Results for “Error Metrics” — Page 6

NASA NTRS2021

The Contributions of Gauge-Based Precipitation and SMAP Brightness Temperature Observations to the Skill of the SMAP Level-4 Soil Moisture Product

Soil Moisture Active Passive (SMAP) mission L-band brightness temperature (Tb) observations are routinely assimilated into the Catchment land surface model to generate Level-4 Soil Moisture (L4_SM) estimates of global surface and root-zone soil moisture at 9-km, 3-hourly resolution with ~2.5-day latency. The Catchment model in the L4_SM algorithm is driven with ¼-degree, hourly surface meteorological forcing data from the Goddard Earth Observing System (GEOS). Outside of Africa and the high latitudes, GEOS precipitation is corrected using Climate Prediction Center Unified (CPCU) gauge-based, ½-degree, daily precipitation. L4_SM soil moisture was previously shown to improve over land model-only estimates that use CPCU precipitation but no Tb assimilation (CPCU_SIM). Here, we additionally examine the skill of model-only (CTRL) and Tb assimilation-only (SMAP_DA) estimates derived without CPCU precipitation. Soil moisture is assessed versus in situ measurements in well-instrumented regions and globally through the Instrumental Variable (IV) method using independent soil moisture retrievals from the Advanced Scatterometer. At the in situ locations, SMAP_DA and CPCU_SIM have comparable soil moisture skill improvements relative to CTRL for the unbiased root-mean-square error (surface and root-zone) and correlation metrics (root-zone only). In the global average, SMAP Tb assimilation increases the surface soil moisture anomaly correlation by 0.10-0.11 compared to an increase of 0.02-0.03 from the CPCU-based precipitation corrections. The contrast is particularly strong in central Australia, where CPCU is known to have errors and observation-minus-forecast Tb residuals are larger when CPCU precipitation is used. Validation versus streamflow measurements in the contiguous U.S. reveals that CPCU precipitation provides most of the skill gained in L4_SM runoff estimates over CTRL.

SMAP↗

NASA NTRS2012

Improving operations: Metrics to Results

As a result of the mission failure of the Mars Climate Orbiter (MCO) spacecraft in 1999, the Jet Propulsion Laboratory (JPL) initiated the development of a Mission Operations Assurance (MOA) program to be implemented across all flight projects managed by JPL. One of the initiatives undertaken in 2001 was the collection of data on command file errors occurring in the operational phase of the mission. This paper defines command file errors and how and where they occur in the operations process. It also describes the problem reporting system (PRS) in use for mission operations at JPL. We examine the recent modifications to the PRS that enable the collection of metrics, specifically on command file errors. This paper discusses what the data show us since metrics have been collected for the operational missions conducted by JPL. We examine the evolution of an operational working group initiative to evaluate proximate, contributing, and root causes for the errors. As part of this discussion we see what the metrics have indicated over a decade. At the macro level, we can say that the aggregate command file error rate has been cut to roughly one third of the initial 2001 level by the end of 2011. Additionally, we explore efficient and innovative means to continually integrate the findings and recommendations from the working group back into the flight operations environment.

command file errors↗

NASA NTRS2005

Passive isolator design for jitter reduction in the Terrestrial Planet Finder Coronagraph

Terrestrial Planet Finder (TPF) is a mission to locate and study extrasolar Earth-like planets. The TPF Coronagraph (TPF-C), planned for launch in the latter half of the next decade, will use a coronagraphic mask and other optics to suppress the light of the nearby star in order to collect visible light from such planets. The required contrast ratio of 5e-11 can only be achieved by maintaining pointing accuracy to 4 milli-arcseconds, and limiting optics jitter to below 5 nm. Numerous mechanical disturbances act to induce jitter. This paper concentrates on passive isolation techniques to minimize the optical degradation introduced by disturbance sources. A passive isolation system, using compliant mounts placed at an energy bottleneck to reduce energy transmission above a certain frequency, is a low risk, flight proven design approach. However, the attenuation is limited, compared to an active system, so the feasibility of the design must be demonstrated by analysis. The paper presents the jitter analysis for the baseline TPF design, using a passive isolation system. The analysis model representing the dynamics of the spacecraft and telescope is described, with emphasis on passive isolator modeling. Pointing and deformation metrics, consistent with the TPF-C error budget, are derived. Jitter prediction methodology and results are presented. Then an analysis of the critical design parameters that drive the TPF-C jitter response is performed.

