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At least 1,135 records · Page 63

Empirical correction for earth sensor horizon radiance variation

A major limitation on the use of infrared horizon sensors for attitude determination is the variability of the height of the infrared Earth horizon. This variation includes a climatological component and a stochastic component of approximately equal importance. The climatological component shows regular variation with season and latitude. Models based on historical measurements have been used to compensate for these systematic changes. The stochastic component is analogous to tropospheric weather. It can cause extreme, localized changes that for a period of days, overwhelm the climatological variation. An algorithm has been developed to compensate partially for the climatological variation of horizon height and at least to mitigate the stochastic variation. This method uses attitude and horizon sensor data from spacecraft to update a horizon height history as a function of latitude. For spacecraft that depend on horizon sensors for their attitudes (such as the Total Ozone Mapping Spectrometer-Earth Probe-TOMS-EP) a batch least squares attitude determination system is used. It is assumed that minimizing the average sensor residual throughout a full orbit of data results in attitudes that are nearly independent of local horizon height variations. The method depends on the additional assumption that the mean horizon height over all latitudes is approximately independent of season. Using these assumptions, the method yields the latitude dependent portion of local horizon height variations. This paper describes the algorithm used to generate an empirical horizon height. Ideally, an international horizon height database could be established that would rapidly merge data from various spacecraft to provide timely corrections that could be used by all.

Hashmall, Joseph A.↗

General Multimechanism Reversible-Irreversible Time-Dependent Constitutive Deformation Model Being Developed

Since most advanced material systems (for example metallic-, polymer-, and ceramic-based systems) being currently researched and evaluated are for high-temperature airframe and propulsion system applications, the required constitutive models must account for both reversible and irreversible time-dependent deformations. Furthermore, since an integral part of continuum-based computational methodologies (be they microscale- or macroscale-based) is an accurate and computationally efficient constitutive model to describe the deformation behavior of the materials of interest, extensive research efforts have been made over the years on the phenomenological representations of constitutive material behavior in the inelastic analysis of structures. From a more recent and comprehensive perspective, the NASA Glenn Research Center in conjunction with the University of Akron has emphasized concurrently addressing three important and related areas: that is, 1) Mathematical formulation; 2) Algorithmic developments for updating (integrating) the external (e.g., stress) and internal state variables; 3) Parameter estimation for characterizing the model. This concurrent perspective to constitutive modeling has enabled the overcoming of the two major obstacles to fully utilizing these sophisticated time-dependent (hereditary) constitutive models in practical engineering analysis. These obstacles are: 1) Lack of efficient and robust integration algorithms; 2) Difficulties associated with characterizing the large number of required material parameters, particularly when many of these parameters lack obvious or direct physical interpretations.

Saleeb, A. F.↗

A Maximum Likelihood Approach to Determine Sensor Radiometric Response Coefficients for NPP VIIRS Reflective Solar Bands

Optical sensors aboard Earth orbiting satellites such as the next generation Visible/Infrared Imager/Radiometer Suite (VIIRS) assume that the sensors radiometric response in the Reflective Solar Bands (RSB) is described by a quadratic polynomial, in relating the aperture spectral radiance to the sensor Digital Number (DN) readout. For VIIRS Flight Unit 1, the coefficients are to be determined before launch by an attenuation method, although the linear coefficient will be further determined on-orbit through observing the Solar Diffuser. In determining the quadratic polynomial coefficients by the attenuation method, a Maximum Likelihood approach is applied in carrying out the least-squares procedure. Crucial to the Maximum Likelihood least-squares procedure is the computation of the weight. The weight not only has a contribution from the noise of the sensor s digital count, with an important contribution from digitization error, but also is affected heavily by the mathematical expression used to predict the value of the dependent variable, because both the independent and the dependent variables contain random noise. In addition, model errors have a major impact on the uncertainties of the coefficients. The Maximum Likelihood approach demonstrates the inadequacy of the attenuation method model with a quadratic polynomial for the retrieved spectral radiance. We show that using the inadequate model dramatically increases the uncertainties of the coefficients. We compute the coefficient values and their uncertainties, considering both measurement and model errors.

