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I was re-reading Missing iris effect as a possible cause of muted hydrological change and high climate sensitivity in models, Thorsten Mauritsen and Bjorn Stevens from 2015 (because I referenced it in a recent comment) and then looked up other recent papers citing it. One interesting review paper is by Stevens et al from 2016. I recognized his name from many other papers and it looks like Bjorn Stevens has been publishing papers since the early 1990s, with almost 200 papers in peer-reviewed journals, mostly on this and related topics. Likewise, Sherwood and Bony (two of the coauthors) are very familiar names from this field.

Many regular readers (and I’m sure new readers of this blog) will understand much more than me about current controversies in climate sensitivity. The question in brief (of course there are many subtleties) – how much will the earth warm if we double CO2? It’s a very important question. As the authors explain at the start:

Nearly 40 years have passed since the U.S. National Academies issued the “Charney Report.” This landmark assessment popularized the concept of the “equilibrium climate sensitivity” (ECS), the increase of Earth’s globally and annually averaged near surface temperature that would follow a sustained doubling of atmospheric carbon dioxide relative to its preindustrial value. Through the application of physical reasoning applied to the analysis of output from a handful of relatively simple models of the climate system, Jule G. Charney and his co-authors estimated a range of 1.5 –4.5 K for the ECS [Charney et al., 1979].

Charney is a eminent name you will know, along with Lorentz, if you read about the people who broke ground on numerical weather modeling. The authors explain a little about the definition of ECS:

ECS is an idealized but central measure of climate change, which gives specificity to the more general idea of Earth’s radiative response to warming. This specificity makes ECS something that is easy to grasp, if not to realize. For instance, the high heat capacity and vast carbon stores of the deep ocean mean that a new climate equilibrium would only be fully attained a few millennia after an applied forcing [Held et al., 2010; Winton et al., 2010; Li et al., 2012]; and uncertainties in the carbon cycle make it difficult to know what level of emissions is compatible with a doubling of the atmospheric CO2 concentration in the first place.

Concepts such as the “transient climate response” or the “transient climate response to cumulative carbon emissions” have been introduced to account for these effects and may be a better index of the warming that will occur within a century or two [Allen and Frame, 2007; Knutti and Hegerl, 2008; Collins et al., 2013;MacDougall, 2016].

But the ECS is strongly related and conceptually simpler, so it endures as the central measure of Earth’s susceptibility to forcing [Flato et al., 2013].

And about the implications of narrowing the range of ECS:

The socioeconomic value of better understanding the ECS is well documented. If the ECS were well below 1.5 K, climate change would be a less serious problem. The stakes are much higher for the upper bound. If the ECS were above 4.5 K, immediate and severe reductions of greenhouse gas emissions would be imperative to avoid dangerous climate changes within a few human generations.

From a mitigation point of view, the difference between an ECS of 1.5 K and 4.5 K corresponds to about a factor of two in the allowable CO2 emissions for a given temperature target [Stocker et al., 2013] and it explains why the value of learning more about the ECS has been appraised so highly [Cooke et al., 2013; Neubersch et al., 2014].

The ECS also gains importance because it conditions many other impacts of greenhouse gases, such as regional temperature and rainfall [Bony et al., 2013; Tebaldi and Arblaster, 2014], and even extremes [Seneviratne et al., 2016], knowledge of which is required for developing effective adaptation strategies. Being an important and simple measure of climate change, the ECS is something that climate science should and must be able to better understand and quantify more precisely.

One of the questions they raise is at the heart of my question about whether climate sensitivity is a constant that we can measure, or a value that has some durable meaning rather than being dependent on the actual climate specifics at the time. For example, there are attempts to measure it via the climate response during an El Nino. We see the climate warm and we measure how the top of atmosphere radiation balance changes. We attempt to measure the difference in ocean temperature between end of the last ice age and today and deduce climate sensitivity. Perhaps I have a mental picture of non-linear systems that is preventing me from seeing the obvious. However, the picture I have in my head is that the dependence of the top of radiation balance on temperature is not a constant.

Here is their commentary. They use the term “pattern effect” for my mental model described above:

Hence, a generalization of the concept of climate sensitivity to different eras may need to account for differences that arise from the different base state of the climate system, increasingly so for large perturbations.

Even for small perturbations, there is mounting evidence that the outward radiation may be sensitive to the geographic pattern of surface temperature changes. Senior and Mitchell [2000] argued that if warming is greater over land, or at high latitudes, different feedbacks may occur than for the case where the same amount of warming is instead concentrated over tropical oceans.

These effects appear to be present in a range of models [Armour et al., 2013; Andrews et al., 2015]. Physically they can be understood because clouds—and their impact on radiation—are sensitive to changes in the atmospheric circulation, which responds to geographic differences in warming [Kang et al., 2013], or simply because an evolving pattern of surface warming weights local responses differently at different times [Armour et al., 2013].

