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# Radiative Transfer - Science topic

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Questions related to Radiative Transfer

Many Monte Carlo methods to solve a given Partial Differential Equation (PDE) are built by sampling the PDE's Green's function. E.g., for heat diffusion, diffusion-convection-reaction type of equations, and so on, have algorithms that can be derived directly from the PDE (i.e., through Ito calculus or stochastic integral). On the other hand, for the Radiative Transfer Equation (RTE), there is an Integral representation. However, the argument for explaining Monte Carlo Radiative Transfer (MCRT) ALWAYS revolves around the physical interpretation.

I even found a review article [1] that states on page 16: "Unlike traditional approaches to RT problems, MCRT calculations do not attempt to solve the RTE directly."

Is there really NO relation (discovered yet) between MCRT and the RTE? or is it just that no one has ever proven this?. I understand the physical interpretation; it is just that having mathematical foundations would also help teach it in class. Can anyone help me by directing me to a reference that derives this?.

[1] Noebauer, U. M., & Sim, S. A. (2019). Monte Carlo radiative transfer.

*Living Reviews in Computational Astrophysics*,*5*(1), 1-103.I'm reading the book of Chandrasekhar "Radiative Transfer" and I have some doubts about some definitions when the Rayleigh scattering is assumed. In particular, when we consider a plane-parallel geometry, the text define the optical thickness as

\tau(z) = \int_{z}^{\infty} \kappa \rho \: d \zeta

where $ \kappa $ is the mass scattering coefficient, and $ \rho $ is the mass density. I think that Chandrasekhar sets the coordinate system as in the attached figure.

Under the hypothesis of Rayleigh scattering, the text states that

\kappa = \frac{8 \pi ^ 3}{3} \frac{(n ^ 2 - 1) ^ 2}{\lambda ^ 4 N \rho}

where $ n $ is the refractive index, $ \lambda $ is the wavelength, and $ N $ is the number of particle per unit volume. Assuming a single homogeneous layer, I think that the optical thickness could be treated as follows

\tau(z) = \int_{z}^{\infty} \kappa \rho \: d \zeta = \kappa \rho \int_{z}^{0} d \zeta = - \kappa \rho z

for $z \leq 0 $. Imposing that the height of the layer is $d$, and substituting the expression of $ \kappa $, the optical thickness of the layer should be

\tau(d) = \frac{8 \pi ^ 3}{3} \frac{(n ^ 2 - 1) ^ 2}{\lambda ^ 4 N} d

The strange thing is that for a higher $ N $, namely for a higher concentration of particles and so a "denser" medium, the optical thickness decreases, and this appears counter-intuitive to me. Is there an error in my development?

Moreover, Chandrasekhar seems to consider only lossless medium, namely with purely real refractive index, to define the mass scattering coefficient, isn't it? Is there a way to consider also lossy medium?

Finally, from $ \kappa $, Chandrasekhar define the following "scattering coefficient per particle"

\sigma = \frac{8 \pi ^ 3}{3} \frac{(n ^ 2 - 1) ^ 2}{\lambda ^ 4 N ^ 2}

This has the dimension of a cross-section, but it can be seen that it depends on $ N $. Therefore, it is not the cross-section that characterizes a single particle (usually treated in the Mie theory), isn't it? Thanks

Many observations and calculations of the atmospheric absorption can be found, but it would appear very few studies on climate had explicitly applied the basic radiative transfer equation in different forms, including scattering and atmospheric radiation. If you know any relevent references or your own papers to share, that would be wonderful.

I need to calculate the radiative properties (emissivity, reflection...) of some specific gas mixtures.

Do you know any appropriate software for this type of calculus?

Thank you.

I am working on aerosol retrieval using a radiative transfer equation with Landsat 8 OLI, and I am having difficulty determining the raster-based path radiance. I am using the formula by Felix C. Seidel (2011); Hadjimitsis (2009); Themistocleous (2016). see attached file. Whenever I try to compute the AOD after inverting the equation, there is always a negative value under the square root. from the image attached file "the last two equations'.

LST Calculator tool developed by Oguz H (2016), which makes the LST retrieval process quite simple. The model in based on Radiative Transfer Equation (RTE) method, which was developed in ArcGIS Model Builder to retrieve LST from Landsat 8 satellite imagery.

I am looking for SBDART model , either online or offline. The online model I found

doesn't seem to work , and the MATLAB code i got from here shows error. Any other source for the model ?

