Search NASASearch

SEARCH · Search NASA

Results for “Radiation processing”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

The Iron Project

Recent advances in theoretical atomic physics have enabled large-scale calculation of atomic parameters for a variety of atomic processes with high degree of precision. The development and application of these methods is the aim of the Iron Project. At present the primary focus is on collisional processes for all ions of iron, Fe I - FeXXVI, and other iron-peak elements; new work on radiative processes has also been initiated. Varied applications of the Iron Project work to X-ray astronomy are discussed, and more general applications to other spectral ranges are pointed out. The IP work forms the basis for more specialized projects such as the RmaX Project, and the work on photoionization/recombination, and aims to provide a comprehensive and self-consistent set of accurate collisional and radiative cross sections, and transition probabilities, within the framework of relativistic close coupling formulation using the Breit-Pauli R-Matrix method. An illustrative example is presented of how the IP data may be utilized in the formation of X-ray spectra of the K alpha complex at 6.7 keV from He-like Fe XXV.

Pradhan, Anil K.

Radio wavelength observations of magnetic fields on active dwarf M, RS CVn and magnetic stars

The dwarf M stars, YZ Canis Minoris and AD Leonis, exhibit narrow-band, slowly varying (hours) microwave emission that cannot be explained by conventional thermal radiation mechanisms. The dwarf M stars, AD Leonis and Wolf 424, emit rapid spikes whose high brightness temperatures similarly require a nonthermal radiation process. They are attributed to coherent mechanisms such as an electron-cyclotron maser or coherent plasma radiation. If the electron-cyclotron maser emits at the second or third harmonic gyrofrequency, the coronal magnetic field strength equals 250 G or 167 G, and constraints on the plasma frequency imply an electron density of 6 x 10 to the 9th/cu cm. Radio spikes from AD Leonis and Wolf 424 have rise times less than or equal to 5 ms, indicating a linear size of less than or equal to 1.5 x 10 to the 8th cm, or less than 0.005 of the stellar radius. Although Ap magnetic stars have strong dipole magnetic fields, they exhibit no detectable gyroresonant radiation, suggesting that these stars do not have hot, dense coronae. The binary RS CVn star UX Arietis exhibits variable emission at 6 cm wavelength on time scales ranging from 30 s to more than one hour.

Lang, Kenneth R.

Enhancing the Design Process for Complex Space Systems through Early Integration of Risk and Variable-Fidelity Modeling

An important enabler of the new national Vision for Space Exploration is the ability to rapidly and efficiently develop optimized concepts for the manifold future space missions that this effort calls for. The design of such complex systems requires a tight integration of all the engineering disciplines involved, in an environment that fosters interaction and collaboration. The research performed under this grant explored areas where the space systems design process can be enhanced: by integrating risk models into the early stages of the design process, and by including rapid-turnaround variable-fidelity tools for key disciplines. Enabling early assessment of mission risk will allow designers to perform trades between risk and design performance during the initial design space exploration. Entry into planetary atmospheres will require an increased emphasis of the critical disciplines of aero- and thermodynamics. This necessitates the pulling forward of EDL disciplinary expertise into the early stage of the design process. Radiation can have a large potential impact on overall mission designs, in particular for the planned nuclear-powered robotic missions under Project Prometheus and for long-duration manned missions to the Moon, Mars and beyond under Project Constellation. This requires that radiation and associated risk and hazards be assessed and mitigated at the earliest stages of the design process. Hence, RPS is another discipline needed to enhance the engineering competencies of conceptual design teams. Researchers collaborated closely with NASA experts in those disciplines, and in overall space systems design, at Langley Research Center and at the Jet Propulsion Laboratory. This report documents the results of this initial effort.

