Specifically, for a differential area of the surface
of a blackbody at a single temperature, the law gives the spectral distribution and the amount of energy radiated from that differential area into a differential solid angle.
Not exact matches
Applying aperture photometry on the azimuthally averaged deconvolved PACS images and using a modified
blackbody of the form Bν · λ − β, as expected for a grain emissivity Qabs ~ λ − β with β equal to 1.2 (representing amorphous carbon, Mennella et al. 1998), we derived a dust temperature between 108 ± 5 K
at 20 ′ ′ and 40 ± 5 K
at 180 ′ ′.
The surface
of the Earth radiates as a
blackbody at its temperature which is continually changing because it is being heated by the sun, or it is cooling during the night.
sigmaT ^ 4 is the upward
blackbody radiation (based on stefan - boltzmann)
at the surface, «a» is the albedo (reflectivity), so (1 - a) is the fraction
of incident solar radiation that is absorbed by the planet.
Now, the best thing would be to be able to take your class into space and point your $ 50 sensor
at the Earth from the Space Station, so you could see that the radiation going out is like a
blackbody at 255K instead
of the actual surface temperature
of the Earth.
The flux F» (relative to the
blackbody value, σ * T ^ 4, for T
at the point
of view) will then be the integral over solid angle
of the intensity (relative to
blackbody intensity for T
at the point
of view) * cos (θ)(this other factor
of cos (θ) is due to the way a unit area facing vertical projects onto a smaller area in other directions), which will be
At equilibrium, it will have a temperature at which the blackbody flux at 15 microns would be half of the actual OLR at 15 micron
At equilibrium, it will have a temperature
at which the blackbody flux at 15 microns would be half of the actual OLR at 15 micron
at which the
blackbody flux
at 15 microns would be half of the actual OLR at 15 micron
at 15 microns would be half
of the actual OLR
at 15 micron
at 15 microns.
Since the 155 W / m2 GHE is the GHE forcing based on the present climate (in the sense that removing all GH agents (only their LW opacity, keeping solar radiation properties constant) results in a forcing
of -155 W / m2
at TOA for the present climate, and we know that without any GHE, in the isothermal
blackbody surface approximation, the temperature will fall approximately 33 K without any non-Planck feedbacks), it can be compared to smaller climate forcings made in the context
of the present climate (such as a doubling CO2.)
Scattering may also drive the distribution over polarizations toward an equilibrium (which would be,
at any given frequency and direction, constant over polarizations so long as the real component
of the index
of refraction is independent
of polarization) Interactions wherein photons are scattered by matter with some exchange
of energy will eventually redistribute photons toward a Planck - function distribution — a
blackbody spectrum — characteristic
of some temperature, and because the exchange involves some other type
of matter, the photon gas temperature (brightness temperature) will approach the temperature
of the material it is interacting with -LRB-?
In a linear approximation (that the
blackbody spectral flux as a function
of local temperature changes linearly over optical thickness going down from TOA, down to a sufficient optical depth), a doubling
of CO2 will bring the depth
of the valley halfway towards half
of the OLR (the OLR
at 15 microns will decrease by 25 % per doubling — remember this is before the temperature responds).
... the intensity will thus be the
blackbody intensity for the temperature found
at unit optical depth distance from the point
of view.
Depending on the lapse rate in the stratosphere, the hill in the downward flux could reverse
at some point, particularly if their is a large negative lapse rate in the base
of the stratosphere — but I don't think this tends to be the case; anyway, let's assume that the CO2 valley in the TRPP net upward flux only deepens until it saturates
at zero (it saturates
at zero because
at that point the upward and downward spectral fluxes
at the center
of the band are equal to the
blackbody value for the temperature
at TRPP).
In Kiehl and Trenberth 1997, they find a 155 W / m2 total greenhouse effect for approximately present - day Earth conditions (among the approximations: surface is a perfect (isothermal **)
blackbody, and the use a representative 1 - dimensional atmospheric column (instead
of seperate calculations for each location over the globe
at each time over the course
of a period
of time sufficient to describe a climatic state — but note righthand side
of p. 200, just past halfway down the column)... a few other things).
But when optical thickness gets to a significant value (such that the overall spatial temperature variation occurs on a spatial scale comparable to a unit
of optical thickness), each successive increment tends to have a smaller effect — when optical thickness is very large relative to the spatial scale
of temperature variation, the flux
at some location approaches the
blackbody value for the temperature
at that location, because the distances photons can travel from where they are emitted becomes so small that everything «within view» becomes nearly isothermal.
