Archive for August, 2017

In XII – Rainfall 2 we saw the results of many models on rainfall as GHGs increase. They project wetter tropics, drier subtropics and wetter higher latitude regions. We also saw an expectation that rainfall will increase globally, with something like 2-3% per ºC of warming.

Here is a (too small) graph from Allen & Ingram (2002) showing the model response of rainfall under temperature changes from GHG increases. The dashed line marked “C-C” is the famous (in climate physics) Clausius–Clapeyron relation which, at current temperatures, shows a 7% change in water vapor per ºC of warming. The red triangles are the precipitation changes from model simulations showing about half of that.

From Allen & Ingram (2002)

Figure 1

Here is another graph from the same paper showing global mean temperature change (top) and rainfall over land (bottom):

From Allen & Ingram (2002)

Figure 2

The temperature has increased over the last 50 years, and models and observations show that the precipitation has.. oh, it’s not changed. What is going on?

First, the authors explain some important background:

The distribution of moisture in the troposphere (the part of the atmosphere that is strongly coupled to the surface) is complex, but there is one clear and strong control: moisture condenses out of supersaturated air.

This constraint broadly accounts for the humidity of tropospheric air parcels above the boundary layer, because almost all such parcels will have reached saturation at some point in their recent history. Physically, therefore, it has long seemed plausible that the distribution of relative humidity would remain roughly constant under climate change, in which case the Clausius-Clapeyron relation implies that specific humidity would increase roughly exponentially with temperature.

This reasoning is strongest at higher latitudes where air is usually closer to saturation, and where relative humidity is indeed roughly constant through the substantial temperature changes of the seasonal cycle. For lower latitudes it has been argued that the real-world response might be different. But relative humidity seems to change little at low latitudes under a global warming scenario, even in models of very high vertical resolution, suggesting this may be a robust ’emergent constraint’ on which models have already converged.

They continue:

If tropospheric moisture loading is controlled by the constraints of (approximately) unchanged relative humidity and the Clausius-Clapeyron relation, should we expect a corresponding exponential increase in global precipitation and the overall intensity of the hydrological cycle as global temperatures rise?

This is certainly not what is observed in models.

To clarify, the point in the last sentence is that models do show an increase in precipitation, but not at the same rate as the expected increase in specific humidity (see note 1 for new readers).

They describe their figure 2 (our figure 1 above) and explain:

The explanation for these model results is that changes in the overall intensity of the hydrological cycle are controlled not by the availability of moisture, but by the availability of energy: specifically, the ability of the troposphere to radiate away latent heat released by precipitation.

At the simplest level, the energy budgets of the surface and troposphere can be summed up as a net radiative heating of the surface (from solar radiation, partly offset by radiative cooling) and a net radiative cooling of the troposphere to the surface and to space (R) being balanced by an upward latent heat flux (LP, where L is the latent heat of evaporation and P is global-mean precipitation): evaporation cools the surface and precipitation heats the troposphere.

[Emphasis added].

Basics Digression

Picture the atmosphere over a long period of time (like a decade), and for the whole globe. If it hasn’t heated up or cooled down we know that the energy in must equal energy out (or if it has only done so only marginally then energy in is almost equal to energy out). This is the first law of thermodynamics – energy is conserved.

What energy comes into the atmosphere?

  1. Solar radiation is partly absorbed by the atmosphere (most is transmitted through and heats the surface of the earth)
  2. Radiation emitted from the earth’s surface (we’ll call this terrestrial radiation) is mostly absorbed by the atmosphere (some is transmitted straight through to space)
  3. Warm air is convected up from the surface
  4. Heat stored in evaporated water vapor (latent heat) is convected up from the surface and the water vapor condenses out, releasing heat into the atmosphere when this happens

How does the atmosphere lose energy?

