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At least 253 records · Page 14

Application of Different Statistical Techniques in Integrated Logistics Support of the International Space Station Alpha

The process to predict the values of the maintenance time dependent variable parameters such as mean time between failures (MTBF) over time must be one that will not in turn introduce uncontrolled deviation in the results of the ILS analysis such as life cycle cost spares calculation, etc. A minor deviation in the values of the maintenance time dependent variable parameters such as MTBF over time will have a significant impact on the logistics resources demands, International Space Station availability, and maintenance support costs. It is the objective of this report to identify the magnitude of the expected enhancement in the accuracy of the results for the International Space Station reliability and maintainability data packages by providing examples. These examples partially portray the necessary information hy evaluating the impact of the said enhancements on the life cycle cost and the availability of the International Space Station.

Sepehry-Fard, F.↗

Impacts of Soil-aquifer Heat and Water Fluxes on Simulated Global Climate

Climate models have traditionally only represented heat and water fluxes within relatively shallow soil layers, but there is increasing interest in the possible role of heat and water exchanges with the deeper subsurface. Here, we integrate an idealized 50m deep aquifer into the land surface module of the GISS ModelE general circulation model to test the influence of aquifer-soil moisture and heat exchanges on climate variables. We evaluate the impact on the modeled climate of aquifer-soil heat and water fluxes separately, as well as in combination. The addition of the aquifer to ModelE has limited impact on annual-mean climate, with little change in global mean land temperature, precipitation, or evaporation. The seasonal amplitude of deep soil temperature is strongly damped by the soil-aquifer heat flux. This not only improves the model representation of permafrost area but propagates to the surface, resulting in an increase in the seasonal amplitude of surface air temperature of >1K in the Arctic. The soil-aquifer water and heat fluxes both slightly decrease interannual variability in soil moisture and in landsurface temperature, and decrease the soil moisture memory of the land surface on seasonal to annual timescales. The results of this experiment suggest that deepening the modeled land surface, compared to modeling only a shallower soil column with a no-flux bottom boundary condition, has limited impact on mean climate but does affect seasonality and interannual persistence.

soil↗

Dynamic large deflection response of composite laminates subjected to impact

Impact responses of composite laminates with and without initial stresses are investigated using the finite element method. A nine-node isoparametric quadrilateral element based on the Mindlin plate theory and the von Karman large deflection assumptions is developed. An experimentally established contact law which accounts for the permanent indentation is incorporated into the finite element program to evaluate the impact force. In the time integration, the Newmark constant acceleration algorithm is used in conjunction with successive iterations within each time step. Numerical results, including the contact force histories, deflections and strains in the plate, are presented.

Chen, J. K.↗

Development of a Test for Evaluation of the Hydrothermal Stability of Sorbents Used in Closed-Loop CO2 Removal Systems

The International Space Station Carbon Dioxide Removal Assembly uses zeolite 5A molecular sieve material packed into beds for the capture of cabin CO2. The beds are cyclically heated to drive off the CO2 and restore the removal capacity. Over time, the sorbent material has been found to break down resulting in dust that restricts flow through the beds. Humidity adsorbed in the 5A zeolite when it is heated is a suspected cause of this sorbent degradation. To evaluate the impact of adsorbed water during thermal cycling, the Hydrothermal Stability Test was developed. The test configuration provides comparative side-by-side flow restriction data for two sorbent materials at specifically controlled humidity levels. While the initial focus of the testing is on 5A zeolite materials currently used on the ISS, the system will also be used to evaluate future candidate materials. This paper describes the approach, the test system, current results, and future testing.

