The Science of Doom

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:

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:

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:

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.

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:

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

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.

Figure 1

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

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:

ΔR_c + ΔR_T = LΔP

where the change in radiative cooling ΔR, is split into two components: ΔR_c that is independent of the change in atmospheric temperature; and ΔR_T 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, ΔR_c = -2 to -3W/m²; prior to a temperature change ΔR_T = 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 ΔR_T:

The enhanced radiative cooling due to tropospheric warming, ΔR_T, is approximately proportional to ΔT: tropospheric temperatures scale with the surface temperature change and warmer air radiates more energy, so ΔR_T = 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:

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:

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:

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:

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:

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:

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:

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:

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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