Radiative Flux Divergence Research Articles

A first order mixing–condensation scheme for nocturnal stratocumulus

A simple closure scheme for nocturnal stratocumulus is proposed. The scheme is formulated in conserved variables. Cloud fraction and cloud water amount are diagnosed assuming a top-hat distribution for total water. Conversion of cloud water into rain water is parameterized in terms of cloud water and the incoming rain flux. Turbulence transport in the cloud layer is accounted for by a first-order vertical diffusion scheme with a profile-type diffusivity. The length scale corresponds to the thickness of the cloud layer. The turbulent velocity scale is directly related to the long wave radiative flux divergence in the cloud. Entrainment at cloud top is implicitly treated by extending the in-cloud mixing profile slightly beyond cloud top. The excess height is derived from the buoyancy frequency at cloud top and a radiative–convective velocity scale. The scheme is capable of simulating realistic profiles of the conserved variables and cloud parameters for a case of nocturnal stratocumulus prepared on the basis of ASTEX data.

COMPARISON OF THE DISCRETE TRANSFER AND MONTE CARLO METHODS FOR RADIATIVE HEAT TRANSFER IN THREE-DIMENSIONAL NONHOMOGENEOUS SCATTERING MEDIA

Modified formulations of the discrete transfer and Monte Carlo methods are presented for the prediction of radiative heat transfer in three-dimensional nonhomogeneous participating media. Numerical solutions found with both algorithms are in good agreement with published benchmark results, which used contemporary methods to determine the radiative transport in a unit cube. New solutions in an arbitrary L-shaped geometry using a nonorthogonal body-fitted mesh are also presented. The average deviation between the two methods is less than 1.2% for both the boundary surface flux and the divergence of radiative flux or gas emissive power within the enclosed, isotropically scattering media.

Boundary Layer Evolution within a Canyonland Basin. Part I: Mass, Heat, and Moisture Budgets from Observations

Abstract Individual terms of the mass, heat, and moisture budget equations are evaluated for an atmospheric control volume in Colorado's Sinbad Basin using tethered balloon and surface energy budget data obtained during a 16.5-h period on 15–16 July 1988. The basin was chosen for its simple topography and arid climate, which simplified the evaluation of some of the budget terms. The paper documents the many assumptions that are required to evaluate the mass, heat, and moisture budget equations in confined terrain using small datasets. The nighttime outflow of air from the basin produced a compensatory mean sinking motion of 0.026 m s−1 at the top of the basin control volume and brought warm air into the top of the basin atmosphere. In contrast to previous reports for well-drained valleys, a high rate of atmospheric cooling continued in this basin throughout the entire night. The cooling is attributed primarily to turbulent sensible heat flux divergence and, to a lesser extent, radiative flux divergence. M...

Determination of Clear-Sky Radiative Flux Profiles, Heating Rates, and Optical Depths Using Unmanned Aerospace Vehicles as a Platform

Abstract In this paper the authors report results obtained using an unmanned aerospace vehicle (UAV) as an experimental platform for atmospheric radiative transfer research. These are the first ever climate measurements made from a UAV and represent a major step forward in realizing the unique potential of long-endurance, high-altitude UAVs to contribute to climate and environmental studies. Furthermore, the radiative flux divergences determined during these experiments are some of the highest quality measurements of this kind obtained from any type of aircraft and constitute an important test of radiative transfer models.

Radiative heating and the buoyant rise of magnetic flux tubes in the solar interior

