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NASA NTRS1991

Quantitative knowledge acquisition for expert systems

A common problem in the design of expert systems is the definition of rules from data obtained in system operation or simulation. While it is relatively easy to collect data and to log the comments of human operators engaged in experiments, generalizing such information to a set of rules has not previously been a direct task. A statistical method is presented for generating rule bases from numerical data, motivated by an example based on aircraft navigation with multiple sensors. The specific objective is to design an expert system that selects a satisfactory suite of measurements from a dissimilar, redundant set, given an arbitrary navigation geometry and possible sensor failures. The systematic development is described of a Navigation Sensor Management (NSM) Expert System from Kalman Filter convariance data. The method invokes two statistical techniques: Analysis of Variance (ANOVA) and the ID3 Algorithm. The ANOVA technique indicates whether variations of problem parameters give statistically different covariance results, and the ID3 algorithms identifies the relationships between the problem parameters using probabilistic knowledge extracted from a simulation example set. Both are detailed.

Belkin, Brenda L.↗
NASA NTRS2017

Assimilation of AERONET and MODIS AOT Observations Using Variational and Ensemble Data Assimilation Methods and Its Impact on Aerosol Forecasting Skill

Data assimilation of Aerosol Robotic Network (AERONET) and Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol optical thickness (AOT) for aerosol forecasting was tested within the Navy Aerosol Analysis Prediction System (NAAPS) framework, using variational and ensemble data assimilation methods. Navy aerosol forecasting currently makes use of a deterministic NAAPS simulation coupled to Navy Variational Data Assimilation System for aerosol optical depth, a two-dimensional variational data assimilation system, for MODIS AOT assimilation. An ensemble version of NAAPS (ENAAPS) coupled to an ensemble adjustment Kalman filter (EAKF) from the Data Assimilation Research Testbed was recently developed, allowing for a range of data assimilation and forecasting experiments to be run with deterministic NAAPS and ENAAPS. The main findings are that the EAKF, with its flow-dependent error covariances, makes better use of sparse observations such as AERONET AOT. Assimilating individual AERONET observations in the two-dimensional variational system can increase the analysis errors when observations are located in high AOT gradient regions. By including AERONET with MODIS AOT assimilation, the magnitudes of peak aerosol events (AOT> 1) were better captured with improved temporal variability, especially in India and Asia where aerosol prediction is a challenge. Assimilating AERONET AOT with MODIS had little impact on the 24 h forecast skill compared to MODIS assimilation only, but differences were found downwind of AERONET sites. The 24 h forecast skill was approximately the same for forecasts initialized with analyses from AERONET AOT assimilation alone compared to MODIS assimilation, particularly in regions where the AERONET network is dense; including the United States and Europe, indicating that AERONET could serve as a backup observation network for over-land synoptic-scale aerosol events.

Rubin, Juli I.↗
NASA NTRS2020

Mechanisms Linked to Recent Ozone Decreases in the Northern Hemisphere Lower Stratosphere

Previous studies have robustly identified a decrease since 1998 in lower stratospheric (LS) ozone in the Northern Hemisphere (NH). While this ozone decrease is qualitatively explained as resulting from changes in the large‐scale circulation, there is not yet a quantitative mechanistic explanation of these changes. Here we explore the drivers of recent ozone changes using two different configurations of the Goddard Earth Observing System (GEOS) general circulation model. The first configuration of GEOS includes a full chemistry module and is constrained with meteorological fields from the Modern‐Era Retrospective analysis for Research and Applications, Version 2 (MERRA‐2). This configuration (M2GMI) is used to analyze an idealized tracer that covaries closely with ozone on interannual and decadal timescales, revealing that recent ozone decreases in the NH subtropics are associated with a poleward expansion of upwelling in the NH LS, with reduced (enhanced) downwelling over northern subtropics (midlatitudes). The second configuration of GEOS is a free‐running version of the GEOS Chemistry‐Climate Model (CCM) that is used to perform a ten‐member ensemble of free‐running simulations. Comparisons of the two configurations reveal that, while the free‐running model can produce negative ozone changes in the NH LS, the magnitude of these changes is significantly weaker, relative to both M2GMI and MERRA‐2; moreover, these weaker ozone decreases are consistent with weaker simulated changes in the residual circulation. Finally, we examine the GEOS model results in the broader context of the hindcast simulations performed as part of Phase 1 of the Chemistry Climate Modeling Initiative. We show that the majority of the free‐running simulations considered here also exhibit weaker long‐term residual circulation changes, compared to reanalyses.