Hence different patterns of warming, occurring on different timescales, may be associated with stronger or weaker radiative responses. This introduces an additional state dependence, one that is not encapsulated by the global mean temperature. We call this a “pattern effect.” Pattern effects are thought to be important for interpreting changes over the instrumental period [Gregory and Andrews, 2016], and may contribute to the state dependence of generalized measures of Earth’s climate sensitivity as inferred from the geological record.

Some of my thoughts are that the insoluble questions on this specific topic are also tied into the question about the climate being chaotic vs just weather being chaotic – see for example, Natural Variability and Chaos – Four – The Thirty Year Myth. In that article we look at the convention of defining climate as the average of 30 years of weather and why that “eliminates” chaos, or doesn’t. Non-linear systems have lots of intractable problems – more on that topic in the whole series Natural Variability and Chaos. It’s good to see it being mentioned in this paper.

Read the whole paper – it reviews the conditions necessary for very low climate sensitivity and for very high climate sensitivity, with the idea being that if one necessary condition can be ruled out then the very low and/or very high climate sensitivity can be ruled out. The paper also includes some excellent references for further insights.

From Stevens et al 2016

Click to enlarge

Happy Thanksgiving to our US readers.

References

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

Prospects for narrowing bounds on Earth’s equilibrium climate sensitivity, Bjorn Stevens, Steven C Sherwood, Sandrine Bony & Mark J Webb, Earth’s
Future (2016) – free paper

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In Part Five – More on Tuning & the Magic Behind the Scenes and also in the earlier Part Four we looked at the challenge of selecting parameters in climate models. A recent 2017 paper on this topic by Frédéric Hourdin and colleagues is very illuminating. One of the co-authors is Thorsten Mauritsen, the principal author of the 2012 paper we reviewed in Part Four. Another co-author is Jean-Christophe Golaz, the principal author of the 2013 paper we reviewed in Part Five.

The topics are similar but there is some interesting additional detail and commentary. The paper is open and, as always, I recommend reading the whole paper.

One of the key points is that climate models need to be specific about their “target” – were they trying to get the model to match recent climatology? top of atmosphere radiation balance? last 100 years of temperature trends? If we know that a model was developed with an eye on a particular target then it doesn’t demonstrate model skill if they get that target right.

Because of the uncertainties in observations and in the model formulation, the possible parameter choices are numerous and will differ from one modeling group to another. These choices should be more often considered in model intercomparison studies. The diversity of tuning choices reflects the state of our current climate understanding, observation, and modeling. It is vital that this diversity be maintained. It is, however, important that groups better communicate their tuning strategy. In particular, when comparing models on a given metric, either for model assessment or for understanding of climate mechanisms, it is essential to know whether some models used this metric as tuning target.

They comment on the paper by Jeffrey Kiehl from 2007 (referenced in The Debate is Over – 99% of Scientists believe Gravity and the Heliocentric Solar System so therefore..) which showed how models with higher sensitivity to CO2 have higher counter-balancing negative forcing from aerosols.

And later in the paper:

The question of whether the twentieth-century warming should be considered a target of model development or an emergent property is polarizing the climate modeling community, with 35% of modelers stating that twentieth-century warming was rated very important to decisive, whereas 30% would not consider it at all during development.

Some view the temperature record as an independent evaluation dataset not to be used, while others view it as a valuable observational constraint on the model development. Likewise, opinions diverge as to which measures, either forcing or ECS, are legitimate means for improving the model match to observed warming.

The question of developing toward the twentieth- century warming therefore is an area of vigorous debate within the community..

..The fact that some models are explicitly, or implicitly, tuned to better match the twentieth-century warming, while others may not be, clearly complicates the interpretation of the results of combined model ensembles such as CMIP. The diversity of approaches is unavoidable as individual modeling centers pursue their model development to seek their specific scientific goals.

It is, however, essential that decisions affecting forcing or feedback made during model development be transparently documented.

And so, onto another recent paper by Sumant Nigam and colleagues. They review the temperature trends by season over the last 100 years and review that against models. They look only at the northern hemisphere over land, due to the better temperature dataset available (compared with the southern hemisphere).

Here are the observations of the trends for each of the four seasons, I find it fascinating to see the difference between the seasonal trends:

From Nigam et al 2017

Figure 1 – Click to enlarge

Then they compare the observations to some of the models used in IPCC AR5 (from the model intercomparison project, CMIP5) – top line is observations, each line below is a different model. When we compare the geographical distribution of winter-summer trend (right column) we can see that the models don’t do very well:

From Nigam et al 2017

Figure 2 – Click to enlarge

From their conclusion:

The urgent need for shifting the evaluative and diagnostic focus away from the customary annual mean toward the seasonal cycle of secular warming is manifest in the inability of the leading climate models (whose simulations inform the IPCC’s Fifth Assessment Report) to generate realistic and robust (large signal-to noise ratio) twentieth-century winter and summer SAT trends over the northern continents. The large intra-ensemble SD of century-long SAT trends in some IPCC AR5 models (e.g., GFDL-CM3) moreover raises interesting questions: If this subset of climate models is realistic, especially in generation of ultra-low-frequency variability, is the century-long (1902–2014) linear trend in observed SAT—a one-member ensemble of the climate record—a reliable indicator of the secular warming signal?

