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NASA NTRS2018

Convergence Analysis of Turbulent Flow Solutions

Data from the "Turbulence Modeling Resource" website for turbulent flow over an NACA-0012 airfoil is analyzed to determine the convergence behavior of three second-order CFD (Computational Fluid Dynamics) codes: CFL3D (Computational Fluids Lab 3 Dimensional flow solver), FUN3D (Fully Unstructured Navier-stokes flow solver), and TAU (German Aerospace Center (DLR) 2 dimensional code for unstructured hybrid grids solving the Reynolds-Averaged Navier-Stokes equations or the Euler equations). The convergence of both integrated properties and pointwise data are examined. Several different methods for estimating errors and computing convergence rates are compared. A high-order extension to the Richardson extrapolation is developed that improves the accuracy of the mesh limit values and provides a quantitative estimate of the threshold of the asymptotic regime. The coefficient of total drag exhibits second-order convergence for all three codes, and convergence is monotone over a sequence of 7 grids. Other force coefficients are not so well behaved. The convergence rates of the viscous component of drag on the three nest grids ranges from 3:0 for CFL3D to 1:0 for FUN3D. The three codes are converging to similar but not identical solutions. The largest differences between the codes are in the coefficient of lift for which the difference between CFL3D and FUN3D is greater than 10 (sup minus 4). The best agreement occurs in the viscous component of drag, which is the only force component for which all three codes are converging towards each other at a rate of second-order. The agreement between the two unstructured grid codes is good with all properties except lift converging towards common values at a rate of second-order. No one code was universally better than the other. The TAU code has the lowest error in total drag, FUN3D has the lowest error in lift, and CFL3D has the lowest error in the viscous component of drag.

Atkins, Harold L.↗
NASA NTRS1999

TRMM Field Campaigns: Objectives and Status Report

The Tropical Rainfall Measuring Mission (TRMM) satellite has been sending valuable data since launch in November 1997. Some of the key goals of the joint NASA (US) and NASDA (Japan) mission are: (1) to estimate the four-dimensional diabatic heating in the tropical and subtropical atmosphere, (2) understand the role of latent heating in driving tropical and extratropical circulations, (3) obtain monthly area-averaged estimates of rainfall over the data-sparse oceans, and (4) estimate the relative contribution of convective and stratiform precipitation over different regions during different seasons. The overarching scientific objective is to understand and improve estimates of rainfall and latent heating profiles throughout the global tropics. This requires observations for fundamental understanding of cloud dynamics and microphysics, as well as for validation, testing assumptions and error estimates of cloud-resolving models, forward radiative transfer models, algorithms used to estimate rainfall statistics and vertical structure of precipitation from surface-based radar, and from satellites. Field experiments designed to contribute to this understanding have been conducted in Texas and the South China Sea in spring of 1998, Florida in summer of 1998, and interior Brazil in (boreal) winter 1999. In summer 1999, a major oceanic campaign will be based at Kwajalein Atoll. Some early results will be highlighted, noting some significant contrasts between oceanic and continental convective systems.

Zipser, Edward I.↗
NASA NTRS2005

Hubble Space Telescope Magnetometer and Two-Gyro Control Law Design, Implementation, and On-Orbit Performance

For f i h years, the science mission of the Hubble Space Telescope (HST) required using at least three of six rate gyros for attitude control. In the past, HST has mitigated gyro hardware failures by replacement of the failed units through Space Shuttle Servicing Missions. Following the tragic loss of Space Shuttle Columbia on STS-107, the desire to have a safe haven for astronauts during missions has resulted in the cancellation of all planned maxu14 missions to HST. While a robotic servicing mission is being currently being planned, controlling with alternate sensors to replace failed gyros can extend the HST Science mission until the robotic mission can be performed and extend science at HST s end of life. A two-gym control law has been designed and implemented using magnetometers (Magnetic Sensing System - MSS), fixed head star trackers (FHSTs), and Fine Guidance Sensors (FGSs) to control vehicle rate about the missing gyro axis. The three aforementioned sensors are used in succession to reduce HST boresight jitter to less than 7 milli-arcseconds rms and attitude error to less than 10 milli-arcseconds prior to science imaging. The MSS and 2-Gyro (M2G) control law is used for large angle maneuvers and attitude control during earth occultation of FHSTs and FGSs. The Tracker and 2-Gyro (T2G) control law dampens M2G rates and corrects the majority of attitude error in preparation for guide star acquisition with the FGSs. The Fine Guidance Sensor and 2-Gyro (F2G) control law d a m p T2G rates and controls HST attitude during science imaging. This paper describes the M2G control law. Details of M2G algorithms are presented, including computation of the HST 3-axis attitude error estimate, design of the M2G control law, SISO hear stability analyses, and restrictions on operations to maintain the h d t h and safety requirement of a 10degree maximum attitude error. Results of simulations performed in HSTSIM, a high-fidelity non-linear time domain simulation, are presented to predict HST on-orbit performance in attitude hold and maneuver modes. Simulation results are compared to on-orbit data from M2G flight tests performed in November and December 2004 and February 2005. Flight telemetry, using a currently available third gyro, shows that HST attitude error with the new M2G control law is maintained below the 10-degree requirement, and attitude errors are under 2 degrees for 95% of the time.

