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NASA NTRS1978

Equations of motion and two-equation turbulence model for plane or axisymmetric turbulent flows in body-oriented orthogonal curvilinear coordinates and mass-averaged dependent variables

The full Navier-Stokes time-dependent, compressible, turbulent, mean-flow equations in mass-averaged variables for plane or axisymmetric flow are presented. The equations are derived in a body-oriented, orthogonal, curvilinear coordinate system. Turbulence is modelled by a system of two equations for mass-averaged turbulent kinetic energy and dissipation rate proposed. These equations are rederived and some new features are discussed. A system of second order boundary layer equations is then derived which includes the effects of longitudinal curvature and the normal pressure gradient. The Wilcox and Chambers approach is used in considering effects of streamline curvature on turbulence phenomena in turbulent boundary layer type flows. Their two-equation turbulence model with curvature terms are rederived for the cases considered in the present report. The derived system equations serves as a basis for an investigation of problems where streamline curvature is of the order of the characteristic length in the longitudinal direction.

Sislian, J. P.↗

NASA NTRSDate not supplied

An Ensemble Investigation of the Causes for Regional Air-Quality Model Critical Load Exceedances Prediction Variability in European and North American Domains Using Diagnostics From Phase 4 of the Air Quality Model Evaluation International Initiative

We summarize tentative findings from multi air quality model ensembles for the years 2009 and 2010 in Europe (EU), and 2010 and 2016 in North America (NA), under AQMEII-4. The model predictions of sulphur and nitrogen deposition were used to estimate exceedances of critical loads for acidification and eutrophication, to show the extent to which the ensemble members agree in the magnitude and the trend of ecologically meaningful impacts. Model exceedance variability was analyzed using AQMEII-4 diagnostics. Evaluation against concentration and wet deposition observations, coupled with these diagnostics, identified specific process representations as the causes for variability between model predictions and for reduced model performance. All models predicted reductions in ecosystem acidification impacts in North America between the years 2010 and 2016, in accord with SO2 emissions reduction legislation which started in 2010 (SO2 SIP) However, all models in EU and NA domains had net negative biases for wet deposition of sulphur and nitrogen relative to observations. The wet S deposition average mean bias for the NA ensemble was -0.17 eq ha-1 d-1, and for the EU ensemble -1.15 eq ha-1 d-1. The NA daily wet deposition average mean bias for NH4+ was -0.37 eq ha-1d-1; EU -1.19 eq ha-1 d-1. The daily NA wet NO3- deposition average mean bias was -0.24 eq ha-1d-1; EU -0.69 eq ha-1 d-1. The members of the ensemble diverged (factor of 10) in their North American predictions for Ndep and consequently their eutrophication exceedances. The models with the highest eutrophication predictions also predicted the highest levels of gas-phase ammonia dry deposition (standard deviation of ammonia dry deposition flux across ensemble members was larger than the ensemble average). These models also had negative biases of predicted ammonia concentrations; average mean biases of -0.63 (satellite NH3) and -0.85 ppbv (surface NH3) compared to ensemble averages of -0.30 and -0.34 ppbv. Diagnostics showed that these differences resulted from the manner in which bidirectional ammonia fluxes were parameterized within these models. The second largest source of NA eutrophication prediction variability were models with positive biases in particulate ammonium and nitrate concentrations, and higher particle nitrogen deposition levels ( particle ammonium concentration bias +0.35 ug m-3; ensemble bias +0.15 ug m-3). We believe two factors may have led to these latter overestimates: higher levels of fine mode particle nitrate formation compared to other models (due to the use of an inorganic heterogeneous chemistry algorithm which did not take base cation chemistry into account), and updates to particle dry deposition velocities carried out in the absence of concurrent updates to wet scavenging algorithms. The relative importance of dry gas, dry particulate, and wet deposition towards total sulphur and nitrogen deposition totals differed between EU and North American domains, though all models had negative biases in wet deposition as noted above. Parallel and subsequent work suggests that multiphase hydrometeor scavenging may improve model wet deposition performance. An increased research focus is recommended for four model processes: multiphase hydrometeor scavenging, ammonia bidirectional fluxes, base cation chemistry and emissions, and particle dry deposition.