Blaurock, Carl↗

NASA NTRS2010

Configurable Multi-Purpose Processor

Advancements in technology have allowed the miniaturization of systems used in aerospace vehicles. This technology is driven by the need for next-generation systems that provide reliable, responsive, and cost-effective range operations while providing increased capabilities such as simultaneous mission support, increased launch trajectories, improved launch, and landing opportunities, etc. Leveraging the newest technologies, the command and telemetry processor (CTP) concept provides for a compact, flexible, and integrated solution for flight command and telemetry systems and range systems. The CTP is a relatively small circuit board that serves as a processing platform for high dynamic, high vibration environments. The CTP can be reconfigured and reprogrammed, allowing it to be adapted for many different applications. The design is centered around a configurable field-programmable gate array (FPGA) device that contains numerous logic cells that can be used to implement traditional integrated circuits. The FPGA contains two PowerPC processors running the Vx-Works real-time operating system and are used to execute software programs specific to each application. The CTP was designed and developed specifically to provide telemetry functions; namely, the command processing, telemetry processing, and GPS metric tracking of a flight vehicle. However, it can be used as a general-purpose processor board to perform numerous functions implemented in either hardware or software using the FPGA s processors and/or logic cells. Functionally, the CTP was designed for range safety applications where it would ultimately become part of a vehicle s flight termination system. Consequently, the major functions of the CTP are to perform the forward link command processing, GPS metric tracking, return link telemetry data processing, error detection and correction, data encryption/ decryption, and initiate flight termination action commands. Also, the CTP had to be designed to survive and operate in a launch environment. Additionally, the CTP was designed to interface with the WFF (Wallops Flight Facility) custom-designed transceiver board which is used in the Low Cost TDRSS Transceiver (LCT2) also developed by WFF. The LCT2 s transceiver board demodulates commands received from the ground via the forward link and sends them to the CTP, where they are processed. The CTP inputs and processes data from the inertial measurement unit (IMU) and the GPS receiver board, generates status data, and then sends the data to the transceiver board where it is modulated and sent to the ground via the return link. Overall, the CTP has combined processing with the ability to interface to a GPS receiver, an IMU, and a pulse code modulation (PCM) communication link, while providing the capability to support common interfaces including Ethernet and serial interfaces boarding a relatively small-sized, lightweight package.

Valencia, J. Emilio↗

NASA NTRS2010

Simulating Future GPS Clock Scenarios with Two Composite Clock Algorithms

Using the GPS Toolkit, the GPS constellation is simulated using 31 satellites (SV) and a ground network of 17 monitor stations (MS). At every 15-minutes measurement epoch, the monitor stations measure the time signals of all satellites above a parameterized elevation angle. Once a day, the satellite clock estimates the station and satellite clocks. The first composite clock (B) is based on the Brown algorithm, and is now used by GPS. The second one (G) is based on the Greenhall algorithm. The composite clock of G and B performance are investigated using three ground-clock models. Model C simulates the current GPS configuration, in which all stations are equipped with cesium clocks, except for masers at USNO and Alternate Master Clock (AMC) sites. Model M is an improved situation in which every station is equipped with active hydrogen masers. Finally, Models F and O are future scenarios in which the USNO and AMC stations are equipped with fountain clocks instead of masers. Model F is a rubidium fountain, while Model O is more precise but futuristic Optical Fountain. Each model is evaluated using three performance metrics. The timing-related user range error having all satellites available is the first performance index (PI1). The second performance index (PI2) relates to the stability of the broadcast GPS system time itself. The third performance index (PI3) evaluates the stability of the time scales computed by the two composite clocks. A distinction is made between the "Signal-in-Space" accuracy and that available through a GNSS receiver.

global positioning system↗

NASA NTRS2017

Adjoint-Based Mesh Adaptation for the Sonic Boom Signature Loudness

The mesh adaptation functionality of FUN3D is utilized to obtain a mesh optimized to calculate sonic boom ground signature loudness. During this process, the coupling between the discrete-adjoints of the computational fluid dynamics tool FUN3D and the atmospheric propagation tool sBOOM is exploited to form the error estimate. This new mesh adaptation methodology will allow generation of suitable meshes adapted to reduce the estimated errors in the ground loudness, which is an optimization metric employed in supersonic aircraft design. This new output-based adaptation could allow new insights into meshing for sonic boom analysis and design, and complements existing output-based adaptation techniques such as adaptation to reduce estimated errors in off-body pressure functional. This effort could also have implications for other coupled multidisciplinary adjoint capabilities (e.g., aeroelasticity) as well as inclusion of propagation specific parameters such as prevailing winds or non-standard atmospheric conditions. Results are discussed in the context of existing methods and appropriate conclusions are drawn as to the efficacy and efficiency of the developed capability.