Knox, James C.↗

Temporal Changes in Left Ventricular Mechanics: Impact of Bed Rest and Exercise

BACKGROUND Current techniques used to assess cardiac function following spaceflight or head-down tilt bed rest (HDTBR) involve invasive and time consuming procedures such as Swan-Ganz catheterization or cardiac magnetic resonance imaging. An alternative approach, echocardiography, can monitor cardiac morphology and function via sequential measurements of left ventricular (LV) mass and ejection fraction (EF). However, LV mass and EF are insensitive measures of early (subclinical) cardiac deconditioning, and a decrease in LV mass and EF become evident only once significant deconditioning has already occurred. The use of more sensitive and specific echocardiographic techniques such as speckle tracking imaging may address the current limitations of conventional cardiac imaging techniques to provide insight into the magnitude and time course of cardiac deconditioning. METHODS Speckle tracking assessment of longitudinal, radial, and circumferential strain and twist was used to evaluate the impact of 70 days of HDTBR (n=7) and HDTBR + exercise (n=11) on temporal changes in LV mechanics. Echocardiograms were performed pre (BR-2), during (BR31, 70), and following (BR+4hr) HDTBR. Multi-level modeling was used to evaluate the effect of HDTBR condition (Control, Exercise) on cardiac variables. RESULTS Compared to BR-2, longitudinal (BR-2: - 19.0 +/- 1.8%; BR31: -15.9 +/- 2.4%; BR70: -14.9 +/- 2.4%; BR+4hr: -16.0 +/- 2.1%) and radial (BR-2: 15.0 +/- 1.9%; BR31: 12.3 +/- 2.4%; BR70: 11.3 +/- 2.2%; BR+4hr: 13.5 +/- 2.5% ) strains were significantly impaired during and following bed rest (p<0.05), while twist (BR-2: 18.0 +/- 4.0deg; BR31: 18.1 +/- 3.8deg; BR70: 17.0 +/- 3.6deg; BR+4hr:18.1 +/- 4.3deg) was significantly decreased at BR70 (p<0.05). In contrast, exercise preserved LV mechanics for longitudinal strain (BR-2: -19.1 +/- 1.5%; BR 31: -19.0 +/- 2.4%; BR70: -19.1 +/- 2.7%; BR+4hr: -17.8 +/- 2.1%), radial strain (BR-2: 13.8 +/- 2.4; BR31: 14.7 +/- 2.4; BR70: 14.4 +/- 1.6; BR+4hr: 14.4 +/- 2.4), and twist (BR-2: 17.8 +/- 3.6deg; BR31: 18.0 +/- 3.6deg; BR70: 18.2 +/- 5.9deg; BR+4hr: 18.3 +/- 4.2deg). CONCLUSIONS Speckle-tracking echocardiography provides important new insight into temporal changes in LV mechanics during disuse and exercise training.

Scott, Jessica M.↗

Assimilation of Cloud- and Land-Affected TOVS/ATOVS Level 1B Radiances in DAO's Next Generation Finite-Volume Data Assimilation System

The Physical-space/Finite-volume Data Assimilation System (fvDAS) is the next generation global atmospheric data assimilation system in development at the Data Assimilation Office (DAO) at NASA's Goddard Space Flight Center. It is based on a new finite-volume general circulation model jointly developed by NASA and NCAR, and on the Physical-Space Statistical Analysis System (PSAS) developed at the DAO. In this talk we will focus on the assimilation of data from the (Advanced) TIROS Operational Vertical Sounder (ATOVS), with emphasis on the impact of cloud- and land-affected level 1B radiances. Recently, it has been shown that the use of observations from satellite-borne microwave and infrared radiometers in data assimilation systems consistently increases forecast skill. Considerable effort has been expended over the past two decades, particularly with the (Advanced) TIROS Operational Vertical Sounder (ATOVS), to achieve this result. The positive impact on forecast skill has resulted from improvements in quality control algorithms, systematic error correction schemes, and more sophisticated data assimilation algorithms. Despite these advances, there are still many issues regarding the use of satellite data in data assimilation systems that remain unresolved. In particular, most operational centers still do not assimilate cloud- and land-affected TOVS data. In this study, we evaluate the impact of assimilating cloud-and land-affected TOVS/ATOVS level 1B data in DAO's next generation fvDAS, using a 1D variational scheme. We will discuss the impact of these data on both tropospheric and stratospheric forecasts, as well as on the general aspects of the earth climate system.

