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Description of data on the Nimbus 7 LIMS map archive tape: Ozone and nitric acid

The Nimbus 7 Limb Infrared Monitor of the Stratosphere (LIMS) data set has been processed into a Fourier coefficient representation with a Kalman filter algorithm applied to profile data at individual latitudes and pressure levels. The algorithm produces synoptic data at noon Greenwich Mean Time (GMT) from the asynoptic orbital profiles. This form of the data set is easy to use and is appropriate for time series analysis and further data manipulation and display. Ozone and nitric acid results are grouped together in this report because the LIMS vertical field of views (FOV's) and analysis characteristics for these species are similar. A comparison of the orbital input data with mixing ratios derived from Kalman filter coefficients indicates errors in mixing ratio of generally less than 5 percent, with 15 percent being a maximum error. The high quality of the mapped data was indicated by coherence of both the phases and the amplitudes of waves with latitude and pressure. Examples of the mapped fields are presented, and details are given concerning the importance of diurnal variations, the removal of polar stratospheric cloud signatures, and the interpretation of bias effects in the data near the tops of profiles.

Remsberg, E. E.↗

Backus Effect on a Perpendicular Errors in Harmonic Models of Real vs. Synthetic Data

Measurements of geomagnetic scalar intensity on a thin spherical shell alone are not enough to separate internal from external source fields; moreover, such scalar data are not enough for accurate modeling of the vector field from internal sources because of unmodeled fields and small data errors. Spherical harmonic models of the geomagnetic potential fitted to scalar data alone therefore suffer from well-understood Backus effect and perpendicular errors. Curiously, errors in some models of simulated 'data' are very much less than those in models of real data. We analyze select Magsat vector and scalar measurements separately to illustrate Backus effect and perpendicular errors in models of real scalar data. By using a model to synthesize 'data' at the observation points, and by adding various types of 'noise', we illustrate such errors in models of synthetic 'data'. Perpendicular errors prove quite sensitive to the maximum degree in the spherical harmonic expansion of the potential field model fitted to the scalar data. Small errors in models of synthetic 'data' are found to be an artifact of matched truncation levels. For example, consider scalar synthetic 'data' computed from a degree 14 model. A degree 14 model fitted to such synthetic 'data' yields negligible error, but amplifies 4 nT (rmss) added noise into a 60 nT error (rmss); however, a degree 12 model fitted to the noisy 'data' suffers a 492 nT error (rmms through degree 12). Geomagnetic measurements remain unaware of model truncation, so the small errors indicated by some simulations cannot be realized in practice. Errors in models fitted to scalar data alone approach 1000 nT (rmss) and several thousand nT (maximum).

Voorhies, C. V.↗

Evaluation of a native vegetation masking technique

A crop masking technique based on Ashburn's vegetative index (AVI) was used to evaluate native vegetation as an indicator of crop moisture condition. A mask of the range areas (native vegetation) was generated for each of thirteen Great Plains LANDSAT MSS sample segments. These masks were compared to the digitized ground truth and accuracies were computed. An analysis of the types of errors indicates a consistency in errors among the segments. The mask represents a simple quick-look technique for evaluating vegetative cover.

Kinsler, M. C.↗

Test and evaluation of the 2.4-micron photorefractor ocular screening system

An improved 2.4-m photorefractor ocular screening system was tested and evaluated. The photorefractor system works on the principal of obtaining a colored photograph of both human eyes; and, by analysis of the retinal reflex images, certain ocular defects can be detected such a refractive error, strabismus, and lens obstructions. The 2.4-m photorefractory system uses a 35-mm camera with a telephoto lens and an electronic flash attachment. Retinal reflex images obtained from the new 2.4-m system are significantly improved over earlier systems in image quality. Other features were also improved, notably portability and reduction in mass. A total of 706 school age children were photorefracted, 211 learning disabled and 495 middle school students. The total students having abnormal retinal reflexes were 156 or 22 percent, and 133 or 85 percent of the abnormal had refractive error indicated. Ophthalmological examination was performed on 60 of these students and refractive error was verified in 57 or 95 percent of those examined. The new 2.4-m system has a NASA patent pending and is authorized by the FDA. It provides a reliable means of rapidly screening the eyes of children and young adults for vision problems. It is especially useful for infants and other non-communicative children who cannot be screened by the more conventional methods such as the familiar E chart.

