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At least 19 records

Using GPUs and the Parameterization Method for Rapid Search and Refinement of Connections between Tori in Periodically Perturbed Planar Circular Restricted 3-Body Problems

When the planar circular restricted 3-body problem is periodically perturbed, most unstable periodic orbits become invariant tori. However, 2D Poincare ́ sections no longer work to find their manifolds’ intersections; new methods are needed. In this study, we first review a method of restricting the intersection search to only certain manifold subsets. We then implement this search using Julia and OpenCL, representing the manifolds as triangular meshes and gaining a 30x speedup using GPUs. We finally show how to use manifold parametrizations to refine the ap- proximate connections found in the mesh search. We demonstrate the tools on the planar elliptic RTBP.

de la Llave, Rafael↗

Controllers, observers, and applications thereof

Controller scaling and parameterization are described. Techniques that can be improved by employing the scaling and parameterization include, but are not limited to, controller design, tuning and optimization. The scaling and parameterization methods described here apply to transfer function based controllers, including PID controllers. The parameterization methods also apply to state feedback and state observer based controllers, as well as linear active disturbance rejection (ADRC) controllers. Parameterization simplifies the use of ADRC. A discrete extended state observer (DESO) and a generalized extended state observer (GESO) are described. They improve the performance of the ESO and therefore ADRC. A tracking control algorithm is also described that improves the performance of the ADRC controller. A general algorithm is described for applying ADRC to multi-input multi-output systems. Several specific applications of the control systems and processes are disclosed.

Gao, Zhiqiang↗

Sensitivity of Spacebased Microwave Radiometer Observations to Ocean Surface Evaporation

Ocean surface evaporation and the latent heat it carries are the major components of the hydrologic and thermal forcing on the global oceans. However, there is practically no direct in situ measurements. Evaporation estimated from bulk parameterization methods depends on the quality and distribution of volunteer-ship reports which are far less than satisfactory. The only way to monitor evaporation with sufficient temporal and spatial resolutions to study global environment changes is by spaceborne sensors. The estimation of seasonal-to-interannual variation of ocean evaporation, using spacebased measurements of wind speed, sea surface temperature (SST), and integrated water vapor, through bulk parameterization method,s was achieved with reasonable success over most of the global ocean, in the past decade. Because all the three geophysical parameters can be retrieved from the radiance at the frequencies measured by the Scanning Multichannel Microwave Radiometer (SMMR) on Nimbus-7, the feasibility of retrieving evaporation directly from the measured radiance was suggested and demonstrated using coincident brightness temperatures observed by SMMR and latent heat flux computed from ship data, in the monthly time scale. However, the operational microwave radiometers that followed SMMR, the Special Sensor Microwave/Imager (SSM/I), lack the low frequency channels which are sensitive to SST. This low frequency channels are again included in the microwave imager (TMI) of the recently launched Tropical Rain Measuring Mission (TRMM). The radiance at the frequencies observed by both TMI and SSM/I were simulated through an atmospheric radiative transfer model using ocean surface parameters and atmospheric temperature and humidity profiles produced by the reanalysis of the European Center for Medium Range Weather Forecast (ECMWF). From the same ECMWF data set, coincident evaporation is computed using a surface layer turbulent transfer model. The sensitivity of the radiance to evaporation over various seasons and geographic locations are examined. The microwave frequencies with radiance that are significant correlated with evaporation are identify and capability of estimating evaporation directly from TMI will be discussed.

Liu, Timothy W.↗

A numerical method for parameterization of atmospheric chemistry - Computation of tropospheric OH

An efficient and stable computational scheme for parameterization of atmospheric chemistry is described. The 24-hour-average concentration of OH is represented as a set of high-order polynomials in variables such as temperature, densities of H2O, CO, O3, and NO(t) (defined as NO + NO2 + NO3 + 2N2O5 + HNO2 + HNO4) as well as variables determining solar irradiance: cloud cover, density of the overhead ozone column, surface albedo, latitude, and solar declination. This parameterization of OH chemistry was used in the three-dimensional study of global distribution of CH3CCl3. The proposed computational scheme can be used for parameterization of rates of chemical production and loss or of any other output of a full chemical model.