I’ve commented a number of times in various articles – people who don’t read climate science papers often have some idea that climate scientists are monolithically opposed to questioning model results or questioning “the orthodoxy”. This is contrary to what you find if you read lots of papers. It might be that press releases that show up in The New York Times, CNN or the BBC (or pick another ideological bellwether) have some kind of monolithic sameness but this just demonstrates that no one interested in finding out anything important (apart from the weather and celebrity news) should ever watch/read media outlets.

They continue:

The relative contribution of both mechanisms to the observed seasonality in century-long SAT trends needs further assessment because of uncertainties in the diagnosis of evapotranspiration and sea level pressure from the century-long observational records. Climate system models—ideal tools for investigation of mechanisms through controlled experimentation—are unfortunately not yet ready given their inability to simulate the seasonality of trends in historical simulations.

Subversive indeed.

Their investigation digs into evapotranspiration – the additional water vapor, available from plants, to be evaporated and therefore to remove heat from the surface during the summer months.

Conclusion

All models are wrong but some are useful” – a statement attributed to a modeler from a different profession (statistical process control) and sometimes quoted also by climate modelers.

This is always a good way to think about models. Perhaps the inability of climate models to reproduce seasonal trends is inconsequential – or perhaps it is important. Models fail on many levels. The question is why, and the answers lead to better models.

Climate science is a real science, contrary to the claims of many people who don’t read much climate science papers, because many published papers ask important and difficult questions, and critique the current state of the science. That is, falsifiability is being addressed. These questions might not become media headlines, or even make it into the Summary for Policymakers in IPCC reports, but papers with these questions are not outliers.

I found both of these papers very interesting. Hourdin et al because they ask valuable questions about how models are tuned, and Nigam et al because they point out that climate models do a poor job of reproducing an important climate trend (seasonal temperature) which provides an extra level of testing for climate models.

References

Striking Seasonality in the Secular Warming of the Northern Continents: Structure and Mechanisms, Sumant Nigam et al, Journal of Climate (2017)

The Art and Science of Climate Model Tuning, Frédéric Hourdin et al, American Meteorological Society (2017) – free paper

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Over in another article, a commenter claims:

..Catastrophic predictions depend on accelerated forcings due to water vapour feedback. This water vapour feedback is simply written into climate models as parameters. It is not derived from any kind simulation of first principles in the General Circulation Model runs (GCMs)..

[Emphasis added]

I’ve seen this article of faith a lot. If you frequent fantasy climate blogs where people learn first principles and modeling basics from comments by other equally well-educated commenters this is the kind of contribution you will be able to make after years of study.

None of us knowed nothing, so we all sat around and teached each other.

Actually how the atmospheric section of climate models work is pretty simple in principle. The atmosphere is divided up into a set of blocks (a grid) with each block having dimensions something like 200 km x 200km x 500m high. The values vary a lot and depend on the resolution of the model, this is just to give you an idea.

Then each block has an E-W wind; a N-S wind; a vertical velocity; temperature; pressure; the concentrations of CO2, water vapor, methane; cloud fractions, and so on.

Then the model “steps forward in time” and uses equations to calculate the new values of each item.

The earth is spinning and conservation of momentum, heat, mass is applied to each block. The principles of radiation through each block in each direction apply via paramaterizations (note 1).

Specifically on water vapor – the change in mass of water vapor in each block is calculated from the amount of water evaporated, the amount of water vapor condensed, and the amount of rainfall taking water out of the block. And from the movement of air via E-W, N-S and up/down winds. The final amount of water vapor in each time step affects the radiation emitted upwards and downwards.

It’s more involved and you can read whole books on the subject.

I doubt that anyone who has troubled themselves to read even one paper on climate modeling basics could reach the conclusion so firmly believed in fantasy climate blogs and repeated above. If you never need to provide evidence for your claims..

For this blog we do like to see proof of claims, so please take a read of Description of the NCAR Community Atmosphere Model (CAM 4.0) and just show where this water vapor feedback is written in. Or pick another climate model used by a climate modeling group.

This is the kind of exciting stuff you find in the 200+ pages of an atmospheric model description:

From CAM4 Technical Note

You can also find details of the shortwave and longwave radiation parameterization schemes and how they apply to water vapor.

Here is a quote from The Global Circulation of the Atmosphere (ref below):

Essentially all GCMs yield water vapor feedback consistent with that which would result from holding relative humidity approximately fixed as climate changes. This is an emergent property of the simulated climate system; fixed relative humidity is not in any way built into the model physics, and the models offer ample means by which relative humidity could change.