Lei, Ning↗

Physics Mining of Multi-Source Data Sets

Powerful new parallel data mining algorithms can produce diagnostic and prognostic numerical models and analyses from observational data. These techniques yield higher-resolution measures than ever before of environmental parameters by fusing synoptic imagery and time-series measurements. These techniques are general and relevant to observational data, including raster, vector, and scalar, and can be applied in all Earth- and environmental science domains. Because they can be highly automated and are parallel, they scale to large spatial domains and are well suited to change and gap detection. This makes it possible to analyze spatial and temporal gaps in information, and facilitates within-mission replanning to optimize the allocation of observational resources. The basis of the innovation is the extension of a recently developed set of algorithms packaged into MineTool to multi-variate time-series data. MineTool is unique in that it automates the various steps of the data mining process, thus making it amenable to autonomous analysis of large data sets. Unlike techniques such as Artificial Neural Nets, which yield a blackbox solution, MineTool's outcome is always an analytical model in parametric form that expresses the output in terms of the input variables. This has the advantage that the derived equation can then be used to gain insight into the physical relevance and relative importance of the parameters and coefficients in the model. This is referred to as physics-mining of data. The capabilities of MineTool are extended to include both supervised and unsupervised algorithms, handle multi-type data sets, and parallelize it.

Helly, John↗

Variability and Predictability of West African Droughts. A Review in the Role of Sea Surface Temperature Anomalies

The Sahel experienced a severe drought during the 1970s and 1980s after wet periods in the 1950s and 1960s. Although rainfall partially recovered since the 1990s, the drought had devastating impacts on society. Most studies agree that this dry period resulted primarily from remote effects of sea surface temperature (SST) anomalies amplified by local land surface-atmosphere interactions. This paper reviews advances made during the last decade to better understand the impact of global SST variability on West African rainfall at interannual to decadal time scales. At interannual time scales, a warming of the equatorial Atlantic and Pacific/Indian Oceans results in rainfall reduction over the Sahel, and positive SST anomalies over the Mediterranean Sea tend to be associated with increased rainfall. At decadal time scales, warming over the tropics leads to drought over the Sahel, whereas warming over the North Atlantic promotes increased rainfall. Prediction systems have evolved from seasonal to decadal forecasting. The agreement among future projections has improved from CMIP3 to CMIP5, with a general tendency for slightly wetter conditions over the central part of the Sahel, drier conditions over the western part, and a delay in the monsoon onset. The role of the Indian Ocean, the stationarity of teleconnections, the determination of the leader ocean basin in driving decadal variability, the anthropogenic role, the reduction of the model rainfall spread, and the improvement of some model components are among the most important remaining questions that continue to be the focus of current international projects.

West Africa↗

Snowfall in the Northern Great Lakes: Lessons Learned from a Multisensor Observatory

A multisensor snowfall observational suite has been deployed at the Marquette, Michigan, National Weather Service Weather Forecast Office (KMQT) since 2014. Micro Rain Radar (MRR; profiling radar), Precipitation Imaging Package (PIP; snow particle imager), and ancillary ground-based meteorological observations illustrate the unique capabilities of these combined instruments to document radar and concomitant microphysical properties associated with northern Great Lakes snowfall regimes. Lake-effect, lake-orographic, and transition event case studies are presented that illustrate the variety of snowfall events that occur at KMQT. Case studies and multiyear analyses reveal the ubiquity of snowfall produced by shallow events. These shallow snowfall features and their distinctive microphysical fingerprints are often difficult to discern with conventional remote sensing instruments, thus highlighting the scientific and potential operational value of MRR and PIP observations. The importance of near-surface lake-orographic snowfall enhancement processes in extreme snowfall events and regime-dependent snow particle microphysical variability controlled by regime and environmental factors are also highlighted.