regional air-quality model↗

DOE OSTI2022

Forecasting distributed energy resources adoption for power systems

Failing to incorporate accurate distributed energy resource penetration forecasts into long-term resource and transmission planning can lead to cost inefficiencies at best and system failures at worst. We have developed an open-source tool that employs an advanced Bass specification to calibrate and forecast technology adoption. The advanced specification includes geographic clustering, exogenously estimated market size, and dynamic time steps. Training on historical adoption of rooftop photovoltaics at the U.S. county-level and using detailed techno-economic estimates, our model achieves a two-year average mean-absolute-percentage-error of 19% in predicting system counts at the county-level, weighted by population. Model error was negatively correlated with market maturity - the error was 12% for counties in states with at least 28 W-per-capita of installed capacity. The advanced specification significantly reduces unweighted forecasting percent error compared to a conventional Bass specification: from 196% to 25% for capacity and from 226% to 22% for system count.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

NASA NTRS1994

Model evaluation of the radiative and temperature effects of the ozone content changes in the global atmosphere of 1980's

Radiative and temperature effects of the observed ozone and greenhouse gas atmospheric content changes in 1980 - 1990 are evaluated using the two-dimensional energy balance radiative-convective model of the zonally and annually averaged troposphere and stratosphere. Calculated radiative flux changes for standard conditions quantitatively agree with their estimates in WMO/UNEP 1991 review. Model estimates indicate rather small influence of ozone depletion in the lower stratosphere on the greenhouse tropospheric warming rate, being more significant in the non-tropical Southern Hemisphere. The calculated cooling of the lower stratosphere is close to the observed temperature trends there in the last decade.

Karol, Igor L.↗

DOE OSTI2021

Transport in Stochastic Media with Random Chord Length Distributions

Thermal radiation transport computations in binary Markovian random mixtures rely almost exclusively on the Levermore-Pomraning (LP) model which is obtained by applying a heuristic closure to the ensemble averaged random medium transport equation. The validity of this model has been extensively tested by comparing numerical results over a broad parameter range (material types and mixing parameters) against benchmark solutions in planar geometry. The conditions under which the LP-model provides useful results and when it breaks down are now well established, but work to date has been largely restricted to homogeneous mixing statistics, i.e., the mean chord lengths of both materials are taken to be spatially constant. In recent work, this limitation was relaxed by allowing the mean chord lengths and, in a consistent fashion, the volume fractions in the LP-model to vary spatially and in a follow-up investigation benchmark solutions were obtained by ensemble averaging results over material realizations sampled from a nonhomogeneous Poisson process (NHPP). Numerical experiments in rod geometry with specifically linear and quadratic spatial dependence of chord lengths showed that the material averaged radiation intensities vary nonmonotonically with depth into the medium, in stark contrast to solutions obtained assuming uniform chord lengths. Moreover, depending on the local optical thickness and strength of scattering, the LP-model results showed locally more nuanced deviations from the benchmark solutions than was the case with constant chord lengths. These limited numerical investigations highlight the nontrivial qualitative and quantitative consequences of nonhomogeneous mixing statistics, in particular that closure approximations may not be uniformly valid or invalid over the problem domain.

42 ENGINEERING↗

DOE OSTI2024

Simulating energetic ions and enhanced fusion rates from ion-cyclotron resonance heating with a full-wave/Fokker–Planck model

Reproducing fast-ion enhanced fusion rates from ion-cyclotron resonance heating (ICRH) in tokamaks requires the self-consistent coupling of a full-wave solver and a Fokker–Planck solver, which evolves multiple simultaneously resonant ion species. We introduce a new self-consistent model that iterates the TORIC full-wave solver with the CQL3D Fokker–Planck solver using the integrated plasma simulator (IPS). This model evolves the bounce-averaged ion distribution functions in both parallel and perpendicular velocity-space with a quasilinear radio frequency (RF) diffusion operator valid in the ion finite Larmor radius (FLR) limit and the RF electric fields with the resultant non-Maxwellian FLR dielectric tensor. This produces non-Maxwellian ICRH simulations that are fully self-consistent, fast, and interoperable with integrated modeling frameworks, such as TRANSP/GACODE/IPS-FASTRAN. We demonstrate our model's capabilities by validating it against experimental data in Alcator C-Mod. We then perform the first RF heating simulations of SPARC using self-consistent non-Maxwellian ion distributions to investigate the potential to enhance fusion rates using ion cyclotron resonance heating generated fast ions.

