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Interdisciplinary applications and interpretations of ERTS data within the Susquehanna River Basin (resource inventory, land use, and pollution)

The author has identified the following significant results. An interdisciplinary group at Penn State University is analyzing ERTS-1 data. The geographical area of interest is that of the Susquehanna River Basin in Pennsylvania. The objectives of the work have been to ascertain the usefulness of ERTS-1 data in the areas of natural resources and land use inventory, geology and hydrology, and environmental quality. Specific results include a study of land use in the Harrisburg area, discrimination between types of forest resources and vegetation, detection of previously unknown geologic faults and correlation of these with known mineral deposits and ground water, mapping of mine spoils in the anthracite region of eastern Pennsylvania, and mapping of strip mines and acid mine drainage in central Pennsylvania. Both photointerpretive techniques and automatic computer processing methods have been developed and used, separately and in a combined approach.

Mcmurtry, G. J.↗

The interpretation of simultaneous soft X-ray spectroscopic and imaging observations of an active region

Simultaneous soft X-ray spectroscopic and broad-band imaging observations of an active region have been analyzed together to determine the parameters which describe the coronal plasma. From the spectroscopic data, models of temperature-emission measure-elemental abundance have been constructed which provide acceptable statistical fits. By folding these possible models through the imaging analysis, models which are not self-consistent can be rejected. In this way, only the oxygen, neon, and iron abundances of Pottasch (1967), combined with either an isothermal or exponential temperature-emission-measure model, are consistent with both sets of data. Contour maps of electron temperature and density for the active region have been constructed from the imaging data. The implications of the analysis for the determination of coronal abundances and for future satellite experiments are discussed.

Davis, J. M.↗

Functional mapping reveals mechanistic clusters for OER catalysis across (Cu–Mn–Ta–Co–Sn–Fe)O x composition and pH space

Identification of stable electrocatalysts for the oxygen evolution reaction (OER) remains a primary challenge in materials for energy. The pH-dependent activity is known for very few catalysts, prompting our exploration of a broad range of catalysts using high throughput experiments and data science. This approach enables the largest screening of OER activity and operational stability to date, as illustrated through investigation of the (Cu-Mn-Ta-Co-Sn-Fe)O x composition space as 15 unique quaternary composition spaces. In total 2121 compositions are tested between pH 3 and 13, creating an extensive dataset whose interpretation requires development and application of data science to provide insights that are both beyond the standard composition-activity relationships and beyond human interpretation due to the dimensionality of the dataset. In this work, three distinct classes of OER catalysts are identified with respect to pH-dependent activity and stability. The large-scale screening reveals a new class of Co-rich OER catalysts that can be compositionally tailored to a specified pH and perform on par with state-of-the-art acid OER catalysts.

36 MATERIALS SCIENCE↗

New heavenly double copies

The double copy relates scattering amplitudes and classical solutions in Yang-Mills theory, gravity, and related field theories. Previous work has shown that this has an explicit realisation in self-dual YM theory, where the equation of motion can be written in a form that maps directly to Plebański’s heavenly equation for self-dual gravity. The self-dual YM equation involves an area-preserving diffeomorphism algebra, two copies of which appear in the heavenly equation. In this paper, we show that this construction is a special case of a wider family of heavenly-type examples, by (i) performing Moyal deformations, and (ii) replacing the area-preserving diffeomorphisms with a less restricted algebra. As a result, we obtain a double-copy interpretation for hyper-Hermitian manifolds, extending the previously known hyper-Kähler case. We also introduce a double-Moyal deformation of the heavenly equation. The examples where the construction of Lax pairs is possible are manifestly consistent with Ward’s conjecture, and suggest that the classical integrability of the gravity-type theory may be guaranteed in general by the integrability of at least one of two gauge-theory-type single copies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Gene content evolution in the arthropods

Background: Arthropods comprise the largest and most diverse phylum on Earth and play vital roles in nearly every ecosystem. Their diversity stems in part from variations on a conserved body plan, resulting from and recorded in adaptive changes in the genome. Dissection of the genomic record of sequence change enables broad questions regarding genome evolution to be addressed, even across hyper-diverse taxa within arthropods. Results: Using 76 whole genome sequences representing 21 orders spanning more than 500 million years of arthropod evolution, we document changes in gene and protein domain content and provide temporal and phylogenetic context for interpreting these innovations. We identify many novel gene families that arose early in the evolution of arthropods and during the diversification of insects into modern orders. We reveal unexpected variation in patterns of DNA methylation across arthropods and examples of gene family and protein domain evolution coincident with the appearance of notable phenotypic and physiological adaptations such as flight, metamorphosis, sociality, and chemoperception. Conclusions: These analyses demonstrate how large-scale comparative genomics can provide broad new insights into the genotype to phenotype map and generate testable hypotheses about the evolution of animal diversity.