Wirzburger, John H.↗
NASA NTRS1999

Crack Turning and Arrest Mechanisms for Integral Structure

In the course of several years of research efforts to predict crack turning and flapping in aircraft fuselage structures and other problems related to crack turning, the 2nd order maximum tangential stress theory has been identified as the theory most capable of predicting the observed test results. This theory requires knowledge of a material specific characteristic length, and also a computation of the stress intensity factors and the T-stress, or second order term in the asymptotic stress field in the vicinity of the crack tip. A characteristic length, r(sub c), is proposed for ductile materials pertaining to the onset of plastic instability, as opposed to the void spacing theories espoused by previous investigators. For the plane stress case, an approximate estimate of r(sub c), is obtained from the asymptotic field for strain hardening materials given by Hutchinson, Rice and Rosengren (HRR). A previous study using of high order finite element methods to calculate T-stresses by contour integrals resulted in extremely high accuracy values obtained for selected test specimen geometries, and a theoretical error estimation parameter was defined. In the present study, it is shown that a large portion of the error in finite element computations of both K and T are systematic, and can be corrected after the initial solution if the finite element implementation utilizes a similar crack tip discretization scheme for all problems. This scheme is applied for two-dimensional problems to a both a p-version finite element code, showing that sufficiently accurate values of both K(sub I) and T can be obtained with fairly low order elements if correction is used. T-stress correction coefficients are also developed for the singular crack tip rosette utilized in the adaptive mesh finite element code FRANC2D, and shown to reduce the error in the computed T-stress significantly. Stress intensity factor correction was not attempted for FRANC2D because it employs a highly accurate quarter-point scheme to obtain stress intensity factors.

Pettit, Richard↗
NASA NTRS1977

Range validation using Kalman filter techniques

Range pseudo-residuals may be improved to the level required for data validation by a measurement updating process which utilizes Bierman's adaptation of the Kalman filter measurement updating algorithms together with process noise compensation to account for model errors. This algorithm involves combining the currently available range predictions and measurements to produce an updated range residual measurement whose accuracy is constrained by the range data quality and by the estimated error in the prediction. The algorithm is compact and fast, and is thus suitable for on-line applications in network control or at the station.

Madrid, G. A.↗
NASA NTRS2008

Five-Year Wilkinson Microwave Anisotropy Probe (WMAP1) Observations: Galactic Foreground Emission

We present a new estimate of foreground emission in the WMAP data, using a Markov chain Monte Carlo (MCMC) method. The new technique delivers maps of each foreground component for a variety of foreground models, error estimates of the uncertainty of each foreground component, and provides an overall goodness-of-fit measurement. The resulting foreground maps are in broad agreement with those from previous techniques used both within the collaboration and by other authors. We find that for WMAP data, a simple model with power-law synchrotron, free-free, and thermal dust components fits 90% of the sky with a reduced X(sup 2) (sub v) of 1.14. However, the model does not work well inside the Galactic plane. The addition of either synchrotron steepening or a modified spinning dust model improves the fit. This component may account for up to 14% of the total flux at Ka-band (33 GHz). We find no evidence for foreground contamination of the CMB temperature map in the 85% of the sky used for cosmological analysis.

