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NASA NTRS2020

Calibration Probe Uncertainty and Validation for the Hypersonic Material Environmental Test System

This paper presents an uncertainty analysis of the stagnation-point calibration probe surface predictions for conditions that span the performance envelope of the Hypersonic Materials Environmental Test System facility located at NASA Langley Research Center. A second-order stochastic expansion was constructed over 47 uncertain parameters to evaluate the sensitivities, identify the most significant uncertain variables, and quantify the uncertainty in the stagnation-point heat flux and pressure predictions of the calibration probe for a low- and high-enthalpy test condition. A sensitivity analysis showed that measurement bias uncertainty is the most significant contributor to the stagnation-point pressure and heat flux variance for the low-enthalpy condition. For the high-enthalpy condition, a paradigm shift in sensitivities revealed the computational fluid dynamics model input uncertainty as the main contributor. A comparison between the prediction and measurement of the stagnation-point conditions under uncertainty showed that there was evidence of statistical disagreement. A validation metric was proposed and applied to the prediction uncertainty to account for the statistical disagreement when compared to the possible stagnation-point heat flux and pressure measurements.

Brune, Andrew J.↗

NASA NTRS2022

Uncertainty Estimation for SMAP Level-1 Brightness Temperature Assimilation at Different Timescales

Soil Moisture Active Passive (SMAP) mission brightness temperature (T(b) ) observations are assimilated into NASA’s Catchment Land Surface Model using an Ensemble Kalman filter to update simulations of surface and root-zone soil moisture. Different time series components of the T(b) observations are assimilated including anomalies, inter-annual variations, and high frequency variations. To optimize the weights that the data assimilation (DA) puts on the observations, the ratio between the uncertainties of modeled and observed T(b) is approximated using modeled and observed soil moisture uncertainties estimated using triple collocation analysis. In a benchmark experiment, T(b) observations are assimilated using a spatially constant 4 Kelvin (K) observation uncertainty, as in the operational SMAP Level-4 algorithm. All DA experiments exhibit notable skill improvements in most regions. Improvements are largest for the inter-annual variations in the simulations of both surface and root-zone soil moisture (mean improvements in terms of Pearson correlation (-) are 0.08 and 0.06, respectively). Anomaly simulations improve similarly (0.07), and improvements in the high-frequency variations are only observed for surface soil moisture simulations (0.06). No notable difference in skill - neither improvement nor deterioration - is observed between the experiments that use optimized observation uncertainty parameters and the 4 K benchmark experiment. This may be explained by the presence of large observation operator errors, which are analytically shown to have the potential to render post-update uncertainty insensitive to inaccuracies in estimates of the Kalman gain. These results have important implications for the design of soil moisture DA systems, in particular for parameterizing model and observation uncertainties.

Hydrology↗

NASA NTRS2022

Ames-2021 CO 2 Dipole Moment Surface and IR Line Lists: Toward 0.1% Uncertainty for CO 2 IR Intensities

