In Part Four we took a first look at overlapping gases. pH2O’s absorption band was changed to overlap pCO2′s absorption band. And remember that pH2O has a much higher concentration in the lower atmosphere.

For those who haven’t followed the series so far, these are fictional molecules with only a passing resemblance to the real molecules H2O and CO2. The massive complexity of real spectral absorption and emission makes it difficult for people to appreciate the key points of radiative transfer in the atmosphere.

And of course, many people don’t want to “just accept” the results of a hugely complex computer model..

The simple model results revealed some interesting points:

- With overlapping bands, increases in pCO2 still led to a reduction in TOA flux.
- With increasing pCO2, DLR (back radiation) remains constant and yet TOA flux reduces.

It’s important to understand these results, because it’s very common to see an implicit belief that the TOA results are some kind of “mirror image” of the surface downward results. They aren’t even though of course they are related.

For the results shown in Figure 7 of Part Four, here is the last TOA spectrum and below, the corresponding DLR spectrum:

*Figure 1*

The balance of energy at TOA is what determines whether the planet warms or cools. Therefore, the spectral values at the surface are **not **the most important for determining which gases make the most contribution to the inappropriately-named “greenhouse” effect.

And the total value of back radiation at the surface is not what determines the long term surface temperature – because it is possible to reduce the TOA flux without increasing the surface downward flux. (Note 1)

Hopefully, this simple model demonstrates those points clearly.

Just for reference I have added this model version, v0.4.0 to the notes.

### Stratospheric Temperatures and “Saturation”

The model results shown in Figure 7 of Part Four show that the TOA flux continues to reduce as the pCO2 concentration increases.

There is an important point here for the ever popular theme of “saturation”.

Let’s take a look at that model again, this time up to very high concentrations of pCO2:

*Figure 2 – Click for a larger image*

Notice that even as the pCO2 concentration has reached 50,000ppm the TOA flux is still reducing for increasing pCO2.

Also notice the temperature profile (5th graph in figure 2) – it’s important.

Now here is a similar model run with a slightly different constraint:

*Figure 3 – Click for a larger image*

These results show that “saturation” is reached much sooner. Notice the temperature profile.

The intensity of radiation is dependent on the temperature of the atmosphere from where the radiation takes place.

So if we have an atmosphere that keeps reducing in temperature as we go higher, then no matter how much the concentration of a “greenhouse” gas increases, the ever-higher radiation will be from a colder temperature – and therefore, will keep reducing in intensity.

Of course, eventually the atmosphere thins out to the point where even this effect disappears.

But hopefully the basic physics behind that idea is clear.

This is why in Figure 3 where the stratospheric temperature is held constant and isothermal (all at the same temperature), the changes in TOA flux level off much sooner. No matter where in the stratosphere the atmosphere radiates from it will be at the same temperature. (See the section “Why the Lapse Rate Matters” in Part Four which is covering a very similar point).

Here is the comparison, of 20 different pCO2 concentrations, where the stratosphere was held at 215K (isothermal) and where the stratospheric temperature was allowed to change according to the radiative heating/cooling:

*Log plot*

*Linear plot*

The temperature profile of the atmosphere does affect the “saturation” or not question by “greenhouse” gases.

Note that this model is still very simplistic – both of the gases have a **fixed absorption within a band and zero outside**. Real gases are much more complex and these complexities are very significant in the “saturation” question.

### Conclusion

This article is more of a summary and consolidation so far, than any new ideas.

The next article, before covering line width issues, will cover some of the basic maths (and an explanation of the maths) behind how radiation moves through the atmosphere. At least that’s the intent at the moment.

*Other articles:*

*Part One – a bit of a re-introduction to the subject
*

*Part Two – introducing a simple model, with molecules pH2O and pCO2 to demonstrate some basic effects in the atmosphere. This part – absorption only*

*Part Three – the simple model extended to emission and absorption, showing what a difference an emitting atmosphere makes. Also very easy to see that the “IPCC logarithmic graph” is not at odds with the Beer-Lambert law.*

*Part Four – the effect of changing lapse rates (atmospheric temperature profile) and of overlapping the pH2O and pCO2 bands. Why surface radiation is not a mirror image of top of atmosphere radiation.*

*Part Six – The Equations – the equations of radiative transfer including the plane parallel assumption and it’s nothing to do with blackbodies*

*Part Seven – changing the shape of the pCO2 band to see how it affects “saturation” – the wings of the band pick up the slack, in a manner of speaking*

*And Also -*

*Theory and Experiment – Atmospheric Radiation – real values of total flux and spectra compared with the theory. *

### Notes

**Note 1**: Reducing the TOA flux = less heat leaves the planet = the planet warms; all other things being equal. More about this idea in The Earth’s Energy Budget – Part Three.

