RealClimate logo


Note 3/23/2021: we had a few hiccups with comments after moving the site to https/SSL. Hopefully they're fixed now. Please let us know if there are remaining issues.

A potential rule of thumb for hourly rainfall?

Future global warming will be accompanied by more intense rainfall and flash floods due to increased evaporation, as a consequence of higher surface temperatures which also lead to a higher turn-around rate for the global hydrological cycle. In other words, we will see changing rainfall patterns. And if the global area of rainfall also shrinks, then a higher regional concentration of the rainfall is bound to lead to more intense downpours (the global rainfall indicator is discussed here). 

Even with successful mitigation and cut in CO2-emissions, there will be a need for climate change adaptation (e.g. keeping the global warming below 2°C according to the Paris accord). We must be better prepared for more water in inconvenient forms and critical infrastructure may need to be upgraded to withstand it.

Engineers typically make use of so-called intensity-duration-frequency (IDF) estimates to design buildings, bridges or roads that are dimensioned to weather these conditions. Farmers need to know how to manage their fields to avoid erosion and loss of crops. Hence, IDF curves are useful for climate adaptation.

The IDF curves traditionally need sub-daily rainfall measurements (e.g. rainfall recorded every hour) which are not so common everywhere. The standard commonplace rain gauge data, however, record the rainfall accumulated over 24-hr segments (Figure 1).


Figure 1. Location of 24-hr rain gauge measurements from the global historical climate network (GHCN). 

The question is whether it is possible to make use of 24-hr rain gauge data to say something about IDF statistics, even if it doesn’t involve measurements accumulated over intervals of minutes to hours.

There have been some attempts to estimate IDF curves based on 24-hr data that recently were accompanied by a new “rule of thumb” that gives approximate results (Benestad et al., 2021):

x_\tau(L) = \alpha \mu \left(L/24\right)^\zeta \ln(f_w \tau).

In this expression(illustrated in Figure 2), x_\tau(L) is the return level for rainfall accumulated over time duration L (units in hours), \alpha is a statistical correction factor (accounting for the fact that rainfall is not really exponentially distributed), \mu is the wet-day mean precipitation (here a threshold of 1 mm/day was used to distinguish ‘wet’ and ‘dry’ days), \zeta describes the dependency between different temporal scales, f_w is the wet-day frequency, and \tau is return interval. 

Figure 2 IDF- curve estimated for a location in Norway. 

The question is whether this formula can quantify sub-daily rainfall statistics outside Norway, so it should be tested for other parts of the world to see if it provides useful information on a more general basis.

It should be fairly straight-forward to calibrate \zeta against already established IDF curves for sites with sub-daily rain measurement (see Benestad et al., (2021) for more details). This timescale dependency is expected to depend on relative occurrences of convective storms, cyclones, atmospheric rivers, weather fronts, and orographic rainfall (rainfall triggered by moist air blowing over hills and mountains forcing air ascent).

An advantage of this “rule of thumb” formula is its simplicity. It needs the two key rain fall parameters wet-day mean precipitation \mu and frequency f_w, and if the correction factor \alpha and the timescale cross-dependency \zeta have similar values across regions, then it may provide a quick first guess of the IDF curves for sites where hourly rainfall measurements are absent.

References

  1. R.E. Benestad, J. Lutz, A.V. Dyrrdal, J.E. Haugen, K.M. Parding, and A. Dobler, "Testing a simple formula for calculating approximate intensity-duration-frequency curves", Environmental Research Letters, vol. 16, pp. 044009, 2021. http://dx.doi.org/10.1088/1748-9326/abd4ab

30 Responses to “A potential rule of thumb for hourly rainfall?”

  1. 1
    Lyle says:

    where radar stations exist hourly rainfall rate measures are taken these could be used to help, A single radar site can catch some of the variations. I do know that for example in the Tx Hill Country you are looking at up to 6-8 inches of rain per hour during some mezocyclone events. (Also see in tropical events where rainfall over a several day period is also needed, for example in the Tx Hill Country again 40 inches over 4 days for example or 50 inches near Houston in 4 days with a tropical storm)

  2. 2
    Susan Anderson says:

    Very useful post. Thanks!