We study the effect of radiative heating on the evolution of thin magnetic flux tubes in the solar interior and on the eruption of magnetic flux loops to the surface. Magnetic flux tubes experience radiative heating because (1) the mean temperature gradient in the lower convection zone and the overshoot region deviates substantially from that of radiative equilibrium, and hence there is a non-zero divergence of radiative heat flux; and (2) the magnetic pressure of the flux tube causes a small change of the thermodynamic properties within the tube relative to the surrounding field-free fluid, resulting in an additional divergence of radiative heat flux. Our calculations show that the former constitutes the dominant source of radiative heating experienced by the flux tube. In the overshoot region, the radiative heating is found to cause a quasi-static rising of the toroidal flux tubes with an upward drift velocity ∼ 10-3|δ| cm s-1, where δ ≡ ∇e − ∇ad < 0 describes the subadiabaticity in the overshoot layer. The upward drift velocity does not depend sensitively on the field strength of the flux tubes. Thus in order to store toroidal flux tubes in the overshoot region for a period comparable to the length of the solar cycle, the magnitude of the subadiabaticity δ(< 0) in the overshoot region must be as large as ∼ 3 × 10−4. We discuss the possibilities for increasing the magnitude of δ and for reducing the rate of radiative heating of the flux tubes in the overshoot region. Using numerical simulations we study the formation of ‘Ω’-shaped emerging loops from toroidal flux tubes in the overshoot region as a result of radiative heating. The initial toroidal tube is assumed to be non-uniform in its thermodynamic properties along the tube and lies at varying depths beneath the base of the convection zone. The tube is initially in a state of neutral buoyancy with the internal density of the tube plasma equal to the local external density. We find from our numerical simulations that such a toroidal tube rises quasi-statically due to radiative heating. The top portion of the nonuniform tube first enters the convection zone and may be brought to an unstable configuration which eventually leads to the eruption of an anchored flux loop to the surface. Assuming reasonable initial parameters, our numerical calculations yield fairly short rise times (2–4 months) for the development of the emerging flux loops. This suggests that radiative heating is an effective way of causing the eruption of magnetic flux loops, leading to the formation of active regions at the surface.

Role of radiative transfer in maintenance and destruction of stratocumulus clouds

A mesoscale numerical model is used to study the physical processes in the maintenance of a stratocumulus topped boundary layer. The model includes a surface energy budget, closure using a scheme based on the turbulence kinetic energy, a five category cloud physics scheme and radiative transfer. Model results demonstrate the role radiative flux divergence plays in the maintenance of a stratocumulus layer. Radiative heating and cooling of the cloud layer destabilizes the upper boundary layer and decouples that portion of the boundary layer from the surface layer. Eventually, sufficient solar radiation reaches the surface to overcome the decoupling and the cloud layer dissipates.

Basic Physics and Numerical Modelling of Climate

Despite the basic significance of the environment to many needs of Mission Earth and humans, attainable climate models are likely to provide only general guidance to world simulation in the desirable time-frame, not detailed changes and statistical properties. Some aspects of climate simulation, however, illustrate difficulties that may appear in other large-scale, complicated simulations. The fundamental physics of atmospheric waves, their forcing functions and their interactions are described. As a thermodynamically open system, the atmosphere is not very close to macroscopic local detailed balance. There are interactions across many scales of physics, particularly in the budgets of latent heat and radiative flux divergence. The carbon dioxide stored in the ocean appears to be much greater than that for equilibrium with the present partial pressure in the atmosphere. Although release of stored methane appears the most likely large-scale violation of Le Châtelier's principle, it is not now known how far the atmosphere is from non-extremality of the entropy generation rate, or other major transition in thermodynamic regime, nor whether such phenomena are attainable beyond a previously suggested duality in ocean transports. One suggestion is that the climate system historically has switched between two major regimes as a result of internal and external fluctuations.

Atmospheric convective plumes emanating from leads: 2. Microphysical and radiative processes

A one‐dimensional, second‐order turbulence model with bulk cloud microphysics and detailed radiative transfer is used to simulate the evolution of a thermal internal boundary layer (TIBL) which develops above a wide, open lead. A mixed‐phase cloud, originally based at the surface, is produced within the TIBL. The cloud initially fills the entire TIBL but is later elevated above the surface with its top coincident with the top of the TIBL. Model‐derived cloud ice and cloud liquid water mixing ratios exceed 0.06 g kg−1 directly above the open lead, with a secondary maximum near the top of the TIBL. In addition, precipitating ice particles or snow fills the TIBL with a maximum snow mixing ratio of about 0.05 g kg−1. Radiative flux divergence results in strong cooling at cloud top (which contributes to the local maxima in cloud water mixing ratio at this level) and warming near the surface. The lead‐induced cloud increases the downwelling long‐wave irradiance received at the surface by up to 70 W m−2 (reducing the surface radiative cooling by over 40%) during the baseline case. This value is quite sensitive to the assumed particle size and cloud particle concentration. The vertical structure and composition of the lead‐induced cloud is shown to strongly depend on the rate of snow production and the cloud water partitioning.