A highly accurate CO 2 ab initio dipole moment surface (DMS), Ames-2021, is reported along with 12 C 16 O 2 infrared (IR) intensity comparisons approaching a 1–4‰ level of agreement and uncertainty. The Ames-2021 DMS was accurately fitted from CCSD(T) finite-field dipoles computed with the aug-cc-pVXZ (X = T, Q, 5) basis for C atom and the d-aug-cc-pVXZ (X = T, Q, 5) basis for O atoms, and extrapolated to the one particle basis set limit. Fitting σ(rms) is 3.8 × 10^(–7) au for 4443 geometries below 15 000 per cm . The corresponding IR intensity, S Ames-2021 , are computed using the Ames-2 potential energy surface (PES), which is the best PES available for CO 2 . Compared to high accuracy IR studies for 2001i–00001 and 3001i–00001 bands, S Ames-2021 matches NIST experiment-based intensities [S NIST-HIT16 or S HIT20 ] to −1.0 ± 1.3‰, or matches DLR experiment-based intensities [S DLR-HIT16/UCL/Ames ] to 1.9 ± 3.7‰. This indicates the systematic deviations and uncertainties have been significantly reduced in S Ames-2021 . The S UCL2015 (or S HITRAN2016 ) have larger deviations (vs S DLR ) and uncertainties (vs S DLR , S NIST ) which are attributed to the less accurate Ames-1 PES adopted in UCL-296 line list calculation. The S Ames-2021 intensity of 12 C 16 O 2 and 13 C 16 O 2 is utilized to derive new absolute 13 C/ 12 C ratios for Vienna PeeDee Belemnite (VPDB) with uncertainty reduced by 1/3 or 2/3. Further evaluation of S Ames-2021 are carried out on those CO 2 bands discussed in the HITRAN2020 update paper. Consistent improvements and better accuracies are found in band-by-band analysis, except for those bands strongly affected by Coriolis couplings, or very weak bands measured with relatively larger experimental uncertainties. The Ames-2021 296 K IR line lists are generated for 13 CO 2 isotopologues, with 18,000 per and S 296K > 1E–31) cm/molecule cutoff and then combined with CDSD line positions (except 14 C 16 O 2 ). The Ames-2021 DMS and 296 K IR line lists represent a major improvement over previous CO 2 theoretical IR intensity studies, including Ames-2016, UCL-296, and recent UCL DMS 2021 update. A real 1 permille level of agreement and uncertainty will definitely require both more accurate PES and more accurate DMS.

Chemical calculations↗

NASA NTRS2021

Trend Detection of Atmospheric Time Series: Incorporating Appropriate Uncertainty Estimates and Handling Extreme Events

This paper is aimed at atmospheric scientists without formal training in statistical theory. Its goal is to, 1) provide a critical review of the rationale for trend analysis of the time series typically encountered in the field of atmospheric chemistry; 2) describe a range of trend-detection methods; and 3) demonstrate effective means of conveying the results to a general audience. Trend detections in atmospheric chemical composition data are often challenged by a variety of sources of uncertainty, which often behave differently to other environmental phenomena such as temperature, precipitation rate, or stream flow, and may require specific methods depending on the science questions to be addressed. Some sources of uncertainty can be explicitly included in the model specification, such as autocorrelation and seasonality, but some inherent uncertainties are difficult to quantify, such as data heterogeneity and measurement uncertainty due to the combined effect of short- and long-term natural variability, instrumental stability, and aggregation of data from sparse sampling frequency. Failure to account for these uncertainties might result in an inappropriate inference of the trends and their estimation errors. On the other hand, the variation in extreme events might be interesting for different scientific questions, for example, the frequency of extremely high surface ozone events and their relevance to human health. In this study we aim to, 1) review trend detection methods for addressing different levels of data complexity in different chemical species; 2) demonstrate that the incorporation of scientifically interpretable covariates can outperform pure numerical curve fitting techniques in terms of uncertainty reduction and improved predictability; 3) illustrate the study of trends based on extreme quantiles that can provide insight beyond standard mean or median based trend estimates; and 4) present an advanced method of quantifying regional trends based on the inter-site correlations of multi-site data. All demonstrations are based on time series of observed trace gases relevant to atmospheric chemistry, but the methods can be applied to other environmental data sets.

Trace gas↗

NASA NTRS2023

Reducing Aerosol Forcing Uncertainty by Combining Models With Satellite and Within-The-Atmosphere Observations: A Three-Way Street

Aerosol forcing uncertainty represents the largest climate forcing uncertainty overall. Its magnitude has remained virtually undiminished over the past 20 years despite considerable advances in understanding most of the key contributing elements. Recent work has produced modest increases only in the confidence of the uncertainty estimate itself. This review summarizes the contributions toward reducing the uncertainty in the aerosol forcing of climate made by satellite observations, measurements taken within the atmosphere, as well as modeling and data assimilation. We adopt a more measurement-oriented perspective than most reviews of the subject in assessing the strengths and limitations of each; gaps and possible ways to fill them are considered. Currently planned programs supporting advanced, global-scale satellite and surface-based aerosol, cloud, and precursor gas observations, climate modeling, and intensive field campaigns aimed at characterizing the underlying physical and chemical processes involved, are all essential. But in addition, new efforts are needed: (a) to obtain systematic aircraft in situ measurements capturing the multi-variate probability distribution functions of particle optical, microphysical, and chemical properties (and associated uncertainty estimates), as well as co-variability with meteorology, for the major aerosol airmass types; (b) to conceive, develop, and implement a suborbital (aircraft plus surface-based) program aimed at systematically quantifying the cloud-scale microphysics, cloud optical properties, and cloud-related vertical velocities associated with aerosol-cloud interactions; and (c) to focus much more research on integrating the unique contributions of satellite observations, suborbital measurements, and modeling, to reduce the persistent uncertainty in aerosol climate forcing.

