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All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Incorporating JULES into NASA's Land Information System (LIS) and Investigations of Land-Atmosphere Coupling

NASA's Land Information System (LIS; lis.gsfc.nasa.gov) is a flexible land surface modeling and data assimilation framework developed over the past decade with the goal of integrating satellite- and ground-based observational data products and advanced land surface modeling techniques to produce optimal fields of land surface states and fluxes. LIS features a high performance and flexible design, and operates on an ensemble of land surface models for extension over user-specified regional or global domains. The extensible interfaces of LIS allow the incorporation of new domains, land surface models (LSMs), land surface parameters, meteorological inputs, data assimilation and optimization algorithms. In addition, LIS has also been demonstrated for parameter estimation and uncertainty estimation, and has been coupled to the Weather Research and Forecasting (WRF) mesoscale model. A visiting fellowship is currently underway to implement JULES into LIS and to undertake some fundamental science on the feedbacks between the land surface and the atmosphere. An overview of the LIS system, features, and sample results will be presented in an effort to engage the community in the potential advantages of LIS-JULES for a range of applications. Ongoing efforts to develop a framework for diagnosing land-atmosphere coupling will also be presented using the suite of LSM and PBL schemes available in LIS and WRF along with observations from the U. S .. Southern Great Plains. This methodology provides a potential pathway to study factors controlling local land-atmosphere coupling (LoCo) using the LIS-WRF system, which will serve as a testbed for future experiments to evaluate coupling diagnostics within the community.

Santanello, Joseph↗
NASA NTRS2007

Comparison of Seasonal Terrestrial Water Storage Variations from GRACE with Groundwater-level Measurements from the High Plains Aquifer (USA)

This study presents the first direct comparison of variations in seasonal GWS derived from GRACE TWS and simulated SM with GW-level measurements in a semiarid region. Results showed that variations in GWS and SM are the main sources controlling TWS changes over the High Plains, with negligible storage changes from surface water, snow, and biomass. Seasonal variations in GRACE TWS compare favorably with combined GWS from GW-level measurements (total 2,700 wells, average 1,050 GW-level measurements per season) and simulated SM from the Noah land surface model (R = 0.82, RMSD = 33 mm). Estimated uncertainty in seasonal GRACE-derived TWS is 8 mm, and estimated uncertainty in TWS changes is 11 mm. Estimated uncertainty in SM changes is 11 mm and combined uncertainty for TWS-SM changes is 15 mm. Seasonal TWS changes are detectable in 7 out of 9 monitored periods and maximum changes within a year (e.g. between winter and summer) are detectable in all 5 monitored periods. Grace-derived GWS calculated from TWS-SM generally agrees with estimates based on GW-level measurements (R = 0.58, RMSD = 33 mm). Seasonal TWS-SM changes are detectable in 5 out of the 9 monitored periods and maximum changes are detectable in all 5 monitored periods. Good correspondence between GRACE data and GW-level measurements from the intensively monitored High Plains aquifer validates the potential for using GRACE TWS and simulated SM to monitor GWS changes and aquifer depletion in semiarid regions subjected to intensive irrigation pumpage. This method can be used to monitor regions where large-scale aquifer depletion is ongoing, and in situ measurements are limited, such as the North China Plain or western India. This potential should be enhanced by future advances in GRACE processing, which will improve the spatial and temporal resolution of TWS changes, and will further increase applicability of GRACE data for monitoring GWS.

Strassberg, Gil↗
NASA NTRS1980

Uncertainty in estimates of the number of extraterrestrial civilizations

Estimation of the number N of communicative civilizations by means of Drake's formula involves the combination of several quantities, each of which is to some extent uncertain. The uncertainty in any quantity may be represented by a probability distribution function, even if that quantity is itself a probability. The uncertainty of current estimates of N is derived principally from uncertainty in estimates of the lifetime of advanced civilizations. It is argued that this is due primarily to uncertainty concerning the existence of a "Galactic Federation" which is in turn contingent upon uncertainty about whether the limitations of present-day physics are absolute or (in the event that there exists a yet-undiscovered "hyperphysics") transient . It is further argued that it is advantageous to consider explicitly these underlying assumptions in order to compare the probable numbers of civilizations operating radio beacons, permitting radio leakage, dispatching probes for radio surveillance or dispatching vehicles for manned surveillance.

