If we double the amount of CO2 in the atmosphere, then
the absorption coefficient only needs to be 1/2 or greater in order to make the atmosphere optically thick.
If you accept Kirchoff's law for the moment, that tells you that the emission is
the absorption coefficient times the very same Planck function B (nu, T) that governs blackbody emission.
In such units, an atmosphere with the present amount of CO2 is optically thick where
the absorption coefficient is one or greater, and optically thin where
the absorption coefficient is less than one.
It follows from this that the logarithmic dependence of the outgoing longwave radiation (which by the way, has to do the the exponential decay of
the absorption coefficient away from the center of the absorption line) can still lead to significant temperature changes, particularly since water vapor enhances the value of λ and smoothes out a plot of the outgoing radiation vs. temperature (making it more linear than T ** 4).
(The old Planck mean
absorption coefficient used by astrophysicist is also not appropriate.)
One of the simplest radiative equilibrium models involves the assumption of a so - called grey atmosphere, where
the absorption coefficient is assumed to be independent of wavelength.
Absorption coefficient of water: Data sources.
In this model it very much depends on the concentration of the absorbing gas and
its absorption coefficient.
Folks who do combustion, solar physics and atmospheric measurements understand that in such systems where the light source (s) are at the same temperature as the absorbers you can not naively use
the absorption coefficient
The absorption coefficient, scattering coefficient, and convective heat transfer coefficients are varied.
Because they knew
the absorption coefficient of Cl2 at the laser wavelengths, they could get the ratio of the ClOOCl to Cl2 cross-sections at each wavelength.
What I was trying to ask, was as the density of the GHGs increase, does Earth's gravity play a roll affecting the solution of
the absorption coefficient integral?
That is really not relevant to the discussion on the real argument for GHE & EHGE, which depends on frequency - specific issues like
the absorption coefficient.
Absorption coefficient of 0.001 1 / cm means that half of energy is absorbed in 7m and 100 1 / cm that half is absorbed in 0.7 mm.
No, the OD (r) is just the integral of
the absorption coefficient, at the frequency of interest, from r = infinity downward towards r = 0.
OD is basically the integral of
the absorption coefficient (which depends on the quantum structure of the molecule, and the effects of temperature, and density) over distance.
We consider just two layers, the surface and the «last» layer, and the emissivity of this outer layer is modulated between 0 and 1 according to
the absorption coefficient α.
Upon increasing CO2 concentration, the layer at which
the absorption coefficient at each wavelength is low enough to let the IR light escape will be found higher in the atmosphere.
At the time of Hulburt the CO2
absorption coefficient was not known very accurately and even less its line shape, forcing Huburt to use a «box - like» shape.
We can crudely model this behavior using the Plank law and a gaussian - shaped
absorption coefficient.
On the contrary, if we recall that
the absorption coefficient is gaussian we would expect an increase in the energy retained by our layer along the wings.
In that case it does not matter how the water is heated but simply the temperature of the layer of surface water down to a few multiples of the inverse of the IR
absorption coefficient which is I think varies from around a few cm to less than 1 mm with increasing wavelength.
An absorption coefficient α of 45 — 66 % was found for the control group.
For example the knowledge of CO2
absorption coefficients at different frequencies can be useful.
The reason is that the Planck function change with height (temperature) is very strong in reducing the intensity of those relatively few lines with large
absorption coefficients.
Comparison of
the absorption coefficients over the full range of 1.5 — 18 µm gave the result: CO2 / H2O = ~ 5.5.
Despite the similar performance between the Brewer and Dobson stations, small differences within ± 0.6 % are introduced due to the use of different wavelengths and different temperature dependence for the ozone
absorption coefficients [Staehelin et al., 2003].
Dobson measurements suffer from a temperature dependence of the ozone
absorption coefficients used in the retrievals which might account for a seasonal variation in the error of ± 0.9 % in the middle latitudes and ± 1.7 % in the Arctic, and for systematic errors of up to 4 % [Bernhard et al., 2005].
There are three reasons for this difference: (i)
The absorption coefficients for CO2 used by Manabe and Wetherald [from G. Yamamoto and T. Sasamori, Sci.
The total radiation leaving the layer in each direction is presented as a function of scattering for a range of
absorption coefficients.
The radiation
absorption coefficients of carbon dioxide and water vapour are used to show the effect of carbon dioxide on «sky radiation.»
Once you have the database of
absorption coefficients and the temperature profile of the atmosphere you can calculate the solution.
The optical thickness is calculated via the weighted integral of the path lengths x
absorption coefficients.
Not exact matches
Some separation methods (
absorption, extraction) rely on differences in solubility, expressed as the distribution
coefficient (ratio of a material's solubilities in two solvents).
Diffuse Attenuation
Coefficient at 490 nm measures
absorption of blue light (490 nm) in the top 50 m or so of seawater (largely) by suspended biomass.
The extinction
coefficient for
absorption is also 5 or 6 orders of magnitude smaller than that for water vapor in the same wavelength range.
For the adiabatic process the formula considers the partial pressures and specific heats of the gases forming the atmosphere, an adiabatic constant and corrective
coefficients for the heating caused by water condensation in the wet atmosphere and for the
absorption of infrared radiation by the atmosphere.
One can for example treat radiative systems using classical
absorption, scattering and transmission
coefficients.
However, warming from a doubling of CO2 would only be about 1oC (based on simple calculations where the radiation altitude and the Planck temperature depend on wavelength in accordance with the attenuation
coefficients of wellmixed CO2 molecules; a doubling of any concentration in ppmv produces the same warming because of the logarithmic dependence of CO2's
absorption on the amount of CO2)(IPCC, 2007).
The coating is assumed to be gray (
absorption and scattering
coefficients are not function of wavelength).
I'm sorry, but I do NOT see CO2's signature
absorption or emission peak at it's most dominant, highest extinction
coefficient band — 15 μ.