Dear Mohan,

I am more specialist of oceanography and radiation over ocean, but I think the problem on land or over an ocean surface is the same. There are lots of parameterization of incoming longwave radiation, some quite old (i.e. Clark et al, 1974; Bunker et al., MWR, 1976;  Bignami et al., JGR 1995; Brunt, QJRMS, 1932; Berliand and Berliand, 1952; Hastenrath and Lamb, 1978; Efimova, Met. Gidrol., 1961; Anderson, USGSC, 1952; Swinbank, QJRMS, 1963; Budyko, 1974). They all take into account air temperature and humidity, latitude AND CLOUD COVER as input parameter. When looking at a chronological series of incoming longwave radiation, air temperature is one important factor of variability, but cloud cover is the most important factor of the short term variability. So if you have not access to an estimate of this parameter (for instance from a satellite cloud classification), I don't know how you can solve your problem. G.C.

Dear Mohan Bahadur Chand,

Unfortunately, this calculation does not belong to my field and therefore I cannot answer your question.

I wish you good work.

Best regards

Márton Veress

Dear Caniaux,

Thank you very much for your response. Yes, I afraid about the could cover how to estimate it for my study site. Though there are many empirical equations to estimate the atmospheric emissivity that somehow consider the effect of cloud cover. Many researcher have estimated like this way. For this, We need theoretical incoming solar radiation (TISR) at the top of the atmosphere. I wonder if somebody can guide me for the estimation of TISR. Caniaux, if you have idea on it, please explain to me.

Thanking you,

Mohan

Hi Mohan,

The incoming infra red radiation from the Sun is so little it is usually ignored. However there is down-welling radiation from the greenhouse gases, which is usually called back radiation Its intensity is usually estimated using Planck's function, however that requires the temperature of the air at the (average?) height from which the gas is emitting.

There are three blog posts here which discuss back radiation:

https://scienceofdoom.com/2010/07/17/the-amazing-case-of-back-radiation/

I have not read them all yet, but they do seem to contain links to peer reviewed literature.

Cheers, Alastair.

Hi again Mohan,

I did not see your reply to Caniaux until after I had posted my reply, which may not be very helpful.

Is this file http://lasp.colorado.edu/lisird/resources/whi_ref_spectra/data/ref_solar_irradiance_whi-2008_ver2.dat what you are looking for?

Dear Alastair Bain,

Thank you very much for the suggestions. Yea, Of course we need vertical temperature profile for the incoming long wave radiation. However, we don't have such measurement and temperature measured at 2 m from the surface is normally used for this, which I have too.  My main question was how to estimate the theoretical incoming radiation at the top of the atmosphere, generally depends upon latitude and may be solar angle as far as I remember. With the help of this I can estimate the atmospheric transmissivity, which can considered for the cloud cover through the ration of incoming solar radiation at the earth surface and theoretical radiation at the top of atmosphere.  I am confused, how to estimate this theoretical incoming solar radiation at the top of atmosphere.

Thank you!

Mohan

Dear Mohan,

I can provide you be email a fortran routine computing theoretical incoming solar radiation (by clear sky) as a function of latitude and time. If it is what you are searching.

Regards, G.C.

Dear Caniaux,

Thank you very much, Yes exactly I need the same, but it should for the top of atmosphere not at the surface of the earth. My email is [email protected].

Regards,

Mohan

Dear Mohan,

The incoming longwave radiation is generally considered to be zero, but if you want to see how close to zero it is at the TOA, then you can get that information here: http://lasp.colorado.edu/lisird/resources/whi_ref_spectra/data/ref_solar_irradiance_whi-2008_ver2.dat 

Dear Alastair Bain,

Yea, that should be like that as generally we assume that Sun don't emit long wave radiation and if it emits that can't reach to the atmosphere. I mean to say incoming solar radiation at top of the atmosphere not long wave radiation. From that we can calculate the incoming long wave radiation at the surface using measured solar radiation at the surface.

Thank you

Mohan

The classic summary  of radiation balance over glaciers is  in "The Physics of Glaciers" 3rd edition chapter 4.

W S B Paterson,  Pergamon 1994. 

There is also a 4th edition

Dear David,

The Physics of Glacier is great book, I went through it 3/4 years back. I have to go through it again. 

Thank you very much for the suggestions. I hope I will be able to follow the method given by Physics of Glacier.

