100 yr Storm (How often Does it Really Occur?)
100 yr Storm (How often Does it Really Occur?)
(OP)
I have heard several times the probability of a 100 yr event is the 1/100 for any given year.
I have also heard that statistically if you look at a period say 30 yrs then the odds of a 100 yr event occurring in that 30 yrs is much greater thant he relative frequancy of the union of events... i.e. one way to look at is that the odds of a 100 yr event over a 30 yr period is 1/100+1/100+1/100 etc for 30 times or 30/100 or 3/10... this makes some sense to me, but I have heard several times that the probability is acutually much higher than 3/10 that a 100 yr storm would occur in over a 30 yr period and that the statement the people always make that "... a 100 yr storm occurs on average once per 100 yrs is generally false."
Anyone good enough with statistics to explain in simple terms which is true?????
I have also heard that statistically if you look at a period say 30 yrs then the odds of a 100 yr event occurring in that 30 yrs is much greater thant he relative frequancy of the union of events... i.e. one way to look at is that the odds of a 100 yr event over a 30 yr period is 1/100+1/100+1/100 etc for 30 times or 30/100 or 3/10... this makes some sense to me, but I have heard several times that the probability is acutually much higher than 3/10 that a 100 yr storm would occur in over a 30 yr period and that the statement the people always make that "... a 100 yr storm occurs on average once per 100 yrs is generally false."
Anyone good enough with statistics to explain in simple terms which is true?????





RE: 100 yr Storm (How often Does it Really Occur?)
Hope this helps, and that the old college brain cells haven't failed me.
Carl
RE: 100 yr Storm (How often Does it Really Occur?)
With that in mind, though, the proverbial 100-year event is "unusual" enough to cause substantial (note: not "significant") damage to life and property, hence, use it for your design loads, winds, floods, etc. and thus storm events/flood events that don't produce the same stages, etc. as the "100-year" event will easily be sustained by whatever project you're working on.
How's that for obfuscation?
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
And no it does not average once every 100-years.
The Houston area has had 3 in the past 10 years, and over
10 in the last 100 years.
RE: 100 yr Storm (How often Does it Really Occur?)
What is a "100-year flood"?
A 100-year flood is a flood that has a 1-percent chance of being equaled or exceeded in any given year. A base flood may also be referred to as a 100-year storm and the area inundated during the base flood is sometimes called the 100-year floodplain.
What does the "100-year flood" mean?
The term "100-year flood" is misleading. It is not the flood that will occur once every 100 years. Rather, it is the flood elevation that has a 1- percent chance of being equaled or exceeded each year. Thus, the 100-year flood could occur more than once in a relatively short period of time. The 100-year flood, which is the standard used by most Federal and state agencies, is used by the National Flood Insurance Program (NFIP) as the standard for floodplain management and to determine the need for flood insurance. A structure located within a special flood hazard area shown on an NFIP map has a 26 percent chance of suffering flood damage during the term of a 30-year mortgage.
Other information can be found at http://www.esri.com/hazards/
Online Harzard Maps http://www.esri.com/hazards/makemap.html
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
Chuck
cgopperton@stantec.com
http://www.stantec.com/
RE: 100 yr Storm (How often Does it Really Occur?)
For example, in this same forum was stated it was not necessary to calculate temporary structures against earthquake (forms specifically), since the probability of the structure taking an earthquake blow during construction is too low. Now in Taiwan tha fall of construction cranes and variegate construction material has caused some deaths and a number of wounded people.
So life safety standard has failed during construction, at least the prevention of fall of objects and cranes, this last one very amenable to computation of the holding devices.
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
I don't think the climate is changing so fast that we cannot deal with it. I wonder if anyone has consider that the probably of an ice age returning is in fact more likely than runaway global warming based on historic data. Do you know what triggered the last ice age? I would have to say that predicting the weather is not very reliable and I would guess that predicting climatic change is not any better. The conservative thing to do is adjust as needed and keep the fear level under control. How many automobiles does it take to release the same amount of co2 as one volcano? In the 16th century it snowed in London in the summer. What are we going to do if Kansas has snow in June and the wheat crop is ruined, give up bread
I don't think the climate is changing so fast that we cannot deal with it. I wonder if anyone has consider that the probability of an ice age returning is in fact more likely than runaway global warming based on historic data. Do you know what triggered the last ice age? I would have to say that predicting the weather is not very reliable and I would guess that predicting climatic change is not any better. The conservative thing to do is adjust as needed and keep the fear level under control. How many automobiles does it take to release the same amount of co2 as one volcano? In the 16th century it snowed in London in the summer. What are we going to do if Kansas has snow in June and the wheat crop is ruined, give up bread
Does anyone here really think that a 20% change in climate is going to out strip the safety factors already in place?
