As I pointed out above ln CO2 is
an additional radiative forcing, therefore you need to integrate it (or differentiate you T model to get dT / dt).
(b) Pistone et al. (2014) shows that the decrease in Arctic albedo (including land snow, sea ice and black carbon effects) beyond that previously assumed results in
additional radiative forcing equal to 1/4 of the CO ₂ in the atmosphere.
The new forcing estimate comes about from a newer understanding of the role of aerosols as well as
the additional radiative forcing from greenhouse gas emissions since 2005.
I was responding to someone who was using an equation that represents a temp differential from one equilibrium state to the next, based on
additional radiative forcing.
You could argue that Sensitivity was.5 and that C02 supplied
no additional radiative forcing, but sensitivity can not be zero.
Because there are overlaps — clouds alone could accomplish more; the presence of the gases reduces
the additional radiative forcing caused by the addition of clouds.
[Response: To pre-empt some mutual incomprehension, note that industrial CO2 rises are certainly an anthropgenic forcing and not a response (see here and here), but clearly CO2 changes over glacial - interglacial cycles is both a response (to Milankovitch - driven changes) and a forcing (since
the additional radiative forcing from CO2 is about a third of that needed to keep the ice ages as cold as they are — see here).
And the post provided an initial explanation as to why and how the global oceans could rise and fall without
additional radiative forcings.
Not exact matches
Observations from earlier periods are limited but suggest an
additional negative
radiative forcing of about — 0.1 W / m2 from 1960 to 1990.
A clear explanation of
radiative forcing, CO2 infrared opacity and how
additional atmospheric CO2 will contribute to significant warming would be important to many of trying to explain the physics of global warming.
As an example of the possible extreme change in
radiative forcing in a 50 - year time horizon for Isaken et al (2011)'s 4 x CH4 (i.e. quadrupling the current atmospheric methane burden) case of
additional emission of 0.80 GtCH4 / yr is 2.2 Wm - 2, and as the
radiative forcing for the current methane emissions of 0.54 GtCH4 / yr is 0.48 Wm - 2, this give an updated GWP for methane, assuming the occurrence of Isaksen et al's 4 x CH4 case in 2040, would be: 33 (per Shindell et al 2009, note that AR5 gives a value of 34) times (2.2 / [0.8 + 0.48]-RRB- divided by (0.54 / 0.48) = 50.
Overall, humans have caused an
additional heating (
radiative forcing) of 2.3 watts per square meter of Earth surface — as of 2011.
The magnitude of the
radiative forcing per doubling is equal to the effect of band widenning, which is (BW1 + BW2) * depth of valley or height of hill, plus some
additional effect in the center of the band, which is on the order of 1/2 * (BW1 + BW2) * increase in height or depth of hill or valley; the central contribution could be more or less than that, but it will be less than double (because the shape of the absorption spectrum won't allow a square shape in the graph of the spectral flux).
If it reverses, we can treat the value at the point of reversal (marking a maximum height or depth of the hill or valley in the net upward flux spectrum) as the saturation value, and then include some
additional effect at the center of the band for
additional increases in CO2 that have the opposite sign as the band widenning in their contributions to
radiative forcing.
So for every
additional ton of CO2 emitted, a larger fraction resides in the atmosphere and contributes to increased
radiative forcing, which would bend the curves in figure 1 upward.
My understanding is that the issue over the theory of CO2
forcing is not disagreement over
radiative energy transport but 1) The
additional forcing required to make
radiative forcing a potential crisis and 2) the lack of consideration of convective heat transfer.
Every further doubling adds an
additional 4 Wm - 2 to the
radiative forcing.
At a regional scale and at the surface,
additional more localised and shorter time - scale processes besides
radiative forcing can affect climate in other ways, and possibly be of comparable importance to the effects of the greenhouse gases.
For RCP8.5,
radiative forcing from tropospheric ozone, according to the CAM3.5 calculations, increases by an
additional 0.2 W / m2 by 2100 (Lamarque et al. 2011).
Additional proxy records that cover the entire CE are needed to investigate decadal - to centennial - scale responses of climate to changes in
radiative forcing as well as internal variability at these time scales.
Conversion from the
forcing to a change in effective
radiative black body temperature is well defined and without any
additional uncertainty, when the effective
radiative temperature is defined as the temperature of a black body that radiates as much IR energy as the Earth.
Methane is an important part of the anthropogenic
radiative forcing Methane emissions have a direct GHG effect, and they effect atmospheric chemistry and stratospheric water vapour which have
additional impacts natural feedbacks involving methane likely to be important in future — via wetland response to temperature / rain change, atmospheric chemistry and, yes, arctic sources There are large stores of carbon in the Arctic, some stored as hydrates, some potentially convertible to CH4 by anaerobic resporation [from wikianswers: Without oxygen.
Additional output from the ACCMIP runs will include concentration / mass of radiatively active species, aerosol optical properties, and
radiative forcings (clear and all sky) as well as important parameters that do not directly influence climate such as hydroxyl, chemical reaction rates, deposition rates, emission rates, surface pollutants and diagnostics of tracer transport.
Additional column calculations show a weakened
radiative forcing when the cloud optical depth is much greater than the aerosol optical depth (Haywood and Shine, 1997; Liao and Seinfeld, 1998) and show that the
forcing is insensitive to the relative vertical position of the cloud and aerosol.
Observations from earlier periods are limited but suggest an
additional negative
radiative forcing of about — 0.1 watt per square meter from 1960 to 1990.
So each
additional doubling in CO-2 adds the same (not half) the effect, in terms of
radiative forcing.
Radiative forcing is a multiplier that is added to the carbon emissions factor, that quantifies these
additional effects; including the fact that emitting GHGs in the upper atmosphere has a greater heat - trapping effect than emitting GHGs at ground level.
But, such a calculation is not what is actually made to determine the
radiative forcing due to
additional CO2.
The
radiative forcing for
additional CO2 is already calculated taking into account the effects of which you speak.
A more likely scenario for interpretation of the observed warming of the early 20th century might be a smaller (and therefore more likely) realization of internal variability coupled with
additional external
radiative forcings.
Unfortunately, the IPCC has chosen to define
radiative forcing as the change in flux at the tropopause, a location where
additional complications may obscure relevance to surface temperature change.