Prototype Packages for Managing and Animating Longitudinal Network Data: dynamicnetwork and rSoNIA

Work with longitudinal network survey data and the dynamic network outputs of the statnet ERGMs has demonstrated the need for consistent frameworks and data structures for expressing, storing, and manipulating information about networks that change in time. Motivated by our requirements for exchanging data among researchers and various analysis and visualization processes, we have created an R package dynamicnetwork that builds upon previous work in the network, statnet and sna packages and provides a limited functional implementation. This paper discusses design issues and considerations, describes classes and forms of dynamic data, and works through several examples to demonstrate the utility of the package. The functionality of the rSoNIA package that uses dynamicnetwork to exchange data with the Social Network Image Animator (SoNIA) software to create animated movies of changing networks from within R is also demonstrated.

Numerical Evidence that the Perturbation Expansion for a Non-Hermitian PT\mathcal{PT}-Symmetric Hamiltonian is Stieltjes

Recently, several studies of non-Hermitian Hamiltonians having $\mathcal{PT}$ symmetry have been conducted. Most striking about these complex Hamiltonians is how closely their properties resemble those of conventional Hermitian Hamiltonians. This paper presents further evidence of the similarity of these Hamiltonians to Hermitian Hamiltonians by examining the summation of the divergent weak-coupling perturbation series for the ground-state energy of the $\mathcal{PT}$-symmetric Hamiltonian $H=p^2+{1/4}x^2+i\lambda x^3$ recently studied by Bender and Dunne. For this purpose the first 193 (nonzero) coefficients of the Rayleigh-Schr\"odinger perturbation series in powers of $\lambda^2$ for the ground-state energy were calculated. Pad\'e-summation and Pad\'e-prediction techniques recently described by Weniger are applied to this perturbation series. The qualitative features of the results obtained in this way are indistinguishable from those obtained in the case of the perturbation series for the quartic anharmonic oscillator, which is known to be a Stieltjes series.Comment: 20 pages, 0 figure

Numerical simulations of tropical cyclone‐ocean interaction with a high‐resolution coupled model

The tropical cyclone‐ocean interaction was investigated using a high‐resolution tropical cyclone ocean coupled model. The model design consisted of the NOAA Geophysical Fluid Dynamics Laboratory tropical cyclone prediction model which was coupled with a multilayer primitive equation ocean model. Coupling between the hurricane and the ocean models was carried out by passing into the ocean model the wind stress, heat, and moisture fluxes computed in the hurricane model. The new sea surface temperature (SST) calculated by the ocean model was then used in the tropical cyclone model. A set of idealized numerical experiments were performed in which a tropical cyclone vortex was embedded in both easterly and westerly basic flows of 2.5, 5, and 7.5 m s−1 with a fourth experiment run with no basic flow specified initially. The profile of the tangential wind for Hurricane Gloria at 1200 UTC 22, September 1985 was used as the initial condition of the tropical cyclone for each of the experiments. The model ocean was initially horizontally homogenous and quiescent. To clarify the impact of the ocean response to the hurricane\u27s behavior, analogous experiments were also carried out with the SST kept constant (control cases). The experiments indicated that the cooling of the sea surface induced by the tropical cyclone resulted in a significant impact on the ultimate storm intensity due to the reduction of total heat flux directed into the tropical cyclone above the regions of decreased SST. The sea surface cooling produced by the tropical cyclones was found to be larger when the storms moved slower. In the experiments run without an initial basic flow, the maximum SST anomaly was about −5.6°C with a resulting difference in the minimum sea level pressure and maximum surface winds of 16.4 hPa and −7 m s−1, respectively. In contrast, in the experiments run with the 7.5 m s −1 basic flow, the maximum SST anomalies ranged from about 2.6° to 3.0°C with a difference in the minimum sea level pressure and maximum surface winds of about 7.3 hPa and −2.7 m s−1. The tropical cyclone‐ocean coupling significantly influenced the storm track only for the case with no basic flow and the 2.5 m s−1 easterly flow. In these cases the storm with the ocean interaction turned more to the north and east (no basic flow) or the north (2.5 m s−1 easterly flow) of the experiments with constant SST. In the first case, the storm by 72 hours was located over 70 km to the east‐southeast of the control case. A possible explanation for this track deviation is related to a systematic weakening of the mean tangential flow at all radii of the storm due to the interaction with the ocean and resulting alteration of the beta drift

Prototype Packages for Managing and Animating Longitudinal Network Data: dynamicnetwork and rSoNIA

Work with longitudinal network survey data and the dynamic network outputs of the statnet ERGMs has demonstrated the need for consistent frameworks and data structures for expressing, storing, and manipulating information about networks that change in time. Motivated by our requirements for exchanging data among researchers and various analysis and visualization processes, we have created an R package dynamicnetwork that builds upon previous work in the network, statnet and sna packages and provides a limited functional implementation. This paper discusses design issues and considerations, describes classes and forms of dynamic data, and works through several examples to demonstrate the utility of the package. The functionality of the rSoNIA package that uses dynamicnetwork to exchange data with the Social Network Image Animator (SoNIA) software to create animated movies of changing networks from within R is also demonstrated

The Operational GFDL Coupled Hurricane–Ocean Prediction System and a Summary of Its Performance

