Trends in extreme rainfall events

Guest essay by Philip Lloyd

There are constant claims that extreme events are becoming more frequent, but when you really dig down, you cannot see any trends even in long-term data. Of course, the scaremongers claim that it hasn’t happened yet, but their models predict it is going to happen any day real soon now, just you wait! All agree it has been warming for at least the past 150 years. If there were any effect such as the models predict, surely we would have seen it by now? It surprises many, but there is no detectable trend in extreme events in the historical data sets.

However, it is not quite straightforward. For instance, how do you define an extreme event, particularly with phenomena that are not normally distributed? Do you only have to consider the high extremes, or must you also consider the low extremes? And how many extreme events does it take to determine a baseline, let alone a trend?


To illustrate the challenges, consider the longest rainfall record we possess, that of England and Wales, which has monthly data back to 1766. The annual totals are close to normally distributed, as shown in the figure. A multi-parameter distribution such as a Weibull would do a better job, but we can treat the distribution as normal for the purposes of this exercise. The average annual rainfall is 918mm with a standard deviation of 119mm.


The next figure plots the annual rainfall since 1766 with the upper and lower 95% (two standard deviations) confidence limits. There is a very slight increase of 0.19 ± 0.11 mm per year which is not statistically significant. However, it is of the order to be expected from the Clausius-Clapeyron relationship for the warming over this 250 years.

We would expect 12.5 extreme events in 250 years, if an extreme event is defined as one that exceeds the 95% confidence limits. The figure shows that there are seven such events above the upper limit and four below the lower, or 11 in total, where 12.5 had been expected. Given the slight skewness of the data and the approximation of normality, the difference is not significant.

What is significant, however, is that there is no detectable change in the frequency of the extreme events. Indeed, to detect such a change with any degree of confidence, you would need far more than eleven events or, in the present case, far longer than 250 years. So those who claim we are facing disaster from “climate change” need to reflect on the fact that even with a generous >95% measure of extremeness, it took 250 data points to approximate a baseline. How can we tell if an event is extreme if we have no baseline?

Is 95% generous? I think it is. Engineers typically design for the 1:100 year event, not 5:100. For really critical structures, they may use the 1:1000 year event. By and large, the engineers have been successful in protecting us against all manner of natural forces. The Great Kanto earthquake of 1923 devastated Tokyo; it had a magnitude of 7.9. The Great Tohoku earthquake of 2011, which caused the tsunami that destroyed the nuclear reactors at Fukushima, had a magnitude of 9.0 and the rebuilt, earthquake-proofed Tokyo was virtually unscathed.

When you hear that the effects of climate change will fall more strongly on poor nations, realize that it is probably true. It has, however, nothing to do with climate change, and everything to do with some poorly engineered infrastructure in those nations.


Philip Lloyd

Energy Institute, Cape Peninsula University of Technology, Cape Town, South Africa


42 thoughts on “Trends in extreme rainfall events

    • Naw, Head for the Balloons (Blimps). The Hills wash away from Rain so If you head for the Hills you might get washed away in the Mudslides. Conversely, if you head for the valleys, this is where the Hills wash away into. So…To avoid the slides, head for the Blimps!!

  1. As a Canadian heading into winter, I demand to know…..Where the hell is that Glo.Bull Warming ????? I’m tired of freezing my nuts off every 6 months for 6 months !! Why am I still seeing snow ? You liberals promised ” NO MORE SNOW ” !!!!………..aaaaaah, thanks. I feel better now..

    • As a Canadian, Surely you also realize that your Annual Average temperature is where TPTB indicate global tamps must be for maximum production of goods and services. 🙁
      Snow mobiles
      Snow Skis
      Snow Shoes
      Trees (Construction supplies)
      Trees (cooking fuel supplies)
      Trees (Home heating supplies)
      Trees (CO2 sinks)
      Tasty Geese
      Popsicle Toes
      Frozen ‘Nads
      Cold Shoulder

      • Now that we have learned that a) there is no methane bomb under the ice and b) that trees emit 4% of their carbon uptake as methane, we can expect a new scare claiming that the rapid expansion of forests into the Canadian tundra is going to cause a massive, runaway explosion in the methane concentration. You just can’t win with nature. She has so many tricks to foil even the most ardent sequesterer.
        As for colds, the Canadian Arctic is the best place to hide from sneezes. No pollen most of the year and virusus don’t do well in the frigid air. Colds needs warmth. I hear the cold viruses union (CVU) is an observer member of Minnesotans for Global Warming (M4GW).

