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.     

The inverse problem for convex bodies

A completely rigorous study of the high frequency asymptotics for the scattering matrix in the exterior of convex bodies is developed. These results are then applied to a variety of inverse problems for convex bodies.     

High skill in low-frequency climate response through fluctuation dissipation theorems despite structural instability

Climate change science focuses on predicting the coarse-grained, planetary-scale, longtime changes in the climate system due to either changes in external forcing or internal variability, such as the impact of increased carbon dioxide. The predictions of climate change science are carried out through comprehensive, computational atmospheric, and oceanic simulation models, which necessarily parameterize physical features such as clouds, sea ice cover, etc. Recently, it has been suggested that there is irreducible imprecision in such climate models that manifests itself as structural instability in climate statistics and which can significantly hamper the skill of computer models for climate change. A systematic approach to deal with this irreducible imprecision is advocated through algorithms based on the Fluctuation Dissipation Theorem (FDT). There are important practical and computational advantages for climate change science when a skillful FDT algorithm is established. The FDT response operator can be utilized directly for multiple climate change scenarios, multiple changes in forcing, and other parameters, such as damping and inverse modelling directly without the need of running the complex climate model in each individual case. The high skill of FDT in predicting climate change, despite structural instability, is developed in an unambiguous fashion using mathematical theory as guidelines in three different test models: a generic class of analytical models mimicking the dynamical core of the computer climate models, reduced stochastic models for low-frequency variability, and models with a significant new type of irreducible imprecision involving many fast, unstable modes.     

From the Cover: 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.     

Correlation of periacinar retraction clefting in needle core biopsies and corresponding prostatectomy specimens of patients with prostatic adenocarcinoma

One of the underemphasized supportive criteria for the diagnosis of prostatic cancer is the presence of retraction clefting around neoplastic glands. We analyzed a series of 152 prostatic cancer cases to determine the frequency, extent, and correlation of periacinar retraction clefting between needle core biopsies (NCB) and corresponding matched radical prostatectomy (RP) specimens. Clefting was significantly more frequent in neoplastic compared to nonneoplastic acini in NBC and RP (p<0.05). There was no significant difference in the frequency of retraction clefting in neoplastic acini between NCB and corresponding RP (p>0.05). We have also found a concordance in matched RP and NCB (Kappa=0.582). We conclude that periacinar retraction clefting appears more frequently in neoplastic acini and could serve as a reliable criterion in the diagnosis of prostatic adenocarcinoma.