  3. 3
    David Willams says:

    Interesting! Have a look at today’s news from Australia to see how the experiment is going!

  4. 4
    James McDonald says:

    The goal of finding “big picture” statistics to summarize global patterns is highly appealing, for multiple reasons.

    Scientifically, such summaries introduce unifying concepts, similar to the way the concept of energy unified notions of heat, work, gravitational potential, etc.

    Economically, they simplify planning for anticipated trends. “Expect more intense rainstorms” is easily digestible and gives actionable intelligence to everyone from famers to bridge builders to sewage treatment plants to airport managers.

    And they provide pithy numbers that can be used to influence political discussions and to let governments understand the magnitude and rate of developing problems.

    Having said that, how do you find such measures? Maybe there are simple ones out there that no one has thought to consider: variations in daily wind speeds, shifts of rainfall at time of day or cloud cover by month, changes in spatial gradients for wind/temperature/humidity, whatever.

    That suggest a possible research program using machine learning to observe the mountains of data out there to extract correlations and produce mathematical abstractions (concepts, if you will) that emphasize terseness. That could be done by prioritizing nets with reduced complexity.

    (As an aside, back in the 70’s I worked on the MetaDendral project at Stanford, which used AI techniques to observe mass spectroscopy data and produce new publishable rules for interfering chemical structures from mass spectra. So there is generic precedence for a machine-based approach to produce new scientific concepts.)

    Food for thought…

  5. 5
    Andy Pitman says:

    The statement: “Future global warming will be accompanied by more intense rainfall and flash floods due to increased evaporation, as a consequence of higher surface temperatures which also lead to a higher turn-around rate for the global hydrological cycle.”

    I have no argument that global warming will lead to more intense rain – the evidence there is strong. The question is the mechanism … and the timescales over which those mechanisms can act.

    So, can someone explain how warmer surface temperatures significantly enhances evaporation? While a higher surface temperature might initially elevate evaporation, the cooling effect of that evaporation is enormous (~2.5E6 J/kg of course which is ~2.5E6 J per mm of water evaporated per m^2). In any case, surface temperature does not appear in the equations for the latent heat flux, except in calculating the vapour pressure of the overlying atmosphere. If evaporation was higher, that would lead to a cooler surface. Broadly, if anything, elevated CO2 reduces land evaporation by reducing transpiration via stomatal closure (or at least likely initially increases water use efficiency).

    So, I accept that rainfall is intensifying, but I suspect it is very weakly related to evaporation from the land surface. The oceans maybe – is the case resented here purely for freely evaporating water bodies?

  6. 6
    J Doug Swallow says:

    #3 23 Mar 2021 at 12:06 PM David Willams says: “Interesting! Have a look at today’s news from Australia to see how the experiment is going!”
    “Climate Commissioner Tim Flannery in 2005: “But since 1998 particularly, we’ve seen just drought, drought, drought, and particularly regions like Sydney and the Warragamba catchment – if you look at the Warragamba catchment figures, since ‘98, the water has been in virtual freefall, and they’ve got about two years of supply left, but something will need to change in order to see the catchment start accumulating water again…. So when the models start confirming what you’re observing on the ground, then there’s some fairly strong basis for believing that we’re understanding what’s causing these weather shifts and these rainfall declines, and they do seem to be of a permanent nature…” :

    So which is it? Is your global warming going to cause more droughts or more flooding? Is it possible that more of the life giving trace gas, carbon dioxide, will produce a Goldilocks effect on Earth?

  7. 7
    James Charles says:

    How does ‘this’ ‘fit in’?
    “Plants will be hit as a warming world turns drier
    March 26th, 2021, by Tim Radford”
    https://climatenewsnetwork.net/plants-will-be-hit-as-a-warming-world-turns-drier/?fbclid=IwAR0FDVhx3xKNnpf9dZAP3cGWknYW8YE0hP3wMFoco2RPCI6HLu89BnyBePM

  8. 8
    Piotr says:

    James Charles (7) “How does ‘this’ ‘fit in’? “Plants will be hit as a warming world turns drier March 26th, 2021, by Tim Radford

    Wasn’t the answer in the …article you refer to? E.g.:
    Climate science also predicts that although those regions already rainy will get rainier, the drylands and arid zones will get even dryer as the thermometer soars.