In an immediate sense the back radiation is one of the mechanisms by which the surface is at the temperature it is.

Think of the TOA flux as determining the long term temperature of the surface, and the back radiation as determining the current temperature of the surface.

And for the many who think that this means I am saying convection is unimportant, no I am not. I am explaining one effect on the surface temperature. The essence of understanding a complex subject is to be able to understand the separate effects, and then how they fit together.

**Note 2**: The Matlab code, v0.4.0:

The code is easiest seen by downloading the word doc, but here it is for reference:

======= v0.4.0 ======================

% RTE = Radiative transfer equations in atmosphere

% Objective – allow progressively more complex applications

% to help people see what happens in practice in the atmosphere

% v0.2 allow iterations of one (or more) parameter to find the TOA flux vs

% changed parameter

% v0.3 add emissivity = absorptivity ; as a function of wavelength. Also

% means that downward and upward radiation must be solved, plus iterations

% to allow temperature to change to find stable solution. Use convective

% adjustment to the lapse rate

% v0.3.1 changes the method of defining the atmosphere layers for radiation

% calculations, to have roughly constant mass for each layer

% v0.3.2 tries changing lapse rates and tropopause heights

% v0.3.3 revises element boundaries as various problems found in testing of

% v0.3.2

% v0.4.0 – introducing overlap of absorption bands

clear % empty all the variables, so previous runs can have no effect

disp(‘ ‘);

disp(['---- New Run ---- ' datestr(now) ' ----']);

disp(‘ ‘);

% SI units used unless otherwise stated

% ============= Define standard atmosphere against height ================

% first a “high resolution” atmosphere

% zr = height, pr = pressure, Tr = temperature, rhor = density

Ts=300; % define surface temperature

ps=1.013e5; % define surface pressure

% nmv=2.079e25; % nmv x rho = total number of molecules per m^3, not yet

% used

maxzr=50e3; % height of atmosphere

numzr=5001; % number of points used to define real atmosphere

zr=linspace(0,maxzr,numzr); % height vector from sea level to maxzr

[pr Tr rhor ztropo] = define_atmos_0_2(zr,Ts,ps); % function to determine (or lookup) p, T & rho

% Create “coarser resolution” atmosphere – this reduces computation

% requirements for absorption & emission of radiation

% z, p,Tinit,rho; subset of values used for RTE calcs

numz=30; % number of boundaries to consider (number of layers = numz-1)

minp=3e3; % top of atmosphere to consider in pressure (Pa)

% want to divide the atmosphere into approximately equal pressure changes

dp=(pr(1)-minp)/(numz); % finds the pressure change for each height change

zi=zeros(1,numz); % zi = lookup vector to “select” heights, pressures etc

for i=1:numz % locate each value

zi(i)=find(pr<=(pr(1)-i*dp), 1); % gets the location in the vector where

% pressure is that value

end

% now create the vectors of coarser resolution atmosphere

% z(1) = surface; z(numz) = TOA

% T, p, rho all need to be in the midpoint between the boundaries

% T(1) is the temperature between z(1) and z(2), etc.

z=zr(zi); % height

pb=pr(zi); % pressure at boundaries

Tb=Tr(zi); % starting temperature at boundaries

rhob=rhor(zi); % density at boundaries

% now calculate density, pressure and temperature within each layer

for i=1:numz-1

dz(i)=z(i+1)-z(i); % precalculate thickness of each layer

Tinit(i)=(Tb(i+1)+Tb(i))/2; % temperature in midpoint of boundary

p(i)=(pb(i+1)+pb(i))/2; % pressure in midpoint of boundary

rho(i)=(rhob(i+1)+rhob(i))/2; % density in midpoint of boundary

end

% ============ Set various values =========================

lapse=6.5e-3; % environmental lapse rate in K/m ** note potential conflict with temp profile already determined

% currently = max lapse rate for convective adjustment, but not used to

% define initial temperature profile

ems=0.98; % emissivity of surface

cp=1000; % specific heat capacity of atmosphere, J/K.kg

convadj=true; % === SET TO true === for convective adjustment to lapse rate = lapse

emission=true; % ==== SET TO true ==== for the atmosphere to emit radiation

tstep=3600*12; % fixed timestep of 1hr

nt=1000; % number of timesteps

% work in wavenumber, cm^-1

dv=5;

v=100:dv:2500; % wavenumber (=50um – 4um)

numv=length(v);

rads=ems.*planckmv(v,Ts); % surface emissive spectral power vs wavenumber, v

disp(['Tstep= ' num2str(tstep/3600) ' hrs , No of steps= ' num2str(nt) ', numz= ' ...

