Results for “collocation techniques” — Page 5

NASA NTRS2002

Consistency of ARESE II Cloud Absorption Estimates and Sampling Issues

Data from three cloudy days (March 3, 21, 29, 2000) of the ARM Enhanced Shortwave Experiment II (ARESE II) were analyzed. Grand averages of broadband absorptance among three sets of instruments were compared. Fractional solar absorptances were approx. 0.21-0.22 with the exception of March 3 when two sets of instruments gave values smaller by approx. 0.03-0.04. The robustness of these values was investigated by looking into possible sampling problems with the aid of 500 nm spectral fluxes. Grand averages of 500 nm apparent absorptance cover a wide range of values for these three days, namely from a large positive (approx. 0.011) average for March 3, to a small negative (approximately -0.03) for March 21, to near zero (approx. 0.01) for March 29. We present evidence suggesting that a large part of the discrepancies among the three days is due to the different nature of clouds and their non-uniform sampling. Hence, corrections to the grand average broadband absorptance values may be necessary. However, application of the known correction techniques may be precarious due to the sparsity of collocated flux measurements above and below the clouds. Our analysis leads to the conclusion that only March 29 fulfills all requirements for reliable estimates of cloud absorption, that is, the presence of thick, overcast, homogeneous clouds.

Oreopoulos, L.↗

NASA NTRS1990

International two-way satellite time transfers using INTELSAT space segment and small Earth stations

The satellite operated by the International Telecommunications Satellite Organization (INTELSAT) provides new and unique capabilities for the coordinates of international time scales on a world wide basis using the two-way technique. A network of coordinated clocks using small earth stations collocated with the scales is possible. Antennas as small as 1.8 m at K-band and 3 m at C-band transmitting powers of less than 1 W will provide signals with time jitters of less than 1 ns existing spread spectrum modems. One way time broadcasting is also possible, under the INTELSAT INTELNET system, possibly using existing international data distribution (press and financial) systems that are already operating spread spectrum systems. The technical details of the satellite and requirements on satellite earth stations are given. The resources required for a regular operational international time transfer service are analyzed with respect to the existing international digital service offerings of the INTELSAT Business Service (IBS) and INTELNET. Coverage areas, typical link budgets, and a summary of previous domestic and international work using this technique are provided. Administrative procedures for gaining access to the space segment are outlined. Contact information for local INTELSAT signatories is listed.

Veenstra, Lester B.↗

NASA NTRS1973

Preliminary numerical analysis of improved gas chromatograph model

A mathematical model for the gas chromatograph was developed which incorporates the heretofore neglected transport mechanisms of intraparticle diffusion and rates of adsorption. Because a closed-form analytical solution to the model does not appear realizable, techniques for the numerical solution of the model equations are being investigated. Criteria were developed for using a finite terminal boundary condition in place of an infinite boundary condition used in analytical solution techniques. The class of weighted residual methods known as orthogonal collocation is presently being investigated and appears promising.

Woodrow, P. T.↗

NASA NTRS2010

Improving Global Mass Flux Solutions from Gravity Recovery and Climate Experiment (GRACE) Through Forward Modeling and Continuous Time Correlation

We describe Earth's mass flux from April 2003 through November 2008 by deriving a time series of mas cons on a global 2deg x 2deg equal-area grid at 10 day intervals. We estimate the mass flux directly from K band range rate (KBRR) data provided by the Gravity Recovery and Climate Experiment (GRACE) mission. Using regularized least squares, we take into account the underlying process dynamics through continuous space and time-correlated constraints. In addition, we place the mascon approach in the context of other filtering techniques, showing its equivalence to anisotropic, nonsymmetric filtering, least squares collocation, and Kalman smoothing. We produce mascon time series from KBRR data that have and have not been corrected (forward modeled) for hydrological processes and fmd that the former produce superior results in oceanic areas by minimizing signal leakage from strong sources on land. By exploiting the structure of the spatiotemporal constraints, we are able to use a much more efficient (in storage and computation) inversion algorithm based upon the conjugate gradient method. This allows us to apply continuous rather than piecewise continuous time-correlated constraints, which we show via global maps and comparisons with ocean-bottom pressure gauges, to produce time series with reduced random variance and full systematic signal. Finally, we present a preferred global model, a hybrid whose oceanic portions are derived using forward modeling of hydrology but whose land portions are not, and thus represent a pure GRACE-derived signal.