Peter A Sturrock↗
NASA NTRS2023

Using Regionalized Air Quality Model Performance and Bayesian Maximum Entropy Data Fusion to Map Global Surface Ozone Concentration and Associated Uncertainty

Estimates of ground-level ozone concentrations have been improved through data fusion of observations and atmospheric chemistry models. Our previous global ozone estimates for the Global Burden of Disease study corrected for bias uniformly across continents and then corrected near monitoring stations using the Bayesian Maximum Entropy (BME) framework for data fusion. Here, we use the Regionalized Air Quality Model Performance (RAMP) framework to correct model bias over a much larger spatial range than BME can, accounting for the spatial inhomogeneity of bias and nonlinearity as a function of modeled ozone. RAMP bias correction is applied to a composite of 9 global chemistry-climate models, based on the nearest set of monitors. These estimates are then fused with observations using BME, which matches observations at measurement stations, with the influence of observations declining with distance in space and time. We create global ozone maps for each year from 1990 to 2017 at fine spatial resolution. RAMP is shown to create unrealistic discontinuities due to the spatial clustering of ozone monitors, which we overcome by applying a weighting for RAMP based on the number of monitors nearby. Incorporating RAMP before BME has little effect on model performance near stations, but strongly increases R 2 by 0.15 at locations farther from stations, shown through a checkerboard cross-validation. Corrections to estimates differ based on location in space and time, confirming heterogeneity. We quantify the likelihood of exceeding selected ozone levels, finding that parts of the Middle East, India, and China are most likely to exceed 55 parts per billion (ppb) in 2017. About 96% of the global population was exposed to ozone levels above the World Health Organization guideline of 60 µg m −3 (30 ppb) in 2017. Our annual fine-resolution ozone estimates may be useful for several applications including epidemiology and assessments of impacts on health, agriculture, and ecosystems.

Ozone↗
NASA NTRS2004

Uncertainties in estimates of the risks of late effects from space radiation

Methods used to project risks in low-Earth orbit are of questionable merit for exploration missions because of the limited radiobiology data and knowledge of galactic cosmic ray (GCR) heavy ions, which causes estimates of the risk of late effects to be highly uncertain. Risk projections involve a product of many biological and physical factors, each of which has a differential range of uncertainty due to lack of data and knowledge. Using the linear-additivity model for radiation risks, we use Monte-Carlo sampling from subjective uncertainty distributions in each factor to obtain an estimate of the overall uncertainty in risk projections. The resulting methodology is applied to several human space exploration mission scenarios including a deep space outpost and Mars missions of duration of 360, 660, and 1000 days. The major results are the quantification of the uncertainties in current risk estimates, the identification of factors that dominate risk projection uncertainties, and the development of a method to quantify candidate approaches to reduce uncertainties or mitigate risks. The large uncertainties in GCR risk projections lead to probability distributions of risk that mask any potential risk reduction using the "optimization" of shielding materials or configurations. In contrast, the design of shielding optimization approaches for solar particle events and trapped protons can be made at this time and promising technologies can be shown to have merit using our approach. The methods used also make it possible to express risk management objectives in terms of quantitative metrics, e.g., the number of days in space without exceeding a given risk level within well-defined confidence limits. Published by Elsevier Ltd on behalf of COSPAR.

Non-NASA Center↗
NASA NTRSDate not supplied

Uncertainty Improvement in the NASA Glenn Research Center 8- by 6-Foot Supersonic Wind Tunnel

Within the past decade, a measurement uncertainty analysis (MUA) team was assembled at the NASA Glenn Research Center to assist the wind tunnel characterization team with quantification of uncertainty estimates for variables of interest in wind tunnels and test cells across the center. The initial analysis performed by the team was conducted on the 8- by 6- Foot Supersonic Wind Tunnel using results from the 1996/97 full calibration test entry. These MUA results were published in 2016 which included recommendations for methods to improve the uncertainty estimates for various variables of interest, such as changes to regression models, tunnel operation philosophy, and instrumentation choices. The wind tunnel characterization team utilized the proposed methods in 2019 during a full characterization test entry. Following publication of the 2019 test section characterization results, the MUA team pursued an update to the uncertainty estimates for the facility, which validated previous recommendations and revealed significantly reduced systematic uncertainties across most variables of interest. Inclusion of within-test repeat points in the 2019 test entry allowed for higher fidelity estimates of random uncertainty to be generated, as well. This collaboration between the facility, wind tunnel characterization, and MUA teams serves as an example of the data quality benefits that can be achieved through rigorous analysis of the sources of uncertainty in a ground-test facility.