Lake effects↗

On Boundary-Value Problems for RANS Equations and Two-Equation Turbulence Models

Currently, in engineering computations for high Reynolds number turbulent flows, turbulence modeling continues to be the most frequently used approach to represent the effects of turbulence. Such models generally rely on solving either one or two transport equations along with the Reynolds-Averaged Navier–Stokes (RANS) equations. The solution of the boundary-value problem of any system of partial differential equations requires the complete delineation of the equations and the boundary conditions, including any special restrictions and conditions. In the literature, such a description is often incomplete, neglecting important details related to the boundary conditions and possible restrictive conditions, such as how to ensure satisfying prescribed values of the dependent variables of the transport equations in the far field of a finite domain. In this article, we discuss the possible influence of boundary values, as well as near-field and far-field behavior, on the solution of the RANS equations coupled with transport equations for turbulence modeling. In so doing, we defne the concept of a welldefined boundary-value problem. Additionally, a three-dimensional, rather than a simpler one-dimensional analysis is performed to analyze the near-wall and far-field behavior of the turbulence model variables. This allows an assessment of the decay rate of these variables required to realize the boundary conditions in the far field. This paper also addresses the impact of various transformations of two-equation models (e.g., the model of Wilcox) to remove the singular behavior of the dissipation rate (ω) at the surface boundary. Finally, the issue of well-posedness regarding the governing equations is considered. A compelling argument (although not a proof) for ill-posedness is made for both direct and inverse problems.

Navier–Stokes equations↗

Applying a Crew Accommodations Resource Model to Future Space Vehicle Research

The success of research and development for human space flight depends heavily on modeling. In addition, the use of such models is especially critical at the earliest phase of research and development of any manned vehicle or habitat. NASA is currently studying various innovative and futuristic propulsion technologies to enable further exploration of space by untended as well as tended vehicles. Details such as vehicle mass, volume, shape and configuration are required variables to evaluate the success of the propulsion concepts. For tended vehicles, the impact of the crew's requirements on those parameters must be included. This is especially important on long duration missions where the crew requirements become more complex. To address these issues, a crew accommodations resource model, developed as a mission planning tool for human spaceflight (Stillwell, Boutros, & Connolly), was applied to a reference mission in order to estimate the volume and mass required to sustain a crew for a variety of long duration missions. The model, which compiled information from numerous different sources and contains various attributes which can be modified to enable comparisons across different dimensions, was instrumental in deriving volume and mass required for a tended long duration space flight. With the inclusion of some additional variables, a set of volume and mass requirements were provided to the project. If due consideration to crew requirements for volume and mass had not been entertained, the assumptions behind validation of the propulsion technology could have been found to be incorrect, possibly far into development of the technology or even into the design and build of test vehicles. The availability and use of such a model contributes significantly by increasing the accuracy of human space flight research and development activities and acts as a cost saving measure by preventing inaccurate assumptions from driving design decisions.

Blume, Jennifer Linda↗

A51F-0123: Model Analysis of Tropospheric Aerosol Variability and Sources over the North Atlantic During NAAMES 2015-2016

The North Atlantic Aerosols and Marine Ecosystems Study (NAAMES) is a five-year Earth-Venture Suborbital-2 Mission to characterize the plankton ecosystems and their influences on remote marine aerosols, boundary layer clouds, and their implications for climate in the North Atlantic. While marine-sourced aerosols have been shown to make important contributions to surface aerosol loading, cloud condensation nuclei and ice nuclei concentrations over remote marine and coastal regions, it is still a challenge to differentiate the marine biogenic aerosol signal from the strong influence of continental pollution outflow. We examine here the spatiotemporal variability and quantify the sources of tropospheric aerosols over the North Atlantic during the first two phases (November 2015 and May-June 2016) of NAAMES using a state-of-the-art chemical transport model (GEOS-Chem). The model is driven by the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) from the NASA Global Modeling and Assimilation Office (GMAO). It includes sulfate-nitrate-ammonium aerosol thermodynamics coupled to ozone-NOx-hydrocarbon-aerosol chemistry, mineral dust, sea salt, elemental and organic carbon aerosols, and especially a recently implemented parameterization for the marine primary organic aerosol emission. The simulated aerosols over the North Atlantic are evaluated with available satellite (e.g., MODIS) observations of aerosol optical depths (AOD), and aircraft and ship aerosol measurements. We diagnose transport pathways for continental pollution outflow over the North Atlantic using carbon monoxide, an excellent tracer for anthropogenic pollution transport. We also conduct model perturbation experiments to quantify the relative contributions of terrestrial and oceanic sources to the aerosol loading, AOD, and their variability over the North Atlantic.

aerosols↗

The Relative Importance of Random Error and Observation Frequency in Detecting Trends in Upper Tropospheric Water Vapor