Mavris, Dimitri

Relative Sputtering Rates of FeS, MgS, and Mg Silicates: Implications for ISM Gas Phase Depletions of Rock-Forming Elements

Astronomical measurements of S abundances in the diffuse interstellar medium (ISM) indicate ionized S is a dominant species with little (< 5%) S residing in grains (e.g. Jenkins 2009). This is an enigmatic result, given that abundant Fe-sulfide grains are observed in dust around pre- and post-main sequence stars and are also observed as major components of primitive meteoritic and cometary samples. These disparate observations suggest that the lifetime of sulfide grains in the ISM is short because of destruction processes. Our previous work has shown that FeS and MgS retain their crystallinity and do not amorphize during radiation processing, whereas enstatite and forsterite are readily amorphized. We have extended this study to measure the relative sputtering rates of FeS and MgS compared to enstatite and forsterite. Irradiation of FeS with 4 keV He+ results in preferential sputtering of S and the formation of a thin 2-3 nm, compact Fe metal layer that armors the surface. The zone of S loss extends to a depth of ~8-10 nm below the exposed surface. Despite this S loss, the FeS retains its crystallinity and shows no sign of incipient amorphization. Irradiation of FeS with 5kV Ga+ in a focused ion beam (FIB) instrument resulted in preferential sputtering of S and the formation of a 5-8-nm thick surface layer of nanophase Fe metal. X-ray mapping shows that the zone of S sputtering extends to a depth of nearly 20 nm, but there is no evidence for FeS amorphization, consistent with our previous work. The irradiation experiments show that the relative sputtering rate of FeS and MgS are much higher than olivine or enstatite. Sputtering experiments utilizing 30 kV and 5 kV Ga ions in the FIB produced volume loss in troilite that was ~4X greater than in enstatite or forsterite. The sputter yield under these conditions is such that for every Si atom sputtered from enstatite, ~14 S atoms are sputtered from FeS. We have performed similar sputtering experiments on Fe-bearing niningerite (MgS) and co-existing enstatite from the ALH 84170 EH3 chondrite. MgS also sputters much more rapidly than enstatite with a relative Si:S sputter yield of 1:8. For MgS, sulfur is highly depleted at the surface and the S-depletion zone extends to a depth of ~15 nm (using 5 kV Ga+). There is a corresponding zone of Mg and especially Fe enrichment that extends from 5 to ~10 nm below the surface, respectively. The dominant grain destruction mechanism in the ISM is sputtering from passage of supernova-generated shock waves. This process also results in the amorphization of crystalline silicates in the ISM. Our results indicate that FeS and MgS grains produced in evolved stars and injected into the ISM will be destroyed more rapidly than crystalline silicates. This process may account for the lack of significant depletion of S from the gas phase in the ISM. However, rare nanophase FeS grains occur as inclusions in circumstellar amorphous silicate grains found in comet dust particles analyzed in the laboratory. These results show that a finite amount of S in the ISM is sequestered in solid grains.

SPUTTERING RATES

Radiative heating-cooling and the energetics of the stratosphere and mesosphere

The principal research activities of the period 1983-1986 directed towards the development of models of middle-atmospheric chemistry and dynamics are described. One of these activities concerns parameterization of IR radiative processes, particularly parameterization for the CO2 15-micron-band emission and absorption, for which various models are discussed. The second line of research centers on the radiative balance in the middle atmosphere and the net radiative drive for the diabatic residual or transport circulation. Finally, theoretical and observational studies of radiative damping of waves propagating through the middle atmosphere, and the parameterization of this process, are discussed.

Strobel, Darrell F.

Cloud 3D Effects Evidenced in Landsat Power Spectra and Autocorrelation Functions

An analysis of nadir reflectivity Fourier spatial power spectra and autocorrelation functions at solar wavelengths and for cloudy conditions has been carried out. The data come from Landsat Thematic Mapper (TM) observations, while Monte Carlo (MC) simulations are used to aid the interpretation of the Landsat results. We show that radiative processes produce consistent signatures on power spectra and autocorrelation functions. The former take a variety of forms not shown or explained in previous observational studies. We demonstrate that the TM spectra can potentially be affected by both radiative "roughening" at intermediate scales (approx. 1 -5 km), being more prevalent at large solar zenith angles, and the already documented radiative "smoothing" at small scales (less than 1 km). These processes are wavelength dependent, as shown by systematic differences between conservative (for cloud droplets) TM band 4 (approx. 0.8 microns) and absorbing band 7 (approx. 2.2 microns): band 7 exhibits more roughening and less smoothing. This is confirmed quantitatively by comparing least-squared fitted power spectral slopes for the two bands. It is also corroborated by a slower decrease with distance of autocorrelation function values for band 4 compared to band 7. The appearance of roughening at large solar zenith angles is a result of side illumination and shadowing and adds an additional complexity to the power spectra. MC spectra are useful in illustrating that scale invariant optical depth fields can produce complex power spectra that take a variety of shapes under different conditions. We show that radiative roughening increases with the decrease of single scattering albedo and with the increase of solar zenith angle (as in the observations). For high Sun there is also a clear shift of the radiative smoothing scale to smaller values as droplet absorption increases. The shape of the power spectrum is sensitive to the magnitude and type of cloud top height variability, with the spectral signatures of decorrelation between reflectance and optical depth at large scales becoming stronger as the magnitude of cloud top variations increase. Finally, the usefulness of power spectral analysis in evaluating the skill of novel optical depth retrieval techniques in removing 3D radiative effects is demonstrated. New techniques using inverse Non-local Independent Pixel Approximation (NIPA) and Normalized Difference of Nadir Reflectivity (NDNR) yield optical depth fields which better match the scale-by-scale variability of the true optical depth field.