Sabaka, T. J.↗

NASA NTRSDate not supplied

TPSAS-NF1676L-10737-DND

The Clouds and the Earth's Radiant Energy System (CERES) project provides the community a quality climate TOA and surface fluxes and cloud properties and are key elements in evaluating the ability of climate models to predict both past and future climate states. One important aspect of successful climate monitoring is satellite calibration. The CERES instantaneous broadband calibration radiance stability is 0.1% per year, whereas the accuracy of the longwave (LW) and shortwave (SW) is better than 0.5% and 1% respectively. CERES uses the 3-hourly GEO fluxes and clouds to provide diurnally averaged daily and monthly TOA flux means from the CERES measurements onboard the Terra (10:30 AM local equator crossing time) and Aqua (13:30 PM) sun-synchronous satellites. The GEO radiances are calibrated against MODIS as a reference to provide consistent GEO retrieved cloud properties and derived broadband fluxes. These fluxes are then carefully normalized against the well-calibrated CERES fluxes to ensure climate quality fluxes, free of GEO artifacts. With the upcoming release of Edition3 products, CERES has just recalibrated all the CERES instruments to ensure that both Terra and Aqua fluxes are on the same radiometric scale and the removal of all known instrument trends. CERES will also recalibrate all GEO satellites using the entire GEO time record. CERES employs collocated, coincident ray-matched GEO/MODIS radiances as its primary technique, calibrating GEO radiances beginning in the year 2000. The advantage of the ray-matching technique is that it provides a full dynamic range of radiances to check the linearity of the GEO visible instrument. CERES uses deep convective clouds and invariant desert sites to validate the primary technique. All three methods can assess the stability of the GEO visible instrument. Examples of the CERES GEO calibration techniques and validation efforts will be shown at the conference. Special emphasis will be given to the newly incorporated desert site methodology.

R. Bhatt↗

NASA NTRS1985

Spectral methods for the Euler equations. I - Fourier methods and shock capturing

Spectral methods for compressible flows are introduced in relation to finite difference and finite element techniques within the framework of the method of weighted residuals. Current spectral collociation methods are put into historical context. The basic concepts of Fourier spectral collocation methods are provided. Filtering strategies for shock-capturing approaches are also presented. Fourier shock-capturing techniques are evaluated using a one-dimensional, periodic astrophysical 'nozzle' problem.

Hussaini, M. Y.↗

NASA NTRS1968

Laser/GRARR collocation experiment

Laser/range and range rate tracking collocation experiments with Explorer 29 to verify accuracy and laser calibration technique

Maresca, P. A.↗

NASA NTRS1994

A spectrally accurate boundary-layer code for infinite swept wings

This report documents the development, validation, and application of a spectrally accurate boundary-layer code, WINGBL2, which has been designed specifically for use in stability analyses of swept-wing configurations. Currently, we consider only the quasi-three-dimensional case of an infinitely long wing of constant cross section. The effects of streamwise curvature, streamwise pressure gradient, and wall suction and/or blowing are taken into account in the governing equations and boundary conditions. The boundary-layer equations are formulated both for the attachment-line flow and for the evolving boundary layer. The boundary-layer equations are solved by marching in the direction perpendicular to the leading edge, for which high-order (up to fifth) backward differencing techniques are used. In the wall-normal direction, a spectral collocation method, based upon Chebyshev polynomial approximations, is exploited. The accuracy, efficiency, and user-friendliness of WINGBL2 make it well suited for applications to linear stability theory, parabolized stability equation methodology, direct numerical simulation, and large-eddy simulation. The method is validated against existing schemes for three test cases, including incompressible swept Hiemenz flow and Mach 2.4 flow over an airfoil swept at 70 deg to the free stream.