Ozone↗
NASA NTRS1998

Effect of altered sensory conditions on multivariate descriptors of human postural sway

Multivariate descriptors of sway were used to test whether altered sensory conditions result not only in changes in amount of sway but also in postural coordination. Eigenvalues and directions of eigenvectors of the covariance of shnk and hip angles were used as a set of multivariate descriptors. These quantities were measured in 14 healthy adult subjects performing the Sensory Organization test, which disrupts visual and somatosensory information used for spatial orientation. Multivariate analysis of variance and discriminant analysis showed that resulting sway changes were at least bivariate in character, with visual and somatosensory conditions producing distinct changes in postural coordination. The most significant changes were found when somatosensory information was disrupted by sway-referencing of the support surface (P = 3.2 x 10(-10)). The resulting covariance measurements showed that subjects not only swayed more but also used increased hip motion analogous to the hip strategy. Disruption of vision, by either closing the eyes or sway-referencing the visual surround, also resulted in altered sway (P = 1.7 x 10(-10)), with proportionately more motion of the center of mass than with platform sway-referencing. As shown by discriminant analysis, an optimal univariate measure could explain at most 90% of the behavior due to altered sensory conditions. The remaining 10%, while smaller, are highly significant changes in posture control that depend on sensory conditions. The results imply that normal postural coordination of the trunk and legs requires both somatosensory and visual information and that each sensory modality makes a unique contribution to posture control. Descending postural commands are multivariate in nature, and the motion at each joint is affected uniquely by input from multiple sensors.

NASA Discipline Neuroscience↗
NASA NTRS2022

Measurement report: Closure Analysis of Aerosol–cloud Composition in Tropical Maritime Warm Convection

Cloud droplet chemical composition is a key observable property that can aid understanding of how aerosols and clouds interact. As part of the Clouds, Aerosols and Monsoon Processes – Philippines Experiment (CAMP2Ex), three case studies were analyzed involving collocated airborne sampling of relevant clear and cloudy air masses associated with maritime warm convection. Two of the cases represented a polluted marine background, with signatures of transported East Asian regional pollution, aged over water for several days, while the third case comprised a major smoke transport event from Kalimantan fires. Sea salt was a dominant component of cloud droplet composition, in spite of fine particulate enhancement from regional anthropogenic sources. Furthermore, the proportion of sea salt was enhanced relative to sulfate in rainwater and may indicate both a propensity for sea salt to aid warm rain production and an increased collection efficiency of large sea salt particles by rain in subsaturated environments. Amongst cases, as precipitation became more significant, so too did the variability in the sea salt to (non-sea salt) sulfate ratio. Across cases, nitrate and ammonium were fractionally greater in cloud water than fine-mode aerosol particles; however, a strong covariability in cloud water nitrate and sea salt was suggestive of prior uptake of nitrate on large salt particles. A mass-based closure analysis of non-sea salt sulfate compared the cloud water air-equivalent mass concentration to the concentration of aerosol particles serving as cloud condensation nuclei for droplet activation. While sulfate found in cloud was generally constrained by the sub-cloud aerosol concentration, there was significant intra-cloud variability that was attributed to entrainment – causing evaporation of sulfate-containing droplets –and losses due to precipitation. In addition, precipitation tended to promote mesoscale variability in the sub-cloud aerosol through a combination of removal, convective downdrafts, and dynamically driven convergence. Physical mechanisms exerted such strong control over the cloud water compositional budget that it was not possible to isolate any signature of chemical production/loss using in-cloud observations. The cloud-free environment surrounding the non-precipitating smoke case indicated sulfate enhancement compared to convective mixing quantified by a stable gas tracer; however, this was not observed in the cloud water (either through use of ratios or the mass closure), perhaps implying that the warm convective cloud timescale was too short for chemical production to be a leading-order budgetary term and because precursors had already been predominantly exhausted. Closure of other species was truncated by incomplete characterization of coarse aerosol (e.g., it was found that only 10 %–50% of sea salt mass found in cloud was captured during clear-air sampling) and unmeasured gasphase abundances affecting closure of semi-volatile aerosol species (e.g., ammonium, nitrate and organic) and soluble volatile organic compound contributions to total organic carbon in cloud water.

