If you pay attention to the media reporting on “climate change” (note 1) you will often read/hear something like this:

Under a business as usual scenario..

And then some very worrying future outcomes. Less misleading, but still very misleading, you might read:

Under a high emissions scenario..

Every time I have checked the papers that are behind the press release faithfully reproduced by the stenographers in the media, they are referring to a model simulation using a scenario of CO2 emissions known as RCP8.5.

This scenario – explained below – is a fantastic scenario, and was not created because it was expected to happen.

So – calling it “business as usual”, charitably speaking, is from climate scientists who know nothing about history, demography, current & past trends. And uncharitably, is from climate scientists who are activists, pressing a cause, knowing that stenographers don’t do research or ask difficult questions.

I have been reading climate science for a long time – textbooks, papers, IPCC reports – and for sure when I read “under a business as usual scenario..” I always thought that climate scientists meant – “if we continue doing what we are doing, and don’t immediately reduce CO2 emissions”.

Then I read the papers on the scenarios.

Let me explain. It’s worth spending a few minutes of your time to understand this important subject..

Pre-industrial levels of CO2 were about 280ppm. Currently we are at just over 400ppm. Half a century ago climate scientists used rudimentary climate models and tried doubling CO2 to find out what the new climate equilibrium would be. Some time later people tried 3x and 4x the amount of CO2. It’s a good test. Do the simulated effects of CO2 on climate keep on increasing once we get past 2x CO2? Do the effects flat-line? Skyrocket?

Very worthwhile simulations.

Today we have lots of climate models. There are about 20 modeling centers around the world, each producing results that often vary significantly from other groups (more on that in future articles). How can we compare the results for 2100 from these different models? We need to know how much CO2 (and methane) will be emitted by human activity. We need to know land use and agricultural changes. Of course, no one knows what they will be, but for the purposes of comparison different modeling groups need to work from identical conditions (note 2).

So a bunch of scenarios were created, too many probably. It takes lots of computing power to run a simulation for 100 years. For IPCC AR5 in 2013 these were slimmed down to four Representative Concentration Pathways, or RCPs. One of these is RCP8.5.

The paper writers didn’t come up with RCP8.5 because they felt this was a likely scenario. They were told to come up with RCP8.5:

By design, the RCPs, as a set, cover the range of radiative forcing levels examined in the open literature and contain relevant information for climate model runs..

..The four RCPs together span the range of year 2100 radiative forcing values found in the open literature, i.e. from 2.6 to 8.5 W/m². The RCPs are the product of an innovative collaboration between integrated assessment modelers, climate modelers, terrestrial ecosystem modelers and emission inventory experts. The resulting product forms a comprehensive data set with high spatial and sectoral resolutions for the period extending to 2100..

..The RCPs are named according to radiative forcing target level for 2100. The radiative forcing estimates are based on the forcing of greenhouse gases and other forcing agents. The four selected RCPs were considered to be representative of the literature, and included one mitigation scenario leading to a very low forcing level (RCP2.6), two medium stabilization scenarios (RCP4.5/RCP6) and one very high baseline emission scenarios (RCP8.5).

From IPCC AR5, chapter 2, p.167 we can see that the change in CO2 per year (the bottom graph) is about 2ppm. The legend means, in English rather than maths, the increase in CO2 concentration in ppm per year:

So a naive expectation based on current increases would be around 570 ppm in 2100 (410ppm + 80 years x 2ppm)

This is pretty close to the scenario RCP6, and a very long way from RCP8.5.

To get to RCP8.5 requires almost 1000ppm of CO2 (plus large increases in methane concentrations). This requires about 7ppm per year increase in CO2 starting soon. It’s a “fantastic” scenario that is extremely unlikely to happen, and if by some strange set of circumstances it was, the world could stop it simply by ensuring that sub-Saharan Africa had access to cheap natural gas, rather than coal (see note 3).

If climate scientists and media outlets wrote “under a very unlikely emissions scenario that we can’t see happening we get a few outlier models that predict..” it wouldn’t make good headlines.

It wouldn’t make good climate advocacy.

When you see a story about possible futures, check what scenario is being used. If it’s RCP8.5 (“business as usual” or “a high emissions scenario”) then you can just ignore it – or be concerned and start petitioning your government to encourage more natural gas production.

– Update Jan 1, 2019 (Dec 31st, 2018 in some parts of the world) -just added Opinions and Perspectives – 3.5 – Follow up to “How much CO2 will there be?” due to comments

Further Reading

Impacts – II – GHG Emissions Projections: SRES and RCP


Note 1: I put “climate change” in quotes to distinguish it from climate change that happened up until 1900 or thereabouts. I’m trying to keep this series non-technical, and also assume that readers haven’t read/remembered previous articles in the series. See Opinions and Perspectives – 2 – There is More than One Proposition in Climate Science

Note 2: A significant part of climate modeling is assessing results and trying to figure out why, say, the GISS model differs substantially from the MPI model. To do that we need to be sure that the model results are based on the same conditions.

Note 3: Natural gas produces about 1/2 the CO2 of coal, per unit of energy produced. If you read the paper for RCP8.5 you will see it depends upon a very high sub-Saharan African population burning huge amounts of coal. No demographic transition. No technological progress. A Victorian technology.

Continuing from Opinions and Perspectives – 1 – The Consensus a friend said to me a little while back, “Oh, you don’t believe in climate change do you?”

Ye gods, where to start?

At some exhibition which included a questionnaire that visitors were encouraged to take, one of the later questions was “Do you believe in climate change?”. My uncle remarked, “A question that reveals more about the questioner than about the respondents”. I wish I had his gift.

Let me outline some propositions required for basic climate literacy. That is, whether you agree or not with these propositions, you should know that they are distinct, and important:

1. Before “climate change” there was lots of climate change. That is, before humans began emitting large quantities of CO2 (and other GHGs) by burning fossil fuels the climate experienced large changes on time scales ranging from decades to centuries to millennia and longer.