Gold, B.↗
NASA NTRS1994

A passive microwave technique for estimating rainfall and vertical structure information from space. Part 2: Applications to SSM/I data

A multi channel physical approach for retrieving rainfall and its vertical structure from Special Sensor Microwave/Imager (SSM/I) observations is examined. While a companion paper was devoted exclusively to the description of the algorithm, its strengths, and its limitations, the main focus of this paper is to report on the results, applicability, and expected accuraciesfrom this algorithm. Some examples are given that compare retrieved results with ground-based radar data from different geographical regions to illustrate the performance and utility of the algorithm under distinct rainfall conditions. More quantitative validation is accomplished using two months of radar data from Darwin, Australia, and the radar network over Japan. Instantaneous comparisons at Darwin indicate that root-mean-square errors for 1.25 deg areas over water are 0.09 mm/h compared to the mean rainfall value of 0.224 mm/h while the correlation exceeds 0.9. Similar results are obtained over the Japanese validation site with rms errors of 0.615 mm/h compared to the mean of 0.0880 mm/h and a correlation of 0.9. Results are less encouraging over land with root-mean-square errors somewhat larger than the mean rain rates and correlations of only 0.71 and 0.62 for Darwin and Japan, respectively. These validation studies are further used in combination with the theoretical treatment of expected accuracies developed in the companion paper to define error estimates on a broader scale than individual radar sites from which the errors may be analyzed. Comparisons with simpler techniques that are based on either emission or scattering measurements are used to illustrate the fact that the current algorithm, while better correlated with the emission methods over water, cannot be reduced to either of these simpler methods.

Kummerow, Christian↗
NASA NTRS1978

A comparative study of optimum and suboptimum direct-detection laser ranging receivers

A summary of previously proposed receiver strategies for direct-detection laser ranging receivers is presented. Computer simulations are used to compare performance of candidate implementation strategies in the 1- to 100-photoelectron region. Under the condition of no background radiation, the maximum-likelihood and minimum mean-square error estimators were found to give the same performance for both bell-shaped and rectangular optical-pulse shapes. For signal energies greater than 100 photoelectrons, the root-mean-square range error is shown to decrease as Q to the -1/2 power for bell-shaped pulses and Q to the -1 power for rectangular pulses, where Q represents the average pulse energy. Of several receiver implementations presented, the matched-filter peak detector was found to be preferable. A similar configuration, using a constant-fraction discriminator, exhibited a signal-level dependent time bias.

Abshire, J. B.↗
NASA NTRS2016

Assimilation of Gridded GRACE Terrestrial Water Storage Estimates in the North American Land Data Assimilation System

The objective of the North American Land Data Assimilation System (NLDAS) is to provide best available estimates of near-surface meteorological conditions and soil hydrological status for the continental United States. To support the ongoing efforts to develop data assimilation (DA) capabilities for NLDAS, the results of Gravity Recovery and Climate Experiment (GRACE) DA implemented in a manner consistent with NLDAS development are presented. Following previous work, GRACE terrestrial water storage (TWS) anomaly estimates are assimilated into the NASA Catchment land surface model using an ensemble smoother. In contrast to many earlier GRACE DA studies, a gridded GRACE TWS product is assimilated, spatially distributed GRACE error estimates are accounted for, and the impact that GRACE scaling factors have on assimilation is evaluated. Comparisons with quality-controlled in situ observations indicate that GRACE DA has a positive impact on the simulation of unconfined groundwater variability across the majority of the eastern United States and on the simulation of surface and root zone soil moisture across the country. Smaller improvements are seen in the simulation of snow depth, and the impact of GRACE DA on simulated river discharge and evapotranspiration is regionally variable. The use of GRACE scaling factors during assimilation improved DA results in the western United States but led to small degradations in the eastern United States. The study also found comparable performance between the use of gridded and basin averaged GRACE observations in assimilation. Finally, the evaluations presented in the paper indicate that GRACE DA can be helpful in improving the representation of droughts.