Hi all ,

How can I consider the Optical properties of a surface into the Stefan-Boltzmann law for a problem of Radiation Heat Transfer between a hot Body and a real Surface (namely, a surface with some Absorptivity, Emissivity and some Transmissivity). ?

Hope someone can help,

Best Regards !

Thank You,

Hello there,

I have a question concerning the emissivity of water. Its value depends on water transparency and surface smoothness. Often, its value is assumed to be close to 1. Brewster gives a value of 0.96 at ambient temperature (Brewster MQ (1992) Thermal radiative transfer and properties. Wiley, New York).

But how about the emissivity close to boiling temperature? I cannot find any reference that provides data for this case.

Does anybody have suggestions for me?

Thanks,

Tobias

I've calculated

**Direct Aerosol Radiative Forcing(DARF)**values (W/m^{2}) for Ahmedabad and Gandhinagar City, Gujarat, India using**SBDART**Model (AOD values as an input) at*Top Of Atmosphere (TOA), Surface (Surf) and net Atmospheric Radiative Forcing(Atm).*Please let me know how to

**interpret**these values and how to f**urther analyse**the data.How radiative transfer equation with monte carlo technique can be started.

At which temperature in participating media of nanofluid the rays or intensity of radiation should be emitted.

Is it possible that all photons absorbed are all emitted or some part will be emitted?

**Is it the reason for that TPS gives the higher conductivity value compared with that of steady state method?**

**In the below reference, Coquard et al (2006) mentioned:**Hot wire method for thermal conductivity measurement has recently known a significant increase. However, this method is theoretically not applicable to materials where radiative heat transfer is not negligible such as low-density thermal insulators.

The theoretical results showed that when the EPS foam is too transparent to behave as an optically thick material (Rosseland approximation) the temperature rise near the wire is noticeably different and reaches higher values than for the corresponding fictitious purely conductive material. The influence of radiative transfer on the evolution of the estimated conductivity khot is then comparable to that observed when the thermal inertia of the wire is increased.

Coquard, R., Baillis, D., & Quenard, D. (2006).

**International journal of heat and mass transfer, 49(23), 4511-4524.***Experimental and theoretical study of the hot-wire method applied to low-density thermal insulators*.I want to measure the radiative transfer of the killauea volcano Hawaii. I am interested in SO2 gases

Dear all,

Can anyone help me , How to perform 6S radiative transfer atmospheric correction of Landsat 8 using GRASS GIS. I am new user of GRASS GIS. Or any easy way to perform 6S radiative transfer. Please looking for your valuable guidance.

Thank You

Regards

Shouvik Jha

I am stuck trying to figure out how to estimate this value.

According to the literature the Sensible heat flux (H) at the cold Pixel for Metric and Sebal Models is

H=Rn-G-1.05λ ETr

where Rn is net radiation (w/m2), G is soil heat flux (W/m2), λ is latent heat of vaporization (aprox. 2,264,760 J/Kg) and ET (mm/hr) is Penman Monteith reference evapotranspiration. My problem is that the value that I get is way too high because of the value of the latent heat of vaporization.

For the people that have worked with these kind of models, am I doing something wrong? I have compared my results with the SEBAL manual (appendix 8), and clearly there is something that isn't working as it should.

Regards

In the Fluent, the WSGG is treated as a gray method. Radiative transfer equation is solved for only one time and the absorption coefficient is obtained by getting the total emissivity of the 3 or 4 gases.

So is there a way to implement the real WSGG in Fluent, namely, solving the RTE for each gray gas?

Thanks!

Hi,

I am looking for night time data of LANDSAT8 in India (Land and water area must be there) and its corresponding day time data of LANDSAT8 or other satellites for the same area and date (if not, within 3 to 5 days) fro estimating Land Surface Temperature (LST) using Radiative Transfer Equation. I browsed for a week and I could not get one. Finding it very hard to get the data. I will be grateful to you if you can help.

I am getting either day time data of an area in 2015 and night time in 2017 which is not desirable. If both day and night are available, that would not be having water and land areas together.

Thanks,

Sundara Bharathi

The weight function acts as a weight that determines the relative contribution of

each layer to the total radiance out the top of the atmosphere

at that wavelength. However, how to plot it by matlab, fortran or other tools? Can you help me?Thank you!

Let me please know, Is a free access to the database of SOIL SPECTRAL LIBRARY ? And which methods are better for correlation between parameters of soils from spectral library and soils that are't included to the specified library ?