Uncertainty↗
NASA NTRSDate not supplied

Uncertainty Improvement in the NASA Glenn Research Center 8- by 6-Foot Supersonic Wind Tunnel

Within the past decade, a measurement uncertainty analysis (MUA) team was assembled at NASA Glenn Research Center to assist the wind tunnel characterization team with quantification of uncertainty estimates for variables of interest in wind tunnels and test cells across the center. The initial analysis performed by the team was conducted on the 8- by 6-Foot Supersonic Wind Tunnel using results from the 1996/97 full calibration test entry. These MUA results were published in 2016 which included recommendations for methods to improve the uncertainty estimates for various variables of interest, such as changes to regression models, tunnel operation philosophy, and instrumentation choices. The wind tunnel characterization team utilized the proposed methods in 2019 during a full characterization test entry. Following publication of the 2019 test section characterization results, the MUA team pursued an update to the uncertainty estimates for the facility, which validated previous recommendations and revealed significantly reduced systematic uncertainties across most variables of interest. Inclusion of within-test repeat points in the 2019 test entry allowed for higher fidelity estimates of random uncertainty to be generated, as well. This collaboration between the facility, wind tunnel characterization, and MUA teams serves as an example of the data quality benefits that can be achieved through rigorous analysis of the sources of uncertainty in a ground-test facility.

Uncertainty↗
NASA NTRS2002

Uncertainties in Estimates of the Risks of Late Effects from Space Radiation

The health risks faced by astronauts from space radiation include cancer, cataracts, hereditary effects, and non-cancer morbidity and mortality risks related to the diseases of the old age. Methods used to project risks in low-Earth orbit are of questionable merit for exploration missions because of the limited radiobiology data and knowledge of galactic cosmic ray (GCR) heavy ions, which causes estimates of the risk of late effects to be highly uncertain. Risk projections involve a product of many biological and physical factors, each of which has a differential range of uncertainty due to lack of data and knowledge. Within the linear-additivity model, we use Monte-Carlo sampling from subjective uncertainty distributions in each factor to obtain a Maximum Likelihood estimate of the overall uncertainty in risk projections. The resulting methodology is applied to several human space exploration mission scenarios including ISS, lunar station, deep space outpost, and Mar's missions of duration of 360, 660, and 1000 days. The major results are the quantification of the uncertainties in current risk estimates, the identification of factors that dominate risk projection uncertainties, and the development of a method to quantify candidate approaches to reduce uncertainties or mitigate risks. The large uncertainties in GCR risk projections lead to probability distributions of risk that mask any potential risk reduction using the "optimization" of shielding materials or configurations. In contrast, the design of shielding optimization approaches for solar particle events and trapped protons can be made at this time, and promising technologies can be shown to have merit using our approach. The methods used also make it possible to express risk management objectives in terms of quantitative objective's, i.e., the number of days in space without exceeding a given risk level within well defined confidence limits.

Cucinotta, F. A.↗
NASA NTRSDate not supplied

Is There A Relationship Between Cornered-Hat Methods and A Residual Approach to Estimate System Uncertainty?

Recently a relationship has been established between a now traditional residual diagnostic used to estimate observation, background and analysis error covariances of interest to data assimilation and the three-cornered hat (3CH) method. An existing extension of the traditional residual diagnostic uses residuals from a fixed lag-1 Kalman smoother to retrieve system (model) error covariance. It is thus natural to ask if an additional relationship can be established between this extended residual method and some form of cornered--hat method. The answer might seem straightforward. Unlike in the standard residual estimation case, attempting to estimate model error amounts to estimating the statistics of a residual quantity itself. As shown in this presentation, in such cases the 3CH method becomes trivial: the sought out uncertainty can be derived directly from the covariance of the residual quantity at hand. In the particular case of estimating model error, one of the corners would have to be composed of vectors providing estimates of model error; these are not typically available in practice. Therefore, at first glance the present work finds no relationship between the lag-1 smoother residual diagnostic for system error estimation and cornered--hat methods. However, the work suggests that a two-tiered 3CH might be all that is necessary for system uncertainty to be obtained with 3CH.