Rallabhandi, Sriram K.↗

NASA NTRS2022

Evaluation of remote sensing-based evapotranspiration products at low-latitude eddy covariance sites

Remote sensing-based evapotranspiration (ET) products have been evaluated primarily using data from northern middle latitudes; therefore, little is known about their performance at low latitudes. To address this bias, an evaluation dataset was compiled using eddy covariance data from 40 sites between latitudes 30° S and 30° N. The flux data were obtained from the emerging network in Mexico (MexFlux) and from openly available databases of FLUXNET, AsiaFlux, and OzFlux. This unique reference dataset was then used to evaluate remote sensing-based ET products in environments that have been underrepresented in earlier studies. The evaluated products were: MODIS ET (MOD16, both the discontinued collection 5 (C5) and the latest collection (C6)), Global Land Evaporation Amsterdam Model (GLEAM) ET, and Atmosphere-Land Exchange Inverse (ALEXI) ET. Products were compared with unadjusted fluxes (ETorig) and with fluxes corrected for the lack of energy balance closure (ETebc). Three common statistical metrics were used: coefficient of determination (R2), root mean square error (RMSE), and percent bias (PBIAS). The effect of a vegetation mismatch between pixel and site on product evaluation results was investigated by examining the relationship between the statistical metrics and product-specific vegetation match indexes. Evaluation results of this study and those published in the literature were used to examine the performance of the products across latitudes. Differences between the MOD16 collection 5 and 6 datasets were generally smaller than differences with the other products. Performance and ranking of the evaluated products depended on whether ETorig or ETebc was used. When using ETorig, GLEAM generally had the highest R2, smallest PBIAS, and best RMSE values across the studied land cover types and climate zones. Neither MOD16 nor ALEXI performed consistently better than the other. When using ETebc, none of the products stood out in terms of both low bias and strong correlations. The use of ETebc instead of ETorig affected the biases more than the correlations. The product evaluation results showed no significant relationship with the degree of match between the vegetation at the pixel and site scale. The latitudinal comparison showed tendencies of lower R2 (all products) but better PBIAS and normalized RMSE values (MOD16 and GLEAM) for forests at low latitudes than for forests at northern middle latitudes. For non-forest vegetation, the products showed no clear latitudinal differences in performance.

Diego Salazar-Martínez↗

NASA NTRS1995

Automated spectral classification and the GAIA project

Two dimensional spectral types for each of the stars observed in the global astrometric interferometer for astrophysics (GAIA) mission would provide additional information for the galactic structure and stellar evolution studies, as well as helping in the identification of unusual objects and populations. The classification of the large quantity generated spectra requires that automated techniques are implemented. Approaches for the automatic classification are reviewed, and a metric-distance method is discussed. In tests, the metric-distance method produced spectral types with mean errors comparable to those of human classifiers working at similar resolution. Data and equipment requirements for an automated classification survey, are discussed. A program of auxiliary observations is proposed to yield spectral types and radial velocities for the GAIA-observed stars.

Lasala, Jerry↗

NASA NTRS1997

An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation. This means that the FW-H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Brentner, Kenneth S.↗

NASA NTRS2014

Link Analysis for Space Communication Links Using ARQ Protocol

In space communications, standard link analysis assumes that messages are sent once. For a communication link that uses an error-correction coding scheme, bit-error-rate (BER) or frame-error-rate (FER), and link margins are common metrics that characterize the quality of a link, and they are used to determine the supportable data rate. With the advent of Automatic Repeat-reQuest (ARQ) protocols, when messages are corrupted during transmission, they can be resent multiple times automatically until they are correctly received and acknowledged. The concept of BER, FER, and link margin cannot be directly applied, and the link analysis approach for ARQ links needs to be re-examined.

Cheung, Kar-Ming↗

NASA NTRS2022

Quantifying and Reducing Uncertainty in Microwave Vegetation Optical Depth and Soil Moisture Retrievals

Soil moisture and vegetation optical depth (VOD; related to vegetation water content) retrieved from SMAP and SMOS satellites are widely used for a range of hydrosphere and biosphere applications. However, while soil moisture has been globally well-validated, VOD validation has been sparse. Furthermore, simultaneously retrieval of these parameters results in uncertainties both individually in soil moisture and VOD retrievals as well as in compensation between the parameters. Here, we show global locations where soil moisture and VOD retrievals will have lower uncertainty, based on complementary brightness temperature information content and signal-to-noise ratio metrics. In these same locations, we show that error still propagates more into VOD. However, using VOD regularization algorithms, this error is greatly reduced, especially at sub-weekly timescales where algorithmic error can be most apparent. Despite these regularization approaches that reduce errors, there are yet vast differences in available global regularized retrievals originating from different algorithmic choices.