Pruett, C. David↗

NASA NTRSDate not supplied

Recent Developments in the Assimilation of Microwave and Radar Observations Into NWP Models

Microwave observations play a very important role in improving the weather forecasts. Although these observations are routinely assimilated into NWP models in clear-sky conditions, assimilation of all-sky microwave observations is very limited. Two main factors contributing to this limitation are inaccuracy in the input cloud and hydrometeor profiles used as input to the radiative transfer model and also error in scattering calculations performed by the radiative transfer model itself. The Mie theory is used by many fast RT models to estimate the optical properties of single particles. The Mie theory assumes spherical shapes for ice or snow particles with mixture of air and ice. However, hydrometeors scattering radiation at microwave frequencies have different shapes, sizes, and orientations. Therefore, using Mie theory to determine their optical properties leads to large uncertainties in all-sky radiative transfer calculations. The discrete dipole approximation (DDA) which approximates the optical properties of large objects in terms of discrete dipoles has shown promise in calculating the scattering properties of particles with different shapes in the microwave frequencies. This presentation focuses on recent advancements in the CRTM scattering calculations for frozen hydrometeors in the microwave frequencies using the DDA technique. In addition to using stand-alone CRTM calculations using collocated ATMS and reanalysis profiles, the data assimilation experiments conducted using the NOAA FV3GFS forecast system are used to evaluate the scattering improvements. Additionally, the backscattering information from the DDA database was used to implement a radar simulator into CRTM. The radar operator takes advantage of CRTM different modules to calculate clouds absorption and scattering properties. In addition to the forward model both adjoint and tangent linear of the radar simulator are implemented and evaluated as well. The radar simulator is currently being tested within the JEDI/GEOS data assimilation framework to facilitate the assimilation of radar measurements such as CloudSat CPR and GPM DPR into the NASA GEOS model.

Isaac Moradi↗

NASA NTRSDate not supplied

Enhancing CRTM All-Sky Simulations and Implementation of A New Active Sensor Module

Microwave observations play a very important role in improving the weather forecasts. Although these observations are routinely assimilated into NWP models in clear-sky conditions, assimilation of all-sky microwave observations is very limited. Two main factors contributing to this limitation are inaccuracy in the input cloud and hydrometeor profiles used as input to the radiative transfer model and also error in scattering calculations performed by the radiative transfer model itself. The Mie theory is used by many fast RT models to estimate the optical properties of single particles. The Mie theory assumes spherical shapes for ice or snow particles with mixture of air and ice. However, hydrometeors scattering radiation at microwave frequencies have different shapes, sizes, and orientations. Therefore, using Mie theory to determine their optical properties leads to large uncertainties in all-sky radiative transfer calculations. The discrete dipole approximation (DDA) which approximates the optical properties of large objects in terms of discrete dipoles has shown promise in calculating the scattering properties of particles with different shapes in the microwave frequencies. This presentation focuses on recent advancements in the CRTM scattering calculations for frozen hydrometeors in the microwave frequencies using the DDA technique. In addition to using stand-alone CRTM calculations using collocated ATMS and reanalysis profiles, the data assimilation experiments conducted using the NOAA FV3GFS forecast system are used to evaluate the scattering improvements. Additionally, the backscattering information from the DDA database was used to implement a radar simulator into CRTM. The radar operator takes advantage of CRTM different modules to calculate clouds absorption and scattering properties. In addition to the forward model both adjoint and tangent linear of the radar simulator are implemented and evaluated as well. The radar simulator is currently being tested within the JEDI/GEOS data assimilation framework to facilitate the assimilation of radar measurements such as CloudSat CPR and GPM DPR into the NASA GEOS model.