num2str(numz) ', minp= ' num2str(minp) ' Pa, Lapse= ' num2str(lapse*1e3) ' K/km']);

% ============== Introducing the molecules ==============================

% need % mixing in the atmosphere vs height, % capture cross section per

% number per frequency, pressure & temperature broadening function

nummol=2; % number of radiatively-active gases

mz=ones(nummol,numz-1); % initialize mixing ratios of the gases

% specific concentrations

% pH2O = pretend H2O

emax=17e-3; % max mixing ratio (surface) of 17g/kg

mz(1,:)=(ztropo-z(1:numz-1)).*emax./ztropo; % straight line reduction from surface to tropopause

mz(1,(mz(1,:)<0))=5e-6; % replace negative values with 5ppm, ie, for heights above tropopause

% pCO2 = pretend CO2

mz(2,:)=3162e-6; % a fixed mixing ratio for pCO2

% absorption coefficients

k1=0.3; % arbitrary pick – in m2/kg while we use rho

k2=0.3; % likewise

a=zeros(nummol,length(v)); % initialize absorption coefficients

a(1,(v>=500 & v<=1500))=k1; % wavelength dependent absorption

a(2,(v>=600 & v<=800))=k2; % ” “

% ========== Scenario loop to change key parameter =======================

% for which we want to see the effect

%

nres=10; % number of results to calculate ******

flux=zeros(1,nres); % TOA flux for each change in parameter

fluxd=zeros(1,nres); % DLR for each change in parameter, not really used yet

par=zeros(1,nres); % parameter we will alter

% this section has to be changed depending on the parameter being changed

% now = pCO2 conc.

par=logspace(-5,-2.5,nres); % values vary from 10^-5 (10ppm) to 10^-2.5 (3200ppm)

% par=1; % kept for when only one value needed

% ================== Define plots required =======================

% last plot = summary but only if nres>1, ie if more than one scenario

% plot before (or last) = temperature profile, if plottemp=true

% plot before then = surface downward radiation

plottemp=false; % === SET TO true === if plot temperature profile at the end

plotdown=true; % ====SET TO true ==== if downward surface radiation required

if nres==1 % if only one scenario

plotix=1; % only one scenario graph to plot

nplot=plottemp+plotdown+1; % number of plots depends on what options chosen

else % if more than one scenario, user needs to put values below for graphs to plot

plotix=[1 round(nres/2) 8 nres]; % graphs to plot – “user” selectable

nplot=length(plotix)+plottemp+plotdown+1; % plot the “plotix” graphs plus the summary

% plus the temperature profile plus downward radiation, if required

end

% work out the location of subplots

if nplot==1

subr=1;subc=1; % 1 row, 1 column

elseif nplot==2

subr=1;subc=2; % 1 row, 2 columns

elseif nplot==3 || nplot==4

subr=2;subc=2; % 2 rows, 2 columns

elseif nplot==5 || nplot==6

subr=2;subc=3; % 2 rows, 3 columns

else

subr=3;subc=3; % 3 rows, 3 columns

end

for n=1:nres % each complete run with a new parameter to try

% — the line below has to change depending on parameter chosen

% to find what the stability problem is we need to store all of the

% values of T, to check the maths when it goes unstable

mz(2,:)=par(n); % this is for CO2 changes

% lapse=par(n); % this is for lapse rate changes each run

disp(['Run = ' num2str(n)]);

T=zeros(nt,numz-1); % define array to store T for each level and time step

T(1,:)=Tinit; % load temperature profile for start of scenario

% remove??? T(:,1)=repmat(Ts,nt,1); % set surface temperature as constant for each time step

% First pre-calculate the transmissivity and absorptivity of each layer

% for each wavenumber. This doesn’t change now that depth of each

% layer, number of each absorber and absorption characteristics are

% fixed.