aerosol climate forcing↗

NASA NTRS2023

Understanding Volume Estimation Uncertainty of Lakes and Wetlands Using Satellites and Citizen Science

We studied variations in the volume of water stored in small lakes and wetlands using satellite remote sensing and lake water height data contributed by citizen scientists. A total of 94 water bodies across the globe were studied using satellite data in the optical and microwave wavelengths from Landsat 8, Sentinel-1, and Sentinel-2. The uncertainty in volume estimation as a function of geography and geophysical factors, such as cloud cover, precipitation, and water surface temperature, was studied. The key finding that emerged from this global study is that uncertainty is highest in regions with a distinct precipitation season, such as in the monsoon dominated South Asia or the Pacific Northwestern region of the USA. This uncertainty is further compounded when small lakes and wetlands are seasonal with alternating land use as a water body and agricultural land, such as the wetlands of Northeastern Bangladesh. On an average, 45% of studied lakes could be estimated of their volume change with a statistical significant uncertainty that is less than the expected volume in South Asia. In North America, this statistically significant uncertainty in volume estimation was found to be around 50% in lakes eastward of the 108th meridian with lowest uncertainty found in lakes along the East coast of the USA. The article provides a baseline for understanding the current state of the art in estimating volumetric change of lakes and wetlands using citizen science in anticipation of the recently launched Surface Water and Ocean Topography Mission.

Shahzaib Khan↗

NASA NTRS2024

Uncertainty Budget for Detector-Based Absolute Radiometric Calibration With GLAMR

The accuracy of the absolute radiometric calibration (RadCal) for remote sensing instruments is essential to their wide range of applications. The uncertainty associated to the traditional source-based RadCal method is assessed at a 2% (k=1) or higher level for radiance measurement. To further improve the accuracy to meet the demands of climate studies, a detector-based approach using tunable lasers as a light source has been devised. The Goddard Laser for Absolute Measurement of Radiance, known as the GLAMR system, is a notable example of the incorporation of such technology. Using transfer radiometers calibrated at NIST as calibration standards, the absolute spectral response (ASR) function of a remote sensing instrument is measured with its uncertainty traceable to the International System of Units. This paper presents a comprehensive uncertainty analysis of the detector-based absolute RadCal using the GLAMR system. It identifies and examines uncertainty sources during the GLAMR RadCal test, including those from the GLAMR system, the testing configuration, and data processing methodologies. Analysis is carried out to quantify the contribution of each source and emphasize the most influential factors. It is shown that the calibration uncertainty of GLAMR RadCal can be better than 0.3% (k=1) in the wavelength range of 350-950 nm and 0.6% (k=1) between 950-2300 nm, with the exception of regions with strong water absorption. In addition, recommendations are made to refine the calibration process to further reduce the uncertainty.

Zhipeng Wang↗

NASA NTRSDate not supplied

Uncertainty Quantification Methodology for Sonic Boom Loudness of a Low-Boom Supersonic Concept

This paper presents a comprehensive analysis of uncertainty quantification for sonic boom loudness metrics associated with the X-59 aircraft during its acoustic validation phase. The study focuses on employing advanced methodologies to characterize uncertainties in key sonic boom parameters predicted from a database derived from a computational fluid dynamics (CFD) solver. These methodologies include creating a polynomial chaos expansion (PCE) surrogate model, which is then used to run a Monte Carlo analysis to obtain 95% uncertainty intervals for sonic boom loudness parameters across the full carpet. Atmospheric uncertainties are rigorously considered, leveraging weather models based on historical data near Edwards Air Force Base to simulate potential flight conditions. The findings include preliminary uncertainty results for the full carpet during the validation phase of the Quesst mission. Additionally, a sensitivity study reveals that the primary sources of uncertainty are humidity and cruise weight.