  1. It radiates downwards to the surface
  2. It radiates out to space

..end of digression

Changing Energy Budget

In a warmer world, if we have more evaporation we have more latent heat transfer from the surface into the troposphere. But the atmosphere has to be able to radiate this heat away. If it can’t, then the atmosphere becomes warmer, and this reduces convection. So with a warmer surface we may have a plentiful potential supply of latent heat (via water vapor) but the atmosphere needs a mechanism to radiate away this heat.

Allen & Ingram put forward a simple conceptual equation:


where the change in radiative cooling ΔR, is split into two components: ΔRc that is independent of the change in atmospheric temperature; and ΔRT that depends only on the temperature

L = latent heat of water vapor (a constant), ΔP = change in rainfall (= change in evaporation, as evaporation is balanced by rainfall)

LΔP is about 1W/m² per 1% increase in global precipitation.

Now, if we double CO2, then before any temperature changes we decrease the outgoing longwave radiation through the tropopause (the top of the troposphere) by about 3-4W/m² and we increase atmospheric radiation to the surface by about 1W/m².

So doubling CO2, ΔRc = -2 to -3W/m²; prior to a temperature change ΔRT = 0; and so ΔP reduces.

The authors comment that increasing CO2 before any temperature change takes place reduces the intensity of the hydrological cycle and this effect was seen in early modeling experiments using prescribed sea surface temperatures.

Now, of course, the idea of doubling CO2 without any temperature change is just a thought experiment. But it’s an important thought experiment because it lets us isolate different factors.

The authors then consider their factor ΔRT:

The enhanced radiative cooling due to tropospheric warming, ΔRT, is approximately proportional to ΔT: tropospheric temperatures scale with the surface temperature change and warmer air radiates more energy, so ΔRT = kΔT, with k=3W/(m²K)..

All this is saying is that as the surface warms, the atmosphere warms at about the same rate, and the atmosphere then emits more radiation. This is why the model results of rainfall in our figure 2 above show no trend in rainfall over 50 years, and also match the observations – the constraint on rainfall is the changing radiative balance in the troposphere.

And so they point out:

Thus, although there is clearly usable information in fig. 3 [our figure 2], it would be physically unjustified to estimate ΔP/ΔT directly from 20th century observations and assume that the same quantity will apply in the future, when the balance between climate drivers will be very different.

There is a lot of other interesting commentary in their paper, although the paper itself is now quite dated (and unfortunately behind a paywall). In essence they discuss the difficulties of modeling precipitation changes, especially for a given region, and are looking for “emergent constraints” from more fundamental physics that might help constrain forecasts.

A forecasting system that rules out some currently conceivable futures as unlikely could be far more useful for long-range planning than a small number of ultra-high-resolution forecasts that simply rule in some (very detailed futures as possibilities).

This is a very important point when considering impacts.


Increasing the surface temperature by 1ºC is expected to increase the humidity over the ocean by about 7%. This is simply the basic physics of saturation. However, climate models predict an increase in mean rainfall of maybe 2-3% per ºC. The fundamental reason is that the movement of latent heat from the surface to the atmosphere has to be radiated away by the atmosphere, and so the constraint is the ability of the atmosphere to do this. And so the limiting factor in increasing rainfall is not the humidity increase, it is the radiative cooling of the atmosphere.

We also see that despite 50 years of warming, mean rainfall hasn’t changed. Models also predict this. This is believed to be a transient state, for reasons explained in the article.


Constraints on future changes in climate and the hydrologic cycle, MR Allen & WJ Ingram, Nature (2002)  – freely available [thanks, Robert]


1 Relative humidity is measured as a percentage. If the relative humidity = 100% it means the air is saturated with water vapor – it can’t hold any more water vapor. If the relative humidity = 0% it means the air is completely dry. As temperature increases the ability of air to hold water vapor increases non-linearly.

For example, at 0ºC, 1kg of air can carry around 4g of water vapor, at 10ºC that has doubled to 8g, and at 20ºC it has doubled again to 15g (I’m using approximate values).

So now imagine saturated air over the ocean at 20ºC rising up and therefore cooling (it is cooler higher up in the atmosphere). By the time the air parcel has cooled down to 0ºC (this might be anything from 2km to 5km altitude) it is still saturated but is only carrying 4g of water vapor, having condensed out 11g into water droplets.