Arthropods↗

Hints of a rotating spiral structure in the innermost regions around IRC +10216

The Atacama Large Millimeter/submillimeter Array is allowing us to study the innermost regions of the circumstellar envelopes of evolved stars with unprecedented precision and sensitivity. Key processes in the ejection of matter and dust from these objects occur in their inner zones. In this work, we present sub-arcsecond interferometric maps of transitions of metal-bearing molecules toward the prototypical C-rich evolved star IRC +10216. While Al-bearing molecules seem to be present as a roughly spherical shell, the molecular emission from the salts NaCl and KCl presents an elongation in the inner regions with a central minimum. In order to accurately analyze the emission from the NaCl rotational lines, we present new calculations of the collisional rates for this molecule based on new spectroscopic constants. The most plausible interpretation for the spatial distribution of the salts is a spiral with a NaCl mass of 0.08 M{sub ⊙}. Alternatively, a torus of gas and dust would result in structures similar to those observed. From the torus scenario we derive a mass of ∼1.1 × 10{sup −4} M{sub ⊙}. In both cases, the spiral and the torus, the NaCl structure presents an inner minimum of 27 AU. In the case of the torus, the outer radius is 73 AU. The kinematics of both the spiral and the torus suggests that they are slowly expanding and rotating. Alternative explanations for the presence of the elongation are explored. The presence of these features only in KCl and NaCl might be a result of their comparatively high dipole moment with respect to the Al-bearing species.

79 ASTRONOMY AND ASTROPHYSICS↗

THE CHARGE STATE OF POLYCYCLIC AROMATIC HYDROCARBONS ACROSS REFLECTION NEBULAE: PAH CHARGE BALANCE AND CALIBRATION

Low-resolution Spitzer spectral map data (>1700 spectra) of ten reflection nebulae (RNe) fields are analyzed using the data and tools available through the NASA Ames PAH IR Spectroscopic Database. The PAH emission is broken down into PAH charge state using a database fitting approach. Here, the physics of the PAH emission process is taken into account and uses target appropriate parameters, e.g., a stellar radiation model for the exciting star. The breakdown results are combined with results derived using the traditional PAH band strength approach, which interprets particular PAH band strength ratios as proxies for the PAH charge state, e.g., the 6.2/11.2 μ m PAH band strength ratio. These are successfully calibrated against their database equivalent; the PAH ionized fraction ( f {sub i} ). The PAH ionized fraction is converted into the PAH ionization parameter, which relates the PAH ionized fraction to the strength of the radiation field, gas temperature and electron density. The behavior of the 12.7 μ m PAH band is evaluated as a tracer for PAH ionization and erosion. The plot of the 8.6 versus 11.2 μ m PAH band strength for the northwest photo-dominated region (PDR) in NGC 7023 is shown to be a robust diagnostic template for the PAH ionized fraction. Remarkably, most of the other RNe fall within the limits set by NGC 7023. Finally, PAH spectroscopic templates are constructed and verified as principal components. Template spectra derived from NGC 7023 and NGC 2023 compare extremely well with each other, with those derived for NGC 7023 successfully reproducing the PAH emission observed from NGC 2023.

79 ASTRONOMY AND ASTROPHYSICS↗

Inventory and monitoring of natural vegetation and related resources in an arid environment: A comprehensive evaluation of ERTS-1 imagery

The author has identified the following significant results. A vegetation classification, with 31 types and compatible with remote sensing applications, was developed for the test site. Terrain features can be used to discriminate vegetation types. Elevation and macrorelief interpretations were successful on ERTS photos, although for macrorelief, high sun angle stereoscopic interpretations were better than low sun angle monoscopic interpretations. Using spectral reflectivity, several vegetation types were characterized in terms of patterns of signature change. ERTS MSS digital data were used to discriminate vegetation classes at the association level and at the alliance level when image contrasts were high or low, respectively. An imagery comparison technique was developed to test image complexity and image groupability. In two stage sampling of vegetation types, ERTS plus high altitude photos were highly satisfactory for estimating kind and extent of types present, and for providing a mapping base.