    • The models keep saying a torch for most of Canada due to El nino. It is anything but a torch there now. Raises serious questions. This el nino will not have the same impacts as previous ones. Canada will likely be in for another cold winter because el nino is not the only factor in global climate.

  2. To be fair…this sort of data is good when looking at drought periods (or their non-existence) but not “extreme rainfall events” that fall over much shorter durations than one year. And extreme example (pun intended) would be getting one 24″ rainfall event and dryness the rest of the year instead of 2″ per month

    • I agree. I would think an extreme event would be the number of inches that fall in a one to three day period from a particular weather event.

      • The counterargument to that is – weather is not climate. And there certainly were extreme events before humans began the Industrial Revolution, so the question to ask is, where do you draw the baseline? What arbitrary value would you assign to describe an “EXTREME” event from one that is merely above normal?

      • AZ1971 you make a good point. An extreme weather event is fundamentally different from an extreme climate event. A 100 year Californian drought is a climate event. The huge flood in the 1850’s is a weather event. Individually we are affected by the weather, collectively we are affected by the climate.

      • I think you folks are chasing unicorns, AFAIK there’s no real meaning to the word “extreme” when applied to statistical events. I doubt anyone will find a “Godzilla” classification either, as in Godzilla = 6 sigma whereas extreme = 3 sigma and somewhere between an extreme event and a Godzilla event there are gonzo events. These are terms invented by climate science I’m afraid and have nothing to do with formal statistical analysis.
        I’m sorry. It is a lot more fun. Maybe we could get together an petition ISO or ANSI to come up with some classes that have a bit more pizazz?

      • OK, I have to comment on this whole “extreme” idea; I think you guys are chasing unicorns. AFAIK there isn’t an official “extreme” category for statistical events. It’s a little like the Godzilla classification– it’s not in the textbooks. Not as if “extreme” = a 3 sigma event and “Godzilla” is reserved for 6 sigma and “gonzo” is somewhere in between. I think these are classes invented specifically by climate researchers and haven’t quite made it into the ISO or ANSI references.
        Maybe we should get together and petition them to come up with some names that are more fun?

    • I talked to the Met Office about this rainfall data base a couple of years ago. There is no such thing as reliable rainfall records back to 1766. (my opinion, not necessarily theirs)
      By definition, hundreds of years ago people generally weren’t living in the wettest and most inhospitable parts of the British Isles. Those that were, are unlikely to have had the time or inclination to reliably record rainfall in sufficient numbers in sufficient locations countrywide to constitute a nationwide like for like record that can be compared to today, with its numerous well distributed rainfall collection points that reach an accepted standard of methodology.
      The observers who did take rainfall records were very mixed. The one in Dawlish Devon taking rainfall data in the mid 19th century was an engineer on the Great Western Railway then being built in the area and might be considered more reliable than his counterpart elsewhere who treated rainfall collection as an occasional hobby.
      Historic spot rainfall records for individual locations for a well populated area (like CET) might have considerable relevance to today if they can be validated. Generally, more reliable nationwide records can perhaps be said to have begun in 1910.
      Before someone else points it out, the 1766 records came about in its modern form largely due to work by Phil Jones and others
      Phil Jones is a good scientist whose often excellent past research should not be minimised because of his reputation with sceptics. My objections are based on the sparse readings for each of the 5 climatological regions identified

    • I have looked at rainfall data all the way down to every-five-minute data points(over four years!). I have also studied wind data. The basic conclusions are unchanged. Check for normality (the five-minute data were very close to log-normal); set a statistical limit (two standard deviations are enough for me) to define what you mean by “extreme”; and see how many “extreme events” you a) can observe and b) require to establish a baseline on the rate of extreme events.

      • Philip
        I have studied the climate records of Britain covering the last 1000 years and do not believe for a moment that the modern era has as many extreme events as those of the past periods I can observe. In fact we seem to be living in a relatively benign climate compared to the past. My overriding impression of the most notable events from the 11th to 18th century are those related to stupendous rainfall over protracted periods, associated flooding and huge storms.
        So I am not disagreeing with you, merely pointing out that the British rainfall records to 1766 can not be seen as a scientific document and that we lack historic data from the wettest parts of Britain as few people were taking reliable readings in them.

