Estimating the time-evolving refractivity of a turbulent medium using optical beam measurements: a data assimilation approach.

In applications such as free-space optical communication, a signal is often recovered after propagation through a turbulent medium. In this setting, it is common to assume that limited information is known about the turbulent medium, such as a space- and time-averaged statistic (e.g.

Scintillation minimization versus intensity maximization in optimal beams.

In free-space optical communications and other applications, it is desirable to design optical beams that have reduced or even minimal scintillation. However, the optimization problem for minimizing scintillation is challenging, and few optimal solutions have been found. Here we investigate the general optimization problem of minimizing scintillation and formulate it as a convex optimization problem.

Convergence to precipitating quasi-geostrophic equations with phase changes: asymptotics and numerical assessment.

The quasi-geostrophic (QG) equations play a crucial role in our understanding of atmospheric and oceanic fluid dynamics. Nevertheless, the traditional QG equations describe 'dry' dynamics that do not account for moisture and clouds. To move beyond the dry setting, precipitating QG (PQG) equations have been derived recently using formal asymptotics.

Global warming precipitation accumulation increases above the current-climate cutoff scale.

Precipitation accumulations, integrated over rainfall events, can be affected by both intensity and duration of the storm event. Thus, although precipitation intensity is widely projected to increase under global warming, a clear framework for predicting accumulation changes has been lacking, despite the importance of accumulations for societal impacts. Theory for changes in the probability density function (pdf) of precipitation accumulations is presented with an evaluation of these changes in global climate model simulations.

Simple stochastic model for El Niño with westerly wind bursts.

Atmospheric wind bursts in the tropics play a key role in the dynamics of the El Niño Southern Oscillation (ENSO). A simple modeling framework is proposed that summarizes this relationship and captures major features of the observational record while remaining physically consistent and amenable to detailed analysis. Within this simple framework, wind burst activity evolves according to a stochastic two-state Markov switching-diffusion process that depends on the strength of the western Pacific warm pool, and is coupled to simple ocean-atmosphere processes that are otherwise deterministic, stable, and linear.

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.

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.

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.