2. Burning fossil fuels like coal and natural gas adds CO2 to the atmosphere.

3.  More CO2, methane and a few other inappropriately-named “greenhouse” gases in the atmosphere increase the surface temperature of the earth.

Items 2 and 3 above can be summarised with the term “anthropogenic global warming” or AGW.

4. Just because there was lots of climate change before AGW doesn’t mean that humans can’t alter the climate.

5. AGW will lead to catastrophe for our planet (perhaps we can call this CAGW).

Each one of these propositions is distinct. And proposition 5 could be broken down into a number of different propositions (which we will look at).

For example, many people “believe in climate change” while refuting even AGW. Their argument is sometimes, “The climate was changing long before we started burning fossil fuels, that’s why I don’t believe in AGW”.

I don’t share that point of view. But wrapping causes around catchy phrases can, of course, backfire.

It is possible to believe in proposition 2 and not proposition 3. It is possible to believe in AGW (2 & 3) and not proposition 5.

Most people, after at least a decade and a half of the media blaring at them (from whatever ideological position), don’t realize that these propositions are not all: “Do you believe in climate change?”

It’s almost as though the media is completely counter-productive for grasping complex issues.

Note to commenters – if you want to question the “greenhouse” effect post your comment in one of the many articles about that, e.g. The “Greenhouse” Effect Explained in Simple Terms. Comments placed here on the science basics will just be deleted.

When I started this blog I said:

Opinions are often interesting and sometimes entertaining. But what do we learn from opinions? It’s more useful to understand the science behind the subject.

Of late I’ve been caught up with work, other intellectual interests and (luckily) some fun stuff and haven’t spent any time on climate. So I feel it’s time to put forward a few opinions on climate.

The often-cited consensus on climate is:

a) we add CO2 and other GHGs to the atmosphere by burning fossil fuels (and other human activity)

b) these increase the inappropriately-named “greenhouse effect”

c) this increases the surface temperature over some time period

This scientific consensus is rock solid, like gravity or momentum. It’s not particularly intuitive, but tough luck, physics is often like that. By itself, the consensus doesn’t tell you a lot. It just says that if we keep burning fossil fuels then the earth’s surface temperature will increase.

This scientific consensus doesn’t say that urgent action is needed on climate, or that without urgent action society is doomed, or that rapid adoption of renewable energy towards 100% of current energy consumption is a net cost benefit.

These are different propositions.

Note to commenters – if you want to question the “greenhouse” effect post your comment in one of the many articles about that, e.g. The “Greenhouse” Effect Explained in Simple Terms. Comments placed here on the science basics will just be deleted.



Recent reports have shown that California knew about the threat of climate change decades ago.

No one could have missed the testimony of James Hansen in 1988 and many excellent papers were published prior to that time (and, of course, subsequently). Californian policymakers cannot claim ignorance.

I’m not a resident of California but I often visit this great state and seeing this new petition I’m hoping that everyone concerned about the climate of California will get onboard to denounce the past and current state governments and, especially, to ensure that current residents get to sue these politicians.

They knew, and yet they kept burning fossil fuel. History will judge them harshly, but in the meantime, the people should ensure these politicians feel the pain.

[Update: small note for readers, see comment]

In Part Seven – Resolution & Convection we looked at some examples of how model resolution and domain size had big effects on modeled convection.

One commenter highlighted some presentations on issues in GCMs. As there were already a lot of comments on that article the relevant points appear a long way down. The issue deserves at least a short article of its own.

The presentations, by Paul Williams, Department of Meteorology, University of Reading, UK – all freely available:

The impacts of stochastic noise on climate models

The importance of numerical time-stepping errors

The leapfrog is dead. Long live the leapfrog!

Various papers are highlighted in these presentations (often without a full reference).

Time-Step Dependence

One of the papers cited: Time Step Sensitivity of Nonlinear Atmospheric Models: Numerical Convergence, Truncation Error Growth, and Ensemble Design, Teixeira, Reynolds & Judd 2007 comments first on the Lorenz equations (see Natural Variability and Chaos – Two – Lorenz 1963):

Figure 3a shows the evolution of X for r =19 for three different time steps (10-2, 10-3, and 10-4 LTU).

In this regime the solutions exhibit what is often referred to as transient chaotic behavior (Strogatz 1994), but after some time all solutions converge to a stable fixed point.

Depending on the time step used to integrate the equations, the values for the fixed points can be different, which means that the climate of the model is sensitive to the time step.

In this particular case, the solution obtained with 0.01 LTU converges to a positive fixed point while the other two solutions converge to a negative value.

To conclude the analysis of the sensitivity to parameter r, Fig. 3b shows the time evolution (with r =21.3) of X for three different time steps. For time steps 0.01 LTU and 0.0001 LTU the solution ceases to have a chaotic behavior and starts converging to a stable fixed point.

However, for 0.001 LTU the solution stays chaotic, which shows that different time steps may not only lead to uncertainty in the predictions after some time, but may also lead to fundamentally different regimes of the solution.

These results suggest that time steps may have an important impact in the statistics of climate models in the sense that something relatively similar may happen to more complex and realistic models of the climate system for time steps and parameter values that are currently considered to be reasonable.

[Emphasis added]

For people unfamiliar with chaotic systems, it is worth reading Natural Variability and Chaos – One – Introduction and Natural Variability and Chaos – Two – Lorenz 1963. The Lorenz system of three equations creates a very simple system of convection where we humans have the advantage of god-like powers. Although, as this paper shows, it seems that even with our god-like powers, under certain circumstances, we aren’t able to confirm

  1. the average value of the “climate”, or even
  2. if the climate is a deterministic or chaotic system

The results depend on the time step we have used to solve the set of equations.