Joiner, J.↗

The Impact and Estimation of Uncertainty Correlation for Multi-Angle Polarimetric Remote Sensing of Aerosols and Ocean Color

Multi-angle polarimetric (MAP) measurements contain rich information for characterization of aerosol microphysical and optical properties that can be used to improve atmospheric correction in ocean color remote sensing. Advanced retrieval algorithms have been developed to obtain multiple geophysical parameters in the atmosphere-ocean system, although uncertainty correlation among measurements is generally ignored due to lack of knowledge on its strength and characterization. In this work, we provide a practical framework to evaluate the impact of the angular uncertainty correlation from retrieval results and a method to estimate correlation strength from retrieval fitting residuals. The Fast Multi-Angular Polarimetric Ocean coLor (FastMAPOL) retrieval algorithm, based on neural network forward models, is used to conduct the retrievals and uncertainty quantification. In addition, we also discuss a flexible approach to include a correlated uncertainty model in the retrieval algorithm. The impact of angular correlation on retrieval uncertainties is discussed based on synthetic AirHARP and HARP2 measurements using a Monte Carlo uncertainty estimation method. Correlation properties are estimated using auto-correlation functions based on the fitting residuals from both synthetic AirHARP and HARP2 data and real AirHARP measurement, with the resulting angular correlation parameters found to be larger than 0.9 and 0.8 for reflectance and DoLP, respectively, which correspond to correlation angles of 10° and 5°. Although this study focuses on angular correlation from HARP instruments, the methodology to study and quantify uncertainty correlation is also applicable to other instruments with angular, spectral, or spatial correlations, and can help inform laboratory calibration and characterization of the instrument uncertainty structure.

PACE↗

TPSAS-NF1676L-19238-DND

The 24-hour cycle of solar insolation drives diurnal cycles in Earth system processes critical to climate: radiation, convection, turbulence, and cloud processes. Cloud properties, temperature, radiative fluxes, and precipitation exhibit robust diurnal cycles as a result. The presence of these robust diurnal cycles fundamentally changes the time mean and variability of the TOA energy budget. Therefore, there is a need to understand the diurnal cycle contributions to the TOA energy budget in both observations and climate models. The first objective of this study is to quantify the diurnal cycle impact on the time mean and variability of the TOA energy budget in observations defined as the difference between TOA fluxes computed with diurnally uniform and diurnally varying cloud properties. The required observational input is observed from the combined Terra+Aqua Cloud and Earth's Radiant Energy System (CERES) data products ranging from June 2002 through October 2012. The second objective of this study is to evaluate the impact of known errors in the model diurnal cycle simulation on the time mean and variability of the TOA energy budget. The results indicate that (1) the diurnal cycle impacts on the regional time mean Tropical longwave and shortwave fluxes range from 1-3 W m 2 and 5 25 W m 2, respectively; (2) the diurnal cycle contributions to TOA flux variability exceeds 50% in land convective regions (e.g., central South America and central Africa);(3) the diurnal cycle contributions to the TOA shortwave and longwave flux time mean and variability in the CanAM4 GCM are too small in land convective regions due to errors in the diurnal distribution of convective clouds grid box errors exceed 100%.

Patrick C Taylor↗

The Impact of Temporal Geopotential Variations on GPS

Lemoine et al. (2006) and Lemoine et al. (2010) showed that applying more detailed models of time-variable gravity (TVG) improved the quality of the altimeter satellite orbits (e.g. TOPEX/Poseidon, Jason-1, Jason-2). This modeling include application of atmospheric gravity derived from 6-hrly pressure fields obtained from the ECMWF and annual gravity variations to degree & order 20x20 in spherical harmonics derived from GRACE data. This approach allowed the development of a consistent geophysical model for application to altimeter satellite orbit determination from 1993 to 2011. In addition, we have also evaluated the impact of TVG modeling on the POD of Jason-1 and Jason-2 by application of a weekly degree & order four gravity coefficient time series developed using data from ten SLR & DORIS-tracked satellites from 1993 to 2011 (Lemoine et al., 2011).

Melachroinos, Stavros↗

Harmonizing Food Systems Emissions Accounting for More Effective Climate Action

Food systems—encompassing activities in food production, land-use change, supply chains and waste management—contribute significantly to climate change. Recent estimates indicate that food systems produce over 30% of annual anthropogenic greenhouse gas (GHG) emissions (about 20% of CO 2 , 50% of CH 4 , and 75% of N 2 O), with the Intergovernmental Panel on Climate Change (IPCC) estimating a notably broad range of 23%–42% of global GHG emissions. This paper synthesizes current research on the contributions of food systems to climate change, highlights challenges in quantifying their impact and proposes a harmonized accounting framework for more effective climate action. We recommend that an expert committee aligned with the IPCC develop guidance for food systems emissions accounting in four key areas, including: (1) defining system boundaries and nomenclature; (2) developing protocols to allocate broader sectoral emissions to food systems; (3) prioritizing critical areas for research into activity data and emissions factors; and (4) developing a balanced framework for evaluating the impact of mitigation interventions in light of other food systems imperatives. The committee should be integrated into two key international policy processes—the United Nations Framework Convention on Climate Change and the United Nations Food Systems Summit—to support coordinated action towards global net-zero goals. Guidance from the committee could significantly improve the ability of governments, companies, and researchers to estimate, report, monitor and ultimately reduce the climate impacts of food systems.