Laura M. White↗

NASA NTRSDate not supplied

Design Under Uncertainty for Conceptual Aircraft Design Leveraging Analytical Gradients

The purpose of this paper is to extend previously demonstrated methodologies for design under uncertainty, leveraging analytical gradients to higher fidelity analysis for use in conceptual aircraft design. Previous work developed methods to generate analytical derivatives through polynomial chaos expansion, eliminating the need to estimate derivatives via complex step or finite difference. In this research, the authors build upon the methods to include physics-based aircraft design codes for aircraft design under uncertainty. This extends the previous work’s case study, which employed analytical aerodynamics and Breguet range estimations for wing design, to a higher fidelity level. In addition, this work extends previous work on interface development between the Uncertainty Quantification with Polynomial Chaos Expansion (UQPCE) software and Model-Based Systems Analysis and Engineering (MBSA&E) frameworks. This paper will discuss the development work necessary to perform multidisciplinary design under uncertainty as well as demonstrate the mechanics of interfacing UQPCE and conceptual aircraft design tools such as NASA’s Aviary code. In a case study, a conceptual aircraft design under uncertainty was conducted and compared against a traditional deterministic design. When given information about the uncertainty space from UQPCE, the optimizer was able to shape the output distribution and produce a more robust design

UQ↗

NASA NTRSDate not supplied

Copula-based Method to Generate Consistent Surface Pressures Under Uncertainty

This paper establishes a method to create surface pressure databases that allow for uncertainty quantification. Aerodynamic databases are critical products for launch vehicles and other aeronautical systems, and surface pressure databases are one such database that constains large quantities of data. The focus of this work is the relationship between the integrated force and moment data base and the surface pressure database. In particular, the work attempts to provide a method that maintains consistency between these two databases when accounting for uncertainty. The integrated force and moment database and surface pressure databases are constructed from CFD data which is high-density but low-trust. However, the force and moment database will often also include data from high-trust but low-density sources such as from wind tunnel experiments. This means that the quantified uncertainty of the force and moment database is higher quality as it includes this high fidelity wind tunnel data. This motivates the idea to use the force and moment database uncertainty when constructing the surface pressure database uncertainty. The method utilizes the statistical idea of a copula in order to generate surface pressures that match with uncertain integrated force and moment distributions as well as being consistent with known CFD data. This statistical consistency is quantified by using the Maximum Mean Discrepancy two-sample test. The predictive error of the method is also approximated using leave-one-out error estimation and the good overall performance of the method is presented using probability boxes in a simulated uncertainty scenario.

SLS↗

NASA NTRSDate not supplied

Design Under Uncertainty for Conceptual Aircraft Design Leveraging Analytical Gradients

UQ↗

NASA NTRS2014

An Uncertainty Quantification Framework for Prognostics and Condition-Based Monitoring

This paper presents a computational framework for uncertainty quantification in prognostics in the context of condition-based monitoring of aerospace systems. The different sources of uncertainty and the various uncertainty quantification activities in condition-based prognostics are outlined in detail, and it is demonstrated that the Bayesian subjective approach is suitable for interpreting uncertainty in online monitoring. A state-space model-based framework for prognostics, that can rigorously account for the various sources of uncertainty, is presented. Prognostics consists of two important steps. First, the state of the system is estimated using Bayesian tracking, and then, the future states of the system are predicted until failure, thereby computing the remaining useful life of the system. The proposed framework is illustrated using the power system of a planetary rover test-bed, which is being developed and studied at NASA Ames Research Center.