Then the paper then goes on to consider a couple of models, including a weather forecasting model. In their summary:

In the weather and climate prediction community, when thinking in terms of model predictability, there is a tendency to associate model error with the physical parameterizations.

In this paper, it is shown that time truncation error in nonlinear models behaves in a more complex way than in linear or mildly nonlinear models and that it can be a substantial part of the total forecast error.

The fact that it is relatively simple to test the sensitivity of a model to the time step, allowed us to study the implications of time step sensitivity in terms of numerical convergence and error growth in some depth. The simple analytic model proposed in this paper illustrates how the evolution of truncation error in nonlinear models can be understood as a combination of the typical linear truncation error and of the initial condition error associated with the error committed in the first time step integration (proportional to some power of the time step).

A relevant question is how much of this simple study of time step truncation error could help in understanding the behavior of more complex forms of model error associated with the parameterizations in weather and climate prediction models, and its interplay with initial condition error.

Another reference from the presentations is Dependence of aqua-planet simulations on time step, Willamson & Olsen 2003.

What is an aquaplanet simulation?

In an aqua-planet the earth is covered with water and has no mountains. The sea surface temperature (SST) is speciŽed, usually with rather simple geometries such as zonal symmetry. The ‘correct’ solutions of aqua-planet tests are not known.

However, it is thought that aqua-planet studies might help us gain insight into model differences, understand physical processes in individual models, understand the impact of changing parametrizations and dynamical cores, and understand the interaction between dynamical cores and parametrization packages. There is a rich history of aqua-planet experiments, from which results relevant to this paper are discussed below.

They found that running different “mechanisms” for the same parameterizations produced quite different precipitation results. In investigating further it appeared that the time step was the key change.

Figure 1 – Click to enlarge

Their conclusion:

When running the Neale and Hoskins (2000a) standard aqua-planet test suite with two versions of the CCM3, which differed in the formulation of the dynamical cores, we found a strong sensitivity in the morphology of the time averaged, zonal averaged precipitation.

The two dynamical cores were candidates for the successor model to CCM3; one was Eulerian and the other semi-Lagrangian.

They were each con􏰜figured as proposed for climate simulation application, and believed to be of comparable accuracy.

The major difference was computational ef􏰜ficiency. In general, simulations with the Eulerian core formed a narrow single precipitation peak centred on the equator, while those with the semi-Lagrangian core produced more precipitation farther from the equator accompanied by a double peak straddling the equator with a minimum centred on the equator..

..We do not know which simulation is ‘correct’. Although a single peak forms with smaller time steps, the simulations do not converge with the smallest time step considered here. The maximum precipitation rate at the equator continues to increase..

..The significance of the time truncation error of parametrizations deserves further consideration in AGCMs forced by real-world conditions.

Stochastic Noise

From Global Thermohaline Circulation. Part I: Sensitivity to Atmospheric Moisture Transport, Xiaoli Wang et al 1999, the strength of the North Atlantic overturning current (the thermohaline circulation) changed significantly with noise:

From Wang et al 1999

Figure 2

The idea behind the experiment is that increasing freshwater fluxes at high latitudes from melting ice (in a warmer world) appear to impact the strength of the Atlantic “conveyor” which brings warm water from nearer the equator to northern Europe (there is a long history of consideration of this question). How sensitive is this to random effects?

In these experiments we also include random variations in the zonal wind stress field north of 46ºN. The variations are uniform in space and have a Gaussian distribution, with zero mean and standard deviation of 1 dyn/cm² , based on European Centre for MediumRange Weather Forecasts (ECMWF) analyses (D. Stammer 1996, personal communication).

Our motivation in applying these random variations in wind stress is illustrated by two experiments, one with random wind variations, the other without, in which μN increases according to the above prescription. Figure 12 shows the time series of the North Atlantic overturning strength in these two experiments. The random wind variations give rise to interannual variations in the strength of the overturning, which are comparable in magnitude to those found in experiments with coupled GCMs (e.g., Manabe and Stouffer 1994), whereas interannual variations are almost absent without them. The variations also accelerate the collapse of the overturning, therefore speeding up the response time of the model to the freshwater flux perturbation (see Fig. 12). The reason for the acceleration of the collapse is that the variations make it harder for the convection to sustain itself.

The convection tends to maintain itself, because of a positive feedback with the overturning circulation (Lenderink and Haarsma 1994). Once the convection is triggered, it creates favorable conditions for further convection there. This positive feedback is so powerful that in the case without random variations the convection does not shut off until the freshening is virtually doubled at the convection site (around year 1000). When the random variations are present, they generate perturbations in the Ekman currents, which are propagated downward to the deep layers, and cause variations in the overturning strength. This weakens the positive feedback.

In general, the random wind stress variations lead to a more realistic variability in the convection sites, and in the strength of the overturning circulation.

We note that, even though the transitions are speeded up by the technique, the character of the model behavior is not fundamentally altered by including the random wind variations.

The presentation on stochastic noise also highlighted a coarse resolution GCM that didn’t show El-Nino features – but after the introduction of random noise it did.

I couldn’t track down the reference – Joshi, Williams & Smith 2010  – and emailed Paul Williams who replied very quickly, and helpfully – the paper is still “in preparation” so that means it probably won’t ever be finished, but instead Paul pointed me to two related papers that had been published:  Improved Climate Simulations through a Stochastic Parameterization of Ocean Eddies – Paul D Williams et al, AMS (2016) and Climatic impacts of stochastic fluctuations in air–sea fluxes, Paul D Williams et al, GRL (2012).

From the 2012 paper:

In this study, stochastic fluctuations have been applied to the air–sea buoyancy fluxes in a comprehensive climate model. Unlike related previous work, which has employed an ocean general circulation model coupled only to a simple empirical model of atmospheric dynamics, the present work has employed a full coupled atmosphere–ocean general circulation model. This advance allows the feedbacks in the coupled system to be captured as comprehensively as is permitted by contemporary high-performance computing, and it allows the impacts on the atmospheric circulation to be studied.