From Water Vapor Feedback and Global Warming, a paper well-worth anyone reading for who wants to understand this key question in climate:

Water vapor is the dominant greenhouse gas, the most important gaseous source of infrared opacity in the atmosphere. As the concentrations of other greenhouse gases, particularly carbon dioxide, increase because of human activity, it is centrally important to predict how the water vapor distribution will be affected. To the extent that water vapor concentrations increase in a warmer world, the climatic effects of the other greenhouse gases will be amplified. Models of the Earth’s climate indicate that this is an important positive feedback that increases the sensitivity of surface temperatures to carbon dioxide by nearly a factor of two when considered in isolation from other feedbacks, and possibly by as much as a factor of three or more when interactions with other feedbacks are considered. Critics of this consensus have attempted to provide reasons why modeling results are overestimating the strength of this feedback..

Remember, just a few years of study at fantasy climate blogs can save an hour or more of reading papers on atmospheric physics.

References

Description of the NCAR Community Atmosphere Model (CAM 4)– free paper

On the Relative Humidity of the Atmosphere, Chapter 6 of The Global Circulation of the Atmosphere, edited by Tapio Schneider & Adam Sobel, Princeton University Press (2007)

Water Vapor Feedback and Global Warming, Held & Soden, Annu. Rev. Energy Environ (2000) – free paper

Radiative forcing by well-mixed greenhouse gases: Estimates from climate models in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4), WD Collins et al, JGR (2006)

Notes

Note 1: The very accurate calculation of radiation transfer is done via line by line calculations but they are computationally very expensive and so a simpler approximation is used in GCMs. Of course there are many studies comparing parameterizations vs line by line calculations. One example is Radiative forcing by well-mixed greenhouse gases: Estimates from climate models in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4), WD Collins et al, JGR (2006).

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In recent articles we have looked at rainfall and there is still more to discuss. This article changes tack to look at tropical cyclones, prompted by the recent US landfall of Harvey and Irma along with questions from readers about attribution and the future.

It might be surprising to find the following statement from leading climate scientists (Kevin Walsh and many co-authors in 2015):

At present, there is no climate theory that can predict the formation rate of tropical cyclones from the mean climate state.

The subject gets a little involved so let’s dig into a few papers. First from Gabriel Vecchi and some co-authors in 2008 in the journal Science. The paper is very brief and essentially raises one question – has the recent rise in total Atlantic cyclone intensity been a result of increases in absolute sea surface temperature (SST) or relative sea surface temperature:

From Vecchi et al 2008

Figure 1

The top graph (above) shows a correlation of 0.79 between SST and PDI (power dissipation index). The bottom graph shows a correlation of 0.79 between relative SST (local sea surface temperature minus the average tropical sea surface temperature) and PDI.

With more CO2 in the atmosphere from burning fossil fuels we expect a warmer SST in the tropical Atlantic in 2100 than today. But we don’t expect the tropical Atlantic to warm faster than the tropics in general.

If cyclone intensity is dependent on local SST we expect more cyclones, or more powerful cyclones. If cyclone intensity is dependent on relative SST we expect no increase in cyclones. This is because climate models predict warmer SSTs in the future but not warmer Atlantic SSTs than the tropics. The paper also shows a few high resolution models – green symbols – sitting close to the zero change line.

Now predicting tropical cyclones with GCMs has a fundamental issue – the scale of a modern high resolution GCM is around 100km. But cyclone prediction requires a higher resolution due to their relatively small size.

Thomas Knutson and co-authors (including the great Isaac Held) produced a 2007 paper with an interesting method (of course, the idea is not at all new). They input actual meteorological data (i.e. real history from NCEP reanalysis) into a high resolution model which covered just the Atlantic region. Their aim was to see how well this model could reproduce tropical storms. There are some technicalities to the model – the output is constantly “nudged” back towards the actual climatology and out at the boundaries of the model we can’t expect good simulation results. The model resolution is 18km.

The main question addressed here is the following: Assuming one has essentially perfect knowledge of large-scale atmospheric conditions in the Atlantic over time, how well can one then simulate past variations in Atlantic hurricane activity using a dynamical model?

They comment that the cause of the recent (at that time) upswing in hurricane activity “remains unresolved”. (Of course, fast forward to 2016, prior to the recent two large landfall hurricanes, and the overall activity is at a 1970 low. In early 2018, this may be revised again..).

Two interesting graphs emerge. First an excellent match between model and observations for overall frequency year on year:

From Knutson et al 2007

Figure 2

Second, an inability to predict the most intense hurricanes. The black dots are observations, the red dots are simulations from the model. The vertical axis, a little difficult to read, is SLP, or sea level pressure:

From Knutson et al 2007

Figure 3

These results are a common theme of many papers – inputting the historical climatological data into a model we can get some decent results on year to year variation in tropical cyclones. But models under-predict the most intense cyclones (hurricanes).