Spivakovsky, C. M.↗

Methods of testing parameterizations: Vertical ocean mixing

The ocean's velocity field is characterized by an exceptional variety of scales. While the small-scale oceanic turbulence responsible for the vertical mixing in the ocean is of scales a few centimeters and smaller, the oceanic general circulation is characterized by horizontal scales of thousands of kilometers. In oceanic general circulation models that are typically run today, the vertical structure of the ocean is represented by a few tens of discrete grid points. Such models cannot explicitly model the small-scale mixing processes, and must, therefore, find ways to parameterize them in terms of the larger-scale fields. Finding a parameterization that is both reliable and plausible to use in ocean models is not a simple task. Vertical mixing in the ocean is the combined result of many complex processes, and, in fact, mixing is one of the less known and less understood aspects of the oceanic circulation. In present models of the oceanic circulation, the many complex processes responsible for vertical mixing are often parameterized in an oversimplified manner. Yet, finding an adequate parameterization of vertical ocean mixing is crucial to the successful application of ocean models to climate studies. The results of general circulation models for quantities that are of particular interest to climate studies, such as the meridional heat flux carried by the ocean, are quite sensitive to the strength of the vertical mixing. We try to examine the difficulties in choosing an appropriate vertical mixing parameterization, and the methods that are available for validating different parameterizations by comparing model results to oceanographic data. First, some of the physical processes responsible for vertically mixing the ocean are briefly mentioned, and some possible approaches to the parameterization of these processes in oceanographic general circulation models are described in the following section. We then discuss the role of the vertical mixing in the physics of the large-scale ocean circulation, and examine methods of validating mixing parameterizations using large-scale ocean models.

Tziperman, Eli↗

Optimization of a Remote Sensing Energy Balance Method over Different Canopy Applied at Global Scale

Parameterization methods which calculate turbulent heat and water fluxes with thermal remote sensing data were evaluated in the revised remote sensing surface energy balance system (SEBS) model (Chen et al., 2013). The model calculates sensible heat (H) based on the Monin-Obukhov similarity theory (MOST) and determines latent heat (LE) as the residual of energy balance. We examined the uncertainties of H and LE in the SEBS model due to five key parameters at the local station point scale. Observations at 27 flux towers located in seven land cover types (needle-leaf forest, broad leaf forest, shrub, savanna, grassland, cropland, and sparsely vegetated land) and an artificial intelligence particle swarm optimization (PSO) algorithm was combined to calibrate the five parameters (leaf drag coefficient, leaf heat transfer coefficients, roughness length for soil, and two parameters for ground heat calculation) in the SEBS model. The root-mean-square error at the site scale was reduced by 9 W/sq.m for H, and 92 W/sq.m for LE, and their correlation coefficients were increased by 0.07 (H) and 0.11 (LE) after using the calibrated parameters. The updated model validation was further conducted globally for the remotely sensed evapotranspiration (ET) calculations. Overestimation of SEBS global ET was significantly improved by using the optimized values of the parameters. The results suggested PSO was able to consistently locate the global optimum of the SEBS model, and appears to be capable of solving the ET model optimization problem.

Chen, Xuelong↗

The Parameterization of Solid Metal-Liquid Metal Partitioning of Siderophile Elements

The composition of a metallic liquid can significantly affect the partitioning behavior of elements. For example, some experimental solid metal-liquid metal partition coefficients have been shown to increase by three orders of magnitude with increasing S-content of the metallic liquid. Along with S, the presence of other light elements, such as P and C, has also been demonstrated to affect trace element partitioning behavior. Understanding the effects of metallic composition on partitioning behavior is important for modeling the crystallization of magmatic iron meteorites and the chemical effects of planetary differentiation. It is thus useful to have a mathematical expression that parameterizes the partition coefficient as a function of the composition of the metal. Here we present a revised parameterization method, which builds on the theory of the current parameterization of Jones and Malvin and which better handles partitioning in multi-light-element systems.