% n = scenario, i = layer, j = wavenumber, k = absorber

trans=zeros(numz-1,numv); abso=zeros(numz-1,numv); % pre-allocate space

for i=1:numz-1 % each layer

for j=1:numv % each wavenumber interval

trans=1; % initialize the amount of transmission within the wavenumber interval

for k=1:nummol % each absorbing molecule

% for each absorber: exp(-density x mixing ratio x

% absorption coefficient x thickness of layer)

trans=trans*exp(-rho(i)*mz(k,i)*a(k,j)*dz(i)); % calculate transmission, = 1- absorption

end

tran(i,j)=trans; % transmissivity = 0 – 1

abso(i,j)=(1-trans)*emission; % absorptivity = emissivity = 1-transmissivity

% if emission=false, absorptivity=emissivity=0

end

end

% === Main loops to calculate TOA spectrum & flux =====

% now (v3) considering emission as well, have to find temperature stability

% first, we cycle around to confirm equilibrium temperature is reached

% second, we work through each layer

% third, through each wavenumber

% fourth, through each absorbing molecule

% currently calculating surface radiation absorption up to TOA AND

% downward radiation from TOA (at TOA = 0)

for h=2:nt % main iterations to achieve equilibrium

radu=zeros(numz,numv); % initialize upward intensity at each boundary and wavenumber

radd=zeros(numz,numv); % initialize downward intensity at each boundary and wavenumber

radu(1,:)=rads; % upward surface radiation vs wavenumber

radd(end,:)=zeros(1,numv); % downward radiation at TOA vs wavenumber

% units of radu, radd are W/m^2.cm^-1, i.e., flux per wavenumber

% h = timestep, i = layer, j = wavenumber

% Upward (have to do upward, then downward)

Eabs=zeros(numz-1); % zero the absorbed energy before we start

for i=1:numz-1 % each layer

for j=1:numv % each wavenumber interval

% first calculate how much of each monochromatic ray is

% transmitted to the next layer

radu(i+1,j)=radu(i,j)*tran(i,j);

% second, add emission at this wavelength:

% planck function at T(i) x emissivity (=absorptivity)

% this function is spectral emissive power (pi x intensity)

radu(i+1,j)=radu(i+1,j)+abso(i,j)*3.7418e-8.*v(j)^3/(exp(v(j)*1.4388/T(h-1,i))-1);

% Change in energy = dI(v) * dv (per second)

% accumulate through each wavenumber

% if the upwards radiation entering the layer is more than

% the upwards radiation leaving the layer, then a heating

Eabs(i)=Eabs(i)+(radu(i,j)-radu(i+1,j))*dv;

end % each wavenumber interval

end % each layer

% Downwards (have to do upward, then downward)

for i=numz-1:-1:1 % each layer from the top down

for j=1:numv % each wavenumber interval

% first, calculate how much of each monochromatic ray is

% transmitted to the next layer, note that the TOA value

% is set to zero at the start

radd(i,j)=radd(i+1,j)*tran(i,j); % attentuation..

% second, calculate how much is emitted at this wavelength,

radd(i,j)=radd(i,j)+abso(i,j)*3.7418e-8.*v(j)^3/(exp(v(j)*1.4388/T(h-1,i))-1); % addition..

% accumulate energy change per second

Eabs(i)=Eabs(i)+(radd(i+1,j)-radd(i,j))*dv;

end % each wavenumber interval

dT=Eabs(i)*tstep/(cp*rho(i)*dz(i)); % change in temperature = dQ/heat capacity

T(h,i)=T(h-1,i)+dT; % calculate new temperature

if T(h,i)>500 % Finite Element analysis problem

disp(['Terminated at n= ' num2str(n) ', h= ' num2str(h) ', z(i)= ' num2str(z(i)) ', i = ' num2str(i)]);

disp(['time = ' num2str(h*tstep/3600) ' hrs; = ' num2str(h*tstep/3600/24) ' days']);

disp(datestr(now));

return

end

% need a step to see how close to an equilibrium we are getting

% not yet implemented

end % each layer

% now need convective adjustment

if convadj==true % if convective adjustment chosen..

for i=2:numz-1 % go through each layer

if (T(h,i-1)-T(h,i))/dz(i)>lapse % too cold, convection will readjust

T(h,i)=T(h,i-1)-(dz(i)*lapse); % adjust temperature

end

end

end

end % iterations to find equilibrium temperature

flux(n)=sum(radu(end,:))*dv; % calculate the TOA flux

fluxd(n)=sum(radd(1,:))*dv; % calculate the DLR total

% === Plotting specific results =======

% Decide if and where to plot

ploc=find(plotix==n); % is this one of the results we want to plot?

if not(isempty(ploc)) % then plot. “Ploc” is the location within all the plots

subplot(subr,subc,ploc),plot(v,radu(end,:)) % plot wavenumber against TOA emissive power

xlabel(‘Wavenumber, cm^-^1′,’FontSize’,8)

ylabel(‘W/m^2.cm^-^1′,’FontSize’,8)

title(['pCO2 @ ' num2str(round(par(n)*1e6)) 'ppm, TOA flux= ' num2str(round(flux(n)))...

