Can variations in lapse rate & cloud cover explain ice-age temperature changes and the inter-glacial "hard stop"?

I woke up this morning thinking about the most fundamental issue of climate:

If the temperature of the earth is set by the blackbody radiation temperature of the earth … and that is fixed in turn by the sun … then how do we see global temperature change.

To rephrase: if there is a greenhouse effect and the temperature of the surface is determined by the black body temperature of the earth + greenhouse effect … how do we see any change of temperature at the surface?
(Personal note to Anthony Watts … unless you believe the blackbody temperature changes, phrasing the issue the way you do implies that ANY & ALL TEMPERATURE CHANGE IS BOTH PROOF OF, AND THE CONSEQUENCE FROM, THE GREENHOUSE EFFECT AND THEREFORE GREENHOUSE GASES).
Just to recap (for those like Anthony who still don’t understand) the way greenhouse warming works. In order for there to be equilibrium, the temperature of the effective radiation surface of the earth must be such that outgoing radiation equals incoming radiation. This temperature is usually given as 255K. But because much of the outgoing radiation occurs from up in  the atmosphere itself where it is cooler, the effective temperature at the effective radiation height is lower than the earth’s surface. The result is that for equilibrium, because the atmosphere is lower in temperature, the surface of the earth must be higher in temperature. This difference (about 32C) is in effect the lapse rate x the effective radiation height.
From this we can see several factors that affect the global temperature:

  1. Solar energy input (which determines the black body temp of 255K)
  2. Effective radiation height (the average height of emitted radiation which in sum has temperature of 255k)
  3. Lapse rate (the temperature from this effective radiation height down to earth).

The effective radiation height is in turn determined the “thickness” of the atmosphere:

  1. Atmospheric pressure (so total atoms which just bulks up atmosphere and raises the height from which IR is emitted – the point the slayer’s keep making)
  2. The relative density of IR interactive molecules like CO2 & H2O (this means emission takes place from less dense layers higher up. This raises average emission height).
  3. The height, density, daily phase (and whether night/day ) of cloud layer

I covered the effect of changing atmospheric pressure before and postulated this as possible (probable?) cause of temperature change. We all know how the relative density of greenhouse gases can affect temperature (but the mechanism is often badly stated on sites like WUWT using the barely scientific model of heat capture). Previously I’ve suggested a global “clouding over” of the earth may be the break that stops the warming at the end of the ice-age and therefore is likely to be the massive negative feedback that prevents further warming in inter-glacials.

Lapse Rate

However, what I’ve not considered so far is a change in the lapse rate – which until now I was considering as a constant.
I’ve previously given a description of why we get a lapse rate before, but to recap, in order for air to rise up against gravity, it must gain potential energy. That potential energy comes via expansion, but originates from the stored heat energy of the air. And because the heat capacity is very close to 1 (of some unit … it must be 0.001 joules/kg/k) … the result when we have a gravitational constant of 9.8 (m/s2) is that we get a dry air lapse rate of 9.8k/km as we rise up through the atmosphere.
However … air is not dry, and when air reaches a height and temperature at which it saturates, water starts to condense. This condensation tends to maintain the temperature. That is to say, evaporating water takes energy so that there is energy stored in the water vapour. So when it condenses this energy is translated into heat energy which maintains the temperature of the air at a higher temperature than it would be if the air were dry and there was no condensation.
The result is that moist air loses less temperature as it rises up in the atmosphere than dry air, so that moist air has a lapse rate of around 5C/km (this varies strongly). Thus if He is the effective radiation height and Hc is the height at which air starts to condense, the overall lapse rate of air up to the effective radiation height He is made up of:

Lapse rate = (9.8 x Hc + ~5 x (He – Hc))/He

The lapse rate is usually stated as being an average of 6.5C/km. If this were the lapse rate to the effective radiation height where the temperature is on average 255k or 32C lower than the earth’s surface, we can calculate what the height of the effective radiation height as 32/6.5 ≈ 5km.
So, by knowing the greenhouse increase and He, we can then work out Hc as:

32 = 9.8 Hc + 5 x(5 – Hc)

Hc = (32-25)/5 ≈ 1.4km

Or to put that another way:

Greenhouse effect = He moist lapse + Hc (dry lapse – moist lapse)

So what does this mean?
One interpretation is that as the average height at which air condenses water (aka cloud base) changes, then this directly affects the greenhouse temperature. As such if the world were to become wetter, then we might assume Hc will drop and so the earth will become cooler. It also follows that when the earth becomes drier, then Hc will rise and so the greenhouse temperature will increase and the earth will become warmer.
This is a very plausible explanation as to why we hit a “dead stop” that stops the temperature rise as we head into an interglacial. But something else must still be causing temperature to rise and that temperature rise then results in more plant growth, plants are a major “polluter” of that toxic greenhouse gas Dihydrogen Monoxide (H2O) and so more plants in turn lead to higher levels of atmospheric humidity. This then would appear to directly moderate Hc thus sharply dropping temperatures.
And we know e.g. that as we came out of the glacial period, areas like the Sahara became very wet and lush.
However whilst this equation can explain the dead stop in the interglacial, it still leaves the massive problem of explaining the large changes going into and out of ice-ages – because we know the climate was drier during the ice-age. This suggests that a drier atmosphere in some way leads to cooling or at least that a drier planet is a consequence of a cooler atmosphere.