Health Monitoring↗

NASA NTRS2016

Conflict Resolution for Wind-Optimal Aircraft Trajectories in North Atlantic Oceanic Airspace with Wind Uncertainties

Air traffic in the North Atlantic oceanic airspace (NAT) experiences very strong winds caused by jet streams. Flying wind-optimal trajectories increases individual flight efficiency, which is advantageous when operating in the NAT. However, as the NAT is highly congested during peak hours, a large number of potential conflicts between flights are detected for the sets of wind-optimal trajectories. Conflict resolution performed at the strategic level of flight planning can significantly reduce the airspace congestion. However, being completed far in advance, strategic planning can only use predicted environmental conditions that may significantly differ from the real conditions experienced further by aircraft. The forecast uncertainties result in uncertainties in conflict prediction, and thus, conflict resolution becomes less efficient. This work considers wind uncertainties in order to improve the robustness of conflict resolution in the NAT. First, the influence of wind uncertainties on conflict prediction is investigated. Then, conflict resolution methods accounting for wind uncertainties are proposed.

wind uncertainties↗

NASA NTRS2016

Spatial and Temporal Uncertainty of Crop Yield Aggregations

The aggregation of simulated gridded crop yields to national or regional scale requires information on temporal and spatial patterns of crop-specific harvested areas. This analysis estimates the uncertainty of simulated gridded yield time series related to the aggregation with four different harvested area data sets. We compare aggregated yield time series from the Global Gridded Crop Model Inter-comparison project for four crop types from 14 models at global, national, and regional scale to determine aggregation-driven differences in mean yields and temporal patterns as measures of uncertainty. The quantity and spatial patterns of harvested areas differ for individual crops among the four datasets applied for the aggregation. Also simulated spatial yield patterns differ among the 14 models. These differences in harvested areas and simulated yield patterns lead to differences in aggregated productivity estimates, both in mean yield and in the temporal dynamics. Among the four investigated crops, wheat yield (17% relative difference) is most affected by the uncertainty introduced by the aggregation at the global scale. The correlation of temporal patterns of global aggregated yield time series can be as low as for soybean (r = 0.28).For the majority of countries, mean relative differences of nationally aggregated yields account for10% or less. The spatial and temporal difference can be substantial higher for individual countries. Of the top-10 crop producers, aggregated national multi-annual mean relative difference of yields can be up to 67% (maize, South Africa), 43% (wheat, Pakistan), 51% (rice, Japan), and 427% (soybean, Bolivia).Correlations of differently aggregated yield time series can be as low as r = 0.56 (maize, India), r = 0.05∗Corresponding (wheat, Russia), r = 0.13 (rice, Vietnam), and r = −0.01 (soybean, Uruguay). The aggregation to sub-national scale in comparison to country scale shows that spatial uncertainties can cancel out in countries with large harvested areas per crop type. We conclude that the aggregation uncertainty can be substantial for crop productivity and production estimations in the context of food security, impact assessment, and model evaluation exercises.

Aggregation uncertainty↗

NASA NTRS2016

Uncertainties in Coastal Ocean Color Products: Impacts of Spatial Sampling

With increasing demands for ocean color (OC) products with improved accuracy and well characterized, per-retrieval uncertainty budgets, it is vital to decompose overall estimated errors into their primary components. Amongst various contributing elements (e.g., instrument calibration, atmospheric correction, inversion algorithms) in the uncertainty of an OC observation, less attention has been paid to uncertainties associated with spatial sampling. In this paper, we simulate MODIS (aboard both Aqua and Terra) and VIIRS OC products using 30 m resolution OC products derived from the Operational Land Imager (OLI) aboard Landsat-8, to examine impacts of spatial sampling on both cross-sensor product intercomparisons and in-situ validations of R(sub rs) products in coastal waters. Various OLI OC products representing different productivity levels and in-water spatial features were scanned for one full orbital-repeat cycle of each ocean color satellite. While some view-angle dependent differences in simulated Aqua-MODIS and VIIRS were observed, the average uncertainties (absolute) in product intercomparisons (due to differences in spatial sampling) at regional scales are found to be 1.8%, 1.9%, 2.4%, 4.3%, 2.7%, 1.8%, and 4% for the R(sub rs)(443), R(sub rs)(482), R(sub rs)(561), R(sub rs)(655), Chla, K(sub d)(482), and b(sub bp)(655) products, respectively. It is also found that, depending on in-water spatial variability and the sensor's footprint size, the errors for an in-situ validation station in coastal areas can reach as high as +/- 18%. We conclude that a) expected biases induced by the spatial sampling in product intercomparisons are mitigated when products are averaged over at least 7 km × 7 km areas, b) VIIRS observations, with improved consistency in cross-track spatial sampling, yield more precise calibration/validation statistics than that of MODIS, and c) use of a single pixel centered on in-situ coastal stations provides an optimal sampling size for validation efforts. These findings will have implications for enhancing our understanding of uncertainties in ocean color retrievals and for planning of future ocean color missions and the associated calibration/validation exercises.