RE: 100 yr Storm (How often Does it Really Occur?)
Your estimation of the probability of a 100 year event happening in 30 years is incorrect. 1% + 1% ... = 30% will not work. If you use this same theory for 100 years, you will get a 100% chance that the event will occure in the 100 years (which isn't true). The probability P of an event having a given return period T occurring at least once in N successive years is given as P=1-(1-(1/T))^N. So, for a 30 year period, the probablity that a 100 year event will occure at least once is 26%. For a period of 100 years, the probability that a 100 year event will occure is 63%.
Brian
RE: 100 yr Storm (How often Does it Really Occur?)
Your calculations are not correct, because your definition of a 100-year storm is incorrect. A 100-year storm does not mean that the storm has a probability of occurring every 100-years. A 100-year storm means that the event has a
1% chance of occurring in ANY GIVEN YEAR.
RE: 100 yr Storm (How often Does it Really Occur?)
Yes, you are correct that the definition of 100-yr event means that it will have a 1% chance of occuring in any year, however, that number is not additive, i.e., there is not a 2% chance that a 100-yr event will occure within two years nor a 50% chance the event will happen within 50 years. The formula I gave gives the probability of an event with a given recurance interval occuring within a givin time period.
Brian
RE: 100 yr Storm (How often Does it Really Occur?)
Just for giggles, the following table is the probability of only x occurrences in 100 and 500 years, so the probability of getting none in 100 yrs is 36.6%, which means that the probability of getting 1 or MORE is 73.4%. The probability of getting none in 500 yrs drops to 0.66%. Note that as the overall period increases, the 1% of the period is the 50% breakpoint in the probability distribution function.
0 36.6032 0.6570
1 36.9730 3.3184
2 18.4865 8.3631
3 6.0999 14.0230
4 1.4942 17.5995
5 0.2898 17.6351
6 0.0463 14.6959
7 0.0063 10.4759
8 0.0007 6.5210
9 0.0001 3.6008
10 0.0000 1.7859
TTFN
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
p = 1/T where p is the probability and T is return period
therefore probability of a 5 year flood in any given year is 1/5 = 0.20
RE: 100 yr Storm (How often Does it Really Occur?)
A probability of this type is called a poisson distribution. You can look up the details in any undergraduate statistics textbook. In this type of distribution the probability of the event occurring in any time frame is independent of it occurring in the next time frame.
Some examples of this type of distribution are the arrival of calls in a telephone exchange, breakdown of a piece of equipment, defect along a wire or rope, manufacturing defects and of course storms and floods.
If a flood occurs one year the possibility that the 1 :100 flood occurs next year is still 0.01. If a flood has not occurred for many years the probability is still 0.01.
The formula is
P(n events in time t)= e exponential (-lambda*t)*(lambda*t)exponential (n) /n!
Where n =0,1,2,3 etc
Lambda=expected number of events per unit time In the storm case 0.01 (for a 30 year period the expected number of floods is 30*0.01=0.3 events)
The probability of zero events in 30 years is:
P(0)=e exponential (-0.01*30) * (0.01*30) exponential (0)/0! = 0.741
The probability of at least one 1:100 event in 30 years is
1-P(0)=1-0.741=0.259
The probability of exactly one event is
P(1)=e exponential (-0.01*30) * (0.01*30) exponential 1 / 1!=0.222
The probability of two events in 30 years is therefore
P(2)=e exponential (-0.01*30)*(0.01*30) exponential 2 / 2!= 0.033
As you can see the probability of additional events drops off quickly as n increases.
The probability of more than two events would be
1-P(0)-P(1)-P(2)= 1-0.741-0.222-0.033=0.004
Rick Kitson MBA P.Eng
Construction Project Management
From conception to completion
www.kitsonengineering.com
RE: 100 yr Storm (How often Does it Really Occur?)
But, is the 1% probability actually backed out from the binomial statistics, or was it a simple thing of looking over 1000 yrs and finding only 10 occurrences?
TTFN
RE: 100 yr Storm (How often Does it Really Occur?)
That is the real problem in generating the 1:100 (or other probability) distribution.
Once the value of the event is known calculating the probabilities is actually a simple matter as I showed above. Its really introductory level statistics.
The real statistical work is in calculating the value of the storm (or in aerospace usage the MTBF which is the same statistical distribution).
You seldom have 100 years of data. You often only have 30 to 50 years of reliable data. Old data is unreliable because the method of taking the samples may be suspect, sample locations may have changed, only extreme data may have been recorder etc. The new hard drive that I bought with a predicted MTBF of 100,000 hours was not run for over 11 years to predict this number.