Effective radiation Height & clouds

Something else I cannot ignore, is that effective radiation height is significantly affected by the clouds. More clouds and the effective height increases. A raised (top of) cloud layer and the effective height increases. And (living in Glasgow) how could I forget … more clouds means less sunshine to heat us!
So, when cloud layer is sparse … increasing humidity increases cloud cover. If this occurs during daylight the net effect is to block out sunlight and reduce temperature. If it occurs at night, the effect is mainly that of raising effective radiation height (it blocks IR emitters at lower levels) and thereby warming the earth**.
If it is drier during glacials, then this suggests less moisture in the atmosphere and so fewer clouds. If this were in some way to be the cause of cooling, it would require that the lack of moisture led to cooling. There seems to be a paradox (requiring e.g. something else like changes to atmospheric pressure).

Possible model

earth_galileoFirst, however I need to introduce you to our planet as we know it today. As shown right, the planet is covered both by areas of cloud and by areas without cloud. In order for cloud to form, moist air must rise and cool. This air must go somewhere, so in other places there is descending cool air. Which either because it has lost its moisture via precipitation or because it is warming and re-absorbing the water droplets through evaporation, are cloudless.
What drives these circulations are heat flows in the atmosphere. Warm air is heated and rises, it then loses its energy via IR emission to space and then is cold enough and so dense enough to sink.
In meteorologist terms, areas of rising warm moist air are (rainy) low pressure regions and areas of descending cold dry are (sunny) high pressure zones.
I’m beginning to visualise a potential model. Starting in the glacial period, the evidence suggests the planet was drier. So in order to get to the inter-glacial we need a number of feedback mechanism and the effect of water must either be positive (making warming more than it would otherwise) – or at least not sharply negative in its effect.
Therefore, I suggest an initial regime in which rising moisture initially causes an increase in cloud cover at night. Night time cloud is largely a result of the atmospheric circulation patterns I describe above. These are driven by rising warm MOIST air – typically over warm seas. So, they are indicative of warm seas. The reverse of this suggests that the glacial period would see a large reduction in cyclones … and this could be explained by the lack of oceanic currents that cause warm seas in colder areas (like e.g. the Atlantic drift – often falsely referred to as Gulf stream). (see posts of Hadley cells to see why this might occur).
But for some reason there is a limit to how much cloud induced positive feedback and so additional warming that can be caused. This could be because there is a “flip” in the Hadley cell structure, it could be because some fundamental physical barrier which effectively means that cloud cannot cover the earth(perhaps because the layer becomes unstable and rains) But the reason that seems most compelling is that put simply: for every place on the planet where moist air is rising creating clouds, there needs to be a place where dry air is descending giving (everyone but us in Glasgow) sunny weather.
So, when around half (ish++) of the planet is covered by cloud … more cloud can only form by there being a thicker layer of cloud. Now instead of spreading outwards where it tends to raise temperatures, the increasingly moisture in the air can only work by condensing at lower levels causing rain to be produced at lower levels and so reducing the effective radiative level and so reducing the greenhouse effect causing a sharp cooling (if moisture increases). So, when the cloud cover is “saturated” … any further increase in temperature (and so water carrying capacity) causes a sharp drop in cloud level and so drop in Greenhouse warming and so stops further warming.

Summary

In this article I have shown that height of cloud formation can directly change the greenhouse temperature of the planet. I have explained how this would lead to the “dead stop” that prevents runaway warming as we reach the inter-glacial temperatures at the end of an ice-age. I’ve also suggested that a change in how increasing moisture in the atmosphere affects cloud cover may be a possible explanation – or at least contribution- to the generally positive feedbacks that must be present as we “flip” from glacial to inter-glacial and the generally negative feedbacks that create the required “dead halt” that stops further warming and stabilises temperatures during the inter-glacials.


**Imagine a planet where there are no clouds and 50% of outgoing IR originates at ground level below the clouds and 50% above at 2xHe. So average radiation height is He. Now we introduce 100% cloud cover at Hc. Now the average radiation height is He + Hc/2. Thus the average height has increased and if the lapse rate remains the same, then  total greenhouse temperature increases leading to a rise in surface temperature.
++Warm air rises rapidly as a result of intense solar heating during the day. Cooling occurs over longer periods with less intense IR. So it requires more time to lose IR than to gain solar. So I would expect the areas of air “losing” heat to be greater than those where air is rising. Thus I would expect to require more clear areas than cloud.

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