Ewan Crosbie↗
NASA NTRS1986

The use of multidate multichannel radiance data in urban feature analysis

Two images were obtained from thematic mappers on Landsats 4 and 5 over the Washington, DC area during November 1982 and March 1984. Selected training areas containing different types of urban land use were examined,one area consisting entirely of forest. Mean digital radiance values for each bandpass in each image were examined, and variances, standard deviations, and covariances between bandpasses were calculated. It has been found that two bandpasses caused forested areas to stand out from other land use types, especially for the November 1982 image. In order to evaluate quantitatively the possible utility of the principal components analysis in selected feature extraction, the eigenvectors were evaluated for principal axes rotations which rendered each selected land use type most separable from all other land use types. The evaluated eigenvectors were plotted as a function of land use type, whose order was decided by considering anticipated shadow component and by examining the relative loadings indicative of vegetation for each of the principal components for the different features considered. The analysis was performed for each seven-band image separately and for the two combined images. It was found that by combining the two images, more dramatic land use type separation could be obtained.

Duggin, M. J.↗
NASA NTRS1999

Launch Collision Probability

This report analyzes the probability of a launch vehicle colliding with one of the nearly 10,000 tracked objects orbiting the Earth, given that an object on a near-collision course with the launch vehicle has been identified. Knowledge of the probability of collision throughout the launch window can be used to avoid launching at times when the probability of collision is unacceptably high. The analysis in this report assumes that the positions of the orbiting objects and the launch vehicle can be predicted as a function of time and therefore that any tracked object which comes close to the launch vehicle can be identified. The analysis further assumes that the position uncertainty of the launch vehicle and the approaching space object can be described with position covariance matrices. With these and some additional simplifying assumptions, a closed-form solution is developed using two approaches. The solution shows that the probability of collision is a function of position uncertainties, the size of the two potentially colliding objects, and the nominal separation distance at the point of closest approach. ne impact of the simplifying assumptions on the accuracy of the final result is assessed and the application of the results to the Cassini mission, launched in October 1997, is described. Other factors that affect the probability of collision are also discussed. Finally, the report offers alternative approaches that can be used to evaluate the probability of collision.