The stochastic fluctuations were introduced as a crude attempt to capture the variability of rapid, sub-grid structures otherwise missing from the model. Experiments have been performed to test the response of the climate system to the stochastic noise.

In two experiments, the net fresh water flux and the net heat flux were perturbed separately. Significant changes were detected in the century-mean oceanic mixed-layer depth, sea-surface temperature, atmospheric Hadley circulation, and net upward water flux at the sea surface. Significant changes were also detected in the ENSO variability. The century-mean changes are summarized schematically in Figure 4. The above findings constitute evidence that noise-induced drift and noise-enhanced variability, which are familiar concepts from simple models, continue to apply in comprehensive climate models with millions of degrees of freedom..

The graph below shows the control experiment (top) followed by the difference between two experiments and the control (note change in vertical axis scale for the two anomaly experiments) where two different methods of adding random noise were included:

From Williams et al 2012

Figure 3

A key element of the paper is that adding random noise changes the mean values.

From Williams et al 2012

Figure 4

From the 2016 paper:

Faster computers are constantly permitting the development of climate models of greater complexity and higher resolution. Therefore, it might be argued that the need for parameterization is being gradually reduced over time.

However, it is difficult to envisage any model ever being capable of explicitly simulating all of the climatically important components on all of the relevant time scales. Furthermore, it is known that the impact of the subgrid processes cannot necessarily be made vanishingly small simply by increasing the grid resolution, because information from arbitrarily small scales within the inertial subrange (down to the viscous dissipation scale) will always be able to contaminate the resolved scales in finite time.

This feature of the subgrid dynamics perhaps explains why certain systematic errors are common to many different models and why numerical simulations are apparently not asymptoting as the resolution increases. Indeed, the Intergovernmental Panel on Climate Change (IPCC) has noted that the ultimate source of most large-scale errors is that ‘‘many important small- scale processes cannot be represented explicitly in models’’.

And they continue with an excellent explanation:

The major problem with conventional, deterministic parameterization schemes is their assumption that the impact of the subgrid scales on the resolved scales is uniquely determined by the resolved scales. This assumption can be made to sound plausible by invoking an analogy with the law of large numbers in statistical mechanics.

According to this analogy, the subgrid processes are essentially random and of sufficiently large number per grid box that their integrated effect on the resolved scales is predictable. In reality, however, the assumption is violated because the most energetic subgrid processes are only just below the grid scale, placing them far from the limit in which the law of large numbers applies. The implication is that the parameter values that would make deterministic parameterization schemes exactly correct are not simply uncertain; they are in fact indeterminate.


The question of whether stochastic closure schemes outperform their deterministic counterparts was listed by Williams et al. (2013) as a key outstanding challenge in the field of mathematics applied to the climate system.

Adding noise with a mean zero doesn’t create a mean zero effect?

The changes to the mean climatological state that were identified in section 3 are a manifestation of what, in the field of stochastic dynamical systems, is called noise-induced drift or noise-induced rectification. This effect arises from interactions between the noise and nonlinearities in the model equations. It permits zero- mean noise to have non-zero-mean effects, as seen in our stochastic simulations.

The paper itself aims..

..to investigate whether climate simulations can be improved by implementing a simple stochastic parameterization of ocean eddies in a coupled atmosphere–ocean general circulation model.

The idea is whether adding noise can improve model results more effectively than increasing model resolution:

We conclude that stochastic ocean perturbations can yield reductions in climate model error that are comparable to those obtained by refining the resolution, but without the increased computational cost.

In this latter respect, our findings are consistent with those of Berner et al. (2012), who studied the model error in an atmospheric general circulation model. They reported that, although the impact of adding stochastic noise is not universally beneficial in terms of model bias reduction, it is nevertheless beneficial across a range of variables and diagnostics. They also reported that, in terms of improving the magnitudes and spatial patterns of model biases, the impact of adding stochastic noise can be similar to the impact of increasing the resolution. Our results are consistent with these findings. We conclude that oceanic stochastic parameterizations join atmospheric stochastic parameterizations in having the potential to significantly improve climate simulations.

And for people who’ve been educated on the basics of fluids on a rotating planet via experiments on the rotating annulus (a 2d model – along with equations – providing great insights into our 3d planet), Testing the limits of quasi-geostrophic theory: application to observed laboratory flows outside the quasi-geostrophic regime, Paul D Williams et al 2010 might be interesting.


Some systems have a lot of non-linearity. This is true of climate and generally of turbulent flows.

In a textbook that I read some time ago on (I think) chaos, the author made the great comment that usually you start out being taught “linear models” and much later come into contact with “non-linear models”. He proposed that a better terminology would be “real world systems” (non-linear) while “simplistic non-real-world teaching models” were the alternative (linear models). I’m paraphrasing.

The point is that most real world systems are non-linear. And many (not all) non-linear systems have difficult properties. The easy stuff you learn – linear systems, aka “simplistic non-real-world teaching models” – isn’t actually relevant to most real world problems, it’s just a stepping stone in giving you the tools to solve the hard problems.

Solving these difficult systems requires numerical methods (there is mostly no analytical solution) and once you start playing around with time-steps, parameter values and model resolution you find that the results can be significantly – and sometimes dramatically – affected by the arbitrary choices. With relatively simple systems (like the Lorenz three-equation convection system) and massive computing power you can begin to find the dependencies. But there isn’t a clear path to see where the dependencies lie (of course, many people have done great work in systematizing (simple) chaotic systems to provide some insights).

GCMs provide insights into climate that we can’t get otherwise.

One way to think about GCMs is that once they mostly agree on the direction of an effect that provides “high confidence”, and anyone who doesn’t agree with that confidence is at best a cantankerous individual and at worst has a hidden agenda.

