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It is shown that when differencing analytic functions using the pseudospectral Fourier or Tchebyshev methods, the error committed decays to zero at an exponential rate.
The use of laser holography for measuring the distortion of antennas under space simulation conditions is described. The subject is the so-called double exposure procedure which allows to measure the distortion in the order of 1 to 30/micrometers + or - 0.5 per hologramme of an area of 4 m diameter max. The method of holography takes into account the constraints of the space simulation facility. The test method, the test set up and the constraints by the space simulation facility are described. The results of the performed tests are presented and compared with the theoretical predictions. The test on the K-Band Antenna e.g., showed a distortion of approximately 140/micrometers + or - 5/micrometers measured during the cool down from -10 C to -120 C.
The systems of truncated differential equations that have been proposed to reduce the complexity and large computational costs of solutions to the full Navier-Stokes equations are considered. These systems are computationally efficient and capture all the physically relevant behavior. The systems follow a certain hierarchy: (1) the classical boundary-layer equations with specified edge properties (usually the streamwise pressure distribution); (2) the coupled boundary-layer/inviscid equations; (3) the so-called thin-layer equations that discard streamwise diffusion; and (4) the Navier-Stokes equations. Consideration is given to each of these approximations applied to an incompressible, laminar-separating flow at low and moderate Reynolds numbers. It is pointed out that for any flow or region of flow for which viscous-inviscid interaction effects are small, classical boundary-layer equations will provide a satisfactory description of the viscous flow at a fraction of the computational cost of any higher approximations.
The impact of satellite data is found to vary considerably from one map to another and from one geographic region to another. However, the impact of satellite data is generally small in comparison with forecast error. On the average, over land areas (where good conventional data permit accurate verification), the impact of satellite data on 48-hr forecasts of 500-mb height is seen to be neutral. Indirect numerical evidence is found, however, that satellite data has a marked positive impact in the lower and middle troposphere in ocean regions, especially those regions where conventional data are sparse. The impact over oceans is found to be especially noticeable in maps depicting the mean differences between the satellite and the conventional-data-only maps averaged over the period of the data set (January 1-14, 1980), both for analyses and for forecasts to 48 hours.
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Estimates of the shape of the sea surface as determined from satellite altimeters have become of increasing importance in geophysics, geodesy and physical oceanography. The most effective error reduction procedures used in producing these surfaces have been some version of a crossing-arc analysis. The problem with this procedure is the absence of an easy means of evaluating the noise structure of the final result. By recasting the problem as one of objective mapping (optimal estimation) the error reduction is optimized and an explicit estimate is obtained of the wave-number structure of the final altimetric surface. Examples, suitable to a small computer, have been generated to show that the error reduction along the sub-satellite tracks is very great, with most of the residual lying in long wavelengths.
Report reviews sources of systematic error in laser radar (lidar) measurements of particles in atmosphere. Report applies particularly to stationary pulsed carbon dioxide lidars of type used to measure backscatter from aerosols in troposphere. Provides information for calibrating such systems accurately and consistently and interpreting their data correctly. Also useful in calibrating mobile and airborne lidars, lidars operating at wavelengths other than those of carbon dioxide lasers, and continuouswave lidars.
The optimum number of ground control points required to rectify a full scene or a portion of a LANDSAT MSS scene was investigated using data from southeastern Louisiana/southwestern Mississippi and eastern Kansas. The ground control points utilized were randomly distributed across the partial or full scene. This work suggest that 24 round control points are more than adequate to rectify a partial or full scene of LANDSAT MSS data. The error incurred in choosing ground control points representing artificial versus natural features was also studied.
Elliptic problems with corner singularities are discussed. Finite element approximations based on variational principles of the least squares type tend to display poor convergence properties in such contexts. Moreover, mesh refinement or the use of special singular elements do not appreciably improve matters. It is shown that if the least squares formulation is done in appropriately weighted space, then optimal convergence results in unweighted spaces like L(2).
Proposed space missions will require large scale, light weight, space based structural systems. Large space structure technology (LSST) systems will have to accommodate (among others): ocean data systems; electronic mail systems; large multibeam antenna systems; and, space based solar power systems. The structures are to be delivered into orbit by the space shuttle. Because of their inherent size, modelling techniques and scaling algorithms must be developed so that system performance can be predicted accurately prior to launch and assembly. When the size and weight-to-area ratio of proposed LSST systems dictate that the entire system be considered flexible, there are two basic modeling methods which can be used. The first is a continuum approach, a mathematical formulation for predicting the motion of a general orbiting flexible body, in which elastic deformations are considered small compared with characteristic body dimensions. This approach is based on an a priori knowledge of the frequencies and shape functions of all modes included within the system model. Alternatively, finite element techniques can be used to model the entire structure as a system of lumped masses connected by a series of (restoring) springs and possibly dampers. In addition, a computational algorithm was developed to evaluate the coefficients of the various coupling terms in the equations of motion as applied to the finite element model of the Hoop/Column.