Recent published work assessed the amount of time to detect trends in atmospheric water vapor over the coming century. We address the same question and conclude that under the most optimistic scenarios and assuming perfect data (i.e., observations with no measurement uncertainty) the time to detect trends will be at least 12 years at approximately 200 hPa in the upper troposphere. Our times to detect trends are therefore shorter than those recently reported and this difference is affected by data sources used, method of processing the data, geographic location and pressure level in the atmosphere where the analyses were performed. We then consider the question of how instrumental uncertainty plays into the assessment of time to detect trends. We conclude that due to the high natural variability in atmospheric water vapor, the amount of time to detect trends in the upper troposphere is relatively insensitive to instrumental random uncertainty and that it is much more important to increase the frequency of measurement than to decrease the random error in the measurement. This is put in the context of international networks such as the Global Climate Observing System (GCOS) Reference Upper-Air Network (GRUAN) and the Network for the Detection of Atmospheric Composition Change (NDACC) that are tasked with developing time series of climate quality water vapor data.

Whiteman, David N.↗

Source Attribution and Interannual Variability of Arctic Pollution in Spring Constrained by Aircraft (ARCTAS, ARCPAC) and Satellite (AIRS) Observations of Carbon Monoxide

We use aircraft observations of carbon monoxide (CO) from the NASA ARCTAS and NOAA ARCPAC campaigns in April 2008 together with multiyear (2003-2008) CO satellite data from the AIRS instrument and a global chemical transport model (GEOS-Chem) to better understand the sources, transport, and interannual variability of pollution in the Arctic in spring. Model simulation of the aircraft data gives best estimates of CO emissions in April 2008 of 26 Tg month-1 for Asian anthropogenic, 9.1 for European anthropogenic, 4.2 for North American anthropogenic, 9.3 for Russian biomass burning (anomalously large that year), and 21 for Southeast Asian biomass burning. We find that Asian anthropogenic emissions are the dominant source of Arctic CO pollution everywhere except in surface air where European anthropogenic emissions are of similar importance. Synoptic pollution influences in the Arctic free troposphere include contributions of comparable magnitude from Russian biomass burning and from North American, European, and Asian anthropogenic sources. European pollution dominates synoptic variability near the surface. Analysis of two pollution events sampled by the aircraft demonstrates that AIRS is capable of observing pollution transport to the Arctic in the mid-troposphere. The 2003-2008 record of CO from AIRS shows that interannual variability averaged over the Arctic cap is very small. AIRS CO columns over Alaska are highly correlated with the Ocean Nino Index, suggesting a link between El Nino and northward pollution transport. AIRS shows lower-than-average CO columns over Alaska during April 2008, despite the Russian fires, due to a weakened Aleutian Low hindering transport from Asia and associated with the moderate 2007-2008 La Nina. This suggests that Asian pollution influence over the Arctic may be particularly large under strong El Nino conditions.

Fisher, J. A.↗

Variability of (O I) 6300-A emission near Io

Observations of (O I) 6300-A emission near Io have been obtained in 1990, 1991, and 1992 by the National Solar Observatory staff using the solar-stellar spectrography on the McMath-Pierce telescope at Kitt Peak. High-resolution spectra with a resolving power of about 1.2 x 10(exp 5) were obtained with an integration time of 10-15 min each. The viewing aperture for the observations was 5.2 arc sec x 5.2 arc sec centered on Io, with spatial resolution limited within this area by seeing conditions. Observations thus far have been reduced to obtain average brightness values over the aperture which range from approximately 200 to 1000 R for a number of different Io phase angles and Io system III longitudes. The (O I) 6300-A emission brightness exhibits an east-west asymmetry, where the average intensity for Io phase angles in the west (receding ansa) is 1.5 times brighter than in the east (approaching ansa). Similar east-west intensity ratios have also been observed for neutrals near Io and ions in the plasma torus for a number of other optical and ultraviolet emission lines which are excited by electron impact. In addition to the east-west asymmetry, the (O I) 6300-A emission brightness exhibits a strong dependence on the Io system III longitude angle, with a maximum value occurring in the range 200 deg +/- 50 deg. Earlier IUE observations of ultraviolet emission lines of O and S near Io obtained over a number of years have measured the east-west asymmetry, but the long IUE integration times of approximately 7-14 hours masked any detection of system III variability. For the (O I) 6300-A emission, the O(1D) state may be excited by electron impact of atomic oxygen and by electron impact dissociation of SO. The molecule SO may be present at the exobase or may be produced above the exobase as the dominant product of SO2 dissociation by electron impact. Preliminary assessment indicates that production of O(1D) by molecular dissociation may be more important. The (O I) 6300-A emission may therefore provide a remote signature for monitoring (1) the upward transport rates of molecular species in Io's atmosphere, (2) the relative abundance and time-variable dissociation of SO2 and/or SO at the exobase and in the corona of Io, and (3) the spatial distribution of these escaping molecular and atomic species and their ion production rates in the planetary magnetosphere.