Another way to think about GCMs is that climate models are mostly at the mercy of unverified parameterizations and numerical methods and anyone who does accept their conclusions is naive and doesn’t appreciate the realities of non-linear systems.

Life is complex and either of these propositions could be true, along with anything inbetween.

More about Turbulence: Turbulence, Closure and Parameterization


Time Step Sensitivity of Nonlinear Atmospheric Models: Numerical Convergence, Truncation Error Growth, and Ensemble Design, Teixeira, Reynolds & Judd, Journal of the Atmospheric Sciences (2007) – free paper

Dependence of aqua-planet simulations on time step, Willamson & Olsen, Q. J. R. Meteorol. Soc. (2003) – free paper

Global Thermohaline Circulation. Part I: Sensitivity to Atmospheric Moisture Transport, Xiaoli Wang, Peter H Stone, and Jochem Marotzke, American Meteorological Society (1999) – free paper

Improved Climate Simulations through a Stochastic Parameterization of Ocean Eddies – Paul D Williams et al, AMS (2016) – free paper

Climatic impacts of stochastic fluctuations in air–sea fluxes, Paul D Williams et al, GRL (2012) – free paper

Testing the limits of quasi-geostrophic theory: application to observed laboratory flows outside the quasi-geostrophic regime, Paul Williams, Peter Read & Thomas Haine, J. Fluid Mech. (2010) – free paper

A couple of recent articles covered ground related to clouds, but under Models –Models, On – and Off – the Catwalk – Part Seven – Resolution & Convection & Part Five – More on Tuning & the Magic Behind the Scenes. In the first article Andrew Dessler, day job climate scientist, made a few comments and in one comment provided some great recent references. One of these was by Paulo Ceppi and colleagues published this year and freely accessible. Another paper with some complementary explanations is from Mark Zelinka and colleagues, also published this year (but behind a paywall).

In this article we will take a look at the breakdown these papers provide. There is a lot to the Ceppi paper so we’re not going to review it all in this article, hopefully in a followup article.

Globally and annually averaged, clouds cool the planet by around 18W/m² – that’s large compared with the radiative effect of doubling CO2, a value of 3.7W/m². The net effect is made up of two larger opposite effects:

  • cooling from reflecting sunlight (albedo effect) of about 46W/m²
  • warming from the radiative effect of about 28W/m² – clouds absorb terrestrial radiation and reemit from near the top of the cloud where it is colder, this is like the “greenhouse” effect

In this graphic, Zelinka and colleagues show the geographical breakdown of cloud radiative effect averaged over 15 years from CERES measurements:

From Zelinka et al 2017

Figure 1 – Click to enlarge

Note that the cloud radiative effect shown above isn’t feedbacks from warming, it is simply the current effect of clouds. The big question is how this will change with warming.

In the next graphic, the inset in the top shows cloud feedback (note 1) vs ECS from 28 GCMs. ECS is the steady state temperature resulting from doubling CO2. Two models are picked out – red and blue – and in the main graph we see simulated warming under RCP8.5 (an unlikely future world confusing described by many as the “business as usual” scenario).

In the bottom graphic, cloud feedbacks from models are decomposed into the effect from low cloud amount, from changing high cloud altitude and from low cloud opacity. We see that the amount of low cloud is the biggest feedback with the widest spread, followed by the changing altitude of high clouds. And both of them have a positive feedback. The gray lines extending out cover the range of model responses.

From Zelinka et al 2017

Figure 2 – Click to enlarge

In the next figure – click to enlarge – they show the progression in each IPCC report, helpfully color coded around the breakdown above:

From Zelinka et al 2017

Figure 3 – Click to enlarge

On AR5:

Notably, the high cloud altitude feedback was deemed positive with high confidence due to supporting evidence from theory, observations, and high-resolution models. On the other hand, continuing low confidence was expressed in the sign of low cloud feedback because of a lack of strong observational constraints. However, the AR5 authors noted that high-resolution process models also tended to produce positive low cloud cover feedbacks. The cloud opacity feedback was deemed highly uncertain due to the poor representation of cloud phase and microphysics in models, limited observations with which to evaluate models, and lack of physical understanding. The authors noted that no robust mechanisms contribute a negative cloud feedback.

And on work since:

In the four years since AR5, evidence has increased that the overall cloud feedback is positive. This includes a number of high-resolution modelling studies of low cloud cover that have illuminated the competing processes that govern changes in low cloud coverage and thickness, and studies that constrain long-term cloud responses using observed short-term sensitivities of clouds to changes in their local environment. Both types of analyses point toward positive low cloud feedbacks. There is currently no evidence for strong negative cloud feedbacks..

Onto Ceppi et al 2017. In the graph below we see climate feedback from models broken out into a few parameters

  • WV+LR – the combination of water vapor and lapse rate changes (lapse rate is the temperature profile with altitude)
  • Albedo – e.g. melting sea ice
  • Cloud total
  • LW cloud – this is longwave effects, i.e., how clouds change terrestrial radiation emitted to space
  • SW cloud- this is shortwave effects, i.e., how clouds reflect solar radiation back to space

From Ceppi et al 2017

Figure 4 – Click to enlarge

Then they break down the cloud feedback further. This graph is well worth understanding. For example, in the second graph (b) we are looking at higher altitude clouds. We see that the increasing altitude of high clouds causes a positive feedback. The red dots are LW (longwave = terrestrial radiation). If high clouds increase in altitude the radiation from these clouds to space is lower because the cloud tops are colder. This is a positive feedback (more warming retained in the climate system). The blue dots are SW (shortwave = solar radiation). If high clouds increase in altitude it has no effect on the reflection of solar radiation – and so the blue dots are on zero.

Looking at the low clouds – bottom graph (c) – we see that the feedback is almost all from increasing reflection of solar radiation from increasing amounts of low clouds.