Physics↗

DOE OSTI2025

Modeling and Simulation of Fuel Dispersal During the Loss-of-Coolant Accident

This document is the compilation of the milestone portion to a larger end of project NEUP report. The executive summary of the modeling portion is provided below: In the event of cladding rupture during a postulated LOCA in a pressurized water reactor, fuel particles, along with fission gases, can be expelled into the reactor core from the fractured fuel rod, a phenomenon referred to as fuel dispersal. The initial stage of fuel dispersal is strongly influenced by the high-pressure ejection of fuel fragments, the size and geometry of the ruptured cladding, and the depressurization history of the fuel rod during the postulated LOCA transient. Depending on the location of the burst orifice relative to the quench front, the dispersal event represents an intricate three-phase flow and heat transfer phenomenon, where high-temperature fuel particles carried by the fission gases interact with the coolant within the narrow subchannels of the fuel assemblies, inducing localized phase change. Given the unique multiphysics nature of this phenomena, the current study develops a dedicated computational framework to predict the mass distribution and cooling of dispersing fuel particles, facilitating post-accident assessment and management of the fuel assemblies. Considering the scale of nuclear reactor applications, a continuum three-fluid model is proposed for simulating the transport of solids within the reactor core. With high-temperature fuel fragments within the liquid media, nucleation sites inducing phase changes are dispersed within the flow domain. Coupled with the fact that the transient dispersal event occurs on different time scales than other three-phase flow applications, this study derives a time-averaged three-fluid flow model without losing generality. The assumptions regarding the continuum treatment of the solid phase and the modeling of fuel dispersal behavior are incorporated to simplify the governing equations and derive applicable closure relations. The computational validation of the model was conducted using adiabatic experimental results obtained from ongoing research at Oregon State University, focusing on characterizing fuel dispersal behavior during simulated LOCA conditions. Settlement characteristics of the solids, quantified by the probability distribution of equivalent particles, closely matched the probability density functions reported in experimental studies. The transport of fuel particles within a scaled 5 × 5 lattice of a pressurized-water reactor rod bundle geometry was modeled through a two-fluid Eulerian framework. The required boundary conditions were evaluated from the fuel performance code BISON in a postulated large-break LOCA scenario. The modeling framework considered solid fuel particles as granular matter, interacting with the gaseous dry steam phase and fission gases through the governing interfacial momentum exchange between the participating fluids. The simulation results provided the volume fraction of the solids obtained at the bottom surface of the enclosing tank geometry. Postulated LOCA leading to fuel dispersal phenomena involves the strong coupling between fuel thermomechanics, cladding deformation, thermal-hydraulics, and fuel particle transport. Incorporation of such a strong coupling in numerical simulation is performed by coupling the multiphysics solvers. In the case of fuel dispersal, a strong coupled simulation can be performed by coupling the BISON code for fuel performance, the TRACE code for system-level thermal hydraulics, and fuel particle transport in Multiphysics Object-Oriented Simulation Environment (MOOSE). For such intricate infrastructure, the MOOSE Framework eases the data transfer between codes. The recent version of MOOSE has incorporated the Navier-Stokes module for the fluid flow. An exploratory exercise was done to gain familiarity with finite volume capabilities in the MOOSE framework to incorporate the Spalart-Allmaras (SA) turbulence model. New finite-volume and auxiliary kernels were introduced to assemble the SA transport equation, compute turbulent viscosity, and evaluate wall distance and diagnostic turbulence terms, fully integrated with existing Navier-Stokes modules. A turbulent lid-driven cavity at a Reynolds number of approximately 10,000 is used for verification. MOOSE shows the robust solver convergence and produces the turbulent features. But it underpredicts the velocity profile and turbulent quantities, emphasizing the need to develop improved SA near-wall treatments (e.g., low-Re corrections or wall functions) as a key direction for future work.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1994