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At least 99.9% of physicists believe the theory of gravity, and the heliocentric model of the solar system. The debate is over. There is no doubt that we can send a manned (and woman-ed) mission to Mars.

Some “skeptics” say it can’t be done. They are denying basic science! Gravity is plainly true. So is the heliocentric model. Everyone agrees. There is an overwhelming consensus. So the time for discussion is over. There is no doubt about the Mars mission.

I create this analogy (note 1) for people who don’t understand the relationship between five completely different ideas:

  • the “greenhouse” effect
  • burning fossil fuels adds CO2 to the atmosphere, increasing the “greehouse” effect
  • climate models
  • crop models
  • economic models

The first two items on the list are fundamental physics and chemistry, and while advanced to prove (see The “Greenhouse” Effect Explained in Simple Terms for the first one) to people who want to work through a proof, they are indisputable. Together they create the theory of AGW (anthropogenic global warming). This says that humans are contributing to global warming by burning fossil fuels.

99.9% of people who understand atmospheric physics believe this unassailable idea (note 2).

This means that if we continue with “business as usual” (note 3) and keep using fossil fuels to generate energy, then by 2100 the world will be warmer than today.

How much warmer?

For that we need climate models.

Climate Models

These are models which break the earth’s surface, ocean and atmosphere into a big grid so that we can use physics equations (momentum, heat transfer and others) to calculate future climate (this class of model is called finite element analysis). These models include giant fudge-factors that can’t be validated (by giant fudge factors I mean “sub-grid parameterizations” and unknown parameters, but I’m writing this article for a non-technical audience).

One way to validate models is to model the temperature over the last 100 years. Another way is to produce a current climatology that matches observations. Generally temperature is the parameter with most attention (note 4).

Some climate models predict that if we double CO2 in the atmosphere (from pre-industrial periods) then surface temperature will be around 4.5ºC warmer. Others that the temperature will be 1.5ºC warmer. And everything in between.

Surely we can just look at which models reproduced the last 100 years temperature anomaly the best and work with those?

From Mauritsen et al 2012

If the model that predicts 1.5ºC in 2100 is close to the past, while the one that predicts 4.5ºC has a big overshoot, we will know that 1.5ºC is a more likely future. Conversely, if the model that predicts 4.5ºC in 2100 is close to the past but the 1.5ºC model woefully under-predicts the last 100 years of warming then we can expect more like 4.5ºC in 2100.

You would think so, but you would be wrong.

All the models get the last 100 years of temperature changes approximately correct. Jeffrey Kiehl produced a paper 10 years ago which analyzed the then current class of models and gently pointed out the reason. Models with large future warming included a high negative effect from aerosols over the last 100 years. Models with small future warming included a small negative effect from aerosols over the last 100 years. So both reproduced the past but with a completely different value of aerosol cooling. You might think we can just find out the actual cooling effect of aerosols around 1950 and then we will know which climate model to believe – but we can’t. We didn’t have satellites to measure the cooling effect of aerosols back then.

This is the challenge of models with many parameters that we don’t know. When a modeler is trying to reproduce the past, or the present, they pick the values of parameters which make the model match reality as best as they can. This is a necessary first step (note 5).

So how warm will it be in 2100 if we double CO2 in the atmosphere?

Somewhat warmer

Models also predict rainfall, drought and storms. But they aren’t as good as they are at temperature. Bray and von Storch survey climate scientists periodically on a number of topics. Here is their response to:

How would you rate the ability of regional climate models to make 50 year projections of convective rain storms/thunder storms? (1 = very poor to 7 = very good)

Similar ratings are obtained for rainfall predictions. The last 50 years has seen no apparent global worsening of storms, droughts and floods, at least according to the IPCC consensus (see Impacts – V – Climate change is already causing worsening storms, floods and droughts).