From Ceppi et al 2017

Figure 5 

Now a couple more graphs from Ceppi et al – the spatial distribution of cloud feedback from models (note this is different from our figure 1 which showed current cloud radiative effect):

From Ceppi et al 2017

Figure 6

And the cloud feedback by latitude broken down into: altitude effects; amount of cloud; and optical depth (higher optical depth primarily increases the reflection to space of solar radiation but also has an effect on terrestrial radiation).

From Ceppi et al 2017

Figure 7

They state:

The patterns of cloud amount and optical depth changes suggest the existence of distinct physical processes in different latitude ranges and climate regimes, as discussed in the next section. The results in Figure 4 allow us to further refine the conclusions drawn from Figure 2. In the multi- model mean, the cloud feedback in current GCMs mainly results from:

  • globally rising free-tropospheric clouds
  • decreasing low cloud amount at low to middle latitudes, and
  • increasing low cloud optical depth at middle to high latitudes

Cloud feedback is the main contributor to intermodel spread in climate sensitivity, ranging from near zero to strongly positive (−0.13 to 1.24 W/m²K) in current climate models.

It is a combination of three effects present in nearly all GCMs: rising free- tropospheric clouds (a LW heating effect); decreasing low cloud amount in tropics to midlatitudes (a SW heating effect); and increasing low cloud optical depth at high latitudes (a SW cooling effect). Low cloud amount in tropical subsidence regions dominates the intermodel spread in cloud feedback.

Happy Christmas to all Science of Doom readers.

Note – if anyone wants to debate the existence of the “greenhouse” effect, please add your comments to Two Basic Foundations or The “Greenhouse” Effect Explained in Simple Terms or any of the other tens of articles on that subject. Comments here on the existence of the “greenhouse” effect will be deleted.


Cloud feedback mechanisms and their representation in global climate models, Paulo Ceppi, Florent Brient, Mark D Zelinka & Dennis Hartmann, IREs Clim Change 2017 – free paper

Clearing clouds of uncertainty, Mark D Zelinka, David A Randall, Mark J Webb & Stephen A Klein, Nature 2017 – paywall paper



The radiative impact of clouds is measured as the cloud-radiative effect (CRE), the difference between clear-sky and all-sky radiative flux at the top of atmosphere. Clouds reflect solar radiation (negative SW CRE, global-mean effect of −45W/m²) and reduce outgoing terrestrial radiation (positive LW CRE, 27W/m²−2), with an overall cooling effect estimated at −18W/m² (numbers from Henderson et al.).

CRE is proportional to cloud amount, but is also determined by cloud altitude and optical depth.

The magnitude of SW CRE increases with cloud optical depth, and to a much lesser extent with cloud altitude.

By contrast, the LW CRE depends primarily on cloud altitude, which determines the difference in emission temperature between clear and cloudy skies, but also increases with optical depth. As the cloud properties change with warming, so does their radiative effect. The resulting radiative flux response at the top of atmosphere, normalized by the global-mean surface temperature increase, is known as cloud feedback.

This is not strictly equal to the change in CRE with warming, because the CRE also responds to changes in clear-sky radiation—for example, due to changes in surface albedo or water vapor. The CRE response thus underestimates cloud feedback by about 0.3W/m² on average. Cloud feedback is therefore the component of CRE change that is due to changing cloud properties only. Various methods exist to diagnose cloud feedback from standard GCM output. The values presented in this paper are either based on CRE changes corrected for noncloud effects, or estimated directly from changes in cloud properties, for those GCMs providing appropriate cloud output. The most accurate procedure involves running the GCM radiation code offline—replacing instantaneous cloud fields from a control climatology with those from a perturbed climatology, while keeping other fields unchanged—to obtain the radiative perturbation due to changes in clouds. This method is computationally expensive and technically challenging, however.

In the comments on Part Five there was some discussion on Mauritsen & Stevens 2015 which looked at the “iris effect”:

A controversial hypothesis suggests that the dry and clear regions of the tropical atmosphere expand in a warming climate and thereby allow more infrared radiation to escape to space

One of the big challenges in climate modeling (there are many) is model resolution and “sub-grid parameterization”. A climate model is created by breaking up the atmosphere (and ocean) into “small” cells of something like 200km x 200km, assigning one value in each cell for parameters like N-S wind, E-W wind and up-down wind – and solving the set of equations (momentum, heat transfer and so on) across the whole earth. However, in one cell like this below you have many small regions of rapidly ascending air (convection) topped by clouds of different thicknesses and different heights and large regions of slowly descending air:

Held and Soden (2000)

Held and Soden (2000)

The model can’t resolve the actual processes inside the grid. That’s the nature of how finite element analysis works. So, of course, the “parameterization schemes” to figure out how much cloud, rain and humidity results from say a warming earth are problematic and very hard to verify.

Running higher resolution models helps to illuminate the subject. We can’t run these higher resolution models for the whole earth – instead all kinds of smaller scale model experiments are done which allow climate scientists to see which factors affect the results.

Here is the “plain language summary” from Organization of tropical convection in low vertical wind shears:Role of updraft entrainment, Tompkins & Semie 2017:

Thunderstorms dry out the atmosphere since they produce rainfall. However, their efficiency at drying the atmosphere depends on how they are arranged; take a set of thunderstorms and sprinkle them randomly over the tropics and the troposphere will remain quite moist, but take that same number of thunderstorms and place them all close together in a “cluster” and the atmosphere will be much drier.

Previous work has indicated that thunderstorms might start to cluster more as temperatures increase, thus drying the atmosphere and letting more infrared radiation escape to space as aresult – acting as a strong negative feedback on climate, the so-called iris effect.