North African savanna fires and atmospheric carbon dioxide

The effect of north African savanna fires on atmospheric CO2 is investigated using a tracer transport model. The model uses winds from operational numerical weather prediction analyses and provides CO2 concentrations as a function of space and time. After a spin-up period of several years, biomass-burning sources are added, and model experiments are run for an additional year, utilizing various estimates of CO2 sources. The various model experiments show that biomass burning in the north African savannas significantly affects CO2 concentrations in South America. The effect is more pronounced during the period from January through March, when biomass burning in South America is almost nonexistent. During this period, atmospheric CO2 concentrations in parts of South America typically may increase by 0.5 to 0.75 ppm at 970 mbar, the average pressure of the lowest model layer. These figures are above the probable uncertainty level, as model runs with biomass-burning sources estimated from independent studies using distinct data sets and techniques indicate. From May through September, when severe biomass burning occurs in South America, the effect of north African savanna fires over South America has become generally small at 970 mbar, but north of the equator it may be of the same magnitude or larger than the effect of South American fires. The CO2 concentration increase in the extreme northern and southern portions of South America, however, is mostly due to southern African fires, whose effect may be 2-3 times larger than the effect of South American fires at 970 mbar. Even in the central part of the continent, where local biomass-burning emissions are maximum, southern African fires contribute to at least 15% of the CO2 concentration increase at 970 mbar. At higher levels in the atmosphere, less CO2 emitted by north African savanna fires reaches South America, and at 100 mbar no significant amount of CO2 is transported across the Atlantic Ocean. The vertical structure of the CO2 concentration increase due to biomass burning differs substantially, depending on whether sources are local or remote. A prominent maximum of CO2 concentration increase in the lower layers characterizes the effect of local sources, whereas a more homogeneous profile of CO2 concentration increase characterizes the effect of remote sources. The results demonstrate the strong remote effects of African biomoass burning which, owing to the general circulation of the atmosphere, are felt as far away as South America.

Iacobellis, Sam F.↗

NASA NTRS1995

On the uniqueness of linear moving-average filters for the solar wind-auroral geomagnetic activity coupling

The relation between the solar wind input to the magetosphere, VB(sub South), and the auroral geomagnetic index AL is modeled with two linear moving-average filtering methods: linear prediction filters and a driven harmonic oscillator in the form of an electric circuit. Although the response of the three-parameter oscillator is simpler than the filter's, the methods yield similar linear timescales and values of the prediction-observation correlation and the prediction Chi(exp 2). Further the filter responses obtained by the two methods are similar in their long-term features. In these aspects the circuit model is equivalent to linear prediction filtering. This poses the question of uniqueness and proper interpretation of detailed features of the filters such as response peaks. Finally, the variation of timescales and filter responses with the AL activity level is discussed.

Vassiliadis, D.↗

NASA NTRS1992

Improvement of observer/Kalman filter identification (OKID) by residual whitening

This paper presents a time-domain method to identify a state space model of a linear system and its corresponding observer/Kalman filter from a given set of general input-output data. The identified filter has the properties that its residual is minimized in the least squares sense, orthogonal to the time-shifted versions of itself, and to the given input-output data sequence. The connection between the state space model and a particular auto-regressive moving average description of a linear system is made in terms of the Kalman filter and a deadbeat gain matrix. The procedure first identifies the Markov parameters of an observer system, from which a state space model of the system and the filter gain are computed. The developed procedure is shown to improve results obtained by an existing observer/Kalman filter identification method, which is based on an auto-regressive model without the moving average terms. Numerical and experimental results are presented to illustrate the proposed method.

Phan, Minh↗

NASA NTRS1988

A numerical model for gravity wave dissipation in the thermosphere

Two simplified models have been developed for the internal gravity wave dissipation due to viscosity, thermal conduction, and ion-drag in a multilayered, isothermal thermosphere. Both models use the WKB approximation, ray theory, and the time-averaged equations of gravity wave energy conservation. One model uses all the equations appropriate to a dissipative atmosphere, while the other uses the dispersion equation and polarization relations applicable to a nondissipative atmosphere, neglecting the viscous and thermal conduction contributions to the energy flux. Results from these models are compared to each other and to the results obtained by Klostermeyer (1973), using a full-wave model.

