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# Radiative Transfer - Science topic

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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.
Stam Nicolis I checked these references thoroughly. Actually, the document written by Duncan Forgan was the one I used to implement (probably) my first Radiative Monte Carlo code about 10 years ago. Still, I couldn't find what I was looking for. Maybe I am not making myself clear, but what I would like to know is if there is a document that clearly and explicitly explains the relation between the MCRT algorithm (i.e. steps involved and the iterative structure) and the Radiative Transfer Equation (e.g. the algorithm's relation to each of the operators present within the equation). I.e. a relation between MCRT and the RTE without resorting to the "imagine what happens to a photon in the physical scenario".
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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
Thanks a lot for your suggestion. I will consult the text of van de Hulst.
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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.
Y.C. Zhong thank you so much for your valuable comments.
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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.
Why don't you design an experiment to measure the changes in those properties in the first place? Then you could build/choose a theoretical model.
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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'.
When inverting the radiative transfer equation (Chandrasekhar radiative transfer equation, eq.(2.3) from Seidel(2011)) you do not need to perform the expansion of an exponent because you can obtain the analytical solution of he equation
(1-N)=exp(-\tau \eta)
Even in this case you will still need to satisfy the condition N<1.
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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.
Thank you, Ismail Mondal!
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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 ?
You can download the SBDART model zip file from this GitHub link:
Then simply in Unix environment you can proceed with SBDART installation using following commands:
unix> gunzip sbdart_2.4.tar.gz
unix> tar xvf sbdart_2.4.tar
unix> make
These documents are very helpful for SBDART installation and input parameters.
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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,
In the the Stefan-Boltzmann law , only one variable parameter is epsilon. This will come under heat exchange between surface. You need to feed the both the emissivity of surfaces which are considered.
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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
Hello Tobias,
I had no idea how difficult your question was until I tried to answer it myself. I tried looking in two books on heat transfer that I normally use:
R. Byron Bird, Warren E. Stewart, Edwin N. Lightfoot; Transport Phenomena; John Wiley & Sons, Inc.; 1960; p. 432 (Table 14.2-1).
Frank P. Incropera, David P. De Witt; Fundamentals of Heat and Mass Transfer, 2nd Edition; John Wiley & Sons, Inc.; 1985; pp. 779-781 (Table A.11).
While the book by Bird, Stewart, and Lightfoot gave the total emissivity for a thick (?) film of water at 495 and 672 degrees Rankine (absolute temperature in degrees Fahrenheit), there were no citations to source literature, only the following rather unhelpful note: "Calculated from spectroscopic data." One can, of course, look at the absorption spectra in the IR (Infra-Red) as measured by a spectrophotometer in standard books on chemical structural analysis, but it is not clear how one goes from the limited spectrum in the IR to the total emissivity. The following book shows the limited IR spectrum for both H2O and D2O:
Daniel J. Pasto, Carl R. Johnson; Organic Structure Determination; Prentice-Hall, inc.; 1969; p. 356.
The book by Incropera and De Witt has a table listing the hemispherical emissivity for ice at 273 Kelvin and liquid water at 300 Kelvin. There is a note claiming that the data from the table came from four different reference books 1, 9, 24, & 25 (see pp. 783-784 for the citations). Unfortunately, I only have access to reference book #1, the 14 volume set of reference books by Y. S. Touloukian et al.; Thermophysical Properties of Matter; Plenum Press; circa 1970s . I have examined volumes 8 and 9, Thermal Radiative Properties, Nonmetallic Solids and Coatings, but there are no entries for ice or liquid water. The other three reference books are as follows:
#9, J. F. Mallory; Thermal Insulation; Van Nostrand Reinhold; 1969.
#24, G. G. Gubareff, J. E. Janssen, R. H. Torborg; Thermal radiation Properties Survey; Minneapolis-Honeywell Regulator Company; 1960.
#25, F. Kreith, J. F. Kreider; Principles of Solar Energy; Hemisphere Publishing Corp.; 1978.
Anyway, I really like your question.