Bollenbacher, Gary↗
NASA NTRS2013

Tuning and Robustness Analysis for the Orion Absolute Navigation System

The Orion Multi-Purpose Crew Vehicle (MPCV) is currently under development as NASA's next-generation spacecraft for exploration missions beyond Low Earth Orbit. The MPCV is set to perform an orbital test flight, termed Exploration Flight Test 1 (EFT-1), some time in late 2014. The navigation system for the Orion spacecraft is being designed in a Multi-Organizational Design Environment (MODE) team including contractor and NASA personnel. The system uses an Extended Kalman Filter to process measurements and determine the state. The design of the navigation system has undergone several iterations and modifications since its inception, and continues as a work-in-progress. This paper seeks to show the efforts made to-date in tuning the filter for the EFT-1 mission and instilling appropriate robustness into the system to meet the requirements of manned space ight. Filter performance is affected by many factors: data rates, sensor measurement errors, tuning, and others. This paper focuses mainly on the error characterization and tuning portion. Traditional efforts at tuning a navigation filter have centered around the observation/measurement noise and Gaussian process noise of the Extended Kalman Filter. While the Orion MODE team must certainly address those factors, the team is also looking at residual edit thresholds and measurement underweighting as tuning tools. Tuning analysis is presented with open loop Monte-Carlo simulation results showing statistical errors bounded by the 3-sigma filter uncertainty covariance. The Orion filter design uses 24 Exponentially Correlated Random Variable (ECRV) parameters to estimate the accel/gyro misalignment and nonorthogonality. By design, the time constant and noise terms of these ECRV parameters were set to manufacturer specifications and not used as tuning parameters. They are included in the filter as a more analytically correct method of modeling uncertainties than ad-hoc tuning of the process noise. Tuning is explored for the powered-flight ascent phase, where measurements are scarce and unmodelled vehicle accelerations dominate. On orbit, there are important trade-off cases between process and measurement noise. On entry, there are considerations about trading performance accuracy for robustness. Process Noise is divided into powered flight and coasting ight and can be adjusted for each phase and mode of the Orion EFT-1 mission. Measurement noise is used for the integrated velocity measurements during pad alignment. It is also used for Global Positioning System (GPS) pseudorange and delta- range measurements during the rest of the flight. The robustness effort has been focused on maintaining filter convergence and performance in the presence of unmodeled error sources. These include unmodeled forces on the vehicle and uncorrected errors on the sensor measurements. Orion uses a single-frequency, non-keyed GPS receiver, so the effects due to signal distortion in Earth's ionosphere and troposphere are present in the raw measurements. Results are presented showing the efforts to compensate for these errors as well as characterize the residual effect for measurement noise tuning. Another robustness tool in use is tuning the residual edit thresholds. The trade-off between noise tuning and edit thresholds is explored in the context of robustness to errors in dynamics models and sensor measurements. Measurement underweighting is also presented as a method of additional robustness when processing highly accurate measurements in the presence of large filter uncertainties.

Holt, Greg N.↗
NASA NTRS2013

Wald Sequential Probability Ratio Test for Analysis of Orbital Conjunction Data

We propose a Wald Sequential Probability Ratio Test for analysis of commonly available predictions associated with spacecraft conjunctions. Such predictions generally consist of a relative state and relative state error covariance at the time of closest approach, under the assumption that prediction errors are Gaussian. We show that under these circumstances, the likelihood ratio of the Wald test reduces to an especially simple form, involving the current best estimate of collision probability, and a similar estimate of collision probability that is based on prior assumptions about the likelihood of collision.

Carpenter, J. Russell↗
NASA NTRS1995

Technical report series on global modeling and data assimilation. Volume 4: Documentation of the Goddard Earth Observing System (GEOS) data assimilation system, version 1

This report describes the analysis component of the Goddard Earth Observing System, Data Assimilation System, Version 1 (GEOS-1 DAS). The general features of the data assimilation system are outlined, followed by a thorough description of the statistical interpolation algorithm, including specification of error covariances and quality control of observations. We conclude with a discussion of the current status of development of the GEOS data assimilation system. The main components of GEOS-1 DAS are an atmospheric general circulation model and an Optimal Interpolation algorithm. The system is cycled using the Incremental Analysis Update (IAU) technique in which analysis increments are introduced as time independent forcing terms in a forecast model integration. The system is capable of producing dynamically balanced states without the explicit use of initialization, as well as a time-continuous representation of non- observables such as precipitation and radiational fluxes. This version of the data assimilation system was used in the five-year reanalysis project completed in April 1994 by Goddard's Data Assimilation Office (DAO) Data from this reanalysis are available from the Goddard Distributed Active Center (DAAC), which is part of NASA's Earth Observing System Data and Information System (EOSDIS). For information on how to obtain these data sets, contact the Goddard DAAC at (301) 286-3209, EMAIL daac@gsfc.nasa.gov.