Hickey, M. P.↗

NASA NTRS1996

Measurements and Modeling of Soot Formation and Radiation in Microgravity Jet Diffusion Flames

This is a computational and experimental study for soot formation and radiative heat transfer in jet diffusion flames under normal gravity (1-g) and microgravity (0-g) conditions. Instantaneous soot volume fraction maps are measured using a full-field imaging absorption technique developed by the authors. A compact, self-contained drop rig is used for microgravity experiments in the 2.2-second drop tower facility at NASA Lewis Research Center. On modeling, we have coupled flame structure and soot formation models with detailed radiation transfer calculations. Favre-averaged boundary layer equations with a k-e-g turbulence model are used to predict the flow field, and a conserved scalar approach with an assumed Beta-pdf are used to predict gaseous species mole fraction. Scalar transport equations are used to describe soot volume fraction and number density distributions, with formation and oxidation terms modeled by one-step rate equations and thermophoretic effects included. An energy equation is included to couple flame structure and radiation analyses through iterations, neglecting turbulence-radiation interactions. The YIX solution for a finite cylindrical enclosure is used for radiative heat transfer calculations. The spectral absorption coefficient for soot aggregates is calculated from the Rayleigh solution using complex refractive index data from a Drude- Lorentz model. The exponential-wide-band model is used to calculate the spectral absorption coefficient for H20 and C02. It is shown that when compared to results from true spectral integration, the Rosseland mean absorption coefficient can provide reasonably accurate predictions for the type of flames studied. The soot formation model proposed by Moss, Syed, and Stewart seems to produce better fits to experimental data and more physically sound than the simpler model by Khan et al. Predicted soot volume fraction and temperature results agree well with published data for a normal gravity co-flow laminar flames and turbulent jet flames. Predicted soot volume fraction results also agree with our data for 1-g and 0-g laminar jet names as well as 1-g turbulent jet flames.

Ku, Jerry C.↗

NASA NTRS2020

Modelling climate change impacts on maize yields under low nitrogen input conditions in sub‐Saharan Africa

Smallholder farmers in sub‐Saharan Africa (SSA) currently grow rainfed maize with limited inputs including fertilizer. Climate change may exacerbate current production constraints. Crop models can help quantify the potential impact of climate change on maize yields, but a comprehensive multimodel assessment of simulation accuracy and uncertainty in these low‐input systems is currently lacking. We evaluated the impact of varying [CO2], temperature and rainfall conditions on maize yield, for different nitrogen (N) inputs (0, 80, 160 kg N/ha) for five environments in SSA, including cool subhumid Ethiopia, cool semi‐arid Rwanda, hot subhumid Ghana and hot semi‐arid Mali and Benin using an ensemble of 25 maize models. Models were calibrated with measured grain yield, plant biomass, plant N, leaf area index, harvest index and in‐season soil water content from 2‐year experiments in each country to assess their ability to simulate observed yield. Simulated responses to climate change factors were explored and compared between models. Calibrated models reproduced measured grain yield variations well with average relative root mean square error of 26%, although uncertainty in model prediction was substantial (CV = 28%). Model ensembles gave greater accuracy than any model taken at random. Nitrogen fertilization controlled the response to variations in [CO2], temperature and rainfall. Without N fertilizer input, maize (i) benefited less from an increase in atmospheric [CO2], (ii) was less affected by higher temperature or decreasing rainfall and (iii) was more affected by increased rainfall because N leaching was more critical. The model inter-comparison revealed that simulation of daily soil N supply and N leaching plays a crucial role in simulating climate change impacts for low-input systems. Climate change and N input interactions have strong implications for the design of robust adaptation practices across SSA, because the impact of climate change will be modified if farmers intensify maize production with more mineral fertilizer.

Crop simulation model↗

NASA NTRSDate not supplied

Aeroheating Predictions for a Hypersonic, Turbulent Near-Wake

The accuracy of heating predictions using various turbulence models is examined for an axisymmetric near-wake at Mach 6. The CFD predictions are compared with experimental data collected under AGARD Working Group 18 on the wake of a 70-degree sphere-cone. The impact of grid resolution and discretization error is estimated, which allows a comparison of stacked-block and conventional structured meshes. The accuracy of steady Reynolds-averaged Navier-Stokes (RANS) models is contrasted with that of a hybrid RANS/Large-Eddy Simulation model. The predictions are made with three different CFD codes (LAURA, FUN3D, and HyperSolve), to demonstrate the code-to-code variation in the results. Steady SST models capture the qualitative nature of the heating in the wake, including the increasing peak heating with increasing Reynolds number. Spalart-Allmaras models, including SA-Catris, under-predicted the peak heating in the wake. Hybrid RANS/LES models improve upon the SA results but have their own modeling difficulties near the shear layer impingement. These results are generally consistent across solvers and grid topologies.