Sea level is expected to rise between around 0.3m to 0.6m (see Impacts – VI – Sea Level Rise 1 and IX – Sea Level 4 – Sinking Megacities) – this is from AR5 of the IPCC (under scenario RCP6). I mention this because the few people I’ve polled thought that sea level was expected to be 5-10m higher in 2100.

Actual reports with uneventful projections don’t generate headlines.

Crop Models

Crop models build on climate models. Once we know rainfall, drought and temperature we can work out how this impacts crops.

Will we starve to death? Or will there be plentiful food?

Past predictions of disaster haven’t been very accurate, although they are wildly popular with generating media headlines and book sales, as Paul Ehrlich found to his benefit. But that doesn’t mean future predictions of disaster are necessarily wrong.

There are a number of problems with trying to answer the question.

Even if climate models could predict the global temperature, when it comes to a region the size of, say, northern California their accuracy is much lower. Likewise for rainfall. Models which produce similar global temperature changes often have completely different regional precipitation changes. For example, from the IPCC Special Report on Extremes (SREX), p. 154:

At regional scales, there is little consensus in GCM projections regarding the sign of future change in monsoon characteristics, such as circulation and rainfall. For instance, while some models project an intense drying of the Sahel under a global warming scenario, others project an intensification of the rains, and some project more frequent extreme events..

In a warmer world with more CO2 (helps some plants) and maybe more rainfall, or maybe less what can we expect out of crop yields? It’s not clear. The IPCC AR5 wg II, ch 7, p 496:

For example, interactions among CO2 fertilization, temperature, soil nutrients, O3, pests, and weeds are not well understood (Soussana et al., 2010) and therefore most crop models do not include all of these effects.

Of course, as climate changes over the next 80 years agricultural scientists will grow different crops, and develop new ones. In 1900, almost half the US population worked in farming. Today the figure is 2-3%. Agriculture has changed unimaginably.

In the left half of this graph we can see global crop yield improvements over 50 years (the right side is projections to 2050):

From Ray et al 2013

Economic Models

What will the oil price be in 2020? Economic models give you the answer. Well, they give you an answer. And if you consult lots of models they give you lots of different answers. When the oil price changes a lot, which it does from time to time, all of the models turn out to be wrong. Predicting future prices of commodities is very hard, even when it is of paramount concern for major economies, and even when a company could make vast profits from accurate prediction.

AR5 of the IPCC report, wg 2, ch 7, p.512, had this to say about crop prices in 2050:

Changes in temperature and precipitation, without considering effects of CO2, will contribute to increased global food prices by 2050, with estimated increases ranging from 3 to 84% (medium confidence). Projections that include the effects of CO2 changes, but ignore O3 and pest and disease impacts, indicate that global price increases are about as likely as not, with a range of projected impacts from –30% to +45% by 2050..

..One lesson from recent model intercomparison experiments (Nelson et al., 2014) is that the choice of economic model matters at least as much as the climate or crop model for determining  price response to climate change, indicating the critical role of economic uncertainties for projecting the magnitude of price impacts.

In 2001, the 3rd report (often called TAR) said, ch 5, p.238, perhaps a little more clearly:

..it should be noted however that hunger estimates are based on the assumptions that food prices will rise with climate change, which is highly uncertain

Economic models are not very good at predicting anything. As Herbert Stein said, summarizing a lifetime in economics:

  • Economists do not know very much
  • Other people, including the politicians who make economic policy, know even less about economics than economists do


Recently a group, Cook et al 2013, reviewed over 10,000 abstracts of climate papers and concluded that 97% believed in the proposition of AGW – the proposition that humans are contributing to global warming by burning fossil fuels. I’m sure if the question were posed the right way directly to thousands of climate scientists, the number would be over 99%.

It’s not in dispute.

AGW is a necessary theory for Catastrophic Anthropogenic Global Warming (CAGW). But not sufficient by itself.

Likewise we know for sure that gravity is real and the planets orbit the sun. But it doesn’t follow that we can get humans safely to Mars and back. Maybe we can. Understanding gravity and the heliocentric theory is a necessary condition for the mission, but a lot more needs to be demonstrated.

