Tropical cyclone intensities from satellite microwave data

Radial profiles of mean 1000 mb to 250 mb temperature from the Nimbus 6 scanning microwave spectrometer (SCAMS) were constructed around eight intensifying tropical storms in the western Pacific. Seven storms showed distinct inward temperature gradients required for intensification; the eighth displayed no inward gradient and was decaying 24 hours later. The possibility that satellite data might be used to forecast tropical cyclone turning motion was investigated using estimates obtained from Nimbus 6 SCAMS data tapes of the mean 1000 mb to 250 mb temperature field around eleven tropical storms in 1975. Analysis of these data show that for turning storms, in all but one case, the turn was signaled 24 hours in advance by a significant temperature gradient perpendicular to the storm's path, at a distance of 9 deg to 13 deg in front of the storm. A thresholding technique was applied to the North Central U.S. during the summer to estimate precipitation frequency. excep

Variational objective analyses for cyclone studies

The basic analysis equations, i.e., the two horizontal momentum equations, the hydrostatic equation, and the integrated continuity equation were derived for the nonlinear vertical coordinate, nondimensionalized, and expressed in finite differences on a staggered grid. Special care was taken to transform the hydrostatic equation and the pressure gradient terms of the horizontal momentum equations to nearly eliminate truncation error over steeply sloping terrain. This formulation also eliminated explicit reference to orographically induced variations in the thermodynamic variables so that the variational adjustments are on the scale of the meteorological perturbations. The analysis equations were subjected to the Euler-Lagrange operations as expressed for finite differences and an additional set of five partial differential equations was derived, bringing to nine the number of equations in Model I. Higher order terms, terms containing observed quantities, and terms containing none of the variables to be adjusted were grouped into forcing functions and the equations were solved for the zero order terms. Zero order variables were eliminated between these equations and there resulted two diagnostic equations which take the form of general linear second order partial differential equations with nonconstant coefficients

Radiation measurements from polar and geosynchronous satellites

The following topics are discussed: (1) cloud effects in climate determination; (2) annual variation in the global heat balance of the earth; (3) the accuracy of precipitation estimates made from passive microwave measurements from satellites; (4) seasonal oceanic precipitation frequencies; (5) determination of mesoscale temperature and moisture fields over land from satellite radiance measurements; and (6) Nimbus 6 scanning microwave spectrometer data evaluation for surface wind and pressure components in tropical storms

Geostationary earth climate sensor: Scientific utility and feasibility, phase A

The possibility of accurate broad band radiation budget measurements from a GEO platform will provide a unique opportunity for viewing radiation processes in the atmosphere-ocean system. The CSU/TRW team has prepared a Phase 1 instrument design study demonstrating that measurements of radiation budget are practical from geosynchronous orbit with proven technology. This instrument concept is the Geostationary Earth Climate Sensor (GECS). A range of resolutions down to 20 km at the top of the atmosphere are possible, depending upon the scientific goals of the experiment. These tradeoffs of resolution and measurement repeat cycles are examined for scientific utility. The design of a flexible instrument is shown to be possible to meet the two goals: long-term, systematic monitoring of the diurnal cycles of radiation budget; and high time and space resolution studies of regional radiation features

Gravity Waves, Chaos, and Spinning Compact Binaries

Spinning compact binaries are shown to be chaotic in the Post-Newtonian expansion of the two body system. Chaos by definition is the extreme sensitivity to initial conditions and a consequent inability to predict the outcome of the evolution. As a result, the spinning pair will have unpredictable gravitational waveforms during coalescence. This poses a challenge to future gravity wave observatories which rely on a match between the data and a theoretical template.Comment: Final version published in PR

Boundary Conditions for the Einstein Evolution System

New boundary conditions are constructed and tested numerically for a general first-order form of the Einstein evolution system. These conditions prevent constraint violations from entering the computational domain through timelike boundaries, allow the simulation of isolated systems by preventing physical gravitational waves from entering the computational domain, and are designed to be compatible with the fixed-gauge evolutions used here. These new boundary conditions are shown to be effective in limiting the growth of constraints in 3D non-linear numerical evolutions of dynamical black-hole spacetimes.Comment: 21 pages, 12 figures, submitted to PR

Evolution systems for non-linear perturbations of background geometries

The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised background geometry approach, for systems where there is non-trivial a priori knowledge about the spacetime under study. The background three-geometry and associated connection are used to express the ADM evolution equations in terms of physical non-linear deviations from that background. Expressing the equations in first order form leads naturally to a system closely linked to the Einstein-Christoffel system, introduced by Anderson and York, and sharing its hyperbolicity properties. We illustrate the drastic alteration of the source structure of the equations, and discuss why this is likely to be numerically advantageous.Comment: 12 pages, 3 figures, Revtex v3.0. Revised version to appear in Physical Review

Introductory lectures on the Effective One Body formalism

The Effective One Body (EOB) formalism is an analytical approach which aims at providing an accurate description of the motion and radiation of coalescing binary black holes. We present a brief review of the basic elements of this approach.Comment: 22 pages, 3 figures, lectures given at the Second ICRANet Stueckelberg Workshop on Relativistic Field Theories (Pescara, Italy, September 3-8, 2007); to be published in the International Journal of Modern Physics

Numerically generated quasi-equilibrium orbits of black holes: Circular or eccentric?

We make a comparison between results from numerically generated, quasi-equilibrium configurations of compact binary systems of black holes in close orbits, and results from the post-Newtonian approximation. The post-Newtonian results are accurate through third PN order (O(v/c)^6 beyond Newtonian gravity), and include rotational and spin-orbit effects, but are generalized to permit orbits of non-zero eccentricity. Both treatments ignore gravitational radiation reaction. The energy E and angular momentum J of a given configuration are compared between the two methods as a function of the orbital angular frequency \Omega. For small \Omega, corresponding to orbital separations a factor of two larger than that of the innermost stable orbit, we find that, if the orbit is permitted to be slightly eccentric, with e ranging from \approx 0.03 to \approx 0.05, and with the two objects initially located at the orbital apocenter (maximum separation), our PN formulae give much better fits to the numerically generated data than do any circular-orbit PN methods, including various ``effective one-body'' resummation techniques. We speculate that the approximations made in solving the initial value equations of general relativity numerically may introduce a spurious eccentricity into the orbits.Comment: 6 pages, 4 figures, to be submitted to Phys. Rev.