Schrumpf, B. J.↗

The Infrared Astronomical Satellite /IRAS/ Scientific Data Analysis System /SDAS/ sky flux subsystem

The sky flux subsystem of the Infrared Astronomical Satellite Scientific Data Analysis System is described. Its major output capabilities are (1) the all-sky lune maps (8-arcminute pixel size), (2) galactic plane maps (2-arcminute pixel size) and (3) regional maps of small areas such as extended sources greater than 1-degree in extent. The major processing functions are to (1) merge the CRDD and pointing data, (2) phase the detector streams, (3) compress the detector streams in the in-scan and cross-scan directions, and (4) extract data. Functional diagrams of the various capabilities of the subsystem are given. Although this device is inherently nonimaging, various calibrated and geometrically controlled imaging products are created, suitable for quantitative and qualitative scientific interpretation.

Stagner, J. R.↗

Search For Effects of an Electrostatic Potential on Clocks in the Frame of Reference of a Charged Particle

The Program Planning meeting was held on Jan 27-28 at the Washington University, Dept. of Physics. Experiment strategies and details were discussed and milestones mapped. Dr. Ringermacher, the program technical leader and Co-Principal Investigator, presented a Physics Department seminar on the theory and experiment in progress. Following the meeting Professor Conradi (CO-PI) and his students designed the NMR probe and electronics required for the experiment and submitted the drawings to the shop for fabrication. Dr. Cassenti, at UTRC, initiated analytic and computer analysis of the experimental conditions in order to anticipate possible classical effects. Dr. Ringermacher, at KRONOTRAN, re-evaluated the experiment interpretation from the theory and continued working to secure its underpinnings.

Ringermacher, Harry I.↗

Origins of Sinuous and Braided Channels on Ascraeus Mons, Mars - A Keck Geology Consortium Undergraduate Research Project

Water has clearly played an important part in the geological evolution of Mars. There are many features on Mars that were almost certainly formed by fluvial processes -- for example, the channels Kasei Valles and Ares Vallis in the Chryse Planitia area of Mars are almost certainly fluvial features. On the other hand, there are many channel features that are much more difficult to interpret -- and have been variously attributed to volcanic and fluvial processes. Clearly unraveling the details of the role of water on Mars is extremely important, especially in the context of the search of extinct or extant life. In this project we built on our recent work in determining the origin of one channel on the southwest rift apron of Ascraeus Mons. This project, funded by the Keck Geology Consortium and involving 4 undergraduate geology majors took advantage of the recently available datasets to map and analyze similar features on Ascraeus Mons and some other areas of Mars. A clearer understanding of how these particular channel features formed might lead to the development of better criteria to distinguish how other Martian channel features formed. Ultimately this might provide us with a better understanding of the role of volcanic and fluvial processes in the geological evolution of Mars.

de Wet, A. P.↗

An AERONET-Based Aerosol Classification Using the Mahalanobis Distance

We present an aerosol classification based on AERONET aerosol data from 1993 to 2012. We used the AERONET Level 2.0 almucantar aerosol retrieval products to define several reference aerosol clusters which are characteristic of the following general aerosol types: Urban-Industrial, Biomass Burning, Mixed Aerosol, Dust, and Maritime. The classification of a particular aerosol observation as one of these aerosol types is determined by its five-dimensional Mahalanobis distance to each reference cluster. We have calculated the fractional aerosol type distribution at 190 AERONET sites, as well as the monthly variation in aerosol type at those locations. The results are presented on a global map and individually in the supplementary material. Our aerosol typing is based on recognizing that different geographic regions exhibit characteristic aerosol types. To generate reference clusters we only keep data points that lie within a Mahalanobis distance of 2 from the centroid. Our aerosol characterization is based on the AERONET retrieved quantities, therefore it does not include low optical depth values. The analysis is based on point sources (the AERONET sites) rather than globally distributed values. The classifications obtained will be useful in interpreting aerosol retrievals from satellite borne instruments.