Scherb, F.↗

Use of TEMPO as a Proxy for Hyperspectral Geostationary Ocean Color Measurements from the GeoXO OCX Instrument: Harnessing Machine Learning and Principal Component Techniques for Atmospheric and Glint Correction

Retrievals of ocean color from space are important for better understanding the ocean ecosystem. The launch of atmospheric geostationary hyperspectral sensors such as TEMPO, provides a unique opportunity to examine the diurnal variability in ocean ecology. While TEMPO does not have as high spatial resolution or full spectral coverage as planned coastal ocean sensors such as the Geosynchronous Littoral Imaging and Monitoring Radiometer (GLIMR) or GeoXO Ocean Color instrument (OCX), its hourly measurements provide coverage of regions such as Lake Erie and the Gulf of Mexico at spatial scales of approximately 5 km. These data can be useful for testing new algorithms. We will apply our newly developed machine learning based atmospheric correction approach for ocean color retrievals to TEMPO data. Our approach begins by decomposing measured radiances from hyperspectral sensors into spectral features that describe the scattering and absorption of the atmosphere as well as the underlying surface reflectance. The coefficients of the principal components are then used to train a neural network to predict ocean color properties derived from collocated MODIS/VIIRS physically-based retrievals. This machine learning approach does not rely on radiative transfer modeling, and the use of MODIS/VIIRS data for training accounts for possible calibration b in hyperspectral data. Previously, we applied our approach using blue and UV wavelengths with the Ozone Monitoring Instrument (OMI) and TROPOspheric Monitoring Instrument (TROPOMI) to show that it can estimate ocean color properties in less-than-ideal conditions such as lightly to moderately clouded conditions as well as sun glint and thus improve the spatial coverage of ocean color measurements. TEMPO provides an opportunity to improve on this approach since it will provide collocated measurements at green and red wavelengths that were not available from OMI and TROPOMI and are important particularly for coastal waters. Additionally, our technique can be applied early in the mission and has potential to demonstrate the value of near real time ocean color products that are important for monitoring of harmful algae blooms and other oceanic phenomena.

Zachary Fasnacht↗

Recent Progress on Deep Blue Aerosol Algorithm as Applied TO MODIS, SEA WIFS, and VIIRS, and Their Intercomparisons with Ground Based and Other Satellite Measurements

The impact of natural and anthropogenic sources of aerosols has gained increasing attention from scientific communities in recent years. Indeed, tropospheric aerosols not only perturb radiative energy balance by interacting with solar and terrestrial radiation, but also by changing cloud properties and lifetime. Furthermore, these anthropogenic and natural air particles, once generated over the source regions, can be transported out of the boundary layer into the free troposphere and can travel thousands of kilometers across oceans and continents resulting in important biogeochemical impacts on the ecosystem. With the launch of SeaWiFS in 1997, Terra/MODIS in 1999, and Aqua/MODIS in 2002, high quality comprehensive aerosol climatology is becoming feasible for the first time. As a result of these unprecedented data records, studies of the radiative and biogeochemical effects due to tropospheric aerosols are now possible. In this talk, we will demonstrate how this newly available SeaWiFS/MODIS aerosol climatology can provide an important piece of puzzles in reducing the uncertainty of estimated climatic forcing due to aerosols. We will start with the global distribution of aerosol loading and their variabilities over both land and ocean on short- and long-term temporal scales observed over the last decade. The recent progress made in Deep Blue aerosol algorithm on improving accuracy of these Sea WiFS / MODIS aerosol products in particular over land will be discussed. The impacts on quantifying physical and optical processes of aerosols over source regions of adding the Deep Blue products of aerosol properties over bright-reflecting surfaces into Sea WiFS / MODIS as well as VIIRS data suite will also be addressed. We will also show the intercomparison results of SeaWiFS/MODIS retrieved aerosol optical thickness with data from ground based AERONET sunphotometers over land and ocean as well as with other satellite measurements. The trends observed in global aerosol loadings of both natural and anthropogenic sources based upon more than a decade of combined MODIS/SeaWiFS data (1997-2011) will be discussed. We will also address the importance of various key issues such as differences in spatial-temporal sampling rates and observation time between different satellite measurements could potentially impact these intercomparisons results, especially for using the monthly mean data, and thus on estimates of long-term aerosol trends.

