Cloud-temperature feedback

In my three feet of global warming note, I mentioned that two processes in the climate system are a) warmer temperatures -> more moisture in the atmosphere, and b) more moisture -> more severe storms.  A commenter followed up wondering how warming could actually take place, if a) more moisture -> more clouds and  b) more clouds -> cooler temperatures.

A key word there is if.  Although warmer temperatures are observed to lead to more moisture in the atmosphere, it isn't clear that more moisture actually leads to more clouds.  Section 3.4.3 of the IPCC report gives you an overview of the literature on the topic.  Depending on which scientific paper you read, it's more cloud, less cloud, or more over one surface type and less over another.  In other words, an area of significant scientific debate.

It's also a question whether more clouds mean cooler temperatures.  If you're from a cold weather climate, you've experienced that on clear days you get a nice warm daytime temperature, but also a blistering cold nighttime.  Because of those very cold nights, cloudy days can actually average warmer than a sunny day.  The daytime isn't quite as warm, but the night time is far warmer.

Let's take a deeper look in to the relationships between clouds, in particular to look at the feedback on temperature.  You'll notice that the commenter's question is about a feedback -- we start with temperature, and processes occur which ultimately lead to an effect on temperature.  What I'd originally talked about was a straightforward chain.  One thing causes another, causes another.  But no effect on the term or process that started us off.  We'll ultimately get back to the simplest climate model, as it can help shed some light on the question as well.

One aspect of the question is, just what do we mean by 'more cloud'?  If it means thicker clouds, but of the same types as already exist, that is indeed 'more'.  But it means little or no change in how much energy the clouds reflect from the sun, or how much of a blanketing effect they provide.  Most clouds are already thick enough that making them a bit thicker doesn't change their behavior as far as radiation is concerned. 

A different type of 'more' is to have more area of some cloud types.  This added area then reflects more solar energy.  But it also provides a better blanket to earthly temperature.  As result of this is, you have to look at the balance between the two effects.  This has been done, and the result is, some cloud types provide net warming of the surface, and some provide net cooling.  So your question in this becomes whether the cloudiness increase, if you do get one (the IPCC report was showing that even for total cloudiness it isn't clear whether there's more or less -- figuring out which type of cloud you have more or less of is even harder), is more of the warming type of cloud or cooling type.

But for now let's assume that warmer temperatures really do lead to more clouds, and in such a way that the net effect of those clouds is a cooling.  Can it still turn out that the climate warms anyhow?

To look at this, I'll return to the simplest climate model.  We'll have to abuse it some -- use it in ways that violate the assumptions we made in developing it.  Consequently, we can't be entirely confident about the results or trust them as closely as we'd like, but, again, it makes for a helpful heuristic to guide our thinking some before we pull out the supercomputer and start it cranking away for a few weeks.

In the simplest model, we balance incoming solar energy at the top of the atmosphere, minus what gets reflected away (among other things, by clouds), with the energy emitted by the earth.  If you the solar constant to be 1367 W/m^2 and the earth's albedo to be 0.300, you arrive at a black body temperature for the earth of 255 K (254.86), which is in fair agreement with the observations.  The earth's surface temperature, on the other hand, actually averages about 288 K.  This is our sign that to understand the surface temperature, we need more than just the black body temperature, and more processes than just the very simple energy in (at the top of the atmosphere) = energy out (at the top of the atmosphere).

Remember that the sun's rays pass through a disk of area pi * r * r, while the earth emits from an area 4 * pi * r * r.  So, if we knew how much effect changing a greenhouse gas at the surface, we could multiply this by 4 (the fact that the surface is that much bigger than what the solar rays go through) and get an equivalent change to the solar constant.  Since doubling CO2 is expected to lead to about 4 W/m^2, this means the climate effect is something like increasing the solar constant by 16 W/m^2.  If you run the simplest model with a solar constant of 1383 W/m^2, you get a black body temperature of 255.6 K, about 3/4ths of a degree warmer.  Again, this is quite different than the expected surface change (about 3 degrees K, 4 times larger), which again tells us that we need to know more than just the simplest model.

Still, it gives us our start for thinking about the effects of clouds.  Clouds do affect the earth's albedo, and that linked-to article will give you some sample numbers for what the albedo is like for different surfaces, clouds included.

Our simple method for looking at the feedback is this:
1) Start with observed solar constant and albedo, compute the earth's black body temperature
2) Increase the solar constant for the enhanced greenhouse effect, compute the new earth temperature
3) Change the albedo to represent the increased (we're assuming it's an increase) in cloud area, and compute that temperature.

If the temperature after step 3 is colder than step 1, clouds have erased the warming from greenhouse gases.  (At least they have for the black body temperature, we clearly have more work to do than this model can help us with in order to decide what happens to the surface temperature.)  If the temperature after step 3 is warmer than step one, then even though we've said that clouds increase (which is not yet observed) and it's the type of clouds that produce cooling (even more questionable), we still wind up with a net warming.