GHG accounting↗

Smart structures research program at Virginia Tech

A review of the smart structures and avionics research and teaching program that started in 1979 at Virginia Tech is described. Current smart structures research include major efforts in the development of embedded and attached optical fiber and acoustic fiber sensors for cure monitoring, in-service lifetime structural testing, nondestructive evaluation, and impact and damage detection and analysis; of gradual material degradation; sensor signal multiplexing, processing and data handling to achieve near real-time distributed structural analysis; and the integration of embedded sensors, actuators and control electronics to achieve controlled structural response. Special campus facilities used for this work include an optical fiber fabrication facility, an autoclave for composite structure fabrication and curing, and laboratories for optical fiber sensor development, materials response and nondestructive evaluation, structural control testing and computer engineering.

Claus, R. O.↗

Tracking Critical Thermal Metrics throughout the Life Cycle of a Large Observatory Thermal Model

Observatory thermal models for large, complex missions, such as the Wide Field InfraRed Survey Telescope (WFIRST) mission, produce an immense amount of data to be processed. Configuration management of the model throughout the project life cycle has mainly focused on which versions of the subsystem models form the current observatory level configuration. However, the results produced by the model are not nearly as well tracked and traceable. Given the various states of design maturity for each of the components in the WFIRST design, an updated component model is nearly ready to be integrated at the next higher level of assembly about every month or two. With each subsystem model delivery, the observatory model needs to remove the old component, integrate the new one, execute the model, and inspect the results. Usually, this inspection focuses primarily on the newly integrated component. Recently, a Metric Tracking Spreadsheet was developed to help provide a “big picture” view of the entire observatory highlighting key parameters critical to mission performance. This spreadsheet helps track impacts on subsystems by updates of other subsystems that were not intuitively obvious. Metrics tracked include: absorbed environmental loading (to determine effectiveness of sunshield), temperatures of critical avionics, electrical dissipations, heater power predictions, stability of critical optics, parasitic heat leaks in cryogenic region, high level heat flows between elements, and model run time. Producing this data for the same operational configuration with each model update has helped produce a trail of data to evaluate the impact of model updates. While the metrics selected are specific for WFIRST, other large, complex observatories could be well served to establish their own metrics early in the project life cycle to track to quickly assess the impact of any subsystem on other subsystems or the overall system itself.

Thermal Desktop↗

PolarMERRA: A Polar-Focused Global Reanalysis Project for Scientific and Stakeholder Needs

The adequate modeling of physical processes in the Arctic and Antarctic is vital for developing prediction capabilities and for obtaining an understanding of rapidly evolving polar conditions, including their potential global impacts. These processes are often poorly represented in global models and reanalyses, owing to a legacy modeling focus on midlatitude processes, as well as a scarcity of observations needed for model development in polar regions. The polarMERRA initiative, a joint effort between NASA’s Cryospheric Sciences and Modeling and Prediction programs, seeks to improve the representation of cryospheric and polar atmospheric processes and to develop an open-source framework for a quantitively evaluation of polar-relevant variables against current and future satellite and in-situ observations, models, and reanalyses. Here, we evaluate the impacts of spatial resolution and modifications to sea ice, ice sheet, and atmospheric parameterizations on the representation of high latitude conditions by using a quantitative scorecard approach that leverages NASA’s extensive satellite record. Investigations are conducted using the NASA Goddard Earth Observing System model (GEOS) and its data assimilation system (GEOS DAS). Through a quantitative identification of process deficiencies, bias reductions in key surface variables, including temperature and precipitation over cryospheric surfaces, may be achieved. The polarMERRA project additionally seeks to identify additional data sources for use in the GEOS DAS, and to incorporate data and parameterization improvements into future model and reanalysis products for scientific and stakeholder use.