Oreopoulos, Lazaros

Using Multi-scale Modeling System to Study the Interactions between Clouds, Precipitation, Aerosols, Radiation and Land Surface

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 kilometers, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-kilometer scales are resolved in horizontal domains as large as 10,000 kilometers in two-dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. A review of developments, improvements and applications of cloud models (GCE and WRF) at Goddard will be presented in this talk. In particular, a new approach to using multi-scale modeling system to study the interactions between clouds, precipitation, aerosols and land will be presented.

Tao, Wei-Kuo

Using Multi-scale Modeling System to Study the Interactions between Clouds, Precipitation, Aerosols, Radiation and Land Surface

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 kilometers, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial-lkm scales are resolved in horizontal domains as large as 10,000 kilometers in two-dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. A review of developments, improvements and applications of cloud models (GCE and WRF) at Goddard wlll be is presented in this talk. In particular, a new approach to using multi-scale modeling system to study the interactions between clouds, precipitation, aerosols and land will be presented.

Tao, Wei-Kuo

Using Multi-scale Modeling System to Study the Interactions between Clouds, Precipitation, Aerosols, Radiation and Land Surface

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 km, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 sq km in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. A review of developments, improvements and applications of cloud models (GCE and WRF) at Goddard will be presented in this talk. In particular, a new approach to using multi-scale modeling system to study the interactions between clouds, precipitation, aerosols and land will be presented.

Tao, Wei-Kuo

The influence of autoionization accompanied by excitation on dielectronic recombination and ionization equilibrium

In the process of dielectronic recombination, the doubly excited state formed by radiationless capture may autoionize preferentially into an excited state of the recombining ion. This additional autoionization process has not been discussed in previous treatments of dielectronic recombination. The dielectronic recombination rates for certain nonhydrogenic Fe ions, although still larger than the direct radiative recombination rates, are found to be substantially reduced by the inclusion of the additional autoionization rate in the branching ratio for the stabilizing radiative transition. Consequently, the temperatures of maximum equilibrium abundance are significantly lower than those predicted by recent calculations. Finally, the radiative energy loss rate coefficients are calculated for radiation processes involving electron Fe-ion collisions in high-temperature plasmas. Electron impact excitation of resonance line radiation is the dominant radiative cooling mechanism in steady-state plasmas at temperatures where ions with bound electrons are abundant. However, it is found that the radiation emitted during dielectronic recombination can be more important than direct recombination radiation and bremsstrahlung.

Jacobs, V. L.

Microphysics, Radiation and Surface Processes in the Goddard Cumulus Ensemble (GCE) Model

The response of cloud systems to their environment is an important link in a chain of processes responsible for monsoons, frontal depression, El Nino Southern Oscillation (ENSO) episodes and other climate variations (e.g., 30-60 day intra-seasonal oscillations). Numerical models of cloud properties provide essential insights into the interactions of clouds with each other, with their surroundings, and with land and ocean surfaces. Significant advances are currently being made in the modeling of rainfall and rain-related cloud processes, ranging in scales from the very small up to the simulation of an extensive population of raining cumulus clouds in a tropical- or midlatitude-storm environment. The Goddard Cumulus Ensemble (GCE) model is a multi-dimensional nonhydrostatic dynamic/microphysical cloud resolving model. It has been used to simulate many different mesoscale convective systems that occurred in various geographic locations. In this paper, recent GCE model improvements (microphysics, radiation and surface processes) will be described as well as their impact on the development of precipitation events from various geographic locations. The performance of these new physical processes will be examined by comparing the model results with observations. In addition, the explicit interactive processes between cloud, radiation and surface processes will be discussed.