Suarez, Max J.↗
NASA NTRSDate not supplied

Reduced Dimensionality Analysis of TEMPO Ozone Profile Retrievals Using the Compact Phase Space (CPSR) Algorithm

TEMPO ozone (O 3 ) profile retrievals are expected to have fidelity in the troposphere due the sensitivities of the associated averaging kernels. However, those averaging kernels are severely rank deficiency meaning that a visual inspection of the vertical structure of the averaging kernel profile sensitivities is misleading due linear dependencies in the profile. The Compact Phase Space Retrieval (CPSR) algorithm use singular value decompositions of the averaging kernels and the ‘compressed’ retrieval solution error covariance to project the transformed averaging kernels into a space that removes the linear dependencies and accounts for the solution error uncertainties. In this oral presentation and poster, we apply the CPSR dimensional reduction analysis to TEMPO and TROPOMI O 3 profile retrievals for 13:45 UTC March 29, 2024 to study the phase space characteristics of the transformed averaging kernels as a function of latitude for North America. Our results show that TEMPO generally has more phase space vertical structure in the troposphere than TROPOMI. TEMPO has four to five dominant modes, and TROPOMI has five to six dominant modes. That means that dimensional reduction can reduce the TEMPO resource requirements by ~77% and the TROPOMI requirements by ~81%. Finally, we found that after removing linear dependences and after accounting for solution uncertainties TEMPO still has sensitivities throughout the troposphere.

TEMPO↗
NASA NTRS2011

Superpixel-Augmented Endmember Detection for Hyperspectral Images

Superpixels are homogeneous image regions comprised of several contiguous pixels. They are produced by shattering the image into contiguous, homogeneous regions that each cover between 20 and 100 image pixels. The segmentation aims for a many-to-one mapping from superpixels to image features; each image feature could contain several superpixels, but each superpixel occupies no more than one image feature. This conservative segmentation is relatively easy to automate in a robust fashion. Superpixel processing is related to the more general idea of improving hyperspectral analysis through spatial constraints, which can recognize subtle features at or below the level of noise by exploiting the fact that their spectral signatures are found in neighboring pixels. Recent work has explored spatial constraints for endmember extraction, showing significant advantages over techniques that ignore pixels relative positions. Methods such as AMEE (automated morphological endmember extraction) express spatial influence using fixed isometric relationships a local square window or Euclidean distance in pixel coordinates. In other words, two pixels covariances are based on their spatial proximity, but are independent of their absolute location in the scene. These isometric spatial constraints are most appropriate when spectral variation is smooth and constant over the image. Superpixels are simple to implement, efficient to compute, and are empirically effective. They can be used as a preprocessing step with any desired endmember extraction technique. Superpixels also have a solid theoretical basis in the hyperspectral linear mixing model, making them a principled approach for improving endmember extraction. Unlike existing approaches, superpixels can accommodate non-isometric covariance between image pixels (characteristic of discrete image features separated by step discontinuities). These kinds of image features are common in natural scenes. Analysts can substitute superpixels for image pixels during endmember analysis that leverages the spatial contiguity of scene features to enhance subtle spectral features. Superpixels define populations of image pixels that are independent samples from each image feature, permitting robust estimation of spectral properties, and reducing measurement noise in proportion to the area of the superpixel. This permits improved endmember extraction, and enables automated search for novel and constituent minerals in very noisy, hyperspatial images. This innovation begins with a graph-based segmentation based on the work of Felzenszwalb et al., but then expands their approach to the hyperspectral image domain with a Euclidean distance metric. Then, the mean spectrum of each segment is computed, and the resulting data cloud is used as input into sequential maximum angle convex cone (SMACC) endmember extraction.

Thompson, David R.↗
NASA NTRS1975

Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.

Menga, G.↗
NASA NTRS1976

Information and display requirements for independent landing monitors

The ways an Independent Landing Monitor (ILM) may be used to complement the automatic landing function were studied. In particular, a systematic procedure was devised to establish the information and display requirements of an ILM during the landing phase of the flight. Functionally, the ILM system is designed to aid the crew in assessing whether the total system (e.g., avionics, aircraft, ground navigation aids, external disturbances) performance is acceptable, and, in case of anomaly, to provide adequate information to the crew to select the least unsafe of the available alternatives. Economically, this concept raises the possibility of reducing the primary autoland system redundancy and associated equipment and maintenance costs. The required level of safety for the overall system would in these cases be maintained by upgrading the backup manual system capability via the ILM. A safety budget analysis was used to establish the reliability requirements for the ILM. These requirements were used as constraints in devising the fault detection scheme. Covariance propagation methods were used with a linearized system model to establish the time required to correct manually perturbed states due to the fault. Time-to-detect and time-to-correct requirements were combined to devise appropriate altitudes and strategies for fault recovery.