Isaac Moradi↗

NASA NTRSDate not supplied

CRTM Microwave Cloud Scattering Lookup Tables and Radar Simulator

Microwave observations play a very important role in improving the weather forecasts. Although these observations are routinely assimilated into NWP models in clear-sky conditions, assimilation of all-sky microwave observations is very limited. Two main factors contributing to this limitation are inaccuracy in the input cloud and hydrometeor profiles used as input to the radiative transfer model and also error in scattering calculations performed by the radiative transfer model itself. The Mie theory is used by many fast RT models to estimate the optical properties of single particles. The Mie theory assumes spherical shapes for ice or snow particles with mixture of air and ice. However, hydrometeors scattering radiation at microwave frequencies have different shapes, sizes, and orientations. Therefore, using Mie theory to determine their optical properties leads to large uncertainties in all-sky radiative transfer calculations. The discrete dipole approximation (DDA) which approximates the optical properties of large objects in terms of discrete dipoles has shown promise in calculating the scattering properties of particles with different shapes in the microwave frequencies. This presentation focuses on recent advancements in the CRTM scattering calculations for frozen hydrometeors in the microwave frequencies using the DDA technique. In addition to using stand-alone CRTM calculations using collocated ATMS and reanalysis profiles, the data assimilation experiments conducted using the NOAA FV3GFS forecast system are used to evaluate the scattering improvements. Additionally, the backscattering information from the DDA database was used to implement a radar simulator into CRTM. The radar operator takes advantage of CRTM different modules to calculate clouds absorption and scattering properties. In addition to the forward model both adjoint and tangent linear of the radar simulator are implemented and evaluated as well. The radar simulator is currently being tested within the JEDI/GEOS data assimilation framework to facilitate the assimilation of radar measurements such as CloudSat CPR and GPM DPR into the NASA GEOS model.

Isaac Moradi↗

NASA NTRS1991

Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming

The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Shi, Yun Yuan↗

NASA NTRS1995

A test of a vortex method for the computation of flap side edge noise

Upon approach to landing, a major source location of airframe noise occurs at the side edges of the part span, trailing edge flaps. In the vicinity of these flaps, a complex arrangement of spanwise flow with primary and secondary tip vortices may form. Each of these vortices is observed to become fully three-dimensional. In the present study, a numerical model is developed to investigate the noise radiated from the side edge of a flap. The inherent three-dimensionality of this flow forces us to carefully consider a numerical scheme which will be both accurate in its prediction of the flow acoustics and also computationally efficient. Vortex methods have offered a fast and efficient means of simulating many two and three-dimensional, vortex dominated flows. In vortex methods, the time development of the flow is tracked by following exclusively the vorticity containing regions. Through the Biot-Savart law, knowledge of the vorticity field enables one to obtain flow quantities at any desired location during the flow evolution. In the present study, a numerical procedure has been developed which incorporates the Lagrangian approach of vortex methods into a calculation for the noise radiated by a flow-surface interaction. In particular, the noise generated by a vortex in the presence of a flat half plane is considered. This problem serves as a basic model of flap edge flow. It also permits the direct comparison between our computed results and previous acoustic analyses performed for this problem. In our numerical simulations, the mean flow is represented by the complex potential W(z) = Aiz(exp l/2), which is obtained through conformal mapping techniques. The magnitude of the mean flow is controlled by the parameter A. This mean flow has been used in the acoustic analysis by Hardin and is considered a reasonable model of the flow field in the vicinity of the edge and away from the leading and trailing edges of the flap. To represent the primary vortex which occurs near the flap, a point vortex is introduced just below the flat half plane. Using a technique from panel methods, boundary conditions on the flap surface are satisfied by the introduction of a row of stationary point vortices along the extent of the flap. At each time step in the calculation, the strength of these vortices is chosen to eliminate the normal velocity at intermediary collocation points. The time development of the overall flow field is then tracked using standard techniques from vortex methods. Vortex trajectories obtained through this computation are in good agreement with those predicted by the analytical solution given by Hardin, thus verifying the viability of this procedure for more complex flow arrangements. For the flow acoustics, the Ffowcs Williams-Hawkings equation is numerically integrated. This equation supplies the far field acoustic pressure based upon pressures occurring along the flap surface. With our vortex method solution, surface pressures may be obtained with exceptional resolution. The Ffowcs Williams-Hawkings equation is integrated using a spatially fourth order accurate Simpson's rule. Rational function interpolation is used to obtain the surface pressures at the appropriate retarded times. Comparisons between our numerical results for the acoustic pressure and those predicted by the Hardin analysis have been made. Preliminary results indicate the need for an improved integration technique. In the future, the numerical procedure developed in this study will be applied to the case of a rectangular flap of finite thickness and ultimately modified for application to the fully three-dimensional problem.