Strongly coupled radiative transfer and Joule heating in an arc heater electrode

Radiation and Joule heating in the electrode region of an arc heater are discussed. Radiative transport equations for a true axisymmetric geometry are used. A subsonic code is developed to numerically solve the fluid equations with strongly coupled radiation, V -qr and Joule heating j -E, representative of a high-pressure and high-current arc heater. Analytic expression for the divergence of radiative heat flux derived in a previous paper is used. Jacobians of the radiation term are derived. The Joule heating term is computed using a previously developed code. The equilibrium gas model consists of seven species. The fluxes are differenced using Van Leer flux splitting. Using this code the effects of radiative cooling on the thermodynamic parameters of the arc core are discussed.

Radiation Heat Transfer in Fluidized Beds: A Comparison of Exact and Simplified Approaches

Radiation heat transfer at heat exchanger walls in fluidized beds has never been examined through a complete formulation of the problem. In this paper a wall-to-bed heat transfer model is proposed to account for particle convection, gas convection, and radiation exchange in a variable porosity medium. Momentum, energy, and intensity equations are solved in order to determine the velocity, temperature, radiative heat flux profiles and heat transfer coefficients. The discrete-ordinates method is used to compute the radiative intensity equation and the radiative flux divergence in the energy equation. Both the gray and the non-gray assumptions are considered, as well as dependent and independent scattering. The exact solution obtained is compared with several simplified approaches. Large differences are shown for small particles at high temperature but the simplified solutions are valid for large particle beds. The dependency of radiative contribution on controlling parameters is discussed.

Radiative heat transfer in finite cylindrical enclosures with nonhomogeneous participating media

Results of a numerical solution for radiative heat transfer in homogeneous and nonhomogeneous participating media are presented. The geometry of interest is a finite axisymmetric cylindrical enclosure. The integral formulation for radiative transport is solved by the YIX method. A three-dimensional solution scheme is applied to two-dimensional axisymmetric geometry to simplify kernel calculations and to avoid difficulties associated with treating boundary conditions. As part of the effort to improve modeling capabilities for turbulent jet diffusion flames, predicted distributions for flame temperature and soot volume fraction are used to calculate radiative heat transfer from soot particles in such flames. It is shown that the nonhomogeneity of radiative property has very significant effects. The peak value of the divergence of radiative heat flux could be underestimated by 2 factor of 7 if a mean homogeneous radiative property is used. Since recent studies have shown that scattering by soot agglomerates is significant in flames, the effect of magnitude of scattering is also investigated and found to be nonnegligible.

Monte Carlo prediction of radiative heat transfer in inhomogeneous, anisotropic, nongray media

A Monte Carlo solution technique has been formulated to predict the radiative heat transfer in three-dimensional, inhomogeneous participating media which exhibit spectrally dependent emission and absorption and anisotropic scattering. Details of the technique and selected numerical sensitivities are discussed. The technique was applied to a problem involving a medium composed of a gas mixture of carbon dioxide and nitrogen and suspended carbon particles. A homogeneous medium was modeled to examine the effect of total pressure and carbon-particle concentration on radiative heat transfer. Variation in total pressure, over the range studied, had minimal effect on the amount of heat radiated to the enclosure walls and on the radiative-flux distribution within the medium. Increases in the carbon particle concentration produced significantly higher heat fluxes at the boundaries and altered the radiative flux distribution. The technique was then applied to an inhomogeneous medium to examine effects of specific temperature and carbon particle concentration distributions on radiative heat transfer. For the inhomogeneous conditions examined, the largest radiative flux divergence occurs near the center of the medium and the regions near some enclosure walls act as energy sinks.

The radiative source term for plane-parallel layers of reacting combustion gases

An expression is derived for the radiative source term governing the interaction of molecular gas band radiation and flow in nonhomogeneous, plane-parallel reacting flow problems. The divergence of the net radiative flux is formulated in terms of wide-band absorptance model parameters for combustion products, and is valid for all degrees of optical thickness. When optical thickness is finite, the net absorption is obtained by integrating the radiation field solution over the band lineshapes and taking hemispherical averages. Illustrative calculations for counterflow diffusion flames will be discussed.

Longitudinal heating gradient: Another possible factor influencing the intensity of the Asian summer monsoon circulation

The largest longitudinal heating gradients in the tropics exist between the African desert and Asian convective regions during summer once the South Asian monsoon is established. The heating gradients are anchored by the latent heat release and net radiative flux convergence over the monsoon region, and by the dominant net radiative flux divergence over the desert.