Now let's think a bit about albedo and how much it might be changing.  I'll take a very simple set of figures for illustration.  Take cloud albedo as 0.5.  Clouds can be over land -- albedo 0.2, or ocean -- albedo 0.05.  Cloud does have to be over a surface!  The importance is, increasing the area of cloud doesn't change the amount of reflected energy by the same amount everywhere.  It matters what the cloud is over.  (Over Antarctica, albedo 0.8 or so, clouds would actually lower the albedo!)  So, if we put more clouds over land (over the US one report suggests a slight increase in clouds, but then over China it's reported a decrease), the energy reflected increases by 0.3 (from 0.2 to 0.5).  On the other hand, if it's over the ocean, the energy reflected increases by 0.45 (0.05 to 0.5).  In other words, it's much more effective, in feeding back on temperature, to increase clouds over ocean than land.

We'll also remember that there's a lot more ocean (70% of the earth's surface) than land (30%).  Unfortunately for this feedback, the observations for land are the ones showing the larger changes.  The US figure (the US being about 2% of the globe) is 1.4% per decade, increase in clouds.  So, in terms of a simple estimate, we'll call it about 3 decades (which is about right), and a 5% increase in clouds.  That's over 0.02 of the globe, and is a 0.3 change in albedo.  We multiply those figures together to get an approximate net effect -- 0.05 * 0.02 * 0.3 = 0.0003.  Change of the albedo from 0.3 to 0.3003.  That cools us back down from 255.6 to 255.58, leaving us with 0.72 degrees warming instead of 0.74 -- even though we declared the feedback to exist and be of a nature to oppose the warming, it was ineffective at moderating the temperature change from greenhouse gases.

Let's make it the entire land surface of the earth (0.3) instead of just the US 2% of the globe.  15 times larger an effect, but then you also have to explain why the Chinese didn't notice it, or the Sahara desert, etc..  That is 0.0045 on albedo (0.05 * 0.3 * 0.3), raising the earth's albedo to 0.3045.  That cools us off to 255.19 K, giving a warming of 0.33.  The feedback still leaves a warming, but does noticeably reduce it.

Now let's be extreme -- distinctly more than is permitted by the observations.  Let's say that there is a 5% increase in clouds and it's over the ocean.  That makes for 0.05 * 0.7 * 0.45 increase in albedo (always I'm taking change in cloud * fraction of earth's surface that the cloud change is over * change in albedo from non-cloud to cloud conditions).  So 0.0158 change in albedo, taking us to a black body temperature of 254.15 -- making the earth 0.71 K cooler than before the greenhouse gases were added.

This points us to the central issue regarding feedbacks.  It was wrong to stop at step 3.  The temperature change due to the new albedo from step 3 has to go back to change how much greenhouse effect we get (the addition to the solar constant that we made).  Feedbacks are loops that we have to keep running around until the changes get small.  A change in warming from 0.74 to 0.72 clearly won't take long for the 0.02 effect to be resolved.  Changing from 0.74 to 0.33, probably going to take a few more cycles.  Changing from +.74 to -.71 may never converge (meaning we might just keep bouncing around, or we might just run away to some impossible answer).  We need at least a step 4 -- re-estimate the net effects on climate, and repeat your estimates in steps 2 and 3.  Repeat until successive cycles give nearly (say within 0.01 K) the same answer.

A different thing these examples point us to is how accurately we want to know albedo -- we want to observe it globally, and to better than 0.005.  In like vein, we want to know cloudiness changes more accurately than 1% per decade.  These both say things about how we need to go about observations and building new observing systems.

In any case, I think this answers anonymous's question as to how it is that we can have warming even if clouds were to have a cooling feedback.  Namely, it can happen if the clouds don't increase fast enough.  There can be a cooling from them, but not enough to offset the full effect of the greenhouse gas warming.  To be sure which way it goes, you have to get quantitative.  (And preferably with a better model than this simplest one!).  Anonymous: do you agree that your question was answered?  If not, what did I miss?


I'll flag this 'project folder' and invite folks to play with these experiments, and to contribute their own situations:

Give yourself a relationship between albedo and temperature.  Maybe it is warmer by 1 K gives higher albedo by 0.001 (this would be clouds being more widespread and of a type to cool climate).  Maybe you take -0.001 (opposite clouds, or thinking about sea ice and its albedo feedback).  Then do step 1, and cycle steps 2-4 until you do converge (give nearly the same answer from cycle to cycle).

You can also have some fun with this and consider an iceball earth.  Start with a global albedo of, say, 0.6 (something appropriate to ice), and an albedo that decreases with increasing temperature (meaning that you melt the ice and show land or ocean instead).  Kick it with some greenhouse warming due to a few hundred thousand or million years of volcanic CO2. Look at the path the temperatures take as you run through the cycles.

For the more mathematically advanced -- let your albedo function be nonlinear.  Clearly a very cold earth has a high albedo (iceball), and a very, very warm has a high albedo (i.e., so warm that we become fully cloud-covered) is also high.  But somewhere between the two, there's at least one minimum, perhaps corresponding to the present day or pre-industrial, where we have neither enormous amounts of cloud or ice.  Have a look at the stability of those conditions w.r.t. the shape of your albedo function.