Samuel N. Stechmann

The skeleton of tropical intraseasonal oscillations

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 present a minimal dynamical model for the MJO that recovers robustly its fundamental features (i.e., its “skeleton”) on intraseasonal/planetary scales: (i) the peculiar dispersion relation of dω/dk ≈ 0, (ii) the slow phase speed of ≈5 m/s, and (iii) the horizontal quadrupole vortex structure. This is accomplished here in a model that is neutrally stable on planetary scales; i.e., it is tacitly assumed that the primary instabilities occur on synoptic scales. The key premise of the model is that modulations of synoptic scale wave activity are induced by low-level moisture preconditioning on planetary scales, and they drive the “skeleton” of the MJO through modulated heating. The “muscle” of the MJO—including tilts, vertical structure, etc.—is contributed by other potential upscale transport effects from the synoptic scales.

Fewest-switches with time uncertainty: A modified trajectory surface-hopping algorithm with better accuracy for classically forbidden electronic transitions

We present a modification of Tully’s fewest-switches (TFS) trajectory surface-hopping algorithm (also called molecular dynamics with quantum transitions) that is called the fewest-switches with time uncertainty (FSTU) method. The FSTU method improves the self-consistency of the fewest-switches algorithm by incorporating quantum uncertainty into the hopping times of classically forbidden hops. This uncertainty allows an electronic transition that is classically forbidden at some geometry to occur by hopping at a nearby classically allowed geometry if an allowed hopping point is reachable within the Heisenberg interval of time uncertainty. The increased accuracy of the FSTU method is verified using a challenging set of three-body, two-state test cases for which accurate quantum-mechanical results are available. The FSTU method is shown to be more accurate than the TFS method in predicting total nonadiabatic quenching probabilities and product branching ratios.

A Simple Dynamical Model with Features of Convective Momentum Transport

Abstract Convective momentum transport (CMT) plays a central role in interactions across multiple space and time scales. However, because of the multiscale nature of CMT, quantifying and parameterizing its effects is often a challenge. Here a simple dynamic model with features of CMT is systematically derived and studied. The model includes interactions between a large-scale zonal mean flow and convectively coupled gravity waves, and convection is parameterized using a multicloud model. The moist convective wave–mean flow interactions shown here have several interesting features that distinguish them from other classical wave–mean flow settings. First an intraseasonal oscillation of the mean flow and convectively coupled waves (CCWs) is described. The mean flow oscillates due to both upscale and downscale CMT, and the CCWs weaken, change their propagation direction, and strengthen as the mean flow oscillates. The basic mechanisms of this oscillation are corroborated by linear stability theory with differe...

Nonlinear Dynamics and Regional Variations in the MJO Skeleton

AbstractA 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−1, (ii) a peculiar dispersion relation with dω/dk ≈ 0, and (iii) a horizontal quadrupole vortex structure. Originally proposed in recent work by the authors, the fundamental mechanism involves neutrally stable interactions between (i) planetary-scale, lower-tropospheric moisture anomalies and (ii) the envelope of subplanetary-scale, convection/wave activity. Here, the model’s nonlinear dynamics are analyzed in a series of numerical experiments, using either a uniform sea surface temperature (SST) or a warm-pool SST. With a uniform SST, the results show significant variations in the number, strength, and/or locations of MJO events, including, for example, cases of a strong MJO event followed by a weaker MJO event, similar to the Tropical Ocean and Global ...

Madden-Julian Oscillation analog and intraseasonal variability in a multicloud model above the equator

The Madden–Julian Oscillation (MJO) is the dominant component of tropical intraseasonal variability, and a theory explaining its structure and successful numerical simulation remains a major challenge. A successful model for the MJO should have a propagation speed of 4–7 m/s predicted by theory; a wavenumber-2 or -3 structure for the planetary-scale, low-frequency envelope with distinct active and inactive phases of deep convection; an intermittent turbulent chaotic multiscale structure within the planetary envelope involving embedded westward- and eastward-propagating deep convection events; and qualitative features of the low-frequency envelope from the observational record regarding, e.g., its zonal flow structure and heating. Here, such an MJO analog is produced by using the recent multicloud model of Khouider and Majda in an appropriate intraseasonal parameter regime for flows above the equator so that rotation is ignored. Key features of the multicloud model are (i) systematic low-level moisture convergence with retained conservation of vertically integrated moist static energy, and (ii) the use of three cumulus cloud types (congestus, stratiform, and deep convective) together with their differing vertical heating structures. Besides all of the above structure in the MJO analog waves, there are accurate predictions of the phase speed from linear theory and transitions from weak, regular MJO analog waves to strong, multiscale MJO analog waves as climatological parameters vary. With all of this structure in a simplified context, these models should be useful for MJO predictability studies in a fashion akin to the Lorenz 96 model for the midlatitude atmosphere.