Chabot, N. L.↗

Developments in variational methods for high performance plate and shell elements

High performance elements are simple finite elements constructed to deliver engineering accuracy with coarse arbitrary grids. This is part of a series on the variational foundations of high-performance elements, with emphasis on plate and shell elements constructed with the free formulation (FF) and assumed natural strain (ANS) methods. Parameterized variational principles are studied that provide a common foundation for the FF and ANS methods, as well as for a combination of both. From this unified formulation a variant of the ANS formulation, called the assumed natural deviatoric strain (ANDES) formulation, emerges as an important special case. The first ANDES element, a high-performance 9 degrees of freedom triangular Kirchhoff plate bending element, is briefly described to illustrate the use of the new formulation.

Felippa, Carlos A.↗

Preliminary Design of Low-Thrust Interplanetary Missions

For interplanetary missions, highly efficient electric propulsion systems can be used to increase the mass delivered to the destination and/or reduce the trip time over typical chemical propulsion systems. This technology is being demonstrated on the Deep Space 1 mission - part of NASA's New Millennium Program validating technologies which can lower the cost and risk and enhance the performance of future missions. With the successful demonstration on Deep Space 1, future missions can consider electric propulsion as a viable propulsion option. Electric propulsion systems, while highly efficient, produce only a small amount of thrust. As a result, the engines operate during a significant fraction of the trajectory. This characteristic makes it much more difficult to find optimal trajectories. The methods for optimizing low-thrust trajectories are typically categorized as either indirect, or direct. Indirect methods are based on calculus of variations, resulting in a two-point boundary value problem that is solved by satisfying terminal constraints and targeting conditions. These methods are subject to extreme sensitivity to the initial guess of the variables - some of which are not physically intuitive. Adding a gravity assist to the trajectory compounds the sensitivity. Direct methods parameterize the problem and use nonlinear programming techniques to optimize an objective function by adjusting a set of variables. A variety of methods of this type have been examined with varying results. These methods are subject to the limitations of the nonlinear programming techniques. In this paper we present a direct method intended to be used primarily for preliminary design of low-thrust interplanetary trajectories, including those with multiple gravity assists. Preliminary design implies a willingness to accept limited accuracy to achieve an efficient algorithm that executes quickly.

Sims, Jon A.↗

Effects of dynamic heat fluxes on model climate sensitivity Meridional sensible and latent heat fluxes

The high- and low-latitude radiative-dynamic (HLRD) climatic model of Wang et al. (1984) was used to study the effect of meridional heat (MH) fluxes on climate changes caused by increases of CO2 abundance and solar constant variations. However, the empirical MH parameterization of the HLRD model was replaced by physically based parameterization, which gives separate meridional sensible and latent heat fluxes and provides a complete representation of the dependence of the flux on the mean temperature field. Both parameterization methods yielded about the same changes in global mean surface temperature and ice line, and both produced only small changes in meridional temperature gradient, although the latter were even smaller with the physically based parameterizations. At any latitude, the hemispheric mean surface temperature, rather than MH fluxes, dominates the surface temperature changes.

Gutowski, W. J., Jr.↗

Determination of monthly mean humidity in the atmospheric surface layer over oceans from satellite data

A simple statistical technique is described to determine monthly mean marine surface-layer humidity, which is essential in the specification of surface latent heat flux, from total water vapor in the atmospheric column measured by space-borne sensors. Good correlation between the two quantities was found in examining the humidity soundings from radiosonde reports of mid-ocean island stations and weather ships. The relation agrees with that obtained from satellite (Seasat) data and ship reports averaged over 2 deg areas and a 92-day period in the North Atlantic and in the tropical Pacific. The results demonstrate that, by using a local regression in the tropical Pacific, total water vapor can be used to determine monthly mean surface layer humidity to an accuracy of 0.4 g/kg. With a global regression, determination to an accuracy of 0.8 g/kg is possible. These accuracies correspond to approximately 10 to 20 W/sq m in the determination of latent heat flux with the bulk parameterization method, provided that other required parameters are known.