  9. 9
    Piotr says:

    Andy Pitman(5):
    So, can someone explain how warmer surface temperatures significantly enhances evaporation? While a higher surface temperature might initially elevate evaporation, the cooling effect of that evaporation is enormous (~2.5E6 J/kg of course which is ~2.5E6 J per mm of water evaporated per m^2).

    The same “enormous cooling” was in place in the world BEFORE global warming – would you then argue that even there should have been hardly evaporation also then?

    In any case, surface temperature does not appear in the equations for the latent heat flux, except in calculating the vapour pressure of the overlying atmosphere.

    because it is not the latent heat that decides about the rate of the evaporation
    but the relative humidity of the air above. And that, for a given concentration of H20 vapour in air, is decided by the temperature.

    Broadly, if anything, elevated CO2 reduces land evaporation by reducing transpiration via stomatal closure (or at least likely initially increases water use efficiency).

    As you have already indicated, this not apply to the massive evaporation from the oceans and from any land surface that is not a plant. I would argue that it does not apply EVEN to the evaporation from most (nearly all?) plants too. Here is why:

    In all ecosystems where the plants are not water limited – there is no incentive to reduce evaporation. In fact higher temps mean lower relative humidity, therefore MORE “room” for plants to evaporate. And why would like to evaporate MORE ?

    1. in the nutrient limited ecosystems, like tropical jungles – the more water you suck in from the ground – the more of the (very diluted) nutrients you can get

    2. in hot places you also want to evaporation to prevent overheating – a problem in the already hot places (like our main evaporator – tropical forests), particularly if we add there global warming …

    3. in temperature-limited ecosystems, like Arctic – the global warming means more time to grow, which mean that you will need more nutrients, which you get by … sucking more water from the soil, and you can suck more, only if you evaporate more.

    4. which leaves us ONLY with plants that are water-limited. Yes, higher CO2 allows you them SHORTEN your opening of stomata to get THE SAME amount of CO2. But the whole point of the CO2-fertilization is that that the growth of those plant INCREASES – which means that you would need MORE CO2 and MORE nutrients from the soil – i.e., you need to keep the stomata open. To sum it up – under high CO2 water-limited plants are more productive – produce more organic matter per the SAME volume water used, in effect – per the same volume water evaporated.

    And that’s “ how warmer surface temperatures significantly enhances evaporation“…

  10. 10
    nigelj says:

    JDS @6, “Is your global warming going to cause more droughts or more flooding”

    Global warming could theoretically cause both more droughts and more flooding (typically more intense) , but at different times and places obviously. Global warming affects both temperatures and atmospheric water content. This is all obvious even to this layperson. Even you should be able to work that out if you try really hard.

  11. 11
    J Doug Swallow says:

    #5 27 Mar 2021 at 6:45 PM Andy Pitman says: “Broadly, if anything, elevated CO2 reduces land evaporation by reducing transpiration via stomatal closure (or at least likely initially increases water use efficiency).” in addition to other valid and interesting observations about this issue that is questionable about; “Future global warming will be accompanied by more intense rainfall and flash floods due to increased evaporation…”

    What Berkeley has figured out makes perfect sense to me; but I wonder how it will fly on this site?
    “It works like this. Stomata control a tradeoff for the plant: they allow carbon dioxide in, but they also let precious water escape. A plant that could get enough carbon dioxide with fewer stomata would have an advantage since it would be better able to conserve its water. Levels of carbon dioxide in Earth’s atmosphere change over time — so at times when the atmosphere is carbon-dioxide-rich, plants can get away with having fewer stomata since each individual stoma will be able to bring in more carbon dioxide. During those high-carbon-dioxide times, plants with fewer stomata will have an advantage and will be common. On the other hand, when carbon dioxide levels are low, plants need many stomata in order to scrape together enough carbon dioxide to survive. During low-carbon-dioxide times, plants with more stomata will have an advantage and will be common.”
    http://evolution.berkeley.edu/evolibrary/article/0_0_0/mcelwain_03