The past decade has been marked by significant advancements in numerical weather prediction of hurricanes, which have greatly contributed to the steady decline in forecast track error. Since its operational implementation by the U.S. National Weather Service (NWS) in 1995, the best-track model performer has been NOAA’s regional hurricane model developed at the Geophysical Fluid Dynamics Laboratory (GFDL). The purpose of this paper is to summarize the major upgrades to the GFDL hurricane forecast system since 1998. These include coupling the atmospheric component with the Princeton Ocean Model, which became operational in 2001, major physics upgrades implemented in 2003 and 2006, and increases in both the vertical resolution in 2003 and the horizontal resolution in 2002 and 2005. The paper will also report on the GFDL model performance for both track and intensity, focusing particularly on the 2003 through 2006 hurricane seasons. During this period, the GFDL track errors were the lowest of all the dynamical model guidance available to the NWS Tropical Prediction Center in both the Atlantic and eastern Pacific basins. It will also be shown that the GFDL model has exhibited a steady reduction in its intensity errors during the past 5 yr, and can now provide skillful intensity forecasts. Tests of 153 forecasts from the 2004 and 2005 Atlantic hurricane seasons and 75 forecasts from the 2005 eastern Pacific season have demonstrated a positive impact on both track and intensity prediction in the 2006 GFDL model upgrade, through introduction of a cloud microphysics package and an improved air–sea momentum flux parameterization. In addition, the large positive intensity bias in sheared environments observed in previous versions of the model is significantly reduced. This led to the significant improvement in the model’s reliability and skill for forecasting intensity that occurred in 2006

Dynamical Downscaling Projections of Late 21st Century U.S. Landfalling Hurricane Activity

U.S. landfalling tropical cyclone (TC) activity was projected for late 21st century conditions using a two-step dynamical downscaling framework. A regional atmospheric model, run for 27 seasons, generated tropical storm cases. Each storm case was re-simulated (up to 15 days) using the higher resolution GFDL hurricane model. Thirteen CMIP3 or CMIP5 modeled climate change projections were explored as scenarios. Robustness of projections was assessed using statistical significance tests and comparing the sign of changes derived from different models. The proportion of TCs (tropical storms and hurricanes) making U.S. landfall increases for the warming scenarios (by order 50% or more). For category 1-3 hurricane frequency, a robust decrease is projected (basin-wide), but robust changes are not projected for U.S. landfalling cases. A relatively robust increase in U.S. landfalling category 4-5 hurricane frequency is projected, averaging about +400% across the models; 10 of 13 models/ensembles project an increase (statistically significant in three individual models), while three models projected no change. The most robust projections overall for U.S. landfalling TC activity are for increased near-storm rainfall rates: these increases average +18% (all tropical storms and hurricanes), +26% (all hurricanes), and +37% (major hurricanes). Landfalling hurricane wind speed intensities show no robust signal, in contrast to a ~5% increase in basin-averaged TC intensity; basin-wide Power Dissipation Index (PDI) is projected to decrease, partly due to decreased duration. TC translation speed increases a few percent in most simulations. A caveat is the framework’s low correlation of modeled U.S. TC landfalls vs. observed interannual variations (1980-2016)

Effective potential in three-dimensional O(N) models

We consider the effective potential in three-dimensional models with O(N) symmetry. For generic values of N, and in particular for the physically interesting cases N=0,1,2,3, we determine the six-point and eight-point renormalized coupling constants which parametrize its small-field expansion. These estimates are obtained from the analysis of their $\epsilon$-expansion, taking into account the exact results in one and zero dimensions, and, for the Ising model (i.e. N=1), the accurate high-temperature estimates in two dimensions. They are compared with the available results from other approaches. We also obtain corresponding estimates for the two-dimensional O($N$) models.Comment: 22 pages, revtex, 2 fig

Wave trains, self-oscillations and synchronization in discrete media

We study wave propagation in networks of coupled cells which can behave as excitable or self-oscillatory media. For excitable media, an asymptotic construction of wave trains is presented. This construction predicts their shape and speed, as well as the critical coupling and the critical separation of time scales for propagation failure. It describes stable wave train generation by repeated firing at a boundary. In self-oscillatory media, wave trains persist but synchronization phenomena arise. An equation describing the evolution of the oscillator phases is derived.Comment: to appear in Physica D: Nonlinear Phenomen

Hurricane Model Development at GFDL: A Collaborative Success Story From a Historical Perspective

The hurricane project at the National Oceanic and Atmospheric Administration (NOAA) Geophysical Fluid Dynamics Laboratory (GFDL) was established in 1970. By the mid-1970s pioneering research had led to the development of a new hurricane model. As the reputation of the model grew, GFDL was approached in 1986 by the director of the National Meteorological Center about establishing a collaboration between the two federal organizations to transition the model into an operational modeling system. After a multiyear effort by GFDL scientists to develop a system that could support rigorous requirements of operations, and multiyear testing had demonstrated its superior performance compared to existing guidance products, operational implementation was made in 1995. Through collaboration between GFDL and the U.S. Navy, the model was also made operational at Fleet Numerical Meteorology and Oceanography Center in 1996. GFDL scientists continued to support and improve the model during the next two decades by collaborating with other scientists at GFDL, the National Centers for Environmental Prediction (NCEP) Environmental Modeling Center (EMC), the National Hurricane Center, the U.S. Navy, the University of Rhode Island (URI), Old Dominion University, and the NOAA Hurricane Research Division. Scientists at GFDL, URI, and EMC collaborated to transfer key components of the GFDL model to the NWS new Hurricane Weather Research and Forecasting Model (HWRF) that became operational in 2007. The purpose of the article is to highlight the critical role of these collaborations. It is hoped that the experiences of the authors will serve as an example of how such collaboration can benefit the nation with improved weather guidance products