Tao, Wei-Kuo

Present state of knowledge of the upper atmosphere: An assessment report; processes that control ozone and other climatically important trace gases

The state of knowledge of the upper atmosphere was assessed as of January 1986. The physical, chemical, and radiative processes which control the spatial and temporal distribution of ozone in the atmosphere; the predicted magnitude of ozone perturbations and climate changes for a variety of trace gas scenarios; and the ozone and temperature data used to detect the presence or absence of a long term trend were discussed. This assessment report was written by a small group of NASA scientists, was peer reviewed, and is based primarily on the comprehensive international assessment document entitled Atmospheric Ozone 1985: Assessment of Our Understanding of the Processes Controlling Its Present Distribution and Change, to be published as the World Meteorological Organization Global Ozone Research and Monitoring Project Report No. 16.

Watson, R. T.

Radiation hardened PMOS process with ion implanted threshold adjust

By including specific process modifications the effect of ion implantation on radiation hardness can be minimized and radiation hard ion implanted MOS circuits can be fabricated. The experimental procedure followed was to examine key processing steps (with respect to radiation hardness) on ion-implanted individual PMOS transistors. The individual transistors were evaluated by continuously monitoring the threshold voltage as the transistors were being irradiated. By comparing runs it was possible to deduce what is considered a radiation hard ion implanted process. Tests with a complex LSI PMOS IC processor chip containing over 2000 transistors and resistors were also conducted

Jhabvala, M.

Clouds in ECMWF's 30 KM Resolution Global Atmospheric Forecast Model (TL639)

Global models of the general circulation of the atmosphere resolve a wide range of length scales, and in particular cloud structures extend from planetary scales to the smallest scales resolvable, now down to 30 km in state-of-the-art models. Even the highest resolution models do not resolve small-scale cloud phenomena seen, for example, in Landsat and other high-resolution satellite images of clouds. Unresolved small-scale disturbances often grow into larger ones through non-linear processes that transfer energy upscale. Understanding upscale cascades is of crucial importance in predicting current weather, and in parameterizing cloud-radiative processes that control long term climate. Several movie animations provide examples of the temporal and spatial variation of cloud fields produced in 4-day runs of the forecast model at the European Centre for Medium-Range Weather Forecasts (ECMWF) in Reading, England, at particular times and locations of simultaneous measurement field campaigns. model resolution is approximately 30 km horizontally (triangular truncation TL639) with 31 vertical levels from surface to stratosphere. Timestep of the model is about 10 minutes, but animation frames are 3 hours apart, at timesteps when the radiation is computed. The animations were prepared from an archive of several 4-day runs at the highest available model resolution, and archived at ECMWF. Cloud, wind and temperature fields in an approximately 1000 km X 1000 km box were retrieved from the archive, then approximately 60 Mb Vis5d files were prepared with the help of Graeme Kelly of ECMWF, and were compressed into MPEG files each less than 3 Mb. We discuss the interaction of clouds and radiation in the model, and compare the variability of cloud liquid as a function of scale to that seen in cloud observations made in intensive field campaigns. Comparison of high-resolution global runs to cloud-resolving models, and to lower resolution climate models is leading to better understanding of the upscale cascade and suggesting new cloud-radiation parameterizations for climate models.

Cahalan, R. F.

Radio and infrared properties of young stars

Observing young stars, or more appropriately, pre-main-sequence (PMS) stars, in the infrared and at radio frequencies has the advantage over optical observation in that the heavy extinction associated with a star forming region is only a minor problem, so that the whole region can be studied thoroughly. Therefore, it means being able to: (1) search for stars and do statistical studies on the rate of star formation; (2) determine their luminosity, hence, to study luminosity functions and initial mass functions down to low masses; and (3) to study their spectra and, thus, to determine the prevailing conditions at and near the surface of a newly born star and its relations with the surrounding environment. The third point is of principal interest. The report limits itself to a consideration of the observations concerning the processes of outflows from, and accretion onto, PMS stars and the theory necessary to interpret them. Section 2 discusses the radiative processes relevant in stellar outflows. The main observational results are presented in Section 3. A discussion of the statistical properties of stellar winds from PMS stars are given in Section 4.