Martin, James E.↗

NASA NTRS2012

A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation

Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.

integration↗

NASA NTRS1994

A strawman SLR program plan for the 1990s

A series of programmatic and technical goals for the satellite laser ranging (SLR) network are presented. They are: (1) standardize the performance of the global SLR network; (2) improve the geographic distribution of stations; (3) reduce costs of field operations and data processing; (4) expand the 24 hour temporal coverage to better serve the growing constellation of satellites; (5) improve absolute range accuracy to 2 mm at key stations; (6) improve satellite force, radiative propagation, and station motion models and investigate alternative geodetic analysis techniques; (7) support technical intercomparison and the Terrestrial Reference Frame through global collocations; (8) investigate potential synergisms between GPS and SLR.

Degnan, John J.↗

NASA NTRS1994

Evaluating the design of an earth radiation budget instrument with system simulations. Part 2: Minimization of instantaneous sampling errors for CERES-I

Much of the new record of broadband earth radiation budget satellite measurements to be obtained during the late 1990s and early twenty-first century will come from the dual-radiometer Clouds and Earth's Radiant Energy System Instrument (CERES-I) flown aboard sun-synchronous polar orbiters. Simulation studies conducted in this work for an early afternoon satellite orbit indicate that spatial root-mean-square (rms) sampling errors of instantaneous CERES-I shortwave flux estimates will range from about 8.5 to 14.0 W/m on a 2.5 deg latitude and longitude grid resolution. Rms errors in longwave flux estimates are only about 20% as large and range from 1.5 to 3.5 W/sq m. These results are based on an optimal cross-track scanner design that includes 50% footprint overlap to eliminate gaps in the top-of-the-atmosphere coverage, and a 'smallest' footprint size to increase the ratio in the number of observations lying within to the number of observations lying on grid area boundaries. Total instantaneous measurement error also depends on the variability of anisotropic reflectance and emission patterns and on retrieval methods used to generate target area fluxes. Three retrieval procedures from both CERES-I scanners (cross-track and rotating azimuth plane) are used. (1) The baseline Earth Radiaton Budget Experiment (ERBE) procedure, which assumes that errors due to the use of mean angular dependence models (ADMs) in the radiance-to-flux inversion process nearly cancel when averaged over grid areas. (2) To estimate N, instantaneous ADMs are estimated from the multiangular, collocated observations of the two scanners. These observed models replace the mean models in computation of satellite flux estimates. (3) The scene flux approach, conducts separate target-area retrievals for each ERBE scene category and combines their results using area weighting by scene type. The ERBE retrieval performs best when the simulated radiance field departs from the ERBE mean models by less than 10%. For larger perturbations, both the scene flux and collocation methods produce less error than the ERBE retrieval. The scene flux technique is preferable, however, because it involves fewer restrictive assumptions.

Stowe, Larry↗

NASA NTRS1993

High-order cyclo-difference techniques: An alternative to finite differences

The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as 'cyclo-difference' techniques. These techniques are constructed cyclically from stable subelements, and require no numerical boundary conditions; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral element techniques and are ideally suited for parallel implementation, but do not require special collocation points or orthogonal basis functions. The principal focus is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy.

Carpenter, Mark H.↗

NASA NTRS1987

Algorithms for adaptive control of two-arm flexible manipulators under uncertainty

A nonlinear extension of model reference adaptive control (MRAC) technique is used to guide a double arm nonlinearizable robot manipulator with flexible links, driven by actuators collocated with joints subject to uncertain payload and inertia. The objective is to track a given simple linear and rigid but compatible dynamical model in real, possible stipulated time and within stipulated degree of accuracy of convergence while avoiding collision of the arms. The objective is attained by a specified signal adaptive feedback controller and by adaptive laws, both given in closed form. A case of 4 DOF manipulator illustrates the technique.

Skowronski, J. M.↗