We investigate the clustering mechanisms using 2km grid resolution simulations, which show that strong turbulent mixing of air between thunderstorms and their surrounding is crucial for organization to occur. However, with grid cells of 2 km this mixing is not modelled explicitly but instead represented by simple model approximations, which are hugely uncertain. We show three commonly used schemes differ by over an order of magnitude. Thus we recommend that further investigation into the climate iris feedback be conducted in a coordinated community model intercomparison effort to allow model uncertainty to be robustly accounted for.

And a little about computation resources and resolution. CRMs are “cloud resolving models”, i.e. higher resolution models over smaller areas:

In summary, cloud-resolving models with grid sizes of the order of 1 km have revealed many of the potential feed-back processes that may lead to, or enhance, convective organization. It should be recalled however, that these studies are often idealized and involve computational compromises, as recently discussed in Mapes [2016]. The computational requirements of RCE experiments that require more than 40 days of integration still largely prohibit horizontal resolutions finer than 1 km. Simulations such as Tompkins [2001c], Bryan et al. [2003], and Khairoutdinov et al. [2009] that use resolutions less than 350 m were restricted to 1 or 2 days. If water vapor entrainment is a factor for either the establishment and/or the amplification of convective organization, it raises the issue that the organization strength in CRMs model using grid sizes of the order of 1 km or larger is likely to be sensitive to the model resolution and simulation framework in terms of the choice of subgrid-scale diffusion and mixing.

In their conclusion on what resolution is needed:

.. and states that convergence is achieved when the most energetic eddies are well resolved, which is not the case at 2 km, and Craig and Dornbrack [2008] also suggest that resolving clouds requires grid sizes that resolve the typical buoyancy scale of a few hundred meters. The present state of the art of LES is represented by Heinze et al. [2016], integrating a model for the whole of Germany with a 100 m grid spacing, for a period of 4 days.

They continue:

The simulations in this paper also highlight the fact that intricacies of the assumptions contained in the parameterization of small- scale physics can strongly impact the possibility of crossing the threshold from unorganized to organized equilibrium states. The expense of such simulations has usually meant that only one model configuration is used concerning assumptions of small-scale processes such as mixing and microphysics, often initialized from a single initial condition. The potential of multiple equilibria and also an hysteresis in the transition between organized and unorganized states [Muller and Held, 2012], points to the requirement for larger integration ensembles employing a range of initial and boundary conditions, and physical parameterization assumptions. The ongoing requirements of large-domain, RCE numerical experiments imply that this challenge can be best met with a community-based, convective organization model intercomparison project (CORGMIP).

Here is Detailed Investigation of the Self-Aggregation of Convection in Cloud-Resolving Simulations, Muller & Held (2012). The second author is Isaac Held, often referenced on this blog who has been writing very interesting papers for about 40 years:

It is well known that convection can organize on a wide range of scales. Important examples of organized convection include squall lines, mesoscale convective systems (Emanuel 1994; Holton 2004), and the Madden– Julian oscillation (Grabowski and Moncrieff 2004). The ubiquity of convective organization above tropical oceans has been pointed out in several observational studies (Houze and Betts 1981; WCRP 1999; Nesbitt et al. 2000)..

..Recent studies using a three-dimensional cloud resolving model show that when the domain is sufficiently large, tropical convection can spontaneously aggregate into one single region, a phenomenon referred to as self-aggregation (Bretherton et al. 2005; Emanuel and Khairoutdinov 2010). The final climate is a spatially organized atmosphere composed of two distinct areas: a moist area with intense convection, and a dry area with strong radiative cooling (Figs. 1b and 2b,d). Whether or not a horizontally homogeneous convecting atmosphere in radiative convective equilibrium self-aggregates seems to depend on the domain size (Bretherton et al. 2005). More generally, the conditions under which this instability of the disorganized radiative convective equilibrium state of tropical convection occurs, as well as the feedback responsible, remain unclear.

We see the difference in self-aggregation of convection between the two domain sizes below:


From Muller & Held 2012

Figure 1

The effect on rainfall and OLR (outgoing longwave radiation) is striking, and also note that the mean is affected:

From Muller & Held 2012

Figure 2

Then they look at varying model resolution (dx), domain size (L) and also the initial conditions. The higher resolution models don’t produce the self-aggregation, but the results are also sensitive to domain size and initial conditions. The black crosses denote model runs where the convection stayed disorganized, the red circles where the convection self-aggregated:

From Muller & Held 2012

Figure 3

In their conclusion:

The relevance of self-aggregation to observed convective organization (mesoscale convective systems, mesoscale convective complexes, etc.) requires further investigation. Based on its sensitivity to resolution (Fig. 6a), it may be tempting to see self-aggregation as a numerical artifact that occurs at coarse resolutions, whereby low-cloud radiative feedback organizes the convection.

Nevertheless, it is not clear that self-aggregation would not occur at fine resolution if the domain size were large enough. Furthermore, the hysteresis (Fig. 6b) increases the importance of the aggregated state, since it expands the parameter span over which the aggregated state exists as a stable climate equilibrium. The existence of the aggregated state appears to be less sensitive to resolution than the self-aggregation process. It is also possible that our results are sensitive to the value of the sea surface temperature; indeed, Emanuel and Khairoutdinov (2010) find that warmer sea surface temperatures tend to favor the spontaneous self-aggregation of convection.

Current convective parameterizations used in global climate models typically do not account for convective organization.

More two-dimensional and three dimensional simulations at high resolution are desirable to better understand self-aggregation, and convective organization in general, and its dependence on the subgrid-scale closure, boundary layer, ocean surface, and radiative scheme used. The ultimate goal is to help guide and improve current convective parameterizations.

From the results in their paper we might think that self-aggregation of convection was a model artifact that disappears with higher resolution models (they are careful not to really conclude this). Tompkins & Semie 2017 suggested that Muller & Held’s results may be just a dependence on their sub-grid parameterization scheme (see note 1).