Regards,
Tom Cuff
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I've calculated Direct Aerosol Radiative Forcing(DARF) values (W/m2) 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 further analyse the data.
Hi... Yash
Aerosol Direct Radiative Forcing (ADRF) depicts the scattering and absorption of solar radiation by aerosols. the positive values of ADRF indicate the warming and negative values indicate the cooling.
I hope that you have calculated ADRF using up and down radiative flux values. SBDART only provides up and down radiative fluxes later you have to calculate radiative forcing using those values. This method is already published by the many aerosol experts. You can refer to those publications.
Estimated TOA and SFC ADRF indicated the change in flux at TOA and SFC by aerosols. ADRF in the ATM indicates the change in flux within the atmosphere.
Further, you can more clearly associate these estimated radiative forcing to the climate by calculating heating rate. heating rate depicts the warming of the atmosphere. This can easily associate with regional or global climate change.
Herewith I have given you a very basic idea, but I will suggest you to read the related publication and their interpretation. This will give you more idea.
Hope this will help. Feel free to ask me, if you have anything
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How radiative transfer equation with monte carlo technique can be started.
It depends very much on what you want to achieve. If, say, you were studying the radiative transfer (RT) through a layer (of clouds, aerosols) in an atmosphere where the profiles of temperature, humidity, and other radiatively active gases and the cloud and/or aerosol optical properties are not perfectly known/measured, over an area where the surface radiative properties are very variable (say, an ice and snow surface with liquid water ponds on top), one could either 1/ run N times the same RT code with a small change in one of the defining properties (with that small change consistent with the overall probability distribution of the variations for that property (PDF)) then look at how the results actually pan out (to figure, for example, what parameters are really dominant to define the result), or 2/ (more efficient) modify the original RT code to include (for the parameters one is interested in) some random number generators to be used to draw values from the PDFs of the relevant parameters.
Method 2 has been used for RT codes in GCMs in a series of publications by Howard Barker, Robert Pincus and collaborators (and some others) in the last 15 years. If your application is GCM-related, you might want to search for « McICA » (Monte-Carlo Independent Column Approximation).
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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?
Dear sir it means reemission in participating nanofluid in receiver with isothermal temperature below 750 K is always neglected?
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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). Experimental and theoretical study of the hot-wire method applied to low-density thermal insulators. International journal of heat and mass transfer, 49(23), 4511-4524.
Answer from Dr. Silas E. Gustafsson - Pioneers of Thermal Conductivity Measurement( silas.gustafsson@thermetrol.se): Silas E. Gustafsson
a) The contact resistance between the probe and the substrate pieces:
When comparisons are made between data obtained with the Hot Disc (HD) method and those of most other methods, it should be remembered that the transport properties measured with this method are the properties of the substrate beyond the surface, where the structure starts to repeat itself and assumes stable or bulk properties. The reason why it is possible to avoid the influence from the thermal contact resistance between the sensing spiral of the probe and the first surface representing the “bulk” properties of the substrate stems from the fact that the transient recording of the thermal transport properties of the substrate is normally much longer than the time it takes to establish a constant temperature difference across the thin layer comprising the probe insulation and the surface roughness of the substrate (cf Gustavsson, J. S., M. Gustavsson, and S. E. Gustafsson. (1998). On the Use of the Hot Disk Thermal Constants Analyser for Measuring the Thermal Conductivity of Thin Samples of Electrically Insulating Materials. Thermal Conductivity 24, Technomic Publ. Co. Inc., pp 116 -122.). In this paper we discussed how to separate the thermal contact resistance between the probe and the substrate from the transiently recorded data in this ITCC communication some 20 years ago. After this conference professor Cahill applied the suggested procedure for all the measurements he has made on very thin insulating layers with his 3-omega method. The reason why it is possible to separate the thermal contact resistance between the probe and the substrate surface from the measurements of the bulk of the substrate is the different time scales we are dealing with.