Radiative effects of the smoke clouds from the Kuwait oil fires

The radiative effects of the smoke from the Kuwait oil fires were assessed by measuring downwelling and upwelling solar flux, as well as spectral solar extinction beneath, above, and within the smoke plume. Radiative flux divergence measurements were made to determine smoke‐induced heating and cooling rates. Seven radiation flight missions were undertaken between May 16 and June 2, 1991, to characterize the plume between the source region in Kuwait and approximately 200 km south, near Manama, Bahrain. We present results from one flight representative of conditions of the composite plume. On May 18, 1991, in a homogeneous, well‐mixed region of smoke approximately 100 km downstream of the fires, visible optical depths as high as 2 were measured, at which time transmission to the surface was 8%, while 78% of the solar radiation was absorbed by the smoke. The calculated instantaneous heating rate inside the plume reached 24 K/d. While these effects are probably typical of those regions in the Persian Gulf area directly covered by the smoke, there is no evidence to suggest significant climatic effects in other regions.

Vertical fluxes in katabatic flows

Katabatic flow is a dynamical process occurring on relatively calm, clear nights above sloping terrain. Its existence is dependent on long-wave radiative transfer, particularly radiative flux divergence within the air itself, for both its generation and (it is concluded here), along with advective warming, for much of its retardation.

Radiation and convection in circular pipe with uniform wall heat flux

The interaction of thermal radiation with laminar forced convection in thermally developing circular pipe flow is analyzed theoretically. The analysis considers an absorbing and emitting gray fluid bounded by a heated black wall having a uniform heat flux subjected at a certain finite length of wall and insulated otherwise. The contribution of thermal radiation is obtained by solving the two-dimensional exact integral equations for the divergence of radiative heat flux with the use of finite element node approximation technique. The governing energy equation is solved numerically by the Crank-Nicolson finite difference method with an iterative procedure. Effects of various radiation and convection parameters such as optical radius. Peclet number, and inlet fluid temperature on wall radiative heat flux are presented. The effects of the parameters on the development of fluid bulk temperature and wall temperature are also analyzed. 37 refs.

A Comparative Study of Daytime Thermally Induced Upslope Flow on Mars and Earth

Abstract Several characteristics of thermally induced mesoscale upslope flow on Mars and its comparison with that on Earth were investigated using both analytical and numerical model approaches. The conclusions obtained from the analytical and the numerical evaluations for Mars are generally in agreement. The main conclusions are (i) the intensity of the Martian summer daytime upslope flow, with a moderate slope, reaches nearly 10 m s−1 and its depth is about 5 km; (ii) the longwave radiation flux divergence heating, within the lower boundary layer of Mars, has a nonnegligible contribution to the intensity of the upslope flows; and (iii) on Mars, the values of upslope wind speed are, typically, about 2.5 times larger than on Earth under similar conditions. The depth of the daytime upslope flow and the air temperature increase near the surface are 3 to 4 times larger. The vertical eddy exchange coefficient for heat and momentum is about 10 times larger on Mars.

Flux divergence of thermal radiation within stratiform clouds

A longwave radiative transfer model based on the narrow‐band transmission functions of Lowtran 6 has been developed to investigate the profile of radiative flux divergence at the tops of stratiform clouds. The model has a vertical resolution of 1 m and a spectral resolution of 20 cm−1. These features are shown to permit modeling of broadband radiative transfer in the presence of a cloud top inversion and finite liquid water gradient. Radiative cooling rates in excess of 40 K hr−1 are shown to be possible for extreme conditions, with values of 10 K hr−1 being representative of more typical conditions. The values obtained are shown to be strongly influenced by the magnitude of liquid water concentration, by the gradient of liquid water in the top 50 m, and by the strength of the temperature inversion.

Solar activity and radiative flux divergence in the tropical middle atmosphere

Results of a study on radiative net flux divergence at various heights of the middle atmosphere (15–80 km) over the tropical station, Thumba (8°N, 77°E), India, for a period of 12 years from 1971 to 1982 using M-100 rocket data are reported. Over Thumba mesospheric net flux divergence occurs during the descending phases and flux convergence takes place during the ascending phases of the solar cycle. The net flux divergence in middle stratosphere seems to have quasi-biennial variations. The total net flux divergence during a 11-year solar cycle is found to be highly negative in the mesosphere and strongly positive in the upper stratosphere, representing the heat source and sink regions in the middle atmosphere.