Panagia, Nino

Mach wave emission from a high temperature supersonic jet

The paper considers the compressible Rayleigh equation as a model for the Mach wave emission mechanism associated with high temperature supersonic jets. Solutions to the compressible Rayleigh equation reveal the existence of several families of supersonically convecting instability waves. These waves directly radiate noise to the jet far field. The predicted noise characteristics are compared to previously acquired experimental data for an axisymmetric Mach 2 fully pressure balanced jet operating over a range of jet operating total temperatures from ambient to 1370 K. The results of this comparison show that the first order supersonic instability wave and the Kelvin-Helmholtz first, second, and third order modes have directional radiation characteristics that are in agreement with observed data. The assumption of equal initial amplitudes for all of the waves leads to the conclusion that the flapping mode of instability dominates the noise radiation process of supersonic jets. At a jet temperature of 1370 K, supersonic instability waves are predicted to dominate the noise radiated at high frequency at narrow angles to the jet axis.

Seiner, J. M.

Sensitivities of Modeled Tropical Cyclones to Surface Friction and the Coriolis Parameter

In this investigation the sensitivities of a 2-D tropical cyclone (TC) model to surface frictional coefficient and the Coriolis parameter are studied and their implication is discussed. The model used is an axisymmetric version of the latest version of the Goddard cloud ensemble model. The model has stretched vertical grids with 33 levels varying from 30 m near the bottom to 1140 m near the top. The vertical domain is about 21 km. The horizontal domain covers a radius of 962 km (770 grids) with a grid size of 1.25 km. The time step is 10 seconds. An open lateral boundary condition is used. The sea surface temperature is specified at 29C. Unless specified otherwise, the Coriolis parameter is set at its value at 15 deg N. The Newtonian cooling is used with a time scale of 12 hours. The reference vertical temperature profile used in the Newtonian cooling is that of Jordan. The Newtonian cooling models not only the effect of radiative processes but also the effect of processes with scale larger than that of TC. Our experiments showed that if the Newtonian cooling is replaced by a radiation package, the simulated TC is much weaker. The initial condition has a temperature uniform in the radial direction and its vertical profile is that of Jordan. The initial winds are a weak Rankin vortex in the tangential winds superimposed on a resting atmosphere. The initial sea level pressure is set at 1015 hPa everywhere. Since there is no surface pressure perturbation, the initial condition is not in gradient balance. This initial condition is enough to lead to cyclogenesis, but the initial stage (say, the first 24 hrs) is not considered to resemble anything observed. The control experiment reaches quasi-equilibration after about 10 days with an eye wall extending from 15 to 25 km radius, reasonable comparing with the observations. The maximum surface wind of more than 70 m/s is located at about 18 km radius. The minimum sea level pressure on day 10 is about 886 hPa. Thus the overall simulation is considered successful and the model is considered adequate for our investigation.

Chao, Winston C.

The use of satellite data in understanding and predicting convective and large-scale dynamical processes

A two-layer truncated baroclinic spectral model was developed to study the long-term evolution of disturbances to a baroclinically unstable mean flow. Topography and crudely-parameterized radiative processes were accounted for. As a result of Robert Schlaak's discovery of the underlying barotropic nature of the index oscillation as well as reviewers suggestions about the original manuscript, the model has been revised to allow for barotropic as well as baroclinic wave-mean flow interactions. The form-drag exerted by the topography on the barotropic part of the mean flow is larger than on the baroclinic part and thus researchers anticipate significant changes from the original calculations on the index oscillation when it is strongly modulated by topography. Researchers believe that since the index oscillation accounts for a significant portion of atmospheric temporal variance, the long term predictability could be improved if reliable forecasts of the index oscillation were available. Two spectral models of the index oscillation, one barotropic and the other baroclinic, have been developed. The latter allows for moisture, radiation, land-sea temperature countrasts, and energy exchanges with the underlying surface.

Dutton, J. A.