Lauren C Andrews↗

Orbital Variations and Impacts on Observations from SNPP, NOAA 18-20, and AQUA Sun-Synchronous Satellites

The AQUA, SNPP, and NOAA 18-20 PM sun-synchronous satellites were designed with similar local time, local solarzenith angles, and overlapping temporal coverage. Although the satellites are expected to have fixed local equator-crossing time, during the satellite lifetime, the equator-crossing times of these satellites drift. For NOAA 18-19, the driftin equator-crossing time is significant (few hours) and no correction has been done over the lifetime. For SNPP andAQUA, correction in the orbital inclination angle was periodically performed to maintain the equator-crossing timearound the designed value. The impact of systematic drift of the local observation time during the satellite life cycle canbe significant and should be accounted for when using multi-year time series of satellite products in long-termenvironmental studies. In this paper, the equator-crossing time drift of AQUA, SNPP, and NOAA 18-20, the correctionof SNPP and AQUA equator-crossing time via orbital inclination angle change, and the consequent local solar zenithangle variation are evaluated. The impact of such drift on low-latitude mean brightness temperature trend derived fromthe similar ~11 μm thermal emissive channel of AQUA MODIS CH31, SNPP Visible Infrared Imaging RadiometerSuite (VIIRS) CH15 and NOAA 18-19 HIRS CH08 are analyzed. The drift in the mean brightness temperature measuredby these sensors is combined as a function of local time and analyzed using diurnal cycle analysis. The mean brightnesstemperature drift for SNPP VIIRS is reconciled within the context of much larger temperature drift of NOAA 18-19.

Shao, Xi↗

Time Variable Gravity modeling for Precise Orbits Across the TOPEX/Poseidon, Jason-l and Jason-2 Missions

Modeling of the Time Variable Gravity (TVG) is believed to constitute one of the the largest remaining source of orbit error for altimeter satellite POD. The GSFC operational TVG model consists of forward modeling the atmospheric gravity using ECMWF 6-hour pressure data, a GRACE derived 20x20 annual field to account for changes in the hydrology and ocean water mass, and linear rates for C20, C30, C40, based on 17 years of SLR data analysis (IERS 2003) using the EIGEN-GL04S1 (a GRACE+Lageos-based geopotential solution). Although the GSFC Operational model can be applied from 1987, there may be long-term variations not captured by these linear models, and more importantly the linear models may not be consistent with more recent surface mass trends due to global climate change, We have evaluated the impact of TVG in two different wavs: (1) by using the more recent EIGEN-6S gravity model developed by the GFZ/GRGS tearm, which consists of annual, semi-annual and secular changes in the coefficients to 50x50 determined over 8(?) years of GRACE+Lageos+GOCE data (2003-200?): (2) Application of 4x4 solutions developed from a multi satellite SLR+DORIS solution based on GGM03S that span the period from 1993 to 2011. We have evaluated the recently released EIGEN6s static and time-varying gravity field for Jason-2 (J2). Jason-I (J1), and TOPEX/Posiedon (TP) Precise Orbit Determination (POD) spanning 1993-2011. Although EIGEN6s shows significant improvement for J2POD spanning 2008 - 2011, it also shows significant degradation for TP POD from 1992. The GSFC 4x4 time SLR+DORIS-based series spans 1993 to mid 2011, and shows promise for POD. We evaluate the performance of the different TVG models based on analysis of tracking data residuals use of independent data such as altimeter crossovers, and through analysis of differences with internally-generated and externally generated orbits.

Zelensky, Nikita P.↗

Impact of Quikscat Data on Numerical Weather Prediction

Scatterometer observations of the ocean surface wind speed and direction improve the depiction and prediction of storms at sea. These data are especially valuable where observations are otherwise sparse ---mostly in the Southern Hemisphere and tropics, but also on occasion in the North Atlantic and North Pacific. The SeaWinds scatterometer on the QuikScat satellite was launched in July 1999 and it represents a dramatic departure in design from the other scatterometer instruments launched during the past decade (ERS-1,2 and NSCAT). The NASA Data Assimilation Office (DAO) was the first data assimilation center to assimilate QuikScat SeaWinds data and evaluate their impact on numerical weather prediction. Several data impact experiments have been performed, using systems from both the DAO (GEOS-3) and from NCEP (GDAS). In general, these experiments have shown a modest impact of SeaWinds data on numerical weather prediction, the magnitude of which appears to be comparable to the magnitude of the impact of AMI scatterometer data from the ERS satellites. Some of the main results from these experiments will be presented at the meeting.