Hamill, Patrick↗

Confirmation of the Stellar Binary Microlensing Event, Macho 97-BLG-28

The high-magnification microlensing event MACHO-97-BLG-28 was previously determined to be a binary system composed of either two M dwarfs or an M dwarf and a brown dwarf. We present a revised light-curve model using additional data from the Mt. Stromlo 74″telescope, model estimates of stellar limb darkening, and fitting of the blend separately for each telescope and passband. We find a lensing system with a larger mass ratio, q=0.28±0.01, and smaller projected separation, s=0.61±0.01, than those presented in the original study. We revise the estimate of the lens–source relative proper motion to μ(rel)=2.8±0.5 mas/yr, which indicates that 16.07 yr after the event maximum the lens and source should have separated by 46±8 mas. We revise the radius of the source star using more recent reddening maps and angular diameter–color relations to R(*)=(10.3±1.9) R(ʘ). K- and J-band adaptive optics images of the field taken at this epoch using the NIRC2 imager on the Keck telescope show that the source and lens are still blended, consistent with our light-curve model. With no statistically significant excess flux detection we constrain the mass, M(L)=0.24 (+0.28, -0.12) M(ʘ), and distance, D(L)=7.0±1.0 kpc, of the lensing system. This supports the interpretation of this event as a stellar binary in the Galactic bulge. This lens mass gives a companion mass of M= 0.07(+0.08,-0.04) M(ʘ), close to the boundary between being a star and a brown dwarf.

W. Blackman↗

Robust Carbon Dioxide Plume Imaging Using Joint Tomographic Inversion of Seismic Onset Time and Distributed Pressure and Temperature Measurements (Final Report)

We develop and demonstrate rapid and cost-effective methodologies for spatiotemporal tracking of CO2 plumes during geologic sequestration using joint inversion of seismic data and distributed pressure and temperature measurements. Key elements of our methodology are: (a) a computationally efficient approach to pressure and temperature propagation, (b) analysis of time lapse seismic data using a novel ‘seismic onset time’ approach to detect fluid front propagation, and (c) data assimilation and uncertainty assessment via joint inversion of pressure, temperature and time lapse seismic data, and (d) validating the numerical tomographic inversion using a CO2 injection demonstration projects, specifically data collected from the from the Petra Nova Parish Holdings CCUS project in the West Ranch Field, Texas and the Chester-16 reef CO2 injection site in Northern Michigan which is part of the DOE Midwestern Carbon Sequestration Project. The research team is led by Texas A&M University and includes Battelle as a subcontractor with support from Shell, Anadarko, Chevron and JX Nippon. A carbon dioxide (CO2) water-alternating-gas (WAG) pilot was conducted to gain insights into tertiary oil recovery potential via CO2 flood in the West Ranch Field as part of the Petra Nova project, the world’s largest post-combustion CO2 capture and utilization initiative. With a fluvial formation geology and large contrasts in permeability, this is a challenging and novel application of CO2 enhanced oil recovery (EOR). We build a predictive dynamic model of the subsurface that incorporates the multiphase and compositional data acquired during the pilot operation. The calibrated model is used for the carbon dioxide plume imaging. The study began with an initialization of the pilot sector model extracted from a calibrated full-field model. The pilot model calibration follows a two-step hierarchical workflow. First, we performed a large-scale update of the permeability distribution by integrating available bottomhole pressure and multiphase production data. In the second step, local permeability field is fine-tuned using a streamline-based method to match CO2 breakthrough times at the producers. The predictive capability of the calibrated model was verified through two blind validation tests: (1) the model showed good agreement with saturation logs acquired at two observation wells; and (2) the model reproduced the CO2 recovery as a fraction of the injected CO2. The use of seismic onset times has shown great promise for integrating near-continuous seismic surveys for updating geologic models. In this study, we analyze the impact of seismic survey frequency on the onset time approach aiming to extend the application of onset time to infrequent seismic surveys. In addition, we quantitatively examine the nonlinearity of the onset time method and compare it to the commonly used amplitude inversion method. We carry out a sensitivity analysis of seismic survey frequency based on the complete seismic survey data (over 175 surveys) of steam injection in a heavy oil reservoir (Peace River Unit) in Canada. Our results show that an adequate onset time map can be obtained from the infrequent seismic surveys by interpolation between seismic surveys as long as there is no change in the dominant underlying physics between the successive surveys. The study also shows that nonlinearity of the onset time method can be -smaller than that of the amplitude inversion method by several orders of magnitude. Application to the Brugge benchmark case shows that the onset time method obtains comparable permeability update as the traditional seismic amplitude inversion method with faster computation and improved convergence characteristics. We extend the streamline-based data integration approach to incorporate distributed temperature sensor (DTS) data using the concept of thermal tracer travel time. Then, a hierarchical workflow composed of evolutionary and streamline methods is employed to jointly history match the DTS and pressure data. Finally, CO2 saturation and streamline maps are used to visualize the CO2 plume movement during the sequestration process. The hierarchical workflow is applied to a carbon sequestration project in a carbonate reef reservoir within the Northern Niagaran Pinnacle Reef Trend in Michigan, USA. The monitoring data set consists of distributed temperature sensing (DTS) data acquired at the injection well and a monitoring well, flowing bottom-hole pressure data at the injection well, and time-lapse pressure measurements at several locations along the monitoring well. The history matching results indicate that the CO2 movement is mostly restricted to the intended zones of injection which is consistent with an independent warm-back analysis of the temperature data. In addition to employing simulation models and inverse methods for CO2 plume imaging, we also initialized a data-driven technology for detecting inter-well connectivity based on production and pressure data. Our machine-learning framework is built on the statistical recurrent unit (SRU) model and interprets well-based injection/production data into inter-well connectivity without relying on a geologic model. We test it on synthetic and field-scale CO2 EOR projects utilizing the water-alternating-gas (WAG) process. The validation of the proposed data-driven inter-well connectivity assessment is performed using synthetic data from simulation models where inter-well connectivity can be easily measured using the streamline-based flux allocation. The SRU model is shown to offer excellent prediction performance on the synthetic case. Despite significant measurement noise and frequent well shut-ins imposed in the field-scale case, the SRU model offers good prediction accuracy, the overall relative error of the phase production rates at most producers ranges from 10% to 30%. It is shown that the dominant connections identified by the data-driven method and streamline method are in close agreement. Texas A&M University, the lead organization in the project, was primarily responsible for the development of tomographic approaches for CO2 plume mapping in conjunction with distributed pressure, temperature and seismic onset time data. Battelle, as a subcontractor, was primarily responsible for the development of analytical and empirical methods for analyzing transient injection rate and pressure data from point/line sources such as injection and monitoring wells. An additional area of emphasis for Battelle was the use of machine learning for such tasks as inferring reservoir connectivity information from injection-production data, and identifying variable importance for machine learning-based proxy models developed from full-physics simulations. The two organizations also collaborated on the application of the tomographic inversion methodology for a field data set.