Im trying to estimate irradiance on earth surface and I'm using a simple radiative transfer model where the extintion coefficient is parametrized as a linear combination of absortion coefficients for air ozone and different gasses. I want to take into account at least absortion coefficients for air, but I need data about its vertical profile by different wavelengths.

Is there some kind of model that describes this phenomenon?

Hello everyone,

I just started to work with SBDART Radiative Transfer Code. I have downloaded the source files (FORTRAN) on my LINUX machine and compiled it. After that I ran the model for a given INPUT (from examples file).However, results generated from my run are different from those given in example output (for same INPUT). Could anybody explain why I am getting different results? Does SBDART calculation depends on machine?

We are attempting to measure the Quantum Yield of a fluorescent acrylic plastic sheet. Will need some theory to link radiometric measurements to QY. Using a monochromator to illuminate the sheet against a Spectralon white reference and measuring radiance with a calibrated spectroradiometer.

can someone tell me how to consider the emissivity of a diffuse surface as a function of corresponding to that surface polished?

In particular I need the emissivity of diffuse SiC as a function of the wavelength (1 to 14) microns and temperature (up to 1100 °C)

thanks

For spray combustion visualization, Mie Scattering is one of the promising methods for measuring the vapor boundary. Peter Frijters (TUe) use Ar+ laser as a light source while Lama M. Itani (IFPEN) using White LED as a light source. Could anyone kindly give me some general guidelines for Mie scattering optical arrangement? Both arrangements are attached here.

Hi, i am calculating radiative properties of matter.during calculation of bound bound contribution i am facing the problem of line broadening.Which broadening should i use for diff temp and density?Is lorentzian line profile suitable for all line widths?

I am asking about the code or software to help me to solve the transient/time-resolved radiative transfer equation with DOM, FVM or other numerical methods. The optical tomography is my research topic, and I want to model the time-dependent radiance or photon density to a collimated source impinged into a scattering medium.

Thank you very much!

I want calculating atmospheric gas in my PhD thesis.

I am asking about the code or software to help me to solve the transient/time-resolved radiative transfer equation with DOM, FVM or other numerical methods. Surely, the provided code source will be illustrated as a citation in our future achievement. Thank you very much!

Has anyone measured or parameterized the atmospheric analogue of well known Mueller matrix for ocean water (Voss and Fry 1984)? I need it for polarization sensitive radiative transfer simulation. I think that the polarization effects of light scattering in the atmosphere, caused mainly by Rayleigh scattering, should be weakened by aerosols, dust and water droplets. But is there any known parameterization (e.g. for optical thickness as a parameter) that results in angular distribution of Mueller matrix?

MODIS provide MOD06 product, which contains cloud optical properties including Cloud Optical Thickness (COT) and effective particle radius. COT is retrieved based on a look-up scheme, which adopts a Look-Up Table (LUT).

LUT is constructed based on a Radiative Transfer Model (RTM), however, some papers dedicating to describe the COT retrieval algorithm don’t explicitly point out the exact name of the RTM and its availability.

Can someone provide me some information about the RTM? Your help would be really appreciated!

What is the role of phonon energy in different glasses? What is the significance of low and high phonon energy in the different glassy system?

Dear,

I am working in the shallow seawater radiative transfer equation RTE for WorldView-2 channels. I have observed a bad fitting in the yellow-red channels, the modelled diffuse attenuation is much bigger than the observed one. I thinks it is due to the raman scattering, but the documentation that I have read has not made
it clear the functioning of the Raman scattering. Can anyone advise me any publication or book in which the Raman scattering modeling is clearly explained?

Thanks and best regards,

Javier

Does any package do both, correctly?

I am studying heat transfer through different agricultural buildings and processes. Trying to optimize usage of energy and cooling/heating at the same time. Keywords: Solar and Thermal radiation, convective and conductive heat transfer modes.

Applications: greenhouses, refrigerating systems, drying, storage and controlled atmosphere.

Many leaves are dorsiventrally asymmetric (bifacial), leading to a difference in reflectance for the adaxial opposed to the abaxial side of the leaf. At the leaf level this difference can be quantified very accurately in function of wavelength and leaf structure.

Question is, how to proceed to determine the boundary conditions for which abaxial adaxial reflectance difference (leaf asymmetry) can be quantified at the top of the canopy of typically a forest with only dorsiventrally asymmetric leaves? What are the boundary conditions for the quantification of leaf bifaciality at the top of the canopy, with respect to the optimal spectral range, the optimal geometry of observation and the optimal LAD (Leaf Angle Distribution)?