Thank you,

Mohan

Still facing the problem of not estimating the incoming long wave radiation. If will have the cloud cover data it was okay, but Unfortunately I don't have that data. Because cloud emissivity is very important, that increases the incoming long wave radiation. I read few papers that consider the ratio of measured shortwave radiation at the earth surface to radiation at the top of atmosphere for the atmosphere emissivity. For this, I have measured radiation for my site, but I am unable to calculate the radiation at the top of atmosphere. I know the relation but can not find the solution. If any body helps me and make more clear on it.

Thank you,

Mohan

Dear Mohan,   There is no incoming longwave radiation! There is only incoming solar radiation which is all short wave radiation. The longwave radiation at the surface is generated within the atmosphere by the greenhouse gases and the clouds.   There is a paper here which might help you: Wild, M., Folini, D., Schär, C., Loeb, N., Dutton, E. G. and König-Langlo, G. (2013) ‘The global energy balance from a surface perspective’, Climate Dynamics, vol. 40, no. 11–12, pp. 3107–3134.   However, they write " The climate models overestimate the downward solar and underestimate the downward thermal radiation, ...", so no one knows how to calculate the downward long-wave radiation, and it has to be measured if you want accurate results.   HTH, Alastair.

Dear McDonald,

Thank you for your response.

Yea, I am talking about down welling longwave radiation from atmosphere, that can be estimated using Boltzmann's Law ( for Black body radiation), taking consideration of atmospheric emissivity. It also needs the air temperature at different height from the surface, but we normally use the air temperature near the surface. Atmosphere can not be 100% black body, so it can not radiate  100%  radiation. Therefore, we need a atmospheric emissivity. In order to estimate the emissivity we need cloud cover fraction. Unfortunately, I don't have this one too. So, need shortwave radiation at the top of atmosphere, which depends upon latitude, seasons, day also. From this, we can calculate atmospheric emissivity as a ratio of shortwave radiation at the surface to the shortwave radiation at the top of atmosphere. I am getting difficulty in estimation shortwave radiation at the top of atmosphere, though I know the relations. I am poor in mathematics.

The equation for thermal radiation is Kirchhoff's law which uses Planck's function for black body radiation. (Boltzmann's law is used to calculate the excited state of the CO2 molecules, which you may not need.)

It is argued in Pierrehumbert's book "Principles of Planetary Climate" that because the absorption is saturated then Planck's function can be used for long-wave emissions from the atmosphere to the surface.

There is a "Simple Approximation for Infrared Emissivity of Water Cloud" described here: http://journals.ametsoc.org/doi/abs/10.1175/1520-0469(1982)039%3C0171%3ASAFIEO%3E2.0.CO%3B2

But you should be able to get answers to all your questions here:

https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0ahUKEwj78LTup7_QAhUMAcAKHcikC-kQFggiMAE&url=http%3A%2F%2Fwww.bartonlevenson.com%2FRCM%2520Tutorial%2520V2.rtf&usg=AFQjCNGAhKhxG0YizVInA5I6QBDa5ecgmw&sig2=lyPfOQle3bA5koNJZHBJsA

which is a tutorial on writing radiation models.

HTH, Alastair.

Mohan

If I understand your question correctly, you want a simple way to estimate downward IR and solar flux at the surface.    There are simple parameterizations of downward IR flux in terms of the near-surface air temperature and specific humidity.  Example, from Fairall et al. JCLIM 2008. 

IRflux=(.52+.13/60*abs(lat)+(.082-.03/60*abs(lat)).*sqrt(qa)).*(5.67e-8*(ta+tdk).^4)

here ta is in Cent, q is in g/kg and lat is latitude in deg.  tdk=273.15.

There is a downward IR flux even in cloud free conditions because of emissions by water vapor, ozone, and some other trace gases.  There are more accurate ways to do this if you have profiles of temperature and humidity (eg, try RRTM).

Solar flux at the surface can be done similarly, but is more complicated because you have to account for the sun's movement across the sky.  A fairly simple way to do this was described by Iqbal (see reference in the attached paper).  This has been coded up in matlab and excel.  You can get the codes at my ftp site:

ftp://ftp1.esrl.noaa.gov/BLO/Air-Sea/radflux/matlab/

The IR formula above has not been optimised for the arctic, so it might need adjustment.  I have attached a paper on arctic radflux observations.

If you want to go this route, contact me at [email protected] for help.

If you dont have local measurements of air temperature and humidity, then you will have to go with a climatology or output from and numerical weather model.  Those are available on line.

Regards, CF