Radiative transfer method

Stamnes, K S.-C. Tsay, W. Wiscombe, and K. Jayaweera, Numerically Stable Algorithm for Discrete-Ordinate-Method Radiative Transfer in Multiple Scattering and Emitting Layered Media, Appl. Opt., 27, 2502-2509 (1988). 

Stammes K., Tsay S., W. Wiscombe and K. Jayaweera, Numerical stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media, Applied Optics 27, 2502-... 

Chance, K., J.P. Burrows, D. Pettier and W. Schneider (1997) Satellite measurements of atmospheric ozone profiles, including tropospheric ozone from UV/visible measurements in the nadir geometry a potential method to retrieve tropospheric ozone. Journal Quantitative Spectroscopy and Radiative Transfer 57 467-476. 

Collin, A., Boulet, P., Lacroix, D., and Jeandel, G. On radiative transfer in water spray curtains using the discrete ordinates method. Journal of Quantitative Spectroscopy Radiative Transfer, 2005. 92, 85-110. 

Equation (5-121) specifically includes those zones which may not have a direct view of the refractory. When Qr = 0, the refractory surface is said to be in radiative equilibrium with the entire enclosure. Equation (5-121) is indeterminate if = 0. If ,. = 0, rdoes indeed exist and may be evaluated with use of the statement Er = Hr = Wr. It transpires, however, that I, is independent of Erfor all 0 < , < 1. Moreover, since Wr = Hr when Q, = 0, for all 0 < ty < I, the value specified for , is irrelevant to radiative transfer in the entire enclosure. In particular it follows that if Qr = 0, then the vectors W, H, and Q for the entire enclosure are also independent of all 0 < e, < 1.0. A surface zone for which e, = 0 is termed a perfect diffuse mirror. A perfect diffuse mirror is thus also an adiabatic surface zone. The matrix method automatically deals with all options for flux and adiabatic refractory surfaces. 

Subject to the restrictions of no scatter and diffuse surface emission and reflection, the above equations are the most general matrix statement possible for the zone method. When P = 1, the directed exchange areas all reduce to the total exchange areas for a single gray gas. If, in addition, K = 0, the much simpler case of radiative transfer in a transparent medium results. If, in addition, all surface zones are black, the direct, total, and directed exchange areas are all identical. 

Radiative transfer models can be very complicated and their solution cumbersome, so it is always desirable to have simplified tools for this analysis. Very simple and intuitive models can be developed in some cases to study radiation transfer inside photocatalytic reactors. However, it must be pointed out that these models must be well grounded in radiative transfer theory, in order to provide results that are consistent and of lasting engineering interest. Here, we present the basic concepts and discuss some approximations and methods that have been used. 

In particular, Cabrera et al. (1996), Brandi et al. (1999), and Satuf et al. (2005) have determined optical parameters for Ti02 particles of several commercial brands. The determinations were carried out by means of spectrophotometry experiments involving the measurement of specular reflectance and beam transmittance, as well as hemispherical transmittance and reflectance, of catalyst suspensions (Cabrera et al., 1996). By radiative transfer calculations with the discrete ordinates method (DOM), the values of the extinction and absorption coefficient and of the asymmetry parameter that better fitted the results of measurements were found. Actually, the extinction coefficients of Satuf et al. (2005) are the same as those of Brandi... 

Photolysis rates (J values) are calculated on-Une every chemical time step using the method of Landgraf and Crutzen (1998). In this method, radiative transfer calculations are done using a delta-two stream approximation for eight spectral... 

Since the Planckian source is a slowly-varying function of frequency, the sharp atmospheric absorption features in the observed data reveal information about the concentration of the absorbers. An iterative method based on the on-resonance off-resonance ratio of intensities at many absorption features was used to compute the concentration of atmospheric H2O, CO2, N2O, and CH4. This method does not require a model for the source intensity term and only assumes that its spectral variation with frequency is slow relative to most atmospheric absorption features. Accurate meteorological data was not available for the field test however, reasonable agreement was found between the calculated H2O concentration and that reported by the nearest weather station. Experimental CO2, N2O and CH4 concentrations were not available, but calculated values were consistent with historical averages. Atmospheric transmission modeling was performed using the Line-by-Line Radiative-Transfer-Model. ... 

H.R. Gordon (1976). Radiative transfer in the ocean a method for determination of absorption and scattering properties. Appl. Opt., 15,2611-2613. 

More precisely, climate modeling consists in the simulation of large-scale atmospheric processes by applying the basic physical principles and the correct initial conditions in a consistent way (Smagorinsky, 1974). An important part of climate modeling is the consideration of the interaction of macro-processes with phenomena taking place on the micro-scale (radiative transfer, turbulence, and processes of cloud physics and air chemistry). In the equations, the horizontal scale of variations is at least 100 km, while the vertical scale lies between 10 m and 100 km. The volume of air taken into account is a measure of the resolution of the calculation. Phenomena of smaller scale can be included in the model by appropriate statistical methods. This procedure is termed the parameterization. 

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