Kumar, Sujay V.↗
NASA NTRS1989

Statistical retrieval of precipitation cell-top altitude using passive 118-GHz observations

A nonlinear statistical-retrieval operator for precipitation cell-top altitude using high-spatial-resolution passive 118-GHz O2 brightness spectra is demonstrated. The retrieval operator consists of a Karhunen-Loeve transformation followed by a rank reduction, a linearization, and a linear minimum mean-square-error estimator. Information from the 118-GHz data on the ambient atmospheric-temperature profile and the precipitation cell size is also incorporated into the linear stage of the retrieval operator. The rms retrieval error is 1.5 km for cumulus-stage cells with tops ranging from 1.5 to 16 km. The sensitivity of nadiral 118-GHz spectra to the cell-top altitude is predominantly due to the scattering and absorption of radiation originating from low, warm atmospheric levels by colder liquid and frozen precipitation This effect causes cold perturbations in the brightness spectrum, which typically become stronger with increasing cell-top altitude.

Gasiewski, A. J.↗
NASA NTRS1990

True covariance simulation of the EUVE (extreme ultra violet explorer) update filter

This paper presents a covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the onboard computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft. The linearized dynamics and measurement equations of the error states are used in formulating the 'truth model' describing the order of the systems involved. The 'design model' used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A 'true covariance analysis' has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, I. Y.↗
NASA NTRS1989

True covariance simulation of the EUVE update filter

A covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft is presented. The linearized dynamics and measurement equations of the error states are derived which constitute the truth model describing the real behavior of the systems involved. The design model used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A true covariance analysis has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, Itzhack Y.↗
NASA NTRS1990

True covariance simulation of the EUVE update filter

This paper presents a covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft. The linearized dynamics and measurement equations of the error states are used in formulating the 'truth model' describing the real behavior of the systems involved. The 'design model' used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A 'true covariance analysis' has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, I. Y.↗
NASA NTRS2005

Validation for the Tropical Rainfall Measuring Mission: Lessons Learned and Future Plans

The Tropical Rainfall Measuring Mission (TRMM) was launched in November 1997 and is a highly regarded and successful mission. A major component of the TRMM program was its Ground Validation (GV) program. Through dedicated research and hard work by many groups, both the GV and satellite-retrieved rain estimates have shown a convergence at key GV sites, lending credibility to the global TRMM estimates. To be sure, there are some regional differences between the various satellite estimates themselves, which still need to be addressed; however, it can be said with some certainty that TRMM has provided a high-quality, long-term climatological data set for researchers that provides errors on the order of 10-20%, rather than pre-TRMM era error estimates on the order of 50-100%. The TRMM GV program's main operational task is to provide rainfall products for four sites: Darwin, Australia (DARW); Houston, Texas (HSTN); Kwajalein, Republic of the Marshall Islands (KWAJ); and, Melbourne, Florida (MELB). A comparison between TRMM Ground Validation (Version 5) and Satellite (Version 6) rain intensity estimates is presented. The gridded satellite product (3668) will be compared to GV Level II rain-intensity and -type maps (2A53 and 2A54, respectively). The 3G68 product represents a 0.5 deg x 0.5 deg data grid providing estimates of rain intensities from the TRMM Precipitation Radar (PR), Microwave Imager (TMI) and Combined (COM) algorithms. The comparisons will be sub-setted according to geographical type (land, coast and ocean). The convergence of the GV and satellite estimates bodes well for expectations for the proposed Global Precipitation Measurement (GPM) program and this study and others are being leveraged towards planning GV goals for GPM. A discussion of lessons learned and future plans for TRMM GV in planning for GPM will also be provided.

Wolff, David B.↗
NASA NTRS1981

Airplane wing vibrations due to atmospheric turbulence

The magnitude of error introduced due to wing vibration when measuring atmospheric turbulence with a wind probe mounted at the wing tip was studied. It was also determined whether accelerometers mounted on the wing tip are needed to correct this error. A spectrum analysis approach is used to determine the error. Estimates of the B-57 wing characteristics are used to simulate the airplane wing, and von Karman's cross spectrum function is used to simulate atmospheric turbulence. It was found that wing vibration introduces large error in measured spectra of turbulence in the frequency's range close to the natural frequencies of the wing.