I.absorbed / I.incident = absorptivity; I.absorbed = I.emitted; I.incident = B.emitted (because they have the same brightness temperature, where B.emitted is what would be emitted by a
blackbody, and is what would be in equilibrium with matter
at that temperature), emissivity = I.emitted / B.emitted; therefore, given that absorptivity is independent
of incident intensity but is fixed for that material
at that temperature
at LTE, and the emitted intensity is also independent
of incident intensity but is fixed for that material
at that temperature, emissivity (into a direction) = absorptivity (from a direction).
So the intensity
of radiation (
at some frequency and polarization) changes over distance, such that, in the direction the intensity is going, it is always approaching the
blackbody value (Planck function) for the local temperature; it approaches this quickly if the absorption cross section density is high; if the cross section density is very high and the temperature doesn't vary much over distance, the intensity may be nearly equal to the Planck function for that location; otherwise its value is a weighted average
of the Planck function
of local temperature extending back over the path in the direction it came from.
... The GHE TOA forcing
of 155 W / m2 is approximatly the difference between the
blackbody fluxes
at 255 K and 288 K; thus if maitaining 288 K surface temperature, removing it...
So while, in the isothermal
blackbody surface approximation, if the starting surface temperature is 288 K and we know the OLR is reduced from surface emission by 150 W / m2 via GHE, we know that removing all greenhouse agents will have a TOA forcing
of -150 W / m2, (and some forcing
at the tropopause, etc.) which will cool the surface temperature to about 255 K
at equilibrium, absent non-Planck feedbacks.
For a small amount
of absorption, the emission upward and downward would be about the same, so if the upward (spectral) flux from below the layer were more than 2 * the (average)
blackbody value for the layer temperature (s), the OLR
at TOA would be reduced more than the net upward flux
at the base
of the layer, decreasing CO2 TOA forcing more than CO2 forcing
at the base, thus increasing the cooling
of the base.
The difference in radiant flux will be smaller between 222 K and 255 K, and larger between 288 K and 321 K, and it will take a greater GHE TOA forcing to reduce the effective radiating temperature (the temperature
of a
blackbody that would emit a radiative flux)
at TOA from 288 K to 277 K as it would to reduce it from 277 K to 266 K, etc..
Let's assume that it is the 15 micron OLR that controls the skin temperature; the
blackbody OLR (
at 15 microns) for the skin temperature will be half
of the actual OLR.
Except for: — Your claims that bidirectional EM violates the 2nd law
of thermodynamics; — Your sentient detector that received no energy from the object it is pointed
at but radiates energy according to the temperature it is point
at allowing you to see beyond the edge
of the observable universe (Still awaiting the Nobel prize for that one no doubt); — Your perfectly radiating
blackbody that does not radiate according to its temperature; — Your claims EM energy interferes which prevents energy from a colder body reaching a warmer one — a concept which would mean it would be impossible to see your reflection in a mirror.
Likewise if I illuminate it with a continuous
blackbody spectrum some number
of photons in the continuous spectrum are
at the absorption frequency.
This was the
blackbody radiator fed with 240 W, that need to transfer 240W
at equilibrium to a reflective blanket that only absorbs 10 %
of the incident energy.
Emissivity = proportion
of emission with reference to a
blackbody (it's a ratio) Emission = emissivity x what a
blackbody would emit
at that temperature (it's an absolute value)
Below that you are no longer
at the shell
of the
blackbody but inside
of the black body where radiant energy bounces around until it it finds a home in some spectrum that adds to the emissivity.
If the radiaitve thermal equilibrium is both with the sun (a
blackbody) and space (a
blackbody), then no matter what kind
of non-
blackbody the earth is, absorptivity must still equal emissivity
at every wavelength, unless someone is arguing that Kirchoff's law no longer holds.
The entire atmosphere surface to 100 km edge
of space is already much much warmer than 193K, and a true or «partial»
blackbody at 193K can not warm a much warmer
blackbody at 255K or 288K.
Beginning around 1 / 10th the air pressure
of the Earth
at sea level, Jupiter's atmospheric temperature rises and easily exceeds its predicted
blackbody temperature
of 110 Kelvin.
Nevertheless,
at a certain point atmospheric temperature rises along with pressure and far exceeds NASA's
blackbody prediction
of 226.6 Kelvin for Venus.
So if total solar flux
at Earth distance is 1360 watts per square meter, the
blackbody would absorb all
of this 1360 watts per square meter
of this energy.