Richardson, J. R.↗

Evaluation of Trajectory Errors in an Automated Terminal-Area Environment

A piloted simulation experiment was conducted to document the trajectory errors associated with use of an airplane's Flight Management System (FMS) in conjunction with a ground-based ATC automation system, Center-TRACON Automation System (CTAS) in the terminal area. Three different arrival procedures were compared: current-day (vectors from ATC), modified (current-day with minor updates), and data link with FMS lateral navigation. Six active airline pilots flew simulated arrivals in a fixed-base simulator. The FMS-datalink procedure resulted in the smallest time and path distance errors, indicating that use of this procedure could reduce the CTAS arrival-time prediction error by about half over the current-day procedure. Significant sources of error contributing to the arrival-time error were crosstrack errors and early speed reduction in the last 2-4 miles before the final approach fix. Pilot comments were all very positive, indicating the FMS-datalink procedure was easy to understand and use, and the increased head-down time and workload did not detract from the benefit. Issues that need to be resolved before this method of operation would be ready for commercial use include development of procedures acceptable to controllers, better speed conformance monitoring, and FMS database procedures to support the approach transitions.

Oseguera-Lohr, Rosa M.↗

Sensitivity of Forecast Skill to Different Objective Analysis Schemes

Numerical weather forecasts are characterized by rapidly declining skill in the first 48 to 72 h. Recent estimates of the sources of forecast error indicate that the inaccurate specification of the initial conditions contributes substantially to this error. The sensitivity of the forecast skill to the initial conditions is examined by comparing a set of real-data experiments whose initial data were obtained with two different analysis schemes. Results are presented to emphasize the importance of the objective analysis techniques used in the assimilation of observational data.

Baker, W. E.↗

Analysis of faults in an N-version software experiment

The authors have conducted a large-scale experiment in N-version programming. A total of 27 versions of a program were prepared independently from the same specification at two universities. The results of executing the versions revealed that the versions were individually extremely reliable but that the number of input cases in which more than one failed was substantially more than would be expected if they were statistically independent. After the versions had been executed, the failures of each version were examined and the associated faults located. The analysis showed that in some cases the programmers made equivalent logical errors, indicating that some parts of the problem were simply more difficult than others. The authors also found cases in which apparently different logical errors yielded faults that caused statistically correlated failures, indicating that there are special cases in the input space that present difficulty in various parts of the solution. A formal model is presented to explain this phenomenon. It appears that minor differences in the software development environment would not have a major impact in reducing the incidence of faults that cause correlated failures.

Brilliant, Susan S.↗

A unified hp-HDG framework for Friedrichs' PDE systems

Here, this work proposes a unified hp-adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations (PDEs) of Friedrichs' type. In particular, we present unified hp-HDG formulations for abstract one-field and two-field structures and prove their well-posedness. In order to handle non-conforming interfaces we simply take advantage of HDG built-in mortar structures. With split-type mortars and the approximation space of trace, a numerical flux can be derived via Godunov approach and be naturally employed without any additional treatment. As a consequence, the proposed formulations are parameter-free. We perform several numerical experiments for time-independent and linear PDEs including elliptic, hyperbolic, and mixed-type to verify the proposed unified hp-formulations and demonstrate the effectiveness of hp-adaptation. Two adaptivity criteria are considered: one is based on a simple and fast error indicator, while the other is rigorous but more expensive using an adjoint-based error estimate. The numerical results show that these two approaches are comparable in terms of convergence rate even for problems with strong gradients, discontinuities, and singularities.

97 MATHEMATICS AND COMPUTING↗

Development of an adaptive hp-version finite element method for computational optimal control

In this research effort, the usefulness of hp-version finite elements and adaptive solution-refinement techniques in generating numerical solutions to optimal control problems has been investigated. Under NAG-939, a general FORTRAN code was developed which approximated solutions to optimal control problems with control constraints and state constraints. Within that methodology, to get high-order accuracy in solutions, the finite element mesh would have to be refined repeatedly through bisection of the entire mesh in a given phase. In the current research effort, the order of the shape functions in each element has been made a variable, giving more flexibility in error reduction and smoothing. Similarly, individual elements can each be subdivided into many pieces, depending on the local error indicator, while other parts of the mesh remain coarsely discretized. The problem remains to reduce and smooth the error while still keeping computational effort reasonable enough to calculate time histories in a short enough time for on-board applications.