Hsu, N. Christina↗

A preliminary study of the variability and magnitude of the flux of biogenic sulfur gases from a New Hampshire salt marsh

Salt marshes have highly variable spatial and temporal fluxes of hydrogen sulfide, carbonyl sulfide, methane thiol, dimethyl sulfide, and carbon disulfide (H2S, COS, MeSH, DMS, and CS2, respectively). This variability was tested at nine emission sites in a New Hampshire, USA salt marsh: three replicates in each of three vegetation zones, Spartina alterniflora, S. patens, and a transition zone. Three sites were sampled simultaneously, either within or across vegetation zones, using a dynamic flux chamber technique. Difficulties with calibration and field equipment resulted in fluxes with maximum absolute uncertainties of greater than plus or minus 200 percent. However, the relative uncertainty between subsequent samples was closer to plus or minus 20 percent. Chambers are expected to affect the natural flux of gases by altering the humidity, temperature, and composition of the gas inside the chamber. Summertime fluxes are highest for all gases except COS which demonstrated evidence of a springtime peak. A summertime background flux of 5 to 100 x 10(exp -9) g S/m(sup -2) min was observed for all gases, while S alternifora fluxes of MeSH and DMS were approximately 8 fold and approximately 100 fold higher than S. patens, respectively. DMS and MeSH fluxes were higher during the day than at night. Evidence of COS uptake by plants was observed. CS2 appeared to be the quantitatively least important sulfur gas emitted. Improved laboratory and sample collection techniques and further data collection in the field will yield information on the details of salt marsh variability, will improve estimates of the error associated with single flux measurements, and will allow a more accurate estimation of sulfur fluxes from salt marshes based on vegetation and area coverage data. Inability to control the temperature and humidity inside of the chamber remain significant problems with the chamber design.

Morrison, Michael Cope↗

An analysis of delamination in angle-ply fiber reinforced composites

An analytical investigation of the mechanics and failure modes of delamination initiated from a service-induced surface flaw in angle-ply fiber reinforced composites is presented. The analysis employs a hybrid-stress finite element method including a crack-tip singular element with its field variables expressed by Muskhelishvili's complex stress functions. Solutions are obtained for delaminated composites with various laminate parameters. The results elucidate unique and important characteristics of delamination crack-tip response and interlaminar stress transfer mechanisms. Of particular interest are the mixed-mode stress intensity factors associated with the delamination crack. The influence of ply orientation on KI and KII and their effects on subsequent crack extension are discussed.

Wang, S. S.↗

Role of the doubly stochastic Neyman type-A and Thomas counting distributions in photon detection

The sums of Meyman type-A and Thomas random variables are shown to retain their form under the constant multiplication parameter constraint. The conditions under which the two random variables converge in distribution to the fixed multiplicative Poisson, and to the Gaussian, are presented. It is shown that the latter result is important, in that it provides a solution to likelihood-ratio detection, estimation and discrimination problems in the presence of many kinds of signal and noise. Among the explicit applications presented are: (1) the photon-counter scintillation detection of nuclear particles when particle flux is low, (2) the photon-counting detection of weak optical signals in the presence of ionizing radiation, and (3) the design of a star-scanner spacecraft guidance system adequate for hostile space environments.

Teich, M. C.↗

Columbia River volcanism - The question of mantle heterogeneity or crustal contamination

It is found that, although crystal fractionation played an important role in producing the chemical characteristics of Columbia River Province basalts displaying a wide range of chemical and isotopic compositions, the isotopic variability calls for the involvement of at least two isotopically distinct components. The major and trace element characteristics of the main volume of the basalts are not consistent with a metasomatized mantle source region, and the presence of a primordial mantel component is not supported by the chemical data. Models of simple binary mixing between a primary magma and Precambrian sialic crustal materials, while satisfying the observed Nd and Sr isotopic variations, fail to account for major trace element abundances. The combination of crustal assimilation and fractional crystalization is found to give a superior fit to the compositional data.

Carlson, R. W.↗