' W/m^2, DLR= ' num2str(round(fluxd(n)))])

% —

%subplot(subr,subc,ploc),plot(T(end,:),z(2:numz)/1000)

%title(['Lapse Rate ' num2str(par(n)*1000) ' K/km, Total TOA flux= ' num2str(round(flux(n))) ' W/m^2'])

%xlabel(‘Temperature, K’,’FontSize’,8)

%ylabel(‘Height, km’,’FontSize’,8)

grid on

end

end % end of each run with changed parameter to see TOA effect

if plotdown==1 % plot downward surface radiation, if requested

plotloc=nplot-plottemp-(nres>1); % get subplot location

subplot(subr,subc,plotloc),plot(v,radd(2,:)) % plot wavenumber against downward emissive power

title(['Surface Downward, W/m^2.cm^-^1, Total DLR flux= ' num2str(round(fluxd(n))) ' W/m^2'])

xlabel(‘Wavenumber, cm^-^1′,’FontSize’,8)

ylabel(‘W/m^2.cm^-^1′,’FontSize’,8)

grid on

end

if plottemp==1 % plot temperature profile vs height, if requested

plotloc=nplot-(nres>1); % get subplot location

subplot(subr,subc,plotloc),plot(T(end,:),z(2:numz)/1000)

title(‘Temperature vs Height (last scenario)’)

xlabel(‘Temperature, K’,’FontSize’,8)

ylabel(‘Height, km’,’FontSize’,8)

grid on

end

if nres>1 % produce summary plot – TOA flux vs changed parameter

subplot(subr,subc,nplot),plot(par*1e6,flux)

title(‘Summary Results’,’FontWeight’,’Bold’)

ylabel(‘TOA Flux, W/m^2′,’FontSize’,8)

xlabel(‘pCO2 concentration, ppm’,’FontSize’,8) % ==== change label for different scenarios =========

grid on

end

disp(['---- Complete End ---- ' datestr(now) ' ----']);

on February 6, 2011 at 1:34 am |Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Four « The Science of Doom[...] « Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Three Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Five [...]

on February 6, 2011 at 3:25 am |JerryI’m not fully across your model, but I have a minor question which may have already been answered.

Do you account for density changes as well? I expect that at any given level of atmosphere at any given temperature, there will be a preferential energy flow in the direction of lower density. Simply because the mean free photon path will be longer in that direction.

Is this assumption correct?

If so, is it accounted for in your model?

on February 6, 2011 at 3:45 am |scienceofdoomJerry:

Yes, you can see it in the pressure graph shown in Figure 2 of Part Two:

But for completeness here is a plot of density vs height:

And with density shown as a log plot:

on February 7, 2011 at 12:51 pm |JerryHello Science of Doom.

Thanks for the response, but I think you missed the point of the question, which was does a density gradient favour photo radiation flow from the more dense to less dense part? If so, do you account for that in your model?

on February 6, 2011 at 9:46 am |ErnestIt is nice to note that “science of doom” uses consequently the quotation marks around the word “greenhouse” when describing the response of the atmosphere to the thermal radiation from the surface. This is because the underlying physics is not about “the glass houses for cultivation of vegetables” but about “the roasting of a chicken in the microwave oven”.

Thus, we have a chicken (here the atmosphere) and the source of microwave radiation (here the thermal radiation from the surface). The differences are that the source of radiation covers a wide range of wavelength, the heater is places inside “the chicken” and the heat is allowed to escape from the system. The latter indicates that we will always expect the appearing of the temperature gradient independently if the “chicken” absorbs radiation or not. Besides, the chicken meat does not allow the convection process, which makes the chicken to be less useful as a model example.

But let’s stop talking about the roasting of a chicken since this will scare people to death.

So back to the real issue. The surface of the Earth has some temperature and warms the surrounding air by convection, conduction and radiation. The addition of the absorbing molecules increases the efficiency of the absorbing process. As a consequence, this leads to the additional raise of the temperature of the air and of the heater itself. The efficiency of the molecules to affect the temperature of the system by radiation can be found by means of, for example, a transient experiment when studying how the temperature of the transient heater is changing as a function of time due to the different concentrations of the molecules in the air. Such an experiment has nothing to do with the temperature lapse across the air and can be performed inside the greenhouse if one lacks the access to a more suitable place for carrying out the experiment.