  12. 12
    J Doug Swallow says:

    #10 28 Mar 2021 at 4:59 PM nigelj says: “Global warming could theoretically cause both more droughts and more flooding (typically more intense) , but at different times and places obviously”. I’m sure that nigelj’s global warming has caused this to recently happen in Denver.
    “As of Tuesday, Denver International Airport was reporting 30.9 inches of snow so far this month, nearly three times the March average. The vast majority of this pow-pow fell over the course of just two days when the one of the biggest snowstorms ever recorded in the city dumped 27.1 inches.
    As it stands, March 2021 holds fourth spot on the list of the snowiest Marches on record; and looking up the list, less than half an inch is needed for Denver to surpass the March of 1891, which holds third spot, while 1944’s 32.5 inches, and 2003’s 35.2 inches are also well within reach.” https://electroverse.net/denver-forecast-to-break-1891-snowfall-record-as-wintry-storms-threaten-north-america/
    Because the truth is a foreign concept on this site, this post will never see the light of day.

  13. 13
    jgnfld says:

    Re. Question: “Is your global warming going to cause more droughts or more flooding?”

    Answer: Speaking scientifically, very likely yes.

  14. 14

    JDS 6: Is your global warming going to cause more droughts or more flooding?

    BPL: The surface of the Earth is two-dimensional. Global warming causes more droughts in continental interiors, more flooding along coastlines. In short, it moves the rain.

  15. 15
    nigelj says:

    J Doug Swallow @12 says

    “As of Tuesday, Denver International Airport was reporting 30.9 inches of snow so far this month, nearly three times the March average”

    Given that warming obviously wont cancel the seasons, and has lead to more water vapour in the atmosphere its not surprising you get a few record snow storms. You cant grasp this can you. Its beyond you.

  16. 16
    William B Jackson says:

    No #12 Even though your post is nonsense it is here before us to prove the ignorance of the poster. Weather is not climate!

  17. 17
    Richard Caldwell says:

    Piotr: In all ecosystems where the plants are not water limited – there is no incentive to reduce evaporation.

    RC: I’ve pondered this and wonder…

    Evapotranspiration requires energy. Plants can lower energy usage by lowering water use. (I’m not sure about the ultimate source of the energy needed to lift the water. Do you?)

    Many (most?) plants are water limited. So in your opinion your “only plants that are water limited” grouping encompasses what percentage of the planet’s plants, taking into account that the globe is currently around 1.5C warmer than plants evolved in?

    Nutrient overload is an issue. Pumping water to stay alive while photosynthesis and other systems are operating suboptimally could result in overfertilization, especially since the native plants were acclimated to the old climate and soil. Sure, 1000 years from now things might shake out, but we’ll all be long dead.

    Increased temperatures increase respiration (especially(?) microbial, as in soil organisms) more than photosynthesis. The Biosphere experiments couldn’t figure out how to maintain oxygen at a level conducive to human health because soil bugs were happier than the plants.

    Nigel: Given that warming obviously wont cancel the seasons, and has lead to more water vapour in the atmosphere its not surprising you get a few record snow storms

    RC: Yep. I lived in Fairbanks, Alaska for a while. It snowed in spring and fall. In winter ya might get a dusting. Snowfall is a “warm weather” thing. It can’t snow more than the amount of excess moisture, and warmer air holds more moisture. Like BPL said, ya get more droughts AND more floods. Bigger and badder events with longer dry spells in between