A Stochastic Model for the Transition to Strong Convection

A simple stochastic model is designed and analyzed in order to further understand the transition to strong convection. The transition has been characterized recently in observational data by an array of statistical measures, including (i) a sharp transition in mean precipitation, and a peak in precipitation variance, at a critical value of column water vapor (CWV), (ii) an approximate power law in the probability density of precipitation event size, (iii) exponential tails in the probability density of CWV values, when conditioned on either precipitating or nonprecipitating locations, and (iv) long and short autocorrelation times of CWV and precipitation, respectively, with approximately exponential and power-law decays in their autocorrelation functions,respectively.Thestochasticmodelpresentedherecapturesthesefourstatisticalfeaturesintimeseries of CWV and precipitation at a single location. In addition, analytic solutions are given for the exponential tails, which directly relates the tails to model parameters. The model parameterization includes three stochastic components: a stochastic trigger turns the convection on and off (a two-state Markov jump process), and stochastic closures represent variability in precipitation and in ‘‘external’’ forcing (Gaussian white noise). This stochastic external forcing is seen to be crucial for obtaining extreme precipitation events with high CWV and longlifetimes,becauseitcanoccasionallycompensatefortheheavyprecipitationandencouragemoreofit.This stochastic model can also be seen as a simplified stochastic convective parameterization, and it demonstrates simple ways to turn a deterministic parameterization—the trigger and/or closure—into a stochastic one.

Climate science in the tropics: waves, vortices and PDEs

Clouds in the tropics can organize the circulation on planetary scales and profoundly impact long range seasonal forecasting and climate on the entire globe, yet contemporary operational computer models are often deficient in representing these phenomena. On the other hand, contemporary observations reveal remarkably complex coherent waves and vortices in the tropics interacting across a bewildering range of scales from kilometers to ten thousand kilometers. This paper reviews the interdisciplinary contributions over the last decade through the modus operandi of applied mathematics to these important scientific problems. Novel physical phenomena, new multiscale equations, novel PDEs, and numerical algorithms are presented here with the goal of attracting mathematicians and physicists to this exciting research area.

A Stochastic Skeleton Model for the MJO

AbstractThe Madden–Julian oscillation (MJO) is the dominant mode of variability in the tropical atmosphere on intraseasonal time scales 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. In recent work by two of the authors, a minimal dynamical model has been proposed that recovers robustly the most fundamental MJO features of (i) a slow eastward speed of roughly 5 m s−1, (ii) a peculiar dispersion relation with dω/dk ≈ 0, and (iii) a horizontal quadrupole vortex structure. This model, the skeleton model, depicts the MJO as a neutrally stable atmospheric wave that involves a simple multiscale interaction between planetary dry dynamics, planetary lower-tropospheric moisture, and the planetary envelope of synoptic-scale activity. In this article, it is shown that the skeleton model can further account for (iv) the intermittent generation of MJ...

Stochastic models for convective momentum transport

The improved parameterization of unresolved features of tropical convection is a central challenge in current computer models for long-range ensemble forecasting of weather and short-term climate change. Observations, theory, and detailed smaller-scale numerical simulations suggest that convective momentum transport (CMT) from the unresolved scales to the resolved scales is one of the major deficiencies in contemporary computer models. Here, a combination of mathematical and physical reasoning is utilized to build simple stochastic models that capture the significant intermittent upscale transports of CMT on the large scales due to organized unresolved convection from squall lines. Properties of the stochastic model for CMT are developed below in a test column model environment for the large-scale variables. The effects of CMT from the stochastic model on a large-scale convectively coupled wave in an idealized setting are presented below as a nontrivial test problem. Here, the upscale transports from stochastic effects are significant and even generate a large-scale mean flow which can interact with the convectively coupled wave.

Multiscale Waves in an MJO Background and Convective Momentum Transport Feedback

AbstractThe authors use linear analysis for a simple model to study the evolution of convectively coupled waves (CCWs) in a background shear and background moisture mimicking the observed structure of the Madden–Julian oscillation (MJO). This is motivated by the observation, in an idealized setting, of intraseasonal two-way interactions between CCWs and a background wind. It is found here that profiles with a bottom-heavy moisture content are more favorable to the development of mesoscale/squall line–like waves whereas synoptic-scale CCWs are typically more sensitive to the shear strength. The MJO envelope is thus divided into three regions, in terms of the types of CCWs that are favored: an onset region in front that is favorable to Kelvin waves, a mature or active region in the middle in which squall lines are prominent, and the stratiform and decay phase region in the back that is favorable to westward inertia–gravity (WIG) waves. A plausible convective momentum transport (CMT) feedback is then provide...