Ricardo Todling↗
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 NTRS1993

Dependence of the interstellar propagation of ultraheavy cosmic-ray nuclei on various parameters

A stepwise program of interstellar-cosmic-ray propagation suitable for implementation on a small work-station has been used to study the sensitivity of propagation models of ultraheavy cosmic-ray nuclei (UH nuclei) on the input parameters. In this program an initial set of relevant parameters describing the astrophysics of the propagations process and the nuclear physics representing the interactions was assumed. These parameters were then varied within the estimated uncertainties in order to evaluate the sensitivity of the predictions on the assumed values. It is shown that current uncertainties in the estimates of the UH nuclei nuclear cross sections for the production of lighter fragments present the most significant sources of error and are sufficient to preclude reaching detailed conclusions about the source composition. Other uncertainties, such as those in the escape probabilities, or the mean interstellar density, while still significant, are less serious.

Clinton, Robert R.↗
NASA NTRS2020

The AERONET Version 3 Aerosol Retrieval Algorithm, Associated Uncertainties and Comparisons to Version 2

The Aerosol Robotic Network (AERONET) Version 3 (V3) aerosol retrieval algorithm is described, which is based on the Version 2 (V2) algorithm with numerous updates. Comparisons of V3 aerosol retrievals to those of V2 are presented, along with a new approach to estimate uncertainties in many of the retrieved aerosol parameters. Changes in the V3 aerosol retrieval algorithm include (1) a new polarized radiative transfer code (RTC), which replaced the scalar RTC of V2, (2) detailed characterization of gas absorption by adding NO2 and H2O to specify total gas absorption in the atmospheric column, specification of vertical profiles of all the atmospheric species, (3) new bidirectional reflectance distribution function (BRDF) parameters for land sites adopted from the MODIS BRDF/Albedo product, (4) a new version of the extraterrestrial solar flux spectrum, and (5) a new temperature correction procedure of both direct Sun and sky radiance measurements. The potential effect of each change in V3 on single scattering albedo (SSA) retrievals was analyzed. The operational almucantar retrievals of V2 versus V3 were compared for four AERONET sites: GSFC, Mezaira, Mongu, and Kanpur. Analysis showed very good agreement in retrieved parameters of the size distributions. Comparisons of SSA retrievals for dust aerosols (Mezaira) showed a good agreement in 440 nm SSA, while for longer wavelengths V3 SSAs are systematically higher than those of V2, with the largest mean difference at 675 nm due to cumulative effects of both extraterrestrial solar flux and BRDF changes. For non-dust aerosols, the largest SSA deviation is at 675 nm due to differences in extraterrestrial solar flux spectrums used in each version. Further, the SSA 675 nm mean differences are very different for weakly (GSFC) and strongly (Mongu) absorbing aerosols, which is explained by the lower sensitivity to a bias in aerosol scattering optical depth by less absorbing aerosols. A new hybrid (HYB) sky radiance measurement scan is introduced and discussed. The HYB combines features of scans in two different planes to maximize the range of scattering angles and achieve scan symmetry, thereby allowing for cloud screening and spatial averaging, which is an advantage over the principal plane scan that lacks robust symmetry. We show that due to an extended range of scattering angles, HYB SSA retrievals for dust aerosols exhibit smaller variability with solar zenith angles (SZAs) than those of almucantar (ALM), which allows extension of HYB SSA retrievals to SZAs less than 50∘ to as small as 25∘. The comparison of SSA retrievals from closely time-matched HYB and ALM scans in the 50 to 75∘ SZA range showed good agreement with the differences below ∼0.005. We also present an approach to estimate retrieval uncertainties which utilizes the variability in retrieved parameters generated by perturbing both measurements and auxiliary input parameters as a proxy for retrieval uncertainty. The perturbations in measurements and auxiliary inputs are assumed as estimated biases in aerosol optical depth (AOD), radiometric calibration of sky radiances combined with solar spectral irradiance, and surface reflectance. For each set of Level 2 Sun/sky radiometer observations, 27 inputs corresponding to 27 combinations of biases were produced and separately inverted to generate the following statistics of the inversion results: average, standard deviation, minimum and maximum values. From these statistics, standard deviation (labeled U27) is used as a proxy for estimated uncertainty, and a lookup table (LUT) approach was implemented to reduce the computational time. The U27 climatological LUT was generated from the entire AERONET almucantar (1993–2018) and hybrid (2014–2018) scan databases by binning U27s in AOD (440 nm), Angström exponent (AE, 440–870 nm), and SSA (440, 675, 870, 1020 nm). Using this LUT approach, the uncertainty estimates U27 for each individual V3 Level 2 retrieval can be obtained by interpolation using the corresponding measured and inverted combination of AOD, AE, and SSA.