  18. 18

    Nigelj@10 – yes that is possible, but just saying it doesn’t make it happen. Take for example Sydney with a beautiful 160 year record of every day’s rain – up until a couple of years ago when they decided to “standardise” it. Get the data from here yourself:-
    http://www.bom.gov.au/climate/data/
    So I took 20 years of daily recordings from 1900 to 1920, and also 2000 to 2020 and did a 2mm binned histogram and guess what…… you are wrong. The histograms were amazingly similar with the earlier years having very slightly higher values at the extremes.
    OK, it’s only one place but at least for Sydney we are not having more dry days, nor more overly wet days.
    Luckily the BoM also have a good record for Broken Hill (for those unfamiliar with Australian geography it is very typically “the Outback”). Unfortunately I could only get a 16 year period 100 years apart but it shows exactly the same non-trend. So we can also ignore BPL’s guess at what the real world does.
    And on that BPL@14, and you have seen this data before, there are parts of Australia that have had a small increase in rainfall over the last 120 years, as well as some that have had a small decrease. But they are NOT related to interiors or coast, or wet or dry areas. It’s just variable – that is climate change. If any of the things you suggest were true, then you could have reason to suggest that global warming were to blame
    http://www.bom.gov.au/climate/change/index.shtml#tabs=Tracker&tracker=trend-maps&tQ=map%3Drain%26area%3Daus%26season%3D0112%26period%3D1900

    Let me make this clear before you all go off and put words in my mouth….. yes, these are selected locations and times. Don’t just say it isn’t valid, if you have a counter example, give it. And if you are going to counter with a paper, make sure it doesn’t have the words “model” or “smooth” in it

    I just love data

  19. 19
    J Doug Swallow says:

    13 & 14 29 Mar 2021 both jgnfld & Barton Paul Levenson say: “Is your global warming going to cause more droughts or more flooding?” It would have been great if they would have offered up some sort of explanation in more detail than; “Answer: Speaking scientifically, very likely yes”. & whatever point that Barton Paul Levenson was attempting to make with his observation that, “The surface of the Earth is two-dimensional.”
    If one had been foolish enough to listen to what was being said in the past about the California drought a few years ago, they would have been seen to have been very foolish because the drought soon turned into floods.
    “California’s drought is the worst in 1,200 years, evidence suggests”
    Date: December 5, 2014
    Source: Woods Hole Oceanographic Institution
    https://www.sciencedaily.com/releases/2014/12/141205124357.htm

    “California Facing Worst Drought on Record”
    January 29, 2014
    https://www.climate.gov/news-features/event-tracker/california-facing-worst-drought-record

    A worst in 1,200 years drought can end suddenly and I imagine that is not good news to the ones who push this doom and gloom scenario of anthropogenic climate change.
    “California and Nevada Pummeled By Flooding Rain, Mudslides and Rockslides; Rain Heads South Until Tuesday”
    Jan 8 2017
    The National Weather Service says that flooding with this event may be the greatest since December 2005 for some locations.”
    https://weather.com/forecast/regional/news/california-atmospheric-river-sierra-snow-flood-forecast-jan2017

    OROVILLE Note the date.
    February 11, 2017 05:24 AM
    Water began pouring over the emergency spillway at Oroville Dam early Saturday for the first time in its 48-year history. State officials continued to say they don’t expect the situation to result in flooding in Oroville or other communities downstream.
    http://www.sacbee.com/news/local/article132154774.html

  20. 20
    John Pollack says:

    The exceptionally wet mid-March storm affecting primarily eastern Colorado and Wyoming, and most of Nebraska, is a specific illustration of the increasing juxtaposition of drought and excess moisture. The area most affected by the storm was in a drought condition before it hit. Despite the heavy snowfall, Colorado and Wyoming are still in a drought. The storm ended the drought in central and eastern Nebraska, although some areas are still rated “abnormally dry” according to the U.S. Drought Monitor. https://droughtmonitor.unl.edu/
    Grand Island, in south central Nebraska, easily exceeded their 125-year 24 hour precipitation total on March 13. On the 14th, they broke the record set the preceding day.

  21. 21
    jgnfld says:

    Re. 19 and “drought in California means that the whole world is suffering a drought”…

    Are you serious? Just how stupid do you think your readership here is?

  22. 22

    JDS, #19–

    If one had been foolish enough to listen to what was being said in the past about the California drought a few years ago, they would have been seen to have been very foolish because the drought soon turned into floods.

    Uh, how is the fact that a drought ended relevant to its intensity while it lasted?

    A worst in 1,200 years drought can end suddenly and I imagine that is not good news to the ones who push this doom and gloom scenario of anthropogenic climate change.