The presence of the lapse makes, however, both the theory and the computations more complex, especially since the change of the lapse influences also the efficiency of convection. However, intuitively one would expect that the impact of the absorbing molecules on the temperature of the system will be stronger when the flow of heat is prohibited out of the system (the system is kept at a constant temperature) than when we allow a part of heat to leave the system through the outer surface. The results presented by “science of doom” confirm this, if I have understood the figures correctly.

I would also like to emphasize what all the other participants are mentioning in their posts, namely that “science of doom” is doing an excellent job.

on February 6, 2011 at 11:46 am |ErnestThe impact of the atmosphere on the climate of the Earth might be more clearly understood from studying the functioning of the electric bulb lamp.

Energy, delivered to the bulb is loosed to the surrounding by the thermal emission. But, notably, the air is evacuated from the bulb in order to achieve the higher temperature of the radiation element. With the air present around the heating element, the temperature of the heating element would be lower. This is due to the fact that the element is now cooling not only by the radiation losses but also by the heat conduction and convection through the air. The doubling of CO2 in the air within the bulb will not change the situation much.

The effect is thus opposite to what the climate science is expecting from the adding of the atmosphere to the radiative system.

But it should be remembered that in the case of the bulb we are talking about very large temperature gradient. The heat convection through the air is in such a case much stronger than the radiation from the air back to the heating element.

If we lower the power input into the heating element, the temperature of the heater will decrease, and the efficiency of the convectional heat losses will decrease, too. This will also decrease the radiation out from the heater and thus the efficiency of heating the air through the absorption of radiation. This drop of efficiency might be compensated by the increase of the absorbing molecules in the air. This will not affect the convection but will increase the amount of radiation that is absorbed by the air.

Assume that we succeed in absorbing all the radiation that leaves the heater. A part of this absorbed radiation will still manage to leave the system through radiation while the rest will be radiated back to the heater. This will certainly slow down the cooling of the air and the heater, but the temperature of the heater will still go down until it has stabilized at the new, now slightly higher level than previous one before enriching the air by the absorbing molecules. But even so, this new temperature will be lower than that before letting air to surround the heater.

Well, this is the problem that makes me uneasy about the explanation given by the climate science, namely, that the variation of the temperature of the Earth is explained by the variation of the absorbing gases in the atmosphere, solely. The changes of the composition of the air might affect the general trend of the temperature changes observed from the diagram of the temperature variations on the million years scale, but the absorbing gases seems not to be the main cause for these general temperature trends. I must therefore agree with DeWitt Payne, mentioning that the dominating factor causing the temperature trends on the Earth might be prescribed to the drifts of the continents and the changes of the energy flow from the inside of the Earth to the surface (which might result in volcanoes and collisions between the continental plates).

on February 6, 2011 at 11:02 pm |FrankSOD: The results are getting more and more elegant.

One caveat: On the real earth, the stratosphere is warmer than the tropopause because oxygen and ozone absorb solar UV at this altitude. Increasing CO2 causes the stratosphere to cool because it is absorbing photons in the CO2 band from locations that are mostly cooler. This phenomena produces small spikes in the TOA spectrum when the spectrum is calculated well above the tropopause. Your model may be incapable of simulating this phenomena and the stratospheric cooling/tropopause warming “fingerprint” of GHG forcing.

However, I am confused about some aspects of your model, which may have changed. In Part II, you showed a temperature profile with a fixed lapse rate in the troposphere ending at about 12 km, a tropopause from 12-17 km, and a rising temperature in the stratosphere. I initially thought this temperature profile with altitude was unchanging. I also assumed that a similar unchanging profile was used by MODTRAN and HITRAN (but changing in the IPCC’s definition of forcing). Now it appears that the temperature profile above the troposphere or tropopause is being allowed to reach radiative equilibrium in your model while the troposphere has a fixed lapse rate. If you want to model the complications introduced by a warm stratosphere, you need to introduce a heat source at these altitudes OR, second-best, have a preset temperature profile with altitude. The model also needs the TOA (which was at 17 km in one case) to be well above the tropopause.

on February 6, 2011 at 11:51 pm |scienceofdoomFrank:

The model is still simple with no solar heating. Effectively the model has a totally transparent atmosphere (to solar radiation). And of course, with no solar heating of ozone the stratosphere won’t increase in temperature. This might be something to be added in due course.

The temperature profile shown in Figure 2 of Part Two is the “starting” profile.

Usually the model then develops its own temperature based on the effect of radiation absorbed vs emitted, with a “convective lapse rate” adjustment.

So if the temperature is too cold as height increases, then the temperature is adjusted to the lapse rate.

The lapse rate is a parameter that can be varied, as shown in Part Four.