Passive microwave radiometry↗

NASA NTRSDate not supplied

Assimilation of SMAP Observations Over Land Improves the Simulation and Prediction of Tropical Cyclone Idai

This work is focused on the role of soil moisture in the prediction of tropical cyclones (TCs) approaching land and after landfall. Soil moisture conditions can impact the circulation and structure of an existing tropical cyclone (TC) when part or all of the circulation is over land. For example, dry land surface conditions may lead to faster dissipation of a TC over land (often associated with changes in precipitation structure), whereas very wet conditions may help sustain or in rare cases re-intensify a TC. Moreover, the presence of strong soil moisture gradients may affect the symmetry and development of the TC circulation leading to changes in its over-land track. While the link between soil moisture conditions and TC evolution in proximity to land is relatively well understood in theory, applications of these findings in the context of numerical weather prediction (NWP) have been limited. Here we present a case study that explores the potential of improving TC predictions through an improved soil moisture initialization in an NWP framework. Specifically, we examine the impact of assimilating observations from the NASA Soil Moisture Active Passive (SMAP) mission into the NASA Goddard Earth Observing System (GEOS) global weather model on the prediction of South-West Indian Ocean TC Idai (2019). SMAP provides accurate L-band (1.4 GHz) brightness temperatures (Tb) observations that are sensitive to soil moisture globally and at high revisit times of 2-3 days. It has previously been shown that the assimilation of SMAP Tb observations significantly improves modeled land surface states. Thus, it is expected that SMAP can be used to constrain land surface initial conditions and potentially benefit TC forecasts. Here we present two sets of retrospective forecasts of TC Idai that are compared in an Observing System Experiment framework at ¼ degree resolution: (i) forecasts initialized from an analysis that is comparable to the GEOS operational analysis (without SMAP Tb assimilation) and (ii) forecasts initialized from an analysis that additionally assimilates SMAP brightness temperature observations over land using a weakly-coupled land analysis. We find that the assimilation of SMAP meaningfully improves the representation of TC Idai’s structure as well as the prediction of its intensity and track. The analyzed TC size, as measured by the wind speed radius, is improved by up to 18% in the analysis with SMAP assimilation relative to the control run. The forecast intensity error, measured against the observed intensity, is reduced by up to 23%. At the 1/4-degree resolution used here, GEOS unavoidably under-estimates TC intensity and over-estimates TC size. The SMAP assimilation therefore corrects the model in the right direction, leading to a storm that is more energetic and more compact. Furthermore, we find that the along-track forecast error is reduced by up to 34%, indicating a more accurate propagation speed, which is consistent with the fact that TC speed over land is strongly affected by surface processes. The impact of SMAP assimilation on the forecast cross-track error is neutral. Across the TC forecast skill metrics used here, the improvements from SMAP DA are largest at lead times of 36 to 72 hours, suggesting that the predictability of forecasts at shorter lead times may be dominated by short-term convective processes, while the land and its longer memory gains in importance as a source of predictability on a 2-3 day timescale. We further investigated the underlying mechanisms leading to the skill improvements from SMAP data assimilation by isolating the land areas that directly influence TC Idai using a back trajectory analysis. We find that the assimilation of SMAP leads to wetter soil moisture conditions that cause an increased latent heat flux, which ultimately results in TC analyzed representation that has higher column-integrated total moisture content and total energy compared to the analysis in the control run without SMAP assimilation. Overall, the results highlight that the assimilation of SMAP observations into a global numerical weather prediction model can lead to pronounced improvements of TC predictions. This is a crucial step towards a better mitigation of the socio-economic impact of landfalling TCs and thus safeguarding human lives. Finally, our study presents an event-based approach that assesses the impact of land data assimilation for a particular weather event rather than by globally averaging differences in skill. We argue that global skill assessments – while necessary – can mute the impact of land data assimilation, because the land’s influence on the atmosphere is constrained to certain locations and certain times. Instead, the event-based approach better highlights the true potential of land data assimilation in the context of NWP, especially for extreme events when accurate predictions are critical.