Here is Morris Bender and co-authors (including Thomas Knutson, Gabriel Vecchi – a frequent author or co-author in this genre, and of course Isaac Held) from 2010:

Some statistical analyses suggest a link between warmer Atlantic SSTs and increased hurricane activity, although other studies contend that the spatial structure of the SST change may be a more important control on tropical cyclone frequency and intensity. A few studies suggest that greenhouse warming has already produced a substantial rise in Atlantic tropical cyclone activity, but others question that conclusion.

This is a very typical introduction in papers on this topic. I note in passing this is a huge blow to the idea that climate scientists only ever introduce more certainty and alarm on the harm from future CO2 emissions. They don’t. However, it is also true that some climate scientists believe that recent events have been accentuated due to the last century of fossil fuel burning and these perspectives might be reported in the media. I try to ignore the media and that is my recommendation to readers on just about all subjects except essential ones like the weather and celebrity news.

This paper used a weather prediction model starting a few days before each storm to predict the outcome. If you understand the idea behind Knutson 2007 then this is just one step further – a few days prior to the emergence of an intense storm, input the actual climate data into a high resolution model and see how well the high res model predicts the observations. They also used projected future climates from CMIP3 models (note 1).

In the set of graphs below there are three points I want to highlight – and you probably need to click on the graph to enlarge it.

First, in graph B, “Zetac” is the model used by Knutson et al 2007, whereas GFDL is the weather prediction model getting better results in this paper – you can see that observations and the GFDL are pretty close in the maximum wind speed distribution. Second, the climate change predictions in E show that predictions of the future show an overall reduction in frequency of tropical storms, but an increase in the frequency of storms with the highest wind speeds – this is a common theme in papers from this genre. Third, in graph F, the results (from the weather prediction model) fed by different GCMs for future climate show quite different distributions. For example, the UKMO model produces a distribution of future wind speeds that is lower than current values.

From Bender et al 2010

Figure 4 – Click to enlarge

In this graph (S3 from the Supplementary data) we see graphs of the difference between future projected climatologies and current climatologies for three relevant parameters for each of the four different models shown in graph F in the figure above:

From Bender et al 2010

Figure 5 – Click to enlarge

This illustrates that different projected future climatologies, which all show increased SST in the Atlantic region, generate quite different hurricane intensities. The paper suggests that the reduction in wind shear in the UKMO model produces a lower frequency of higher intensity hurricanes.

Conclusion

This article illustrates that feeding higher resolution models with current data can generate realistic cyclone data in some aspects, but less so in other aspects. As we increase the model resolution we can get even better results – but this is dependent on inputting the correct climate data. As we look towards 2100 the questions are – How realistic is the future climate data? How does that affect projections of hurricane frequencies and intensities?

Articles in this Series

Impacts – I – Introduction

Impacts – II – GHG Emissions Projections: SRES and RCP

Impacts – III – Population in 2100

Impacts – IV – Temperature Projections and Probabilities

Impacts – V – Climate change is already causing worsening storms, floods and droughts

Impacts – VI – Sea Level Rise 1

Impacts – VII – Sea Level 2 – Uncertainty

Impacts – VIII – Sea level 3 – USA

Impacts – IX – Sea Level 4 – Sinking Megacities

Impacts – X – Sea Level Rise 5 – Bangladesh

Impacts XI – Rainfall 1

Impacts – XII – Rainfall 2

Impacts – XIII – Rainfall 3

References

Hurricanes and climate: the US CLIVAR working group on hurricanes, American Meteorological Society, Kevin Walsh et al (2015) – free paper

Whither Hurricane Activity? Gabriel A Vecchi, Kyle L Swanson & Brian J. Soden, Science (2008) – free paper

Simulation of the Recent Multidecadal Increase of Atlantic Hurricane Activity Using an 18-km-Grid Regional Model, Thomas Knutson et al, American Meteorological Society, (2007) – free paper

Modeled Impact of Anthropogenic Warming on the Frequency of Intense Atlantic Hurricanes, Morris A Bender et al, Science (2010) – free paper

Notes

Note 1: The scenario is A1B, which is similar to RCP6 – that is, an approximate doubling of CO2 by the end of the century. The simulations came from the CMIP3 suite of model results.

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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:

ΔRc + ΔRT = LΔP

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.

Conclusion

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.

References

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

Notes

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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I probably should have started a separate series on rainfall and then woven the results back into the Impacts series. It might take a few articles working through the underlying physics and how models and observations of current and past climate compare before being able to consider impacts.

There are a number of different ways to look at rainfall models and reality:

  • What underlying physics provides definite constraints regardless of individual models, groups of models or parameterizations?
  • How well do models represent the geographical distribution of rain over a climatological period like 30 years? (e.g. figure 8 in Impacts XI – Rainfall 1)
  • How well do models represent the time series changes of rainfall?
  • How well do models represent the land vs ocean? (when we think about impacts, rainfall over land is what we care about)
  • How well do models represent the distribution of rainfall and the changing distribution of rainfall, from lightest to heaviest?

In this article I thought I would highlight a set of conclusions from one paper among many. It’s a good starting point. The paper is A canonical response of precipitation characteristics to global warming from CMIP5 models by Lau and his colleagues, and is freely available, and as always I recommend people read the whole paper, along with the supporting information that is also available via the link.