RANS↗

NASA NTRSDate not supplied

Aeroheating Predictions for a Hypersonic, Turbulent Near-Wake

RANS↗

DOE OSTI2023

Automatic detection of cataclysmic variables from SDSS images

Abstract Investigating rare and new objects have always been an important direction in astronomy. Cataclysmic variables (CVs) are ideal and natural celestial bodies for studying the accretion process of semi-detached binaries with accretion processes. However, the sample size of CVs must increase because a lager gap exists between the observational and the theoretical expanding CVs. Astronomy has entered the big data era and can provide massive images containing CV candidates. CVs as a type of faint celestial objects, are highly challenging to be identified directly from images using automatic manners. Deep learning has rapidly developed in intelligent image processing and has been widely applied in some astronomical fields with excellent detection results. YOLOX, as the latest YOLO framework, is advantageous in detecting small and dark targets. This work proposes an improved YOLOX-based framework according to the characteristics of CVs and Sloan Digital Sky Survey (SDSS) photometric images to train and verify the model to realise CV detection. We use the Convolutional Block Attention Module to increase the number of output features with the feature extraction network and adjust the feature fusion network to obtain fused features. Accordingly, the loss function is modified. Experimental results demonstrate that the improved model produces satisfactory results, with average accuracy (mean average Precision at 0.5) of 92.0%, Precision of 92.9%, Recall of 94.3%, and $F1-score$ of 93.6% on the test set. The proposed method can efficiently achieve the identification of CVs in test samples and search for CV candidates in unlabeled images. The image data vastly outnumber the spectra in the SDSS-released data. With supplementary follow-up observations or spectra, the proposed model can help astronomers in seeking and detecting CVs in a new manner to ensure that a more extensive CV catalog can be built. The proposed model may also be applied to the detection of other kinds of celestial objects.

Astronomy & Astrophysics↗

DOE OSTI2022

Verification and Validation Activities for the Multi-Fidelity Toolkit

The Multi-Fidelity Toolkit (MFTK) is a simulation tool being developed at Sandia National Laboratories for aerodynamic predictions of compressible flows over a range of physics fidelities and computational speeds. These models include the Reynolds-Averaged-Navier-Stokes (RANS) equations, the Euler equations, and modified Newtonian aerodynamics (MNA) equations, and they can be invoked independently or coupled with hierarchical Kriging to interpolate between high-fidelity simulations using lower-fidelity data. However, as with any new simulation capability, verification and validation are necessary to gather credibility evidence. This work describes formal code- and solution-verification activities as well as model validation with uncertainty considerations. Code verification is performed on the MNA model by comparing with an analytical solution for flat-plate and inclined-plate geometries. Solution-verification activities include grid-refinement studies of HIFiRE-1 wind tunnel measurements, which are used for validation, for all model fidelities. A thorough treatment of the validation comparison with prediction error and validation uncertainty is also presented.

42 ENGINEERING↗

NASA NTRS1989

Ozone precursors and ozone photochemistry over eastern North Pacific during the spring of 1984 based on the NASA GTE/CITE 1 airborne observations

Simultaneous high-resolution measurements of O3, NO, CO, dew point temperature, and UV flux obtained during the NASA Global Tropospheric Experiment Chemical Instrumentation Test and Evaluation (GTE/CITE 1) spring 1984 airborne field exercise over the eastern North Pacific Ocean are analyzed. Mid-tropospheric CO, O3, and NO mixing ratios averaged about 120 parts per billion by volume (ppbv), 50 ppbv, and 10 parts per trillion by volume (pptv), respectively. Statistical analysis of the high-resolution data indicates the existence of two ozone sources, one related to the downward transport of ozone-rich air from the upper troposphere and stratosphere, and the other to the transport of ozone-rich air from the continents. Modeling calculations based on these average levels imply that, from the surface to about 8 km, photochemical reactions probably supplied a net sink of ozone to the region overlying the eastern North Pacific Ocean during the sampling period. However, because the NO levels measured during the flights were frequently at or near the detection limit of the instruments and because the results are very sensitive to the absolute NO levels and their temporal variability, the conclusion must be considered provisional.

Chameides, W. L.↗