At equilibrium with cell contents and source at the same temperature, the spectrophotometer will see the same blackbody curve and total energy flux for T whether the cell is evacuated or filled with any gas or mixture of gase
At equilibrium with cell contents and source
at the same temperature, the spectrophotometer will see the same blackbody curve and total energy flux for T whether the cell is evacuated or filled with any gas or mixture of gase
at the same temperature, the spectrophotometer will see the same
blackbody curve and total energy flux for T whether the cell is evacuated or filled with any gas or mixture
of gases.
I'm not going to review the various arguments that indicate that this is indeed the equilibrium — they are straightforward consideration
of the integrals over the
blackbody spectra from the two bodies that shows that the hotter one loses heat (on average) and the colder one gains heat (on average) until they are
at the same temperature and have identical spectra, where the (time / frequency averaged integral
of the) flux
of the Poynting vector vanishes within microscopic thermal fluctuations
of the sort that are routinely ignored in thermodynamics.
My understanding is that approximately 85 %
of all photons in the Earth's
blackbody spectrum that are also in the absorbtion spectrum
of CO2 are already presently being absorbed
at the present concentration
of atmospheric CO2.
Let's look
at the
blackbody flux densities
of objects
of the temperatures we have been discussing (you can multiply by a 0.95 emissivity if you want to get to real surface values, but it doesn't matter:
The GHGs mean that the atmosphere is essentially opaque to outgoing long - wavelength radiation (approximatelt) and there is a height in the troposphere
at which we effectively emit as a
blackbody with a temperature
of 255 K.
So I cranked the numbers, and showed you that the radiation, even for a
blackbody,
of surfaces
at liquid nitrogen temperatures could not exceed 2 W / m2, trivial compared to the 400 W / m2
of real surfaces
at earth ambient temperatures.
For example, a flat, perfect,
blackbody, receiving 965 W / m ^ 2 would,
at equilibrium, have a temperature
of 361.2 K (88 ºC, 190.5 ºF)
A spherical cavity with a hole is an example and is «close» to a
blackbody, therefore
at MOST we can expect the earth to have energy densities
of a black body (yes gravity complicates the actual temperature on the surface).
Blackbody temperature
at 235 W / m2, the amount
of incoming solar radiation entering our planetary system, is 255K, or -19 C. Thus the earth has «an internal temperature higher than a black body», something which you claim is impossible under any conditions.
For our thought experiment, imagine a planet the size
of the Earth, a perfect
blackbody, heated from the interior
at 235 watts per square metre
of surface area.
looking
at another analogy, the energy emitted by a 100 watt incandescent lightbulb, that emits heat and light across a wide range
of frequencies, but lets just use heat and say that three feet from the bulb, it is IR, and we were to put a globe
of aluminium foil around it to prevent convection, and in another simultaneous experiment we were to line the foil
at the same distance with black paper or another
blackbody material.
Instead
of looking
at the GHE and assuming it is a constant 33 ºC, I have applied the monthly
blackbody temperature
of the Earth to the actual temperature
of the Earth and from that have the monthly
blackbody temperature
of the Earth.
After all, it makes perfect sense that something that is nearly a
blackbody at a temperature
of about 15 C will emit only 50 W / m ^ 2
of emission (gross)...
at least once you repeal a few laws
of physics that were never much use to us anyway!
The
blackbody temperature isn't particularly relevant
at a single point
at the surface because there are lots
of different heat transport mechanisms that affect the local surface energy balance and there's lots
of thermal inertia
at the surface, particularly the oceans.
Now you are saying I can not add the power from the sun to the power from backradiation to get a new total — and then back - calculate the temperature
of a
blackbody which would irradiate
at that temperature.
6) Thus, if we assume, as a first approximation, that the Surface approximates a
blackbody at 288 K, with a spectrum something like the smooth blue curve in my illustration above, we see that the Atmosphere passes the ~ 10μm region (except for part
of the ~ 9.5 μm oxygen / ozone «bite») and, from the Perry plot
of Surface looking UP, re-emits much
of the ~ 7μm and ~ 15μm region back down to the Surface.
Dave in Delaware says: May 9, 2011
at 7:37 am Ira — regarding your summary comment 4)
at May 8, 2011
at 7:51 pm my comment — NO, the atmosphere does NOT emit LWIR across a distribution
of wavelengths like a
blackbody...
The earth is almost a perfect
blackbody emitter in the mid & far - IR and since Kirchkoff's Law imply that the emissivity and absorptivity must be equal
at each wavelength, the means that essentially all
of the radiation that is incident on these objects is absorbed.
If CO2 absorbs
at 15 micron, it also emits
at 15 micron (not a
blackbody distribution
of all wavelengths based on atmospheric temperature).