Jana Kolassa↗

NASA NTRSDate not supplied

Assimilation of SMAP Observations Over Land Improves the Simulation and Prediction of Tropical Cyclone Idai

This work is focused on the role of soil moisture in the prediction of tropical cyclones (TCs) approaching land and after landfall. Soil moisture conditions can impact the circulation and structure of an existing tropical cyclone (TC) when part or all of the circulation is over land. For example, dry land surface conditions may lead to faster dissipation of a TC over land (often associated with changes in precipitation structure), whereas very wet conditions may help sustain or in rare cases re-intensify a TC. Moreover, the presence of strong soil moisture gradients may affect the symmetry and development of the TC circulation leading to changes in its over-land track. While the link between soil moisture conditions and TC evolution in proximity to land is relatively well understood in theory, applications of these findings in the context of numerical weather prediction (NWP) have been limited. Here we present a case study that explores the potential of improving TC predictions through an improved soil moisture initialization in an NWP framework. Specifically, we examine the impact of assimilating observations from the NASA Soil Moisture Active Passive (SMAP) mission into the NASA Goddard Earth Observing System (GEOS) global weather model on the prediction of South-West Indian Ocean TC Idai (2019). SMAP provides accurate L-band (1.4 GHz) brightness temperatures (Tb) observations that are sensitive to soil moisture globally and at high revisit times of 2-3 days. It has previously been shown that the assimilation of SMAP Tb observations significantly improves modeled land surface states. Thus, it is expected that SMAP can be used to constrain land surface initial conditions and potentially benefit TC forecasts. Here we present two sets of retrospective forecasts of TC Idai that are compared in an Observing System Experiment framework at ¼ degree resolution: (i) forecasts initialized from an analysis that is comparable to the GEOS operational analysis (without SMAP Tb assimilation) and (ii) forecasts initialized from an analysis that additionally assimilates SMAP brightness temperature observations over land using a weakly-coupled land analysis. We find that the assimilation of SMAP meaningfully improves the representation of TC Idai’s structure as well as the prediction of its intensity and track. The analyzed TC size, as measured by the wind speed radius, is improved by up to 18% in the analysis with SMAP assimilation relative to the control run. The forecast intensity error, measured against the observed intensity, is reduced by up to 23%. At the 1/4-degree resolution used here, GEOS unavoidably under-estimates TC intensity and over-estimates TC size. The SMAP assimilation therefore corrects the model in the right direction, leading to a storm that is more energetic and more compact. Furthermore, we find that the along-track forecast error is reduced by up to 34%, indicating a more accurate propagation speed, which is consistent with the fact that TC speed over land is strongly affected by surface processes. The impact of SMAP assimilation on the forecast cross-track error is neutral. Across the TC forecast skill metrics used here, the improvements from SMAP DA are largest at lead times of 36 to 72 hours, suggesting that the predictability of forecasts at shorter lead times may be dominated by short-term convective processes, while the land and its longer memory gains in importance as a source of predictability on a 2-3 day timescale. We further investigated the underlying mechanisms leading to the skill improvements from SMAP data assimilation by isolating the land areas that directly influence TC Idai using a back trajectory analysis. We find that the assimilation of SMAP leads to wetter soil moisture conditions that cause an increased latent heat flux, which ultimately results in TC analyzed representation that has higher column-integrated total moisture content and total energy compared to the analysis in the control run without SMAP assimilation. Overall, the results highlight that the assimilation of SMAP observations into a global numerical weather prediction model can lead to pronounced improvements of TC predictions. This is a crucial step towards a better mitigation of the socio-economic impact of landfalling TCs and thus safeguarding human lives. Finally, our study presents an event-based approach that assesses the impact of land data assimilation for a particular weather event rather than by globally averaging differences in skill. We argue that global skill assessments – while necessary – can mute the impact of land data assimilation, because the land’s influence on the atmosphere is constrained to certain locations and certain times. Instead, the event-based approach better highlights the true potential of land data assimilation in the context of NWP, especially for extreme events when accurate predictions are critical.