In the case of

Stratospheric Temperatures and “Saturation”, I then added the ability in the model to fix the temperature of the stratosphere at one value. This helps to see how “saturation” can occur – at least in the case of an absorption band with very simple characteristics.The model runs since Part Four have had the TOA lifted, usually above 30km. It is the parameter called “minp” in the code – which is in pressure, in v4.0 it is 3000Pa, or 3% of the surface pressure.

on February 7, 2011 at 9:03 am |FrankSOD: If you are looking for more things to try with your model, I’d love to see the pCO2 band broken up into 9 or 19 sub-bands of 20 or 10 cm-1 and one central band (680-720 or 690-710) twice as wide as the others. If the central band has an absorption coefficient of 0.8 or 1.6 and dropping two-fold each step from the center, the average absorption will remain about the current 0.3. With 32-fold or 512-fold changes in absorption, as CO2 increases we may see the center of the band saturate, while some section of the “wings” continues to grow with changes of a few W/m2 at the TOA. With modest changes in CO2 (2-3 fold), you might need to superimpose plots to see the difference or plot the differences. (I won’t be surprised to find that you are already several steps ahead of these suggestions.)

on February 7, 2011 at 9:11 am |FrankSOD’s model allows atmospheric temperature to reach radiative equilibrium above the top end of the fixed lapse rate. Does anyone know what happens with MODTRAN or HITRAN? Do these use a fixed temperature vs altitude profile (a “standard atmosphere” representing some sort of global average) or a “radiatively equilibrating” atmosphere or can you select from a variety of options? The IPCC defines forcing after radiative equilibration in the stratosphere, so this capability exists somewhere.

on February 7, 2011 at 10:06 am |ErnestI have mentioned previously about ”the roasting of a chicken in the microwave oven” and “bulb lamp”. These two examples relate mainly to the rubric “Understanding …..” rather than to the actual problem of the temperature gradient across the atmosphere. So let me finish quickly my digression by being more precise on how these examples might contribute to the Understanding.

The example with roasting of a chicken shows that the effects of absorption of radiation can be explained, and even studied, in a quite simple manner. The simplicity of it is that a part of radiation from the heater is used for the raising of the temperature of the chicken instead of being emitted “unused” out to the space as it would be in the case if the chicken had lacked the absorbing molecules. This is as simple as that, so the climate scientists must stop using the word greenhouses, which is only misleading in this connection, and makes people to treat these scientists as being completely ignorants. The experiments by use of the microwave oven (not necessary with a chicken) might help a) to study the “saturation” effects, b) to check both the different theories and results of computational calculations concerning the formation and maintaining of the lapse across the object of study and c) to investigate the “TOA” effects.

The example with the bulb lamp points on the risks for misunderstanding the real processes when presenting explanations with convection and radiation being separated from each other. The evacuation of the air from the around of the filament reduces to zero (more or less) the contribution from the convection without changing the “back radiation” from the surrounding, here coming from the glass housing. This is pointing on the importance of convection and on its role in counteracting the influence of the downward radiation on the temperature of the source. On the experimental level, one is talking about the line source experiments, which are a well-known technique for studying the thermal properties of gases and liquids. Such a method might be used for the determination of the properties of air with or without different absorbing agents in the air. The experimental creates also the lapse across the material under the study which might be studied by means of the optical interferometric technique.

on February 7, 2011 at 12:09 pm |David ReeveSOD, I’m having trouble with the DLR being independent of pCO2 concentration. I can see that Part 4 started with a dependence which was lost in the last simulation run, yet I can’t see what changed in the model to make it so.

on February 7, 2011 at 12:25 pm |scienceofdoomDavid Reeve:

Problems in understanding are critical to making progress – it’s a serious point. At least, I have generally found this to be the case for myself.

Mathematically the answer is correct. Nothing has changed in the underlying physics of the model.

What you seek is conceptual understanding of how this can happen.

Here is my best attempt at a conceptual model for you. Picture a lot of pH2O in the lower troposphere. And picture a lot of pCO2 in the upper troposphere.

The pCO2 radiates into the pH2O which absorbs it all – and IN TURN – radiates down to the ground.

The pCO2 radiates up to the sky, which doesn’t absorb anything, so this is the radiation to space, or TOA flux, or “cooling to space”.

The pH2O in the lower troposphere radiates down to the ground ACCORDING to its temperature.

The temperature of pH2O is determined (primarily) by the surface temperature (and the radiative/convective linkage between the surface and the lower troposphere).

So pCO2 – in the SHORT TERM – cannot affect the downward radiation of the pH2O, because the temperature of the surface is the main determinant of the pH2O temperature.