Hodges, Dewey H.↗

Estimating Climatological Bias Errors for the Global Precipitation Climatology Project (GPCP)

A procedure is described to estimate bias errors for mean precipitation by using multiple estimates from different algorithms, satellite sources, and merged products. The Global Precipitation Climatology Project (GPCP) monthly product is used as a base precipitation estimate, with other input products included when they are within +/- 50% of the GPCP estimates on a zonal-mean basis (ocean and land separately). The standard deviation s of the included products is then taken to be the estimated systematic, or bias, error. The results allow one to examine monthly climatologies and the annual climatology, producing maps of estimated bias errors, zonal-mean errors, and estimated errors over large areas such as ocean and land for both the tropics and the globe. For ocean areas, where there is the largest question as to absolute magnitude of precipitation, the analysis shows spatial variations in the estimated bias errors, indicating areas where one should have more or less confidence in the mean precipitation estimates. In the tropics, relative bias error estimates (s/m, where m is the mean precipitation) over the eastern Pacific Ocean are as large as 20%, as compared with 10%-15% in the western Pacific part of the ITCZ. An examination of latitudinal differences over ocean clearly shows an increase in estimated bias error at higher latitudes, reaching up to 50%. Over land, the error estimates also locate regions of potential problems in the tropics and larger cold-season errors at high latitudes that are due to snow. An empirical technique to area average the gridded errors (s) is described that allows one to make error estimates for arbitrary areas and for the tropics and the globe (land and ocean separately, and combined). Over the tropics this calculation leads to a relative error estimate for tropical land and ocean combined of 7%, which is considered to be an upper bound because of the lack of sign-of-the-error canceling when integrating over different areas with a different number of input products. For the globe the calculated relative error estimate from this study is about 9%, which is also probably a slight overestimate. These tropical and global estimated bias errors provide one estimate of the current state of knowledge of the planet's mean precipitation.

Global Precipitation Climatology Project (GPCP)↗

Estimation and Simulation of Slow Crack Growth Parameters from Constant Stress Rate Data

Closed form, approximate functions for estimating the variances and degrees-of-freedom associated with the slow crack growth parameters n, D, B, and A(sup *) as measured using constant stress rate ('dynamic fatigue') testing were derived by using propagation of errors. Estimates made with the resulting functions and slow crack growth data for a sapphire window were compared to the results of Monte Carlo simulations. The functions for estimation of the variances of the parameters were derived both with and without logarithmic transformation of the initial slow crack growth equations. The transformation was performed to make the functions both more linear and more normal. Comparison of the Monte Carlo results and the closed form expressions derived with propagation of errors indicated that linearization is not required for good estimates of the variances of parameters n and D by the propagation of errors method. However, good estimates variances of the parameters B and A(sup *) could only be made when the starting slow crack growth equation was transformed and the coefficients of variation of the input parameters were not too large. This was partially a result of the skewered distributions of B and A(sup *). Parametric variation of the input parameters was used to determine an acceptable range for using closed form approximate equations derived from propagation of errors.

Salem, Jonathan A.↗

Creating a Satellite-Based Record of Tropospheric Ozone

The TES retrieval algorithm has been applied to IASI radiances. We compare the retrieved ozone profiles with ozone sonde profiles for mid-latitudes for the year 2008. We find a positive bias in the IASI ozone profiles in the UTLS region of up to 22 %. The spatial coverage of the IASI instrument allows sampling of effectively the same air mass with several IASI scenes simultaneously. Comparisons of the root-mean-square of an ensemble of IASI profiles to theoretical errors indicate that the measurement noise and the interference of temperature and water vapour on the retrieval together mostly explain the empirically derived random errors. The total degrees of freedom for signal of the retrieval for ozone are 3.1 +/- 0.2 and the tropospheric degrees of freedom are 1.0 +/- 0.2 for the described cases. IASI ozone profiles agree within the error bars with coincident ozone profiles derived from a TES stare sequence for the ozone sonde station at Bratt's Lake (50.2 deg N, 104.7 deg W).

