Myhre came up with a figure of 3.7 W/m2 for the forcing from 2XCO2 by considering a collection of 1D models that covered various latitudes and seasons. Both K19 and WH20 consider only a single 1D column (and not identical columns). Therefore neither study can be considered to provide a “global” forcing for 2XCO2. This is unfortunate, but may be fixed in follow on publications using a collection of 1D models

Of course, the ultimate collection of 1D models is an AOGCM. Those models given us a “global” Planck feedback of 3.2 W/m2 that takes into account the variation in surface temperature (and surface emissivity) everywhere on the at roughly 1,000,000 surface locations and radiative transfer from there to space. The 1D equivalent of this is a graybody model with Ts = 288 K, emissivity 0.615 and a Planck feedback (dW/dTs) = 3.3 W/m2. The 1D model works surprisingly well given that Ts varies from almost 100 degK over the planet.

However water vapor and lapse rate feedbacks in the output from climate models are now being analyzed in terms of the combined WV+LR feedback expected for a planet were relative humidity remains constant and the lapse rate is isentropic or pseudoadiabatic. (K19 uses the former term and WH20 the latter term. I would benefit from a review of this terminology, but I assume the two are equivalent.). So, if we think of AOGCMs being composed of a million or so 1D columns, current analysis can produce a global WV+LR feedback at constant RH and isentropic lapse rate (“CRH+ILR WV+LR”), and model-specific deviations in WV and LR feedbacks from this ideal. Next time I’m looking at a paper that analyzes feedbacks from models, I’ll need to study this more closely.

If I had my own climate model, at each time point I would artificially raise and lower the temperature by 1, 2, 3, 4, and 5 degC in each grid cell and use the radiation transfer model to calculate pdW/pdTs for every grid cell at that timepoints. Then I’d calculate dW/dTs for the same temperature steps after adjusting to constant relative humidity and isentropic lapse rate in each column of grid cells. Then I’d move on to as many time points over as many decades as needed. I’m fairly sure that the partial derivatives that come from “radiative kernels” are not calculated this way, but instead abstracted from the changes in temperature the model produces by a process I don’t fully understand.

]]>Or as Madame Curry says: Uncertainty is the enemy of established orthodoxy.

]]>Thank you for your comment Frank.

I think the work of Kluft et al is very important. It is climate science at its best.

It make me wonder why it has taken so long to get some reasonable research about forcing and feedback. Perhaps the politicization of science has lagged the development of climate knowledge by 10 to 20 years?

Link to paper Wijngaarden and Happer (2020), WH20: https://arxiv.org/pdf/2006.03098.pdf

NK: Climate sensitivity normally refers to a three-dimensional model of our planet with clouds and atmospheric temperature profiles and composition generated by the model. The authors of WH20 calculated climate sensitivity for three ONE-DIMENSIONAL MODELS of the atmosphere with NO CLOUDS (and no cloud feedback). In one model, there is no water vapor feedback (fixed absolute humidity) or lapse rate feedback (6.5 K/km fixed lapse rate). In the second model, water vapor feedback is added by changing to fixed relative humidity. In the third model, lapse rate feedback is added by using a pseudoadiabatic lapse rate. WH20 uses more sophisticated radiative transfer calculations than earlier groups: more weak lines, no water vapor continuum, 500 levels of atmosphere to a 85 km TOA, and improved line shape (?) further from the line center.

Similar radiation transfer calculations were performed with one-dimensional models nearly fifty years ago and in 2019 by Kluft et al (K19) using the Rapid Radiative Transfer Model for GCMs (RRTMG) being used by many AOGCMs. In a sense, radiative transfer calculations with such one-dimensional models serve as a benchmark for effect of changing methodology in radiative transfer calculations – or would be a benchmark, if there weren’t minor differences in the vertical profile of water vapor and temperature near the tropopause. (The K19 model may be slanted towards a 1D model for tropical oceans rather than the planet as a whole.)

K19: https://journals.ametsoc.org/view/journals/clim/32/23/jcli-d-18-0774.1.xml?tab_body=fulltext-display

Is there anything critically new in these papers or their [minor] disagreements? Probably not. However, from K19, I gained a greater appreciation for the fact that the forcing from 2XCO2 is not a fixed 3.7 W/m2/doubling. That value comes from radiative transfer calculations for change in the net LWR flux at the tropopause or at the TOA after the stratosphere adjusts. The forcing for 2XCO2 can also be calculated for these one dimensional models and forcing changes as water vapor feedback and lapse rate feedback can added to these one-dimensional models. When changes to the troposphere are allowed to influence forcing, we refer to effective radiative forcing. Every climate model has different effective radiative forcing for CO2 and other GHGs and agents. I thought these differences arose in some mysterious was from changes in clouds and other phenomena associated with climate change that models might not get right, since ERFs do differ substantially from model to model. However, the K19 one-dimensional model shows that the instantaneous forcing for 2XCO2 is 2.9 W/m2, but rises to 4.7 W/m2 when water vapor and lapse rate feedbacks are operating. So these differences between iRF and ERF are not necessarily the result of mysterious processes in AOGCMs. These differences can be the result of well understood changes in water vapor and lapse rate. K19 notes that the instantaneous forcing for 2XCO2 in the average CMIP5 model is down to 2.9 W/m2, while ERFs vary widely but average 3.45 W/m2.

]]>SoD: “Doubling CO2 from pre-industrial levels will lead to an increased “radiative forcing” of around 3.7 W/m2, and this part of climate science at least, is well understood.” This doubling is from 280 to 560 ppm CO2.

One interesting calculation in the Wijngaarden/Happer paper is the decreased radiative forcing in the middle of the broadest CO2 band: “An exception is the band of frequencies near the center of the exceptionally strong bending-mode band of CO2 at 667 cm−1 . Here doubling CO2 moves the emission heights to higher, warmer altitudes of the stratosphere, where molecules can more efficiently radiate heat to space.” ]]>

Steve,

Explained simply in Opinions and Perspectives – 7 – Global Temperature Change from Doubling CO2

]]>To wit:

“Doubling CO2 from pre-industrial levels will lead to an increased “radiative forcing” of around 3.7 W/m2, and this part of climate science at least, is well understood.”

Elsewhere, my favorite quote is from Dr. Hansen in chapter 8 of the IPCC’s AR4 page 631:

“In the idealised situation … the climate response to a doubling of atmospheric CO2 … would be around 1.2°C”

Is that about right, basic climate sensitivity of CO2 is about 1.2°C?

]]>kereng,

You might find that the series Visualizing Atmospheric Radiation is a help.

I wrote it sometime after this series, with the aid of a line-by-line model (in MATLAB) to calculate all kinds of interesting results.

Results include demonstrating how “saturation” is something that is so wavelength dependent – see Visualizing Atmospheric Radiation – Part Seven – CO2 increases, which includes graphs like this one:

]]>The difference will be no problem when MODTRAN is used to examine the impact of greenhouse gases. But I tried to calculate the blackbody radiation for some temperatures and thought “why not just use MODTRAN with 0 km?”

Now I see, that is not what it is made for. ]]>

Pekka is correct. I’ve actually done the calculation from 5-5000cm-1 using the Planck function and the MODTRAN curve from 100-1500cm-1 is the same. The Stefan-Boltzmann integration is from 0 to ∞ cm-1. The MODTRAN curves are not equal to zero at 100 and 1500cm-1 so you would expect that some of the emission is missed.

However, the atmosphere is completely opaque at frequencies <100cm-1 and >1500cm-1 so you’re not really missing any information.

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