Pastel, R. L.↗
NASA NTRS2011

Use of GRACE Terrestrial Water Storage Retrievals to Evaluate Model Estimates by the Australian Water Resources Assessment System

Terrestrial water storage (TWS) estimates retrievals from the Gravity Recovery and Climate Experiment (GRACE) satellite mission were compared to TWS modeled by the Australian Water Resources Assessment (AWRA) system. The aim was to test whether differences could be attributed and used to identify model deficiencies. Data for 2003 2010 were decomposed into the seasonal cycle, linear trends and the remaining de-trended anomalies before comparing. AWRA tended to have smaller seasonal amplitude than GRACE. GRACE showed a strong (greater than 15 millimeter per year) drying trend in northwest Australia that was associated with a preceding period of unusually wet conditions, whereas weaker drying trends in the southern Murray Basin and southwest Western Australia were associated with relatively dry conditions. AWRA estimated trends were less negative for these regions, while a more positive trend was estimated for areas affected by cyclone Charlotte in 2009. For 2003-2009, a decrease of 7-8 millimeter per year (50-60 cubic kilometers per year) was estimated from GRACE, enough to explain 6-7% of the contemporary rate of global sea level rise. This trend was not reproduced by the model. Agreement between model and data suggested that the GRACE retrieval error estimates are biased high. A scaling coefficient applied to GRACE TWS to reduce the effect of signal leakage appeared to degrade quantitative agreement for some regions. Model aspects identified for improvement included a need for better estimation of rainfall in northwest Australia, and more sophisticated treatment of diffuse groundwater discharge processes and surface-groundwater connectivity for some regions.

van Dijk, A. I. J. M.↗
NASA NTRS2021

ICESat-2 Pointing Calibration and Geolocation Performance

ICESat-2 science requirements are dependent on the accurate real-time pointing control (i.e. geolocation control) and post-processed geolocation knowledge of the laser altimeter surface returns. Pre-launch pointing alignment errors and post-launch pointing alignment variation result in large geolocation errors that must be calibrated on orbit. In addition, the changing sun-orbit geometry causes thermal-mechanical forced laser frame alignment variations at the orbit period and trends from days, weeks and months. Early mission analysis computed precise post-launch laser beam alignment calibration. The alignment calibration was uploaded to the spacecraft and enabled the pointing control performance to achieve 4.4 ± 6.0 m, a significant improvement over the 45 m (1 σ) mission requirement. Laser frame alignment calibrations are used to reduce the alignment bias and time variation, as well as the orbital variation contributions to geolocation knowledge error from 6 m to 1.7 m (1 σ). Relative beam alignment of the six beams is calibrated and shown to contribute between 0.5 ± 0.1 m and 2.4 ± 0.2 m of remaining geolocation knowledge error. Independent geolocation assessment based on comparison to high-resolution digital elevation models agrees well with the calibration geolocation error estimates. The analysis demonstrates the ICESat-2 mission is performing far better than its geolocation knowledge requirement of 6.5 m (1 σ) after the laser frame alignment bias variation and orbital variation calibrations have been applied. Remaining geolocation error is beam dependent and ranges from 2.5 m for beam 6 to 4.4 m for beam 2 (mean + 1 σ).

S. B. Luthcke↗
NASA NTRS2021

ICESat-2 Pointing Calibration and Geolocation Performance

ICESat-2 science requirements are dependent on the accurate real-time pointing control (i.e., geolocation control) and postprocessed geolocation knowledge of the laser altimeter surface returns. Prelaunch pointing alignment errors and postlaunch pointing alignment variation result in large geolocation errors that must be calibrated on orbit. In addition, the changing sun-orbit geometry causes thermal-mechanical forced laser frame alignment variations at the orbit period and trends from days, weeks, and months. Early mission analysis computed precise postlaunch laser beam alignment calibration. The alignment calibration was uploaded to the spacecraft and enabled the pointing control performance to achieve 4.4 ± 6.0 m, a significant improvement over the 45 m (1 σ) mission requirement. Laser frame alignment calibrations are used to reduce the alignment bias and time variation, as well as the orbital variation contributions to geolocation knowledge error from 6 to 1.7 m (1 σ). Relative beam alignment of the six beams is calibrated and shown to contribute between 0.5 ± 0.1 m and 2.4 ± 0.2 m of remaining geolocation knowledge error. Independent geolocation assessment based on comparison to high-resolution digital elevation models agrees well with the calibration geolocation error estimates. The analysis demonstrates the ICESat-2 mission is performing far better than its geolocation knowledge requirement of 6.5 m (1 σ) after the laser frame alignment bias variation and orbital variation calibrations have been applied. Remaining geolocation error is beam dependent and ranges from 2.5 m for beam 6 to 4.4 m for beam 2 (mean + 1 σ).

S B Luthcke↗