But pCO2 – in the long term – CAN affect the surface temperature because less outgoing radiation (less cooling to space) means the climate heats up.

Exactly how that is “mediated” to the surface depends on many factors, but ultimately the surface will keep warming until the TOA flux balances the absorbed solar radiation (all other things being equal).

So long term (all other things being equal) an increase in pCO2 will cause more DLR from the pH2O. But it won’t show up in the short term, it is all “blocked” by the pH2O.

on February 7, 2011 at 1:07 pm |scienceofdoomJerry:

Thanks for the response, but I think you missed the point of the question, which was does a density gradient favour photo radiation flow from the more dense to less dense part? If so, do you account for that in your model?

Yes.

The absorption and emission is dependent on density.

There is a term in the code, called “trans”:

trans=trans*exp(-rho(i)*mz(k,i)*a(k,j)*dz(i)); % calculate transmission, = 1- absorptionThis is the calculated transmittance, dependent on density for that layer x concentration of that gas in air.

So the equations automatically take care of effect of the density changes.

on February 8, 2011 at 12:28 pm |David ReeveSOD, thanks for the explanation. I now can see that what has changed in the model is the fact the pH20 absorption band overlaps the pCO2 band.

When the bands are separate, the two components independently contribute to DLR from the lower (and presumably different, ie optical range will differ with wavelength) layers of the troposphere, regardless of the fact that pH20 is at a far higher concentration than pCO2. Thus changes in pCO2 must impact the DLR.

However, when the absorption band of pH20 overlaps that of pCO2, the high pH2O concentration means pCO2 will have minimal impact on the signal. I can see this is not a simple relationship and is safer to model than it is to work out on the back of an envelope.

on February 8, 2011 at 9:05 pm |scienceofdoomDavid Reeve:

Glad my comment was some help.

on February 8, 2011 at 10:36 pm |DeWitt PayneFrank,

HITRAN is a database of molecular absorption lines, not a program to calculate atmospheric emission and absorption. Talking about a temperature profile in HITRAN has no meaning. SpectralCalc is a line by line program that uses the HITRAN database. That program does use different temperature profiles as does MODTRAN, which is a band model rather than line by line.. The standard profiles are tropical, mid-latitude summer and winter, sub-Arctic summer and winter and US 1976 standard atmosphere (SpectralCalc also has a Martian atmosphere). In MODTRAN when you change the surface temperature offset, it changes the temperature in the troposphere for altitudes from 0-11 km only by the magnitude of the surface temperature offset. The temperature (and pressure, concentration, etc.) profiles in MODTRAN can be accessed by selecting the save text output for later retrieval option and then clicking on the link at the bottom of the right hand pane after results have been calculated.

SpectralCalc

http://www.spectralcalc.com/info/about.php

MODTRAN

http://geoflop.uchicago.edu/forecast/docs/Projects/modtran.orig.html

on February 10, 2011 at 3:10 am |FrankThanks DeWitt. SOD’s model makes me wonder what I’ve been looking at. There are a variety of possible temperature vs altitude profiles. Do these profiles adjust to radiative equilibrium above the tropopause (as required for calculating radiative forcing according to the IPCC’s definition) or are we seeing a fixed profile until the TOA.

on February 13, 2011 at 3:53 pmDeWitt PayneThe profiles are fixed above the tropopause (actually 12 km and up for MODTRAN as implemented on the web) so forcings calculated using MODTRAN or SpectralCalc do not correspond to the IPCC definition.

The lapse rate doesn’t change either. You don’t get the upper tropical troposphere warming faster than the surface when you change the surface temperature using the surface offset. You need a radiative/convective model for that. Except no such thing actually exists. Convection is handled by a kludge in GCM’s. The entire 100 km2 cell is convectively re-arranged whenever some stability parameter is exceeded.

Some argue (Gerald Browning for example in several long threads at Climate Audit) that even weather forecasting models don’t properly model convection. The needed resolution may be on the order of 1 mm. While weather models are much finer than GCM’s they’re still orders of magnitude away from that. Then there’s the problem that as you go to finer resolution, the stability of the solution gets worse exponentially. Spatio-temporal chaos is really messy.

http://judithcurry.com/2011/02/10/spatio-temporal-chaos/

on April 8, 2011 at 6:08 am |Jochen EbelThe density of the molecules is essential for the greenhouse effect. The amount of the molecules determines the pressure increase. Therefore the following diagram:

http://www.bilder-hochladen.net/files/h9qc-b-jpg.html

[img]http://www.bilder-hochladen.net/files/h9qc-b-jpg.html[/img]