    Bemused all over again… but #1, vide supra. And #2, why would relief from a crippling (and probably for some, tragic) drought ever be bad news for anybody?

  23. 23
    Steven Emmerson says:

    Piotr at #9 wrote:

    In all ecosystems where the plants are not water limited – there is no incentive to reduce evaporation.

    In general, but there are nuances. The tamarisk plant, for example, thrives in relatively water-limited areas but has relatively high evapotranspiration rates.

  24. 24
    Piotr says:

    RC(17) Evapotranspiration requires energy. Plants can lower energy usage by lowering water use.

    What for? It’s not their energy. They don’t need to SPEND any of their own (chemical) energy to evaporate the water. All the energy needed for the evaporation is in the water itself (kinetic energy of the H20 molecules).

    The only (minor in comparison) plant energy expenditure is at the other end – to actively pump ions into the root (so water follows into the root by osmosis).
    But even then, you want these ions (your nutrients) in anyway.

    RC(17) your “only plants that are water limited” grouping encompasses what percentage of the planet’s plants

    Irrelevant to the subject of the discussion:
    a) no reduction or even an increase of transpiration in ecosystems that are not water-limited, and
    b) in those place that are water-limited:
    – in the arid and semi-arid there is so little precipitation – that the role of its transpiration one way or another – at the global scale is also minimal.
    – in the remaining water-limited ecosystems – as previously answered:
    Piotr(9): “[under CO2-fertilization] the growth of plants INCREASES – they produce more organic matter per the SAME volume water used [~= evaporated]

    RC(17)”Nutrient overload is an issue. Pumping water to stay alive while photosynthesis and other systems are operating suboptimally could result in overfertilization

    Most of the water is pumped to get more of the very diluted nutrients from the soil
    so in no danger of overloading with nutrients there. If you have enough – then turn down pumping. And plants have control what ions they are getting in, by screening them out by endodermis, only ions that have cross-membrane carriers can get through and into plant plumbing system.

    More importantly – what is the relevance of that to discussed here claim (that in the future the transpiration will significantly decrease)?

    RC(17) Increased temperatures increase respiration (especially(?) microbial, as in soil organisms) more than photosynthesis.

    Again, how does it relate to the subject of the discussion (the postulated sharp decrease in transpiration)

  25. 25
    David Willams says:

    # 6 J. Doug Swallow: So which is it? Is your global warming going to cause more droughts or more flooding?

    I’m reminded of Tamino’s comment several years back: I’ll continue to do what I can come hell or high water. Expect both.

  26. 26

    JDS 19: A worst in 1,200 years drought can end suddenly and I imagine that is not good news to the ones who push this doom and gloom scenario of anthropogenic climate change.

    BPL: Unbelievable.

    JDS apparently STILL thinks a 1,000 year drought means “a drought that lasts 1,000 years.”

    The man cannot learn.

  27. 27
    Piotr says:

    Steven Emmerson (23) In general, but there are nuances.

    but do you have an example of such nuance that applies to my general statement:
    Piotr(9): “In all ecosystems where the plants are not water limited – there is no incentive to reduce evaporation.” ?

    Your current example: “tamarisk plant” is in … “in water-limited area“, so it does not apply my above statement.
    But there is silver lining – your example does support my complementary argument from (9) (i.e. p.4 about the “water-limited systems”)…

  28. 28
    Oxyaena says:

    Well, on the bright side if you’re a gardener in Florida prospects are looking good. ;)

  29. 29
    Piotr says:

    Oxyaena says (28)”Well, on the bright side if you’re a gardener in Florida prospects are looking good. ;)

    Well, if you are into underwater gardening…
    Or into halophytes (with the seawater intrusion into the groundwater) ;-)

  30. 30
    Jim Eager says:

    Barton, what do you expect from someone who salts their comment with the double red herring “life giving trace gas”?

    As if either are at all relevant.

Leave a Reply

Comment policy. Please note that if your comment repeats a point you have already made, or is abusive, or is the nth comment you have posted in a very short amount of time, please reflect on the whether you are using your time online to maximum efficiency. Thanks.