As an introduction, the underlying physics perhaps provides some constraints. This is strongly believed in the modeling community. The constraint is a simple one – if we warm the ocean by 1K (= 1ºC) then the amount of water vapor above the ocean surface increases by about 7%. So we expect a warmer world to have more water vapor – at least in the boundary layer (typically 1km) and over the ocean. If we have more water vapor then we expect more rainfall. But GCMs and also simple models suggest a lower value, like 2-3% per K, not 7%/K. We will come back to why in another article.

It also seems from models that with global warming, rainfall increases more in regions and times of already high rainfall and reduces in regions and times of low rainfall – the “wet get wetter and the dry get drier”. (Also a marketing mantra that introducing a catchy slogan ensures better progress of an idea). So we also expect changes in the distribution of rainfall. One reason for this is a change in the tropical circulation. All to be covered later, so onto the paper..

We analyze the outputs of 14 CMIP5 models based on a 140 year experiment with a prescribed 1% per year increase in CO2 emission. This rate of CO2 increase is comparable to that prescribed for the RCP8.5, a relatively conservative business-as-usual scenario, except the latter includes also changes in other GHG and aerosols, besides CO2.

A 27-year period at the beginning of the integration is used as the control to compute rainfall and temperature statistics, and to compare with climatology (1979–2005) of rainfall data from the Global Precipitation Climatology Project (GPCP). Two similar 27-year periods in the experiment that correspond approximately to a doubling of CO2 emissions (DCO2) and a tripling of CO2 emissions (TCO2) compared to the control are chosen respectively to compute the same statistics..

Just a note that I disagree with the claim that RCP8.5 is a “relatively conservative business as usual scenario” (see Impacts – II – GHG Emissions Projections: SRES and RCP), but that’s just an opinion, as are all views about where the world will be in population, GDP and cumulative emissions 100-150 years from now. It doesn’t detract from the rainfall analysis in the paper.

For people wondering “what is CMIP5?” – this is the model inter-comparison project for the most recent IPCC report (AR5) where many models have to address the same questions so they can be compared.

Here we see (and along with other graphs you can click to enlarge) what the models show in temperature (top left), mean global rainfall (top right), zonal rainfall anomaly by latitude (bottom left) and the control vs the tripled CO2 comparison (bottom right). The many different colors in the first three graphs are each model, while the black line is the mean of the models (“ensemble mean”). The bottom right graph helps put the changes shown in the bottom left into a perspective – with the different between the red and the blue being the difference between tripling CO2 and today:

From Lau et al 2013

Figure 1 – Click to enlarge

In the figure above, the bottom left graph shows anomalies. We see one of the characteristics of models as a result of more GHGs – wetter tropics and drier sub-tropics, along with wetter conditions at higher latitudes.

From the supplementary material, below we see a better regional breakdown of fig 1d (bottom right in the figure above). I’ll highlight the bottom left graph (c) for the African region. Over the continent, the differences between present day and tripling CO2 seem minor as far as model predictions go for mean rainfall:

From Lau et al 2013

Figure 2 – Click to enlarge

The supplementary material also has a comparison between models and observations. The first graph below is what we are looking at (the second graph we will consider afterwards). TRMM (Tropical Rainfall Measuring Mission) is satellite data and GPCP one rainfall climatology that we met in the last article – so they are both observational datasets. We see that the models over-estimate tropic rainfall, especially south of the equator:

From Lau et al 2013

Figure 3 – Click to enlarge

Rainfall Distribution from Light through to Heavy Rain

Lau and his colleagues then look at rainfall distribution in terms of light rainfall through to heavier rainfall. So, take global rainfall and divide it into frequency of occurrence, with light rainfall to the left and heavy rainfall to the right. Take a look back at the bottom graph in the figure above (figure 3, their figure S1). Note that the horizontal axis is logarithmic, with a ratio of over 1000 from left to right.

It isn’t an immediately intuitive graph. Basically there are two sets of graphs. The left “cluster” is how often that rainfall amount occurred, and the black line is GPCP observations. The “right cluster” is how much rainfall fell (as a percentage of total rainfall) for that rainfall amount and again black is observations.

So lighter rainfall, like 1mm/day and below accounts for 50% of time, but being light rainfall accounts for less than 10% of total rainfall.

To facilitate discussion regarding rainfall characteristics in this work, we define, based on the ensemble model PDF, three major rain types: light rain (LR), moderate rain (MR), and heavy rain (HR) respectively as those with monthly mean rain rate below the 20th percentile (<0.3 mm/day), between response (TCO2 minus control, black) and the inter-model 1s the 40th–70th percentile (0.9–2.4mm/day), and above the 98.5% percentile (>9mm/day). An extremely heavy rain (EHR) type defined at the 99.9th percentile (>24 mm day1) will also be referred to, as appropriate.