The uncertainties in CAGW are huge.

Economic models that have no predictive skill are built on limited crop models which are built on climate models which have a wide range of possible global temperatures and no consensus on regional rainfall.

Human ingenuity somehow solved the problem of going from 2.5bn people in the middle of the 20th century to more than 7bn people today, and yet the proportion of the global population in abject poverty (note 6) has dropped from over 40% to maybe 15%. This was probably unimaginable 70 years ago.

Perhaps reasonable people can question if climate change is definitely the greatest threat facing humanity?

Perhaps questioning the predictive power of economic models is not denying science?

Perhaps it is ok to be unsure about the predictive power of climate models that contain sub-grid parameterizations (giant fudge factors) and that collectively provide a wide range of forecasts?

Perhaps people who question the predictions aren’t denying basic (or advanced) science, and haven’t lost their reason or their moral compass?


[Note to commenters, added minutes after this post was written – this article is not intended to restart debate over the “greenhouse” effect, please post your comments in one of the 10s (100s?) of articles that have covered that subject, for example – The “Greenhouse” Effect Explained in Simple Terms – Comments on the reality of the “greenhouse” effect posted here will be deleted. Thanks for understanding.]


Twentieth century climate model response and climate sensitivity, Jeffrey Kiehl (2007)

Tuning the climate of a global model, Mauritsen et al (2012)

Yield Trends Are Insufficient to Double Global Crop Production by 2050, Deepak K. Ray et al (2013)

Quantifying the consensus on anthropogenic global warming in the scientific literature, Cook et al, Environmental Research Letters (2013)

The Great Escape, Angus Deaton, Princeton University Press (2013)

The various IPCC reports cited are all available at their website


1. An analogy doesn’t prove anything. It is for illumination.

2. How much we have contributed to the last century’s warming is not clear. The 5th IPCC report (AR5) said it was 95% certain that more than 50% of recent warming was caused by human activity. Well, another chapter in the same report suggested that this was a bogus statistic and I agree, but that doesn’t mean I think that the percentage of warming caused by human activity is lower than 50%. I have no idea. It is difficult to assess, likely impossible. See Natural Variability and Chaos – Three – Attribution & Fingerprints for more.

3. Reports on future climate often come with the statement “under a conservative business as usual scenario” but refer to a speculative and hard to believe scenario called RCP8.5 – see Impacts – II – GHG Emissions Projections: SRES and RCP. I think RCP 6 is much closer to the world of 2100 if we do little about carbon emissions and the world continues on the kind of development pathways that we have seen over the last 60 years. RCP8.5 was a scenario created to match a possible amount of CO2 in the atmosphere and how we might get there. Calling it “a conservative business as usual case” is a value-judgement with no evidence.

4. More specifically the change in temperature gets the most attention. This is called the “temperature anomaly”. Many models that do “well” on temperature anomaly actually do quite badly on the actual surface temperature. See Models, On – and Off – the Catwalk – Part Four – Tuning & the Magic Behind the Scenes – you can see that many “fit for purpose” models have current climate halfway to the last ice age even though they reproduce the last 100 years of temperature changes pretty well. That is, they model temperature changes quite well, but not temperature itself.

5. This is a reasonable approach used in modeling (not just climate modeling) – the necessary next step is to try to constrain the unknown parameters and giant fudge factors (sub-grid parameterizations). Climate scientists work very hard on this problem. Many confused people writing blogs think that climate modelers just pick the values they like, produce the model results and go have coffee. This is not the case, and can easily be seen by just reviewing lots of papers. The problem is well-understood among climate modelers. But the world is a massive place, detailed past measurements with sufficient accuracy are mostly lacking, and sub-grid parameterizations of non-linear processes are a very difficult challenge (this is one of the reasons why turbulent flow is a mostly unsolved problem).

6. This is a very imprecise term. I refer readers to the 2015 Nobel Prize winner Angus Deaton and his excellent book, The Great Escape (2013) for more.

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