pollutant↗

Tolerating memory stack failures in multi-stack systems

Memory management circuitry and processes operate to improve reliability of a group of memory stacks, providing that if a memory stack or a portion thereof fails during the product's lifetime, the system may still recover with no errors or data loss. A front-end controller receives a block of data requested to be written to memory, divides the block into sub-blocks, and creates a new redundant reliability sub-block. The sub-blocks are then written to different memory stacks. When reading data from the memory stacks, the front-end controller detects errors indicating a failure within one of the memory stacks, and recovers corrected data using the reliability sub-block. The front-end controller may monitor errors for signs of a stack failure and disable the failed stack.

Mappouras, Georgios↗

Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries

This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using tau-extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive h-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from 10(exp 6), to 10(exp 7) cells.

Aftosmis, M. J.↗

Space structure vibration modes: How many exist? Which ones are important?

Several assertions are argued regarding mode analysis of structural vibration. The idea of a "mode' is, in essence, a mathematical one. It is highly unlikely that any real structure can vibrate exactly so that all its points move in unison; in other words, it is highly unlikely that any structure has any modes. As an approximation, however, the use of a mode is an excellent one for many structures, especially for the "lower modes'. The agreement between experiment and theory for the "higher modes' tends to become weaker. In this approximate sense, most structures have a very large number of modes. It is elementary to show, however, that no real structure has an infinite number of modes. The only utility of the "infinite modes' idea is within the purely mathematical domain. Many "error indices' can be defined as guidelines for structural modal order reduction. Simple modal truncation, although suggested by experience with slender rods, is naive. The proper process is mode selection, based on a appropriate error criterion.

Hughes, P. C.↗

Columnar Aerosol Single-Scattering Albedo and Phase Function Retrieved from Sky Radiance Over the Ocean: Measurements of African Dust

The single-scattering albedo and phase function of African mineral dust are retrieved from ground-based measurements of sky radiance collected in the Florida Keys. The retrieval algorithm employs the radiative transfer equation to solve by iteration for these two properties which best reproduce the observed sky radiance using an assumed aerosol vertical structure and measured aerosol optical depth. Thus, no assumptions regarding particle size, shape, or composition are required. The single-scattering albedo, presented at fourteen wavelengths between 380 and 870 nm, displays a spectral shape expected of iron-bearing minerals but is much higher than current dust models allow. This indicates the absorption of light by mineral dust is significantly overestimated in climate studies. Uncertainty in the retrieved albedo is less than 0.02 due to the small uncertainty in the solar-reflectance-based calibration (12.2%) method employed. The phase function retrieved at 860 nm is very robust under simulations of expected experimental errors, indicating retrieved phase functions at this wavelength may be confidently used to describe aerosol scattering characteristics. The phase function retrieved at 443 nm is very sensitive to expected experimental errors and should not be used to describe aerosol scattering. Radiative forcing by aerosol is the greatest source of uncertainty in current climate models. These results will help reduce uncertainty in the absorption of light by mineral dust. Assessment of the radiative impact of aerosol species is a key component to NASA's Earth System Enterprise.

Cattrall, Christopher↗

L-/S-band calibration error analysis.

Results of a statistical error analysis performed to determine the degree of uncertainty encountered when calibrating steerable receiving antennas with the solar calibration method. The analysis considers the propagation of precision error indices. It is shown that a worst-case one-sigma (1 sigma) uncertainty of plus or minus 0.8 dB in system noise temperature occurs for a solar calibration at L-band. Somewhat better precision can be achieved by monitoring the antenna gain-to-noise temperature ratio at a station; a worst-case uncertainty of plus or minus 0.5 dB (1 sigma) can be realized. An error analysis is made of a method to determine absolute antenna gain based upon solar flux density. The uncertainty in this type of measurement is plus or minus 0.7 dB (1 sigma) at L- and S-band frequencies.

Taylor, R. E.↗

gLaSDI: Parametric physics-informed greedy latent space dynamics identification

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. Here, an interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a -nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658× speed-up with 1 to 5% relative errors.

97 MATHEMATICS AND COMPUTING↗