Here is a geographical breakdown of the total and then the rainfall in these three categories, model mean on the left and observations on the right:

From Lau et al 2013

Figure 4 – Click to enlarge

We can see that the models tend to overestimate the heavy rain and underestimate the light rain. These graphics are excellent because they help us to see the geographical distribution.

Now in the graphs below we see at the top the changes in frequency of mean precipitation (60S-60N) as a function of rain rate; and at the bottom we see the % change in rainfall per K of temperature change, again as a function of rain rate. Note that the bottom graph also has a logarithmic scale for the % change, so as you move up each grid square the value is doubled.

The different models are also helpfully indicated so the spread can be seen:

From Lau et al 2013

Figure 5 – Click to enlarge

Notice that the models are all predicting quite a high % change in rainfall per K for the heaviest rain – something around 50%. In contrast the light rainfall is expected to be up a few % per K and the medium rainfall is expected to be down a few % per K.

Globally, rainfall increases by 4.5%, with a sensitivity (dP/P/dT) of 1.4% per K

Here is a table from their supplementary material with a zonal breakdown of changes in mean rainfall (so not divided into heavy, light etc). For the non-maths people the first row, dP/P is just the % change in precipitation (“d” in front of a variable means “change in that variable”), the second row is change in temperature and the third row is the % change in rainfall per K (or ºC) of warming from GHGs:

From Lau et al 2013

Figure 6 – Click to enlarge

Here are the projected geographical distributions of the changes in mean (top left), heavy (top right), medium (bottom left) and light rain (bottom right) – using their earlier definitions – under tripling CO2:

From Lau et al 2013

Figure 7 – Click to enlarge

And as a result of these projections, the authors also show the number of dry months and the projected changes in number of dry months:

From Lau et al 2013

Figure 8 – Click to enlarge

The authors conclude:

The IPCC CMIP5 models project a robust, canonical global response of rainfall characteristics to CO2 warming, featuring an increase in heavy rain, a reduction in moderate rain, and an increase in light rain occurrence and amount globally.

For a scenario of 1% CO2 increase per year, the model ensemble mean projects at the time of approximately tripling of the CO2 emissions, the probability of occurring of extremely heavy rain (monthly mean >24mm/day) will increase globally by 100%–250%, moderate rain will decrease by 5%–10% and light rain will increase by 10%–15%.

The increase in heavy rain is most pronounced in the equatorial central Pacific and the Asian monsoon regions. Moderate rain is reduced over extensive oceanic regions in the subtropics and extratropics, but increased over the extratropical land regions of North America, and Eurasia, and extratropical Southern Oceans. Light rain is mostly found to be inversely related to moderate rain locally, and with heavy rain in the central Pacific.

The model ensemble also projects a significant global increase up to 16% more frequent in the occurrences of dry months (drought conditions), mostly over the subtropics as well as marginal convective zone in equatorial land regions, reflecting an expansion of the desert and arid zones..

 

..Hence, the canonical global rainfall response to CO2 warming captured in the CMIP5 model projection suggests a global scale readjustment involving changes in circulation and rainfall characteristics, including possible teleconnection of extremely heavy rain and droughts separated by far distances. This adjustment is strongly constrained geographically by climatological rainfall pattern, and most likely by the GHG warming induced sea surface temperature anomalies with unstable moister and warmer regions in the deep tropics getting more heavy rain, at the expense of nearby marginal convective zones in the tropics and stable dry zones in the subtropics.

Our results are generally consistent with so-called “the rich-getting-richer, poor-getting-poorer” paradigm for precipitation response under global warming..

Conclusion

This article has basically presented the results of one paper, which demonstrates consistency in model response of rainfall to doubling and tripling of CO2 in the atmosphere. In subsequent articles we will look at the underlying physics constraints, at time-series over recent decades and try to make some kind of assessment.

Articles in this Series

Impacts – I – Introduction

Impacts – II – GHG Emissions Projections: SRES and RCP

Impacts – III – Population in 2100

Impacts – IV – Temperature Projections and Probabilities

Impacts – V – Climate change is already causing worsening storms, floods and droughts

Impacts – VI – Sea Level Rise 1

Impacts – VII – Sea Level 2 – Uncertainty

Impacts – VIII – Sea level 3 – USA

Impacts – IX – Sea Level 4 – Sinking Megacities

Impacts – X – Sea Level Rise 5 – Bangladesh

Impacts XI – Rainfall 1

References

A canonical response of precipitation characteristics to global warming from CMIP5 models, William K.-M. Lau, H.-T. Wu, & K.-M. Kim, GRL (2013) – free paper

Further Reading

Here are a bunch of papers that I found useful for readers who want to dig into the subject. Most of them are available for free via Google Scholar, but one of the most helpful to me (first in the list) was Allen & Ingram 2002 and the only way I could access it was to pay $4 to rent it for a couple of days.