  3. What do I know? – after all, I am just an engineer. But this statement – “How can we tell if an event is extreme if we have no baseline?’ – seems to get to the crux of the matter. And if you don’t where you have been, how can you tell where you are going?

    • Greg W
      Using stats (good stats) it is possible to determine from a historically incomplete but contiguous record the likelihood of rainfall outside the normal range. There is a small chance that it will rain on London two meters in a day. The likelihood of that happening is small but quantifiable. That says nothing about when, but the likelihood at all can be used to create a baseline. Frequency is another matter. That requires data.
      A big storm need never have happened on record for the chance of one to be real.

  4. For the climate chapter of Arts of Truth, I did a similar but more local analysis for Lincoln Nebraska using the University’s records going back to the 1890s. No trend in temp, 90F summer days, 100F summer days, winter lows, first 90F day, or precipitation.

  5. Thanks Philip, for the tour down memory rain. It seems that in a warmer world there will be slightly more rain. Hardly a daunting prospect.
    Having spent yesterday afternoon on the beach at Kuta, Bali we remarked on the peaceful blue skies. I reminded the group that this paradisical weather was in fact interrupted now and then by gentle warm rain and the occasional thud of falling fruit.
    Sorry to be heading into winter in a couple of days.

  6. some poorly engineered infrastructure in those nations
    compare Katrina, Sandy and Patricia. The poorly engineered technology of the US collapsed like a house of cards, with thousands killed. In contrast the Mexican technology survived the “Strongest Hurricane Ever” with barely a scratch and only 2 deaths.

    • Compare two cities woefully unprepared for hurricanes (New Orleans legendarily so) getting hit by relatively week storms with a city that routinely gets hit by a hurricane. To compare, Florida regularly gets major hurricanes, and even category 5 impacts with relatively little damage compared to the devastation caused by sub-tropical-storm Sandy.

      • Sorry, I didn’t mean to be insensitive. There is only so much you can do to prepare for a category 5 hurricane. However, Andrew was a gigantic hurricane that blew houses clean off their foundations. Katrina was much smaller and weaker, but more devastating due to poor management of the New Orleans dikes
        Note my tagline. I lived through Ike too.

  7. But the alarmist could argue that the extremes are hidden in the data which represent a large area (Wales and England). If one would look at the records of smaller areas extremes may be more apparent. For instance if London would suffer from an event with extreme rain it may not show up in the data of for the whole of England anf Wales. Of course this way there is an infinite number of possibilities to find somewhere an extreme event of whatever nature.

  8. What appears to be more frequent are the numbers and variety of chickens sqwauking about the sky falling in.

  9. The comparison of Katrina , Sandy and Patricia is not really valid. Patricia hit a thinly populated area and dissipated quickly in mountainous terrain. indeed houses in the direct path were destroyed. Houses in the NE and New Orleans were old and probably built only slightly better than those in Mexico (and of course we know the real culprit in NO was the Corp of Engineers). By comparison, my house near Galveston, which we modernized and brought entirely up to coastal storm code two years before Ike (lucky timing), suffered slightly from rising water but had no other damages, while numerous of our neighbors had damages ranging from major to complete destruction.

  10. What is often forgotten when claims of increasing extreme rainfall are made, is that during the 1960’s and 70’s global cooling brought extended drough belts across a swathe of Africa and Asia. Effectively, the tropical rainzones were squeezed towards the equator.
    Since then rainfall has increased again in the regions, inevitable making rainfall look “more extreme”.
    These places are of course only too delighted. Just ask the Indians, who had repeated monsoon failures then.
    All this was known at the time by Lamb and others.

  11. Very interesting article from Philip Lloyd. It’s a pity that Philip’s study on the centennial deviation of temp over the last 8,000 years has not resulted in more comment from scientists around the world.
    We know that HAD 4 data shows about 0.8 C warming since 1850 and the recent Concordia Uni study claims about 0.7 C warming since 1800. But Philip’s study found about 1 C deviation in temp over the last 80 centuries using Antarctic and Greenland ice core studies.

    • Thanks, Neville. In fact, that paper has had quite a good reception, with over 8000 downloads and eleven citations to date. Importantly, from my point of view, is that the findings have not been challenged by the warm brigade (though the reviewers for Nature Climate Change declared it rubbish!)