Karmarker, J. S.↗
NASA NTRS1994

A new approach to the photon localization problem

Since wavelets form a representation of the Poincare group, it is possible to construct a localized superposition of light waves with different frequencies in a Lorentz-covariant manner. This localized wavelet satisfies a Lorentz-invariant uncertainty relation, and also the Lorentz-invariant Parseval's relation. A quantitative analysis is given for the difference between photons and localized waves. It is then shown that this localized entity corresponds to a relativistic photon with a sharply defined momentum in the non-localization limit. Waves are not particles. It is confirmed that the wave-particle duality is subject to the uncertainty principle.

Han, D.↗
NASA NTRS2000

Adjoints and Low-rank Covariance Representation

Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.

Tippett, Michael K.↗
NASA NTRS1994

The updated statistical inversion technique to the evaluation of Umkehr observations

In the present study the standard retrieval Umkehr method to estimate the vertical distribution of ozone was updated using a statistical approach to the mathematical inversion scheme. The vertical ozone profile covariance matrix was used as a priori information for the inverse problem. A new method of the ozonesonde data organization according to air mass types helped to improve the covariance matrix quality. A retrieval method was developed using eigenvector technique. An optimal vertical ozone profile resolution was determined from the mathematical inversion scheme analysis based on the same technique. The sun radiation transfer was accounted for multiple scattering and atmospheric sphericity in this calculation. The retrievals using actual Umkehr Dobson spectrophotometer observations were also performed to provide the comparison of the standard and updated methods with concurrent ozone sound data at Boulder U.S. The comparison has revealed that the present method has some advantages in both resolution and accuracy, as compared to the standard one, especially for the atmospheric layers below ozone maximum.

Frolov, Alexander D.↗
NASA NTRS2000

Preliminary Results from an Assimilation of Saharan Dust Using TOMS Radiances and the GOCART Model

At NASA Goddard we are developing a global aerosol data assimilation system that combines advances in remote sensing and modeling of atmospheric aerosols. The goal is to provide high resolution, 3-D aerosol distributions to the research community. Our first step is to develop a simple assimilation system for Saharan mineral aerosol. The Goddard Chemistry and Aerosol Radiation model (GOCART) provides accurate 3-D mineral aerosol size distributions. Surface mobilization, wet and dry deposition, convective and long-range transport are all driven by assimilated fields from the Goddard Earth Observing System Data Assimilation System, GEOS-DAS. Our version of GOCART transports sizes from .08-10 microns and only simulates Saharan dust. We draw the assimilation to two observables in this study: the TOMS aerosol index (Al) which is directly related to the ratio of the 340 and 380 radiances and the 380 radiance alone. The forward model that simulates the observables requires the aerosol optical thickness, the single scattering albedo and the height of the aerosol layer from the GOCART fields. The forward model also requires a refractive index for the dust. We test three index values to see which best fits the TOMS observables. These are 1) for Saharan dust reported by Patterson, 2) for a mixture of Saharan dust and a highly reflective material (sea salt or sulfate) and 3) for pure illite. The assimilation works best assuming either pure illite or the dust mixture. Our assimilation cycle first determines values of the aerosol index (Al) and the radiance at 380 nm based on the GOCART aerosol fields. Differences between the observed and GOCART model calculated Al and 380 nm radiance are first analyzed horizontally using the Physical-space Statistical Analysis System (PSAS). A quasi-Newton iteration is then performed to produce analyzed 3D aerosol fields according to parameterized background and observation error covariances. We only assimilate observations into the the GOCART model over regions of Africa and the Atlantic where mineral aerosols are dominant and carbonaceous aerosols are minimal.

Weaver, C. J.↗