From Hohenegger & Stevens 2016, how convection self-aggregates over time in their model:

From Hohenegger & Stevens 2016

Figure 4 – Click to enlarge

From a review paper on the same topic by Wing et al 2017:

The novelty of self-aggregation is reflected by the many remaining unanswered questions about its character, causes and effects. It is clear that interactions between longwave radiation and water vapor and/or clouds are critical: non-rotating aggregation does not occur when they are omitted. Beyond this, the field is in play, with the relative roles of surface fluxes, rain evaporation, cloud versus water vapor interactions with radiation, wind shear, convective sensitivity to free atmosphere water vapor, and the effects of an interactive surface yet to be firmly characterized and understood.

The sensitivity of simulated aggregation not only to model physics but to the size and shape of the numerical domain and resolution remains a source of concern about whether we have even robustly characterized and simulated the phenomenon. While aggregation has been observed in models (e.g., global models) in which moist convection is parameterized, it is not yet clear whether such models simulate aggregation with any real fidelity. The ability to simulate self-aggregation using models with parameterized convection and clouds will no doubt become an important test of the quality of such schemes.

Understanding self-aggregation may hold the key to solving a number of obstinate problems in meteorology and climate. There is, for example, growing optimism that understanding the interplay among radiation, surface fluxes, clouds, and water vapor may lead to robust accounts of the Madden Julian oscillation and tropical cyclogenesis, two long-standing problems in atmospheric science.

Indeed, the difficulty of modeling these phenomena may be owing in part to the challenges of simulating them using representations of clouds and convection that were not designed or tested with self-aggregation in mind.

Perhaps most exciting is the prospect that understanding self-aggregation may lead to an improved understanding of climate. The strong hysteresis observed in many simulations of aggregation—once a cluster is formed it tends to be robust to changing environmental conditions—points to the possibility of intransitive or almost intransitive behavior of tropical climate.

The strong drying that accompanies aggregation, by cooling the system, may act as a kind of thermostat, if indeed the existence or degree of aggregation depends on temperature. Whether or how well this regulation is simulated in current climate models depends on how well such models can simulate aggregation, given the imperfections of their convection and cloud parameterizations.

Clearly, there is much exciting work to be done on aggregation of moist convection.

[Emphasis added]


Climate science asks difficult questions that are currently unanswerable. This goes against two myths that circulate media and many blogs: on the one hand the myth that the important points are all worked out; and on the other hand the myth that climate science is a political movement creating alarm, with each paper reaching more serious and certain conclusions than the paper before. Reading lots of papers I find a real science. What is reported in the media is unrelated to the state of the field.

At the heart of modeling climate is the need to model turbulent fluid flows (air and water) and this can’t be done. Well, it can be done, but using schemes that leave open the possibility or probability that further work will reveal them to be inadequate in a serious way. Running higher resolution models helps to answer some questions, but more often reveals yet new questions. If you have a mathematical background this is probably easy to grasp. If you don’t it might not make a whole lot of sense, but hopefully you can see from the papers that very recent papers are not yet able to resolve some challenging questions.

At some stage sufficiently high resolution models will be validated and possibly allow development of more realistic parameterization schemes for GCMs. For example, here is Large-eddy simulations over Germany using ICON: a comprehensive evaluation, Reike Heinze et al 2016, evaluating their model with 150m grid resolution – 3.3bn grid points on a sub-1 second time step over 4 days over Germany:

These results consistently show that the high-resolution model significantly improves the representation of small- to mesoscale variability. This generates confidence in the ability to simulate moist processes with fidelity. When using the model output to assess turbulent and moist processes and to evaluate and develop climate model parametrizations, it seems relevant to make use of the highest resolution, since the coarser-resolved model variants fail to reproduce aspects of the variability.

Related Articles

Ensemble Forecasting – why running a lot of models gets better results than one “best” model

Latent heat and Parameterization – example of one parameterization and its problems

Turbulence, Closure and Parameterization – explaining how the insoluble problem of turbulence gets handled in models

Part Four – Tuning & the Magic Behind the Scenes – how some important model choices get made

Part Five – More on Tuning & the Magic Behind the Scenes – parameterization choices, aerosol properties and the impact on temperature hindcasting, plus a high resolution model study

Part Six – Tuning and Seasonal Contrasts – model targets and model skill, plus reviewing seasonal temperature trends in observations and models


Missing iris efect as a possible cause of muted hydrological change and high climate sensitivity in models, Thorsten Mauritsen and Bjorn Stevens, Nature Geoscience (2015) – free paper

Organization of tropical convection in low vertical wind shears:Role of updraft entrainment, Adrian M Tompkins & Addisu G Semie, Journal of Advances in Modeling Earth Systems (2017) – free paper

Detailed Investigation of the Self-Aggregation of Convection in Cloud-Resolving Simulations, Caroline Muller & Isaac Held, Journal of the Atmospheric Sciences (2012) – free paper

Coupled radiative convective equilibrium simulations with explicit and parameterized convection, Cathy Hohenegger & Bjorn Stevens, Journal of Advances in Modeling Earth Systems (2016) – free paper

Convective Self-Aggregation in Numerical Simulations: A Review, Allison A Wing, Kerry Emanuel, Christopher E Holloway & Caroline Muller, Surv Geophys (2017) – free paper

Large-eddy simulations over Germany using ICON: a comprehensive evaluation, Reike Heinze et al, Quarterly Journal of the Royal Meteorological Society (2016)

Other papers worth reading:

Featured Article Self-aggregation of convection in long channel geometry, Allison A Wing & Timothy W Cronin, Quarterly Journal of the Royal Meteorological Society (2016) – paywall paper


Note 1: The equations for turbulent fluid flow are insoluble due to the computing resources required. Energy gets dissipated at the scales where viscosity comes into play. In air this is a few mm. So even much higher resolution models like the cloud resolving models (CRMs) with scales of 1km or even smaller still need some kind of parameterizations to work. For more on this see Turbulence, Closure and Parameterization.