Jana Kolassa↗

NASA NTRSDate not supplied

TBIRD, a rapid prototyping approach for design, assembly, and test of a LEO-to-ground lasercom CubeSat

The TeraByte InfraRed Delivery (TBIRD) system is a 3U payload on a 6U CubeSat launched in May 2022 which has now demonstrated space to ground links of >1 Terabyte (TB) per pass at a max data rate of 200Gbps. As a CubeSat mission, the development of the TBIRD payload was focused on low SWaP and a “rapid prototyping” approach which accepted higher risks to accelerate the schedule and reduce costs. The optomechanical design process followed standard in-house processes to develop a system that would be robust to LEO environmental loads, with a focus on the stability of the transmit (Tx) and receive (Rx) channel performance metrics. The driving requirement of maintaining 20μrad pointing error between the TX and Rx channels forced specific attention to thermal and mechanical load changes over operational conditions, which drove major design decisions. This paper describes some of engineering challenges overcome and approaches used to make TBIRD a successful program, as well as some of the tradeoffs of rapid prototyping precision optical payloads. TBIRD successfully met and exceeded the total downlink requirements listed above, with a bandwidth of 200Gbps and a total downlink of 4.8TB of information in a single pass.

TBIRD↗

NASA NTRS1972

Variable-length codes and the Fano metric.

It is shown that the metric proposed originally by Fano for sequential decoding is precisely the required statistic for minimum-error-probability decoding of variable-length codes. The analysis shows further that the 'natural' choice of bias in the metric is the code rate and gives insight into why the Fano metric has proved to be the best practical choice in sequential decoding. The recently devised Jelinek-Zigangirov 'stack algorithm' is shown to be a natural consequence of this interpretation of the Fano metric. Finally, it is shown that the elimination of the bias in the 'truncated' portion of the code tree gives a slight reduction in average computation at the sacrifice of increased error probability.

Massey, J. L.↗

NASA NTRSDate not supplied

Discretization Error Estimation and Control for Farfield Acoustic Signatures

We investigate the utility of adjoint-based error estimates for sonic boom farfield simulations governed by solutions of the augmented Burgers’ equation. Solution of this nonlinear system uses operator splitting with a second-order finite volume discretization in space and second-order Runge-Kutta time marching, while the absorption and molecular relaxation are solved using second-order central differencing. The discretization error in selected ground sonic boom cost functionals is estimated using the method of adjoint-weighted residuals. Key elements of the implementation process are emphasized with details provided on the practical aspects as appliedto the sonic boom farfield propagation. We establish the accuracy of the adjoint solutions usingcomplex step and finite difference approaches, and examine the accuracy of the error estimates using analytical N-wave solutions. We then apply it to a pressure waveform corresponding to the X-59 research aircraft. The investigations demonstrate that the method of adjoint-weighted residuals accurately predicts the level of discretization error present in sonic boom farfield simulations while offering insight into which features of the near field signal are the primary drivers of ground noise metrics. The numerical results indicate that at sampling frequencies as low as50kHz, discretization error in the propagation is under 0.01 dB[A] for realistically complex examples.

CST↗

NASA NTRS2017

A new concept of stability in orbit propagation, useful for quantifying numerical errors

We present the concept of topological stability in the numerical propagation of orbits, and show how it results in a useful new method for measuring the global numerical error of an orbit propagation. The concept applies to any problem in orbital dynamics. Moreover, it can be extended to any three-dimensional system of di erential equations of second order. In order to assess the topological stability of a given integration a special metric is introduced, which can be used to estimate the numerical errors robustly. The method is particularly well suited for dealing with strongly perturbed and chaotic systems. The construction is based on the constraint imposed by the Hopf map that supports the Kustaanheimo-Stiefel transformation. Generic concepts of stability are translated to KS space.

Pelaez, Jesus↗

NASA NTRS2007

Anisotropic Solution Adaptive Unstructured Grid Generation Using AFLR

An existing volume grid generation procedure, AFLR3, was successfully modified to generate anisotropic tetrahedral elements using a directional metric transformation defined at source nodes. The procedure can be coupled with a solver and an error estimator as part of an overall anisotropic solution adaptation methodology. It is suitable for use with an error estimator based on an adjoint, optimization, sensitivity derivative, or related approach. This offers many advantages, including more efficient point placement along with robust and efficient error estimation. It also serves as a framework for true grid optimization wherein error estimation and computational resources can be used as cost functions to determine the optimal point distribution. Within AFLR3 the metric transformation is implemented using a set of transformation vectors and associated aspect ratios. The modified overall procedure is presented along with details of the anisotropic transformation implementation. Multiple two-and three-dimensional examples are also presented that demonstrate the capability of the modified AFLR procedure to generate anisotropic elements using a set of source nodes with anisotropic transformation metrics. The example cases presented use moderate levels of anisotropy and result in usable element quality. Future testing with various flow solvers and methods for obtaining transformation metric information is needed to determine practical limits and evaluate the efficacy of the overall approach.

Marcum, David L.↗