics. We first define primary, terminal, and full events in the NLSA-based indices, and then examine their statistics through the associated two-dimensional phase space representations. Roughly one full event per year was detected for the Madden-Julian oscillation (MJO), and 1.3 full events per year for the boreal summer ISO.We also find that 91%of the recovered full MJO events are circumnavigating and exhibit very little to no retrograde (westward) propagation. The Indian Ocean emerges as the most active region in terms of both the onset and decay of events, however relevant activity occurs over all phases, consistent with previous work.
4
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Multiscale asymptotics for the Skeleton of the Madden-Julian Oscillation and Tropical–Extratropical Interactions

81%
Chen S., Majda A. J., Stechmann S. N.
Mathematics of Climate and Weather Forecasting
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2015
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tom 1
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nr 1
EN
Anew model is derived and analyzed for tropical–extratropical interactions involving the Madden– Julian oscillation (MJO). The model combines (i) the tropical dynamics of the MJO and equatorial baroclinic waves and (ii) the dynamics of barotropic Rossby waves with significant extratropical structure, and the combined system has a conserved energy. The method of multiscale asymptotics is applied to systematically derive a system of ordinary differential equations (ODEs) for three-wave resonant interactions. Two novel features are (i) a degenerate auxiliary problem with overdetermined equations due to a compatibility condition (meridional geostrophic balance) and (ii) cubic self-interaction terms that are not typically found in threewave resonance ODEs. Several examples illustrate applications to MJO initiation and termination, including cases of (i) the MJO, equatorial baroclinic Rossbywaves, and barotropic Rossbywaves interacting, and (ii) the MJO, baroclinic Kelvinwaves, and barotropic Rossbywaves interacting. Resonance with the Kelvinwave is not possible here if only dry variables are considered, but it occurs in the moist model here through interactions with water vapor and convective activity.
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