02 PETROLEUM↗

Photoinduced coherent acoustic phonon dynamics inside Mott insulator Sr 2 IrO 4 films observed by femtosecond X-ray pulses

We investigate the transient photoexcited lattice dynamics in a layered perovskite Mott insulator Sr 2 IrO 4 film by femtosecond X-ray diffraction using a laser plasma-based X-ray source. The ultrafast structural dynamics of Sr 2 IrO 4 thin films are determined by observing the shift and broadening of (0012) Bragg diffraction after excitation by 1.5 eV and 3.0 eV pump photons for films with different thicknesses. The observed transient lattice response can be well interpreted as a distinct three-step dynamics due to the propagation of coherent acoustic phonons generated by photoinduced quasiparticles (QPs). Employing a normalized phonon propagation model, we found that the photoinduced angular shifts of the Bragg peak collapse into a universal curve after introducing normalizedn coordinates to account for different thicknesses and pump photon energies, pinpointing the origin of the lattice distortion and its early evolution. In addition, we report a transient photocurrent measurement indicates that the photoinduced QPs are charge neutral excitons. Mapping the phonon propagation and correlating its dynamics with the QP by ultrafast X-ray diffraction (UXRD) establish a powerful way to study electron-phonon coupling and uncover the exotic physics in strongly correlated systems under nonequilibrium conditions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Central and Eastern North America Ground-Motion Characterization (NGA-East)