Aliaksandr Siniuk↗
NASA NTRS2006

Verification and Validation in NASA-CUIP LOX/methane Injector Research Efforts

The NASA-CUIP program is supporting experimental and modeling/computational research efforts investigating wall heat flux characteristics of LOX/methane single-element injectors. A Verification and Validation (V&V) task has begun with the objective of quantifying the degree of accuracy of the models for wall heat flux distributions at specific sets of conditions. The V&V approach used is that being drafted as a standard by the ASME Performance Test Codes Committee, PTC 61: Verification and Validation in Computational Fluid Dynamics and Heat Transfer. The approach is based on well-established concepts from experimental uncertainty analysis. Initially the V&V and uncertainty estimation efforts will use data obtained previously in the same facility using oxygen/hydrogen in single-element injector testing. In this paper the V&V process, experimental facility, and computer code are described, and approaches to estimating the associated uncertainties are discussed.

Coleman, Hugh W.↗
NASA NTRS2009

Aeroheating Testing and Predictions for Project Orion CEV at Turbulent Conditions

An investigation of the aeroheating environment of the Project Orion Crew Exploration Vehicle was performed in the Arnold Engineering Development Center Hypervelocity Wind Tunnel No. 9 Mach 8 and Mach 10 nozzles and in the NASA Langley Research Center 20 - Inch Mach 6 Air Tunnel. Heating data were obtained using a thermocouple-instrumented approx.0.035-scale model (0.1778-m/7-inch diameter) of the flight vehicle. Runs were performed in the Tunnel 9 Mach 10 nozzle at free stream unit Reynolds numbers of 1x10(exp 6)/ft to 20x10(exp 6)/ft, in the Tunnel 9 Mach 8 nozzle at free stream unit Reynolds numbers of 8 x 10(exp 6)/ft to 48x10(exp 6)/ft, and in the 20-Inch Mach 6 Air Tunnel at free stream unit Reynolds numbers of 1x10(exp 6)/ft to 7x10(exp 6)/ft. In both facilities, enthalpy levels were low and the test gas (N2 in Tunnel 9 and air in the 20-Inch Mach 6) behaved as a perfect-gas. These test conditions produced laminar, transitional and turbulent data in the Tunnel 9 Mach 10 nozzle, transitional and turbulent data in the Tunnel 9 Mach 8 nozzle, and laminar and transitional data in the 20- Inch Mach 6 Air Tunnel. Laminar and turbulent predictions were generated for all wind tunnel test conditions and comparisons were performed with the experimental data to help define the accuracy of computational method. In general, it was found that both laminar data and predictions, and turbulent data and predictions, agreed to within less than the estimated 12% experimental uncertainty estimate. Laminar heating distributions from all three data sets were shown to correlate well and demonstrated Reynolds numbers independence when expressed in terms of the Stanton number based on adiabatic wall-recovery enthalpy. Transition onset locations on the leeside centerline were determined from the data and correlated in terms of boundary-layer parameters. Finally turbulent heating augmentation ratios were determined for several body-point locations and correlated in terms of the boundary-layer momentum Reynolds number.