Liu, W. T.↗

Large-scale experimental technology with remote sensing in land surface hydrology and meteorology

Two field experiments to study atmospheric and land surface processes and their interactions are summarized. The Hydrologic-Atmospheric Pilot Experiment, which tested techniques for measuring evaporation, soil moisture storage, and runoff at scales of about 100 km, was conducted over a 100 X 100 km area in France from mid-1985 to early 1987. The first International Satellite Land Surface Climatology Program field experiment was conducted in 1987 to develop and use relationships between current satellite measurements and hydrologic, climatic, and biophysical variables at the earth's surface and to validate these relationships with ground truth. This experiment also validated surface parameterization methods for simulation models that describe surface processes from the scale of vegetation leaves up to scales appropriate to satellite remote sensing.

Brutsaert, Wilfried↗

Absolute extinction and the influence of environment - Dark cloud sight lines toward VCT 10, 30, and Walker 67

The range of validity of the average absolute extinction law (AAEL) proposed by Cardelli et al. (1988 and 1989) is investigated, combining published visible and NIR data with IUE UV observations for three lines of sight through dense dark cloud environments with high values of total-to-selective extinction. The characteristics of the data sets and the reduction and parameterization methods applied are described in detail, and the results are presented in extensive tables and graphs. Good agreement with the AAEL is demonstrated for wavelengths from 3.4 microns to 250 nm, but significant deviations are found at shorter wavelengths (where previous studies of lines of sight through bright nebulosity found good agreement with the AAEL). These differences are attributed to the effects of coatings on small-bump and FUV grains.

Cardelli, Jason A.↗

Adaptive defuzzification for fuzzy systems modeling

We propose a new parameterized method for the defuzzification process based on the simple M-SLIDE transformation. We develop a computationally efficient algorithm for learning the relevant parameter as well as providing a computationally simple scheme for doing the defuzzification step in the fuzzy logic controllers. The M-SLIDE method results in a particularly simple linear form of the algorithm for learning the parameter which can be used both off- and on-line.

Yager, Ronald R.↗

Parameterizing Coefficients of a POD-Based Dynamical System

A method of parameterizing the coefficients of a dynamical system based of a proper orthogonal decomposition (POD) representing the flow dynamics of a viscous fluid has been introduced. (A brief description of POD is presented in the immediately preceding article.) The present parameterization method is intended to enable construction of the dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers. The need for this or a similar method arises as follows: A procedure that includes direct numerical simulation followed by POD, followed by Galerkin projection to a dynamical system has been proven to enable representation of flow dynamics by a low-dimensional model at the Reynolds number of the simulation. However, a more difficult task is to obtain models that are valid over a range of Reynolds numbers. Extrapolation of low-dimensional models by use of straightforward Reynolds-number-based parameter continuation has proven to be inadequate for successful prediction of flows. A key part of the problem of constructing a dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers is the problem of understanding and providing for the variation of the coefficients of the dynamical system with the Reynolds number. Prior methods do not enable capture of temporal dynamics over ranges of Reynolds numbers in low-dimensional models, and are not even satisfactory when large numbers of modes are used. The basic idea of the present method is to solve the problem through a suitable parameterization of the coefficients of the dynamical system. The parameterization computations involve utilization of the transfer of kinetic energy between modes as a function of Reynolds number. The thus-parameterized dynamical system accurately predicts the flow dynamics and is applicable to a range of flow problems in the dynamical regime around the Hopf bifurcation. Parameter-continuation software can be used on the parameterized dynamical system to derive a bifurcation diagram that accurately predicts the temporal flow behavior.

Kalb, Virginia L.↗

A method for coupling a parameterization of the planetary boundary layer with a hydrologic model

Deardorff's parameterization of the planetary boundary layer is adapted to drive a hydrologic model. The method converts the atmospheric conditions measured at the anemometer height at one site to the mean values in the planetary boundary layer; it then uses the planetary boundary layer parameterization and the hydrologic variables to calculate the fluxes of momentum, heat and moisture at the atmosphere-land interface for a different site. A simplified hydrologic model is used for a simulation study of soil moisture and ground temperature on three different land surface covers. The results indicate that this method can be used to drive a spatially distributed hydrologic model by using observed data available at a meteorological station located on or nearby the site.

Lin, J. D.↗