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I want to measure the radiative transfer of the killauea volcano Hawaii. I am interested in SO2 gases
I recommend Frank's answer
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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
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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
1 Watt /m2 = 0.0864 MJ /m2/day
1 MJ /m2/day  =0.408 mm /day
For a ETr of 0.2mm/h, LEcold in METRIC should be around ~ 143 W/m2 (1.05*0.2*681.6, where 681.6 is the scale factor to convert mm/h to W/m2). In SEBAL, LEcold is typically taken as Rn-G (i.e. H = 0).
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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!
This is a real interesting topic. Have you find a solution by chance?
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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
Sundara, as far as I remember, night time Landsat 8 acquisitions are made by special requests only. USGS also makes already requested night time Landsat scenes available for download. But so far out of the 1 million plus scenes acquired with Landat 8 hardly 0.01 % are night time scenes. I imagine for thermal inertia and diurnal surface temperature studies, day and night lst pairs would be very useful but I don't know if we can expect night acquisitions regularly. ASTER is another alternative but I am not sure how many night time scenes are available for India. Are you looking for night time scenes for the entire country or specific area in India? In any case, try the special request option with USGS.
And what do you mean by, '(Land and water area must be there)' and 'that would not be having water and land areas together' in your question?
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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!
what are your inputs? What operating system do you use? If you manage to get (x,y) columns in ASCII format, you can use something like Origin under Windows or xmgrace under Linux.
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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 ?
I would also recommend to use the ASTER Spectral Library. From my own experience the spectra you can find in the mentioned library are in very good correlation to spectra of the same soils measured by Diffuse Reflectance Infrared Fourier Transform Spectroscopy. Therefore we used a Praying Mantis™ from Harrick in the MIR spectral region.
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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.
A great textbook describing calculation of the radiative transfer / absorption of various atmospheric gases in clear and scattering conditions is "Atmospheric Radiation: Theoretical Basis," by Goody and Yung. It should have the information you're looking for.
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Is there some kind of model that describes this phenomenon?
By improving the optical density in the vicinity of plasmonic nanoparticle by means of Surface Plasmon Polariton (SPP). SPP is the collective oscillation of the surface charges of the metal nanoparticle coupled with the electromagnetic wave for a specific frequency.... So,  increase in optical density may leads to the increased light-matter interaction and hence it improves the radiative transitions....
Regards
Sivan
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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?
It's probably not related to the platform (Linux), but there might be differences in Fortran compilers.
Unfortunately, the developer of SBDART has lost his job many years ago, so the code is not supported and should be considered antiquated.
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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.
Dear Derek,
I assume you know about ESA's recently approved Explorer mission 'FLEX', but if not, you'll find more information about it here:
Of course, a web search for "esa explorer fluorescence" will generate thousands of pages... Now, plant materials are quite different from an acrylic plastic sheet, but perhaps some of the physics may be relevant.
Good luck with your investigation. Cheers, Michel.
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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
I have found an interesting paper regarding this topic
International Journal of Heat and Mass Transfer 49 (2006) 4279–4289 www.elsevier.com/locate/ijhmt
Modeling the eﬀects of surface roughness on the emissivity of aluminum alloys Chang-Da Wen, Issam Mudawar
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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, as far as i know, normaly Mie-scattering is used for measuring liquid phase. if you want to measure the vapor phase, Schlieren technique is one of the options. I do not know why does Peter Frijters use so complicated setup to do the Mie-scattering. Usually we use  similar setup as IFPEN to measure the liquid length.  It does not matter you use the LED or laser or other kinds of lamps as the light source, as long as the intensity is strong enough
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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?
It depends on the species and line you  want. 1-1000eV is  very large range. At 1000eV you probably have highly ionized  heavier Z species for which  natural broadenig which scales as Z**4 can be important. At 1 eV on the other hand  you probably do not have ion lines. I assume you imply LTE and hence Doppler, ion and  electron temperatures are more or less equal.  I believe if you are more specific on lines and species (e.g.  FeXV 3p2-3p3d) you can get more useful replies. Generally Voigt=Gaussian(Doppler) +Lorenzian(Stark&natural), neglecting any coupling which is usually small. As for fine structure in many cases if other broadening mechanisms like Stark and Doppler are significant, they will mask fine structure differences and you will see a big blob. But if they are not, then you might see fine structure too. I would check how large is the fine structure splitting and compare it to Stark and Doppler width. If eiher of them dominates fine structure, I would -at least to your level of approximation- neglect fine structure.