Hollis, Brian R.↗
NASA NTRS2023

The CHROMA Cloud-Top Pressure Retrieval Algorithm for the Plankton, Aerosol, Cloud, Ocean Ecosystem (PACE) Satellite Mission

This paper provides the theoretical basis and simulated retrievals for the Cloud Height Retrieval from O2 Molecular Absorption (CHROMA) algorithm. Simulations are performed for the Ocean Color Instrument (OCI), which is the primary payload on the forthcoming NASA Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission, and the Ocean Land Colour Instrument (OLCI) currently flying on the Sentinel 3 satellites. CHROMA is a Bayesian approach which simultaneously retrieves cloud optical thickness (COT), cloud-top pressure and height (CTP and CTH respectively), and (with a significant prior constraint) surface albedo. Simulated retrievals suggest that the sensor and algorithm should be able to meet the PACE mission goal for CTP error, which is ±60 mb for 65 % of opaque (COT ≥3) single-layer clouds on global average. CHROMA will provide pixel-level uncertainty estimates, which are demonstrated to have skill at telling low-error situations from high-error ones. CTP uncertainty estimates are well-calibrated in magnitude, although COT uncertainty is overestimated relative to observed errors. OLCI performance is found to be slightly better than OCI overall, demonstrating that it is a suitable proxy for the latter in advance of PACE's launch. CTP error is only weakly sensitive to correct cloud phase identification or assumed ice crystal habit/roughness. As with other similar algorithms, for simulated retrievals of multi-layer systems consisting of optically thin cirrus clouds above liquid clouds, retrieved height tends to be underestimated because the satellite signal is dominated by the optically thicker lower layer. Total (liquid plus ice) COT also becomes underestimated in these situations. However, retrieved CTP becomes closer to that of the upper ice layer for ice COT ≈3 or higher.

PACE↗
NASA NTRS2002

Estimate of Top-of-Atmosphere Albedo for a Molecular Atmosphere over Ocean using Clouds and the Earth's Radiant Energy System (CERES) Measurements

The shortwave broadband albedo at the top of a molecular atmosphere over ocean between 40deg N and 40deg S is estimated using radiance measurements from the Clouds and the Earth's Radiant Energy System (CERES) instrument and the Visible Infrared Scanner (VIRS) aboard the Tropical Rainfall Measuring Mission (TRMM) satellite. The albedo monotonically increases from 0.059 at a solar zenith angle of 10deg to 0.107 at a solar zenith angle of 60deg. The estimated uncertainty in the albedo is 3.5 x 10(exp -3) caused by the uncertainty in CERES-derived irradiances, uncertainty in VIRS-derived aerosol optical thicknesses, variations in ozone and water vapor, and variations in surface wind speed. The estimated uncertainty is similar in magnitude to the standard deviation of 0.003 that is derived from 72 areas divided by 20deg latitude by 20deg longitude grid boxes. The empirically estimated albedo is compared with the modeled albedo using a radiative transfer model combined with an ocean surface bidirectional reflectivity model. The modeled albedo with standard tropical atmosphere is 0.061 and 0.111 at the solar zenith angles of 10deg and 60deg, respectively. This empirically estimated albedo can be used to estimate the direct radiative effect of aerosols at the top of the atmosphere over oceans.

Kato, S.↗
NASA NTRS1996

Determination of Uncertainties for the New SSME Model

This report discusses the uncertainty analysis performed in support of a new test analysis and performance prediction model for the Space Shuttle Main Engine. The new model utilizes uncertainty estimates for experimental data and for the analytical model to obtain the most plausible operating condition for the engine system. This report discusses the development of the data sets and uncertainty estimates to be used in the development of the new model. It also presents the application of uncertainty analysis to analytical models and the uncertainty analysis for the conservation of mass and energy balance relations is presented. A new methodology for the assessment of the uncertainty associated with linear regressions is presented.

Coleman, Hugh W.↗
NASA NTRS2002

Error Estimation and Uncertainty Propagation in Computational Fluid Mechanics

Numerical simulation has now become an integral part of engineering design process. Critical design decisions are routinely made based on the simulation results and conclusions. Verification and validation of the reliability of the numerical simulation is therefore vitally important in the engineering design processes. We propose to develop theories and methodologies that can automatically provide quantitative information about the reliability of the numerical simulation by estimating numerical approximation error, computational model induced errors and the uncertainties contained in the mathematical models so that the reliability of the numerical simulation can be verified and validated. We also propose to develop and implement methodologies and techniques that can control the error and uncertainty during the numerical simulation so that the reliability of the numerical simulation can be improved.

Zhu, J. Z.↗