Atlas, Robert↗

GRACE Improves Seasonal Groundwater Forecast Initialization Over the United States

We evaluate the impact of Gravity Recovery and Climate Experiment data assimilation (GRACE-DA) on seasonal hydrological forecast initialization over the United States, focusing on groundwater storage. GRACE-based terrestrial water storage (TWS) estimates are assimilated into a land surface model for the2003–16 period. Three-month hindcast (i.e., forecast of past events) simulations are initialized using states from the reference (no data assimilation) and GRACE-DA runs. Differences between the two initial hydrological condition (IHC) sets are evaluated for two forecast techniques at 305 wells where depth to water table measurements are available. Results show that using GRACE-DA-based IHC improves seasonal groundwater forecast performance in terms of both RMSE and correlation. While most regions show improvement, degradation is common in the High Plains, where withdrawals for irrigation practices affect groundwater variability more strongly than the weather variability, which demonstrates the need for simulating such activities. These findings contribute to recent efforts toward an improved U.S. drought monitoring and forecast system.

Augusto Getirana↗

Modeling Macro- and Micro-Scale Turbulent Mixing and Chemistry in Engine Exhaust Plumes

Simulation of turbulent mixing and chemical processes in the near-field plume and plume-vortex regimes has been successfully carried out recently using a reduced gas phase kinetics mechanism which substantially decreased the computational cost. A detailed mechanism including gas phase HOx, NOx, and SOx chemistry between the aircraft exhaust and the ambient air in near-field aircraft plumes is compiled. A reduced mechanism capturing the major chemical pathways is developed. Predictions by the reduced mechanism are found to be in good agreement with those by the detailed mechanism. With the reduced chemistry, the computer CPU time is saved by a factor of more than 3.5 for the near-field plume modeling. Distributions of major chemical species are obtained and analyzed. The computed sensitivities of major species with respect to reaction step are deduced for identification of the dominant gas phase kinetic reaction pathways in the jet plume. Both the near field plume and the plume-vortex regimes were investigated using advanced mixing models. In the near field, a stand-alone mixing model was used to investigate the impact of turbulent mixing on the micro- and macro-scale mixing processes using a reduced reaction kinetics model. The plume-vortex regime was simulated using a large-eddy simulation model. Vortex plume behind Boeing 737 and 747 aircraft was simulated along with relevant kinetics. Many features of the computed flow field show reasonable agreement with data. The entrainment of the engine plumes into the wing tip vortices and also the partial detrainment of the plume were numerically captured. The impact of fluid mechanics on the chemical processes was also studied. Results show that there are significant differences between spatial and temporal simulations especially in the predicted SO3 concentrations. This has important implications for the prediction of sulfuric acid aerosols in the wake and may partly explain the discrepancy between past numerical studies (that employed parabolic or temporal approximations) and the measured data. Finally to address the major uncertainty in the near-field plume modeling related to the plume processing of sulfur compounds and advanced model was developed to evaluate its impact on the chemical processes in the near wake. A comprehensive aerosol model is developed and it is coupled with chemical kinetics and the axisymmetric turbulent jet flow models. The integrated model is used to simulate microphysical processes in the near-field jet plume, including sulfuric acid and water binary homogeneous nucleation, coagulation, non-equilibrium heteromolecular condensation, and sulfur-induced soot activation. The formation and evolution of aerosols are computed and analyzed. The computed results show that a large number of ultra-fine (0.3--0.6 nm in radius) volatile HSO4 - HO embryos are generated in the near-field plume. These embryos further grow in size by self coagulation and condensation. Soot particles can be activated by both heterogeneous nucleation and scavenging of H2SO4-H2O aerosols. These activated soot particles can serve as water condensation nuclei for contrail formation. Conditions under which ice contrails can form behind aircrafts are studied. The sensitivities of the threshold temperature for contrail formation with respect to aircraft propulsion efficiency, relative humidity, and ambient pressure are evaluated. The computed aerosol properties for different extent of fuel sulfur conversion to S(VI) (SO3 and H2SO4) in engine are examined and the results are found to be sensitive to this conversion fraction.

Menon, Suresh↗