Allen MR, Ingram WJ (2002) Constraints on future changes in climate and the hydrologic cycle. Nature 419:224–232

Allan RP (2006) Variability in clear-sky longwave radiative cooling of the atmosphere. J Geophys Res 111:D22, 105

Allan, R. P., B. J. Soden, V. O. John, W. Ingram, and P. Good (2010), Current changes in tropical precipitation, Environ. Res. Lett., doi:10.1088/ 1748-9326/5/52/025205

Physically Consistent Responses of the Global Atmospheric Hydrological Cycle in Models and Observations, Richard P. Allan et al, Surv Geophys (2014)

Held IM, Soden BJ (2006) Robust responses of the hydrological cycle to global warming. J Clim 19:5686–5699

Changes in temperature and precipitation extremes in the CMIP5 ensemble, VV Kharin et al, Climatic Change (2013)

Energetic Constraints on Precipitation Under Climate Change, Paul A. O’Gorman et al, Surv Geophys (2012) 33:585–608

Trenberth, K. E. (2011), Changes in precipitation with climate change, Clim. Res., 47, 123–138, doi:10.3354/cr00953

Zahn M, Allan RP (2011) Changes in water vapor transports of the ascending branch of the tropical circulation. J Geophys Res 116:D18111

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If we want to assess forecasts of floods, droughts and crop yields then we will need to know rainfall. We will also need to know temperature of course.

The forte of climate models is temperature. Rainfall is more problematic.

Before we get to model predictions about the future we need to review observations and the ability of models to reproduce them. Observations are also problematic – rainfall varies locally and over short durations. And historically we lacked effective observation systems in many locations and regions of the world, so data has to be pieced together and estimated from reanalysis.

Smith and his colleagues created a new rainfall dataset. Here is a comment from their 2012 paper:

Although many land regions have long precipitation records from gauges, there are spatial gaps in the sampling for undeveloped regions, areas with low populations, and over oceans. Since 1979 satellite data have been used to fill in those sampling gaps. Over longer periods gaps can only be filled using reconstructions or reanalyses..

Here are two views of the global precipitation data from a dataset which starts with the satellite era, that is, 1979 onwards – GPCP (Global Precipitation Climatology Project):

From Adler et al 2003

Figure 1

From Adler et al 2003

Figure 2

For historical data before satellites we only have rain gauge data. The GPCC dataset, explained in Becker et al 2013, shows the number of stations over time by region:

From Becker et al 2013

Figure 3- Click to expand

And the geographical distribution of rain gauge stations at different times:

From Becker et al 2013

Figure 4 – Click to expand

The IPCC compared the global trends over land from four different datasets over the last century and the last half-century:

From IPCC AR5 Ch. 2

Figure 5 – Click to expand

And the regional trends:

From IPCC AR5 Ch. 2

Figure 6 – Click to expand

The graphs for the annual change in rainfall, note the different scales for each region (as we would expect given the difference in average rainfall in different region):

From IPCC AR5 ch 2

Figure 7

We see that the decadal or half-decadal variation is much greater than any apparent long term trend. The trend data (as reviewed by the IPCC in figs 5 & 6) shows significant differences in the datasets but when we compare the time series it appears that the datasets match up better than indicated by the trend comparisons.

The data with the best historical coverage is 30ºN – 60ºN and the trend values for 1951-2000 (from different reconstructions) range from an annual increase of 1 to 1.5 mm/yr per decade (fig 6 / table 2.10 of IPCC report). This is against an absolute value of about 1000 mm/yr in this region (reading off the climatology in figure 2).

This is just me trying to put the trend data in perspective.

Models

Here is the IPCC AR5 chapter 9 on model comparisons to satellite-era rainfall observations. Top left is observations (basically the same dataset as figure 1 in this article over a slightly longer period with different colors) and bottom right is percentage error of model average with respect to observations:

From IPCC AR5 ch 9

Figure 8 – Click to expand

We can see that the average of all models has substantial errors on mean rainfall.

Articles in this Series

Impacts – I – Introduction

Impacts – II – GHG Emissions Projections: SRES and RCP

Impacts – III – Population in 2100

Impacts – IV – Temperature Projections and Probabilities

Impacts – V – Climate change is already causing worsening storms, floods and droughts

Impacts – VI – Sea Level Rise 1

Impacts – VII – Sea Level 2 – Uncertainty

Impacts – VIII – Sea level 3 – USA

Impacts – IX – Sea Level 4 – Sinking Megacities

Impacts – X – Sea Level Rise 5 – Bangladesh

References

IPCC AR5 Chapter 2

Improved Reconstruction of Global Precipitation since 1900, Smith, Arken, Ren & Shen, Journal of Atmospheric and Oceanic Technology (2012)

The Version-2 Global Precipitation Climatology Project (GPCP) Monthly Precipitation Analysis (1979–Present), Adler et al, Journal of Hydrometeorology (2003)

A description of the global land-surface precipitation data products of the Global Precipitation Climatology Centre with sample applications including centennial (trend) analysis from 1901–present, A Becker, Earth Syst. Sci. Data (2013)

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