When designing a Mesosphere-Stratosphere-Troposphere (MST) radar antenna one has to trade between the choices to optimize the effective aperture or to optimize the sidelobe suppression. An optimization of the aperture increases the sensitivity. Suppression of side-lobes by tapering attenuates undesirable signals which spoil the estimates of reflectivity and velocity. Generally, any sidelobe effects are equivalent to a broadening of the antenna beam. The return signal is due to a product of the antenna pattern with the varying atmospheric reflectivity structures. Thus, knowing the antenna pattern, it is in principle possible to find the signal spectra, which, however, may be a tedious computational and ambiguous procedure. For vertically pointing main beams the sidelobe effects are efficiently suppressed because of the aspect sensitivity. It follows that sidelobes are a minor problem for spaced antenna methods. However, they can be crucial for Doppler methods, which need off-vertical beams. If a sidelobe is pointing towards the zenith a larger power may be received from the vertical than off-vertical directions, but quantitative estimates of this effect are not yet known. To get an error estimate of sidelobe effects with an off-vertical main beam a 1-dimensional example is considered.
An analysis was performed on the P-format computer compatible tapes for the Landsat-4 Thematic Mapper (TM) scene 40109-15140 acquired November 2, 1982 over Washington, D.C. and environs. Three tests of sensor geometry were undertaken: (1) band-to-band registration, (2) line-to-line registration between swaths, and (3) geometric correction of sensor and spacecraft/ephemeris characteristics. The band-to-band and line-to-line registration was measured at one hundred pixel spacings along a line using the phase correlation image alignment method developed by Kuglin and Hines and adapted to a one-dimensional FFT correlation technique. The sensor and spacecraft geometric calibration analysis was checked by identifying 75 ground control points in the TM scene and on 1:24,000 topographic maps. A least squares fit of the gaps was computed and the vector offsets of the residuals was tabulated and plotted.
In 1977 and 1978, general purpose centrally space differenced implicit finite difference codes in two and three dimensions have been introduced. These codes, now called ARC2D and ARC3D, can run either in inviscid or viscous mode for steady or unsteady flow. Since the introduction of the ARC2D and ARC3D codes, overall computational efficiency could be improved by making use of a number of algorithmic changes. These changes are related to the use of a spatially varying time step, the use of a sequence of mesh refinements to establish approximate solutions, implementation of various ways to reduce inversion work, improved numerical dissipation terms, and more implicit treatment of terms. The present investigation has the objective to describe the considered improvements and to quantify advantages and disadvantages. It is found that using established and simple procedures, a computer code can be maintained which is competitive with specialized codes.
A Landsat Image Data Quality Analysis (LIDQA) Program is conducted by NASA. One part of this program forms studies which are being performed with the objective to evaluate the geometric fidelity of Landsat-4 and Landsat-5 Thematic Mapper (TM) data in computer tape (CCT-pt) formats. It is pointed out that the Landsat-4 and Landsat-5 systems provide image data of significantly better geometric fidelity than were obtained from the earlier Landsat missions. Attention is given to the factors which influence the geometric fidelity of the Landsat TM data, the study areas and data sets, the rectification procedures, the rectification of Landsat-4 TM data and comparisons of the Scrounge and the TM Image Processing System (TIPS), the rectification of system and scene corrected Landsat-5 data processed on TIPS, and the cartographic potential of TM data.
In an attempt to increase computational efficiency in the numerical solution of highly nonlinear problems in solid and fluid mechanics, underintegrated finite element methods have been employed by many analysts. Underintegration refers to the use of a rule of an order lower than that required to integrate polynomial integrands exactly. The main drawback of this technique is related to the production of rank-deficient stiffness matrices, or equivalently an expanded kernel of the governing linear momentum operators. Such a development can introduce numerical instabilities. In order to overcome this difficulty, artificial stiffness or viscosity methods, or other stabilization methods have been proposed. One approach involves the elimination of spurious modes in a postprocessing operation. The present study is concerned with this a posteriori elimination method, taking into account the results which can be expected from it, and some of its possible extensions.
This research project proposed a modified unit commitment that schedules connection and disconnection of generating units in response to load. A modified generation control is also proposed that controls steam units under automatic generation control, fast responding diesels, gas turbines and hydro units under a feedforward control, and wind turbine array output under a closed loop array control. This modified generation control and unit commitment require prediction of trend wind power variation one hour ahead and the prediction of error in this trend wind power prediction one half hour ahead. An improved meter for predicting trend wind speed variation is developed. Methods for accurately simulating the wind array power from a limited number of wind speed prediction records was developed. Finally, two methods for predicting the error in the trend wind power prediction were developed. This research provides a foundation for testing and evaluating the modified unit commitment and generation control that was developed to maintain operating reliability at a greatly reduced overall production cost for utilities with wind generation capacity.
All three flowmeter concepts (vortex, dual turbine, and angular momentum) were subjected to experimental and analytical investigation to determine the potential portotype performance. The three concepts were subjected to a comprehensive rating. Eight parameters of performance were evaluated on a zero-to-ten scale, weighted, and summed. The relative ratings of the vortex, dual turbine, and angular momentum flowmeters are 0.71, 1.00, and 0.95, respectively. The dual turbine flowmeter concept was selected as the primary candidate and the angular momentum flowmeter as the secondary candidate for prototype development and evaluation.