This document is the final project report of the Next Generation Attenuation for Central and Eastern North America (CENA) project (NGA-East). The NGA-East objective was to develop a new ground-motion characterization (GMC) model for the CENA region. The GMC model consists of a set of new ground-motion models (GMMs) for median and standard deviation of ground motions and their associated weights to be used with logic-trees in probabilistic seismic hazard analyses (PSHA). NGA-East is a large multidisciplinary project coordinated by the Pacific Earthquake Engineering Research Center (PEER), at the University of California. The project has two components: (1) a set of scientific research tasks, and (2) a model-building component following the framework of the “Seismic Senior Hazard Analysis Committee (SSHAC) Level 3” (Budnitz et al. 1997; NRC 2012). Component (2) is built on the scientific results of component (1) of the NGA-East project. This report documents the tasks under component (2) of the project. Under component (1) of NGA-East, several scientific issues were addressed, including: (a) development of a new database of ground motion data recorded in CENA; (b) development of a regionalized ground-motion map for CENA, (c) definition of the reference site condition; (d) simulations of ground motions based on different methodologies; and (e) development of numerous GMMs for CENA. The scientific tasks of NGA-East were all documented as a series of PEER reports. The scope of component (2) of NGA-East was to develop the complete GMC. This component was designed as a SSHAC Level 3 study with the goal of capturing the ground motions’ center, body, and range of the technically defensible interpretations in light of the available data and models. The SSHAC process involves four key tasks: evaluation, integration, formal review by the Participatory Peer Review Panel (PPRP), and documentation (this report). Key tasks documented in this report include review and evaluation of the empirical groundmotion database, the regionalization of ground motions, and screening sets of candidate GMMs. These are followed by the development of new median and standard deviation GMMs, the development of new analyses tools for quantifying the epistemic uncertainty in ground motions, and the documentation of implementation guidelines of the complete GMC for PSHA computations. Appendices include further documentation of the relevant SSHAC process and additional supporting technical documentation of numerous sensitivity analyses results. The PEER reports documenting component (1) of NGA-East are also considered “attachments” to the current report and are all available online on the PEER website (https://peer.berkeley.edu/). The final NGA-East GMC model includes a set of 17 GMMs defined for 24 ground-motion intensity measures, applicable to CENA in the moment magnitude range of 4.0 to 8.2 and covering distances up to 1500 km. Standard deviation models are also provided for site-specific analysis (single-station standard deviation) and for general PSHA applications (ergodic standard deviation). Adjustment factors are provided for consideration of source-depth effects and hanging-wall effects, as well as for hazard computations at sites in the Gulf Coast region.

58 GEOSCIENCES↗

Radio and X-ray observations of the radio halo source in A1367

Radio and X-ray observations of the 'radio halo' in A1367 are presented. The radio spectral index distribution is derived combining data at 610 and 1415 MHz taken with the Westerbork Synthesis Radio Telescope (WSRT). A high-resolution Very Large Array (VLA) map allows us to discriminate between the extended cluster emission and a triple radio source associated with a background stellar object (most probably a QSO) which appears projected onto it. X-ray observations taken with the high-resolution imager on board the Einstein satellite reveal an X-ray source associated with this background object. A second weak X-ray enhancement is found projected onto the extended radio component. Inverse Compton scattering of the synchrotron-emitting particles provides a possible interpretation of such a source. The presence of large-scale magnetic fields and particle acceleration due to the turbulent motion of galaxies through the intergalactic medium is discussed in relationship to the observed peculiarities of the galaxies found in this region.

Gavazzi, G.↗

Minimal upper mantle temperature variations consistent with observed heat flow and plate velocities

Heat-flow and plate-velocity measurements are used to model upper-mantle temperature variations; the results are intended to form the basis for a gravity-field-variation model and are also applicable to the interpretation of petrological and seismological data. A 5-deg grid is used, a depth of 280 km is chosen as the fully convecting level, and it is assumed that 85 percent of the global heat production (4.0 x 10 to the 13th W) comes from below this level. The velocity field is calculated by integrating the momentum equations down to 280 km (assuming laterally homogeneous viscosity and density) and then used to determine the temperature fields. The results are presented in graphs, tables, and maps. The largest lateral temperature differences are about 1500 C and occur in the top 20 km, where the largest (about 200 C/Myr) nonlinear terms of the energy equation are also found. Below 50 km, heat transfer becomes more convective than conductive, and the most significant temperature variation appears in the form of negative 'tongues' as cold as -825 C at about 100 km. Temperature variations of at least + or - 180 C are calculated at the fully convecting level.

Kaula, W. M.↗