  12. Extreme rain events and annual rain fall are not the same thing at all. The comparison is completely nonsensical.

    Comparing the effects of the Great Kanto Earthquake on Tokyo and with those of the Tohoku (Great East Japan) Earthquake on the same isn’t exactly fair. The epicenter of the Great Kanto was on Izu Oshima (around 100 miles from Tokyo), while that of the Tohoku was offshore and much farther (231 miles from Tokyo).

    • Katherine, is there a thumb-suck formula for the loss of energy into the ground based on radial distance? Something like 2/R^2 etc? I am trying to get a grip on what the effect of being 2.3 times farther away would have. Maybe the rock structure overwhelms all such generalisations.

      • The main killer in the Great Kanto earthquake was the fire storm that swept through the buildings of old Tokyo. The main killer in the Tohoku earthquake was the tsunami it generated, as Philip Lloyd mentioned.
        In both 1923 and 2011, the earthquake itself wasn’t the main problem.
        Of course, when Tokyo was rebuilt after 1924, there were many who claimed that the disaster was Divine Retribution for whatever and the rebuilding plans were scaled down and down. Leaving a city that was still highly vulnerable to fire storms, as 1945 proved.

  14. Actually Philip Lloyd is a little adrift in the probabilities / return periods of weather events when designing structures and infrastructure, although this in no way detracts from his reasoning. For the design of highway drainage (leading to localised flooding of the highway), even 1 in 100 would be hard to justify in cost terms.
    But really critical structures (nuclear engineering and large dam spillways, for example) are usually designed for events with a probability on 1 in 10,000. The difficulty here is obvious for anyone who gives it a moment’s thought. Taking the dam spillway example, how on earth do you predict a 1 in 10,000 year flood? Unfortunately, Noah’s detailed records seem to be unavailable. But there are folk out there who have made a good living theorising how to predict extreme rainfall and flooding events. Whether the results of their (extremely complicated) prognostication programmes give you any real feel for an event that might occur once in 10,000 years, (or, of course, a 1 in 10,000 risk of happening next year, or maybe the year after) is to my way of thinking, a tad doubtful. But, in fairness, the designer has to start somewhere.
    I remember a few years ago that a new computerised extreme flood prediction tool has been developed in the UK and there was a meeting of the British Dam Society which had this new method on the agenda. I think it is fair to say that some design consultants and dam construction company executives were jointly salivating at the thoughts of the fat juicy contracts that might be forthcoming in re-appraising all dam spillways and re-constructing some of them.
    But, as in the tale of the Emperor’s new clothes, there is unfortunately often a rude urchin who points out the obvious. At that meeting, I fear I adopted the rude urchin role and pointed out that (a) it might not be the best use of public money to rebuild a major dam spillway if analysis of the latest super dooper prediction tool suggested that the spillway would “only” pass a 1 in 9,900 flood. And (b), that there were many other problems which could cause a dam to fail, other than the crest over-topping in an extreme flood. How about piping failures for example? How sure were we that all British dams achieved at least a 1 in 10,000 probability of resisting piping failure collapse?
    This didn’t make me popular, but I suggest it was a point worth making. At Fukushima, the backup emergency generators were sited where they could be knocked out by floodwater. Everything else (in a nuclear reactor designed perhaps 60 years ago) seems to have worked according to plan. A pity there wasn’t a rude urchin who had wondered why the generators were down there……
    I apologise that this comment is a bit off topic. But maybe some of the thoughts are applicable elsewhere?

  15. I was part of consultant team doing an analysis of the potential impacts of climate change and sea level rise on the wastewater infrastructure of New York City, and one topic we investigated was the adequacy of the existing drainage network in light of projections of increased intensity of precipitation in the future. This condition, if it were realized, might overwhelm the sewer system which was designed on the basis of old rainfall data.
    The city bases its sewer designs on a series of intensity-duration-frequency (IDF) curves that were created using long-term precipitation data spanning the period of roughly 1900-1950. We had access to additional high-quality data for the period from 1950-2010, so we aggregated the data to run the numbers again: Would the resulting IDF curves reflect a trend towards increased intensity, i.e. more frequent storms with high values of inches-per-hour of rain? We found no such trend at all.
    The modelers who work for the city, and their friends at GISS, had said that such a trend was inevitable: when we reported our findings, the project managers were not happy. “But THEY said …!” Well, that’s the models, this is the hard data.
    The department engineers were happy. They could continue to use their old IDF curves: they deeply resent the meddling of non-engineers who they feel are out of touch with reality.
    So it goes…

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