Coastal ocean color↗

NASA NTRS2019

Uncertainties in Evapotranspiration Estimates over West Africa

An evapotranspiration (ET) ensemble composed of 36 land surface model (LSM) experiments and four diagnostic datasets (GLEAM, ALEXI, MOD16, and FLUXNET) is used to investigate uncertainties in ET estimate over five climate regions in West Africa. Diagnostic ET datasets show lower uncertainty estimates and smaller seasonal variations than the LSM-based ET values, particularly in the humid climate regions. Overall, the impact of the choice of LSMs and meteorological forcing datasets on the modeled ET rates increases from north to south. The LSM formulations and parameters have the largest impact on ET in humid regions, contributing to 90% of the ET uncertainty estimates. Precipitation contributes to the ET uncertainty primarily in arid regions. The LSM-based ET estimates are sensitive to the uncertainty of net radiation in arid region and precipitation in humid region. This study serves as support for better determining water availability for agriculture and livelihoods in Africa with earth observations and land surface models.

land surface model↗

NASA NTRSDate not supplied

Automation of the Uncertainty Quantification Process Based on Probability Boxes with DAKOTA

To date, while the use of CFD is prevalent, very few efforts have been undertaken that truly attempt to document all (or even most) of the sources of uncertainty in the simulations. Instead, the current state-of-the-art relies heavily on the experience of the CFD practitioner to estimate the uncertainty associated with their simulations through simple sensitivity studies or subject matter expertise. This practice will have to be replaced with a formal uncertainty quantification (UQ) process if CFD is to play an expanded role in the design research and engineering community, test and evaluation community, and ultimately certification for flight. This is especially true for hypersonic air-breathing propulsion systems due to the environment, scale, and duration limitations of ground test facilities. Accounting for uncertainties in a formal manner is a tedious process. Moreover, the typical CFD practitioner is not likely to be familiar with formal UQ methods. Hence, a major obstacle that has prevented the adoption of UQ methods for engineering design and development work is the lack of a tool set to automate most (if not all) of the UQ workflow. Towards this end, the SANDIA package DAKOTA (which has been developed to drive both UQ and optimization processes) will be tightly wrapped around the VULCAN-CFD code to automate the uncertainty quantification process. The automated process will be applied to an isolator turbulence model validation exercise that has previously been documented using a manual approach to the UQ process. Hence, the focus of this paper will be documenting the level to which automation can hide the UQ process details from the CFD practitioner rather than the UQ method itself.

CFD↗

NASA NTRSDate not supplied

Uncertainty Quantification of Expected Time-of-Arrival in UAV Flight Trajectory

One of the foremost requirements for accurate in-flight safety monitoring of autonomous unmanned aerial vehicles (UAVs) is tracking of their flight trajectory. Existing UAVs leverage autonomous flight functionalities based on trajectory generation algorithms developed in robotic applications such as polynomial or spline curves in order to facilitate kinematic smoothness, minimum vibrations and fuel efficiency. However in practice, the actual path may be subjected to unexpected local weather conditions, unexpected obstacles along the path or abrupt traffic changes in the low-altitude airspace resulting in large errors of the predicted time-of-arrival at way-points. In this study, an approach to quantify and propagate uncertainty in 4D trajectories is proposed. The paper presents a simple error interval propagation method based on the expected cruise speed of the UAV and its associated uncertainty. The uncertainty is then propagated in time to estimate reasonable confidence intervals on the times-of-arrival of the vehicle at each way-point as well as along the entire flight-path. The uncertainty propagation is demonstrated on a state-of-the-art trajectory generation algorithm based on non-uniform rational B-spline (NURBS) curves. Further, the effect of a stationary wind field is incorporated in the uncertainty propagation approach. The proposed method is implemented on synthetic and real data obtained from flight experiments with a small UAV.

Uncertainty Quantification↗