So I would  suggest you post the specific lines (you should know that because presumably you are looking at a given spectral range) to get more helpful answers
P.S. Typically one does not use density, but electron density (e/cc) because only the ionized part perturbs the emitter and at 1 eV  you may not have that much ionization.
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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!
You can use Fluent. Here is a Thesis link for your help :
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I want calculating atmospheric gas in my PhD thesis.
If you want to compute vertical profiles of shortwave and longwave radiative fluxes, you could have a look at rtweb.aer.com
There are a lot of information on various pieces of codes, and most of them can be downloaded for free after registration. The codes are in Fortran.
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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!
For publicly available three-dimensional radiative transfer codes check http://i3rc.gsfc.nasa.gov/Public_codes_3DRT.htm
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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?
Probably, there are many works related to your question in the JQSRT, some of them by M. Mischenko et al. (http://www.giss.nasa.gov/staff/mmishchenko/mishchenko.html). Also, the Amsterdam database is a database of the scattering matrices and optical properties of aerosol and hydrosol particles cited in several articles (http://www.iaa.es/scattering/amsterdam/index.html).
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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!
Try these:
Tsay, S. C., K. Stamnes and K. Jayaweera, 1990: Radiative transfer in planetary atmospheres: Development and verification of a unified model. J. Quant. Spectrosc. Radiat. Transfer, 43, 133–148.
Chenxi Wang, Ping Yang, Steven Platnick, Andrew K. Heidinger, Bryan A. Baum, Thomas Greenwald, Zhibo Zhang, and Robert E. Holz, 2013: Retrieval of Ice Cloud Properties from AIRS and MODIS Observations Based on a Fast High-Spectral-Resolution Radiative Transfer Model. J. Appl. Meteor. Climatol., 52, 710–726.
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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?
Hanno, I understand your problem and I have never seen its clarification.  Here is my own version:
For any finite set of masses and springs, no matter how irregular, we can find its eigenfrequencies, right?  This is what is called phonons (usually).  But you probably expect some relation with reciprocal lattice?  Well, the reciprocal lattice is more or less the Fourier transform of primary lattice nodes.  Thus exactly the same qualitative picture may be obtained considering irregular set of atoms, just like it takes place in glasses.  The bad news is that when going to infinite glass we obtain not a discrete but continuous set of reciprocal lattice points (k-vectors).  As the distances between real atoms cannot be arbitrarily small, then such k-spectrum should be bounded, even in infinite glass.  Therefore we can talk about the maximum energy of mechanical vibrations in glasses ("phonons").  In this picture, however, there is no place (at least I can't see it) for microscopic polarization of such "phonons".
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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
Dear JAvier,
Raman scattering will only impact your upwelling radiances (and then reflectance) in clear to relatively clear waters and from about 490 nm. Typically water with Chlorophyll concentration lower than 0.3 mg.m-3. It can affect the remote sensing reflectance up to 10% (perhaps 20% in very clear). Raman is an inelastic process (as fluorescence) due to the excitation of water molecules. Due to the relatively low sea water temperature "Raman photons" only appear at longer wavelengths compared to the excitation wavelength. It is therefore more and more visible at higher wavelengths. However, the increasing absorption of water molecules toward high wavelengths compensate this effect (Some Raman photons get absorb by water).
If you want more details you can read the book of C. Mobley: Light and water.
or/and the following papers:
Morel, A., Antoine, D. and B. Gentili (2002). Bidirectional reflectance of oceanic waters: Accounting for Raman emission and varying particle phase function, Appied Optics, 41, 6289-6306
hope it helps
best
hubert
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Does any package do both, correctly?
I have made this kind of calculation (a paper is available on my account) with my own code. I have no experience of calculation with commercial codes.
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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.
What makes you feel that the heat transfer may really not matter in the varied agricultural applications mentioned?
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Question
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)?