What often happens is that the 30 years of valid data is extrapolated to predict a rare occurrence. (or many drives are run for a couple of months) As in all extrapolations accuracy degrades the further out from the data that you have collected.
If the forecasters are scientifically honest instead of stating that the 1:100 storm is x mm/hr they would state that they are say 95% confident that that the 1:100 storm is between x and y mm /hr. They could also predict that a 99% confidence interval was some larger range.
More data points would decrease the range and higher confidence intervals would increase the range. This would allow users of the data to determine their own risk assessment.
Statistics of this nature are quite complex and beyond my statistical ability to do or explain. Complex computer programs are often used. One that will do this analysis that I have used in the past is SPSS (Statistical Package for the Social Sciences.) Don’t let the name fool you, it’s a powerful and complete statistical package.
If you search for rainfall IDF (intensity, duration and frequency) curves on line you will find some samples of the output from these programs.
Rick Kitson MBA P.Eng
Construction Project Management
From conception to completion
www.kitsonengineering.com
RE: 100 yr Storm (How often Does it Really Occur?)
At least, with the hard drive, there are a couple of factors that allow one to do a better job of predicting the MTBF:
> There are actually thousands of harddrives manufactured, so the failure database could be quite substantial.
> The individual components of the hardrives can be individually tested for their MTBF and the system MTBF could be calculated from them. That's the basis of MIL-HDBK-217 and other prediction approaches.
> Actual accelerated and highly accelerated life tests can be performed. The activation energies of failures can be determined and time-temp acceleration factors are calculable. This could be done with a few hundred harddrives.
TTFN
RE: 100 yr Storm (How often Does it Really Occur?)
My main point is that the data is extrapolated from a shorter time frame and a finite number of tests to predict the actual failure frequency in real life and that these predictive methods involve complicated statistical techniques.
While there may be thousands of drives manufactured, the MTBF is usually published before they are made or subjected to any real world use. The high numbers will simply serve to reduce the confidence interval in predicting the actual MTBF.
Tests like the time-temp acceleration factor are in themselves based on a statistical correlation between the increase in failures and the increase in temperatures.
Calculating assembly failures from component failures is also a statistical technique. A simplified example is if I have two components and both have to fail for the assembly to fail and the probability of failure is 50% for each then the probability of assembly failure is 25%.
Even if a extremely large number of drives was tested or you had the complete storm data for some location, it would be a statistical exercise to predict failure rates.
The predicted storm frequency or drive failure rates could also be totally nullified by some change in the underlying conditions like climate change that had an effect on rainfall or a new motherboard that had some effect on drive reliability.
Any time you use a statistic you should ask a couple of questions. (First you have to realize that the number you are using is a statistical based number.)
What is the sample size? Is the 1:100 year storm based on 30 or 200 years of data?
How reliable is the data? Are all data points relating to the same measurement? Did they use a different type of rain gauge 150 years ago?
Has some underlying factor changed that makes the data worthless as a predictor of future events? I.e. global warming
What is the confidence interval at some statistical level of assurance? Is the range x to y and you are 95% sure that the true value lies in this range?
How important is the potential variance in the analysis to what you are doing? I can live with a wide range of storm rainfalls without any significant impact. Often a storm sewer designed for the 5 year rainfall will also accommodate the 10 or 20 year rainfall because the 5 year number forces me to use a pipe size that will carry larger flows. In this case I really don’t care about the confidence interval. If the pipe size is just big enough for the 5 year flow then I might be concerned if the actual flow exceeds the predicted 5 year flows.
If you are doing any regression analysis how strong is the correlation between the independent and the dependant variable? In a weak correlation the effect of a third variable may nullify all conclusions.
Is there some logical reason for a correlation to exist? Someone once did a correlation analysis between the length of Vanna White’s hemlines on Wheel of Fortune (a US game show for those outside North America) and the next day’s performance in the stock market. The cause and effect here is hard to see so this could simply be a statistical anomaly.
Rick Kitson MBA P.Eng
Construction Project Management
From conception to completion
www.kitsonengineering.com
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
100 year flood
probability of equaling or exceeding = .01
consequence = $200,000 damage
risk = .01 x 200,000 = $2,000
for the airliner
probablility of failure = .000000001
consequence = $100,000,000 plus all passengers lost
risk = "acceptable"?
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
Even worse we don't have hardly any data on what the cost of over designing at one location has on the ability to maintain the entire infrastructure of society is.
RE: 100 yr Storm (How often Does it Really Occur?)
If you design a 100 year drainage solution, but you use conservative assumptions, provide plenty of freeboard, and use safety factors. Do you have a 100 year system, or maybe it has 200 year capacity?
Or - you design 2 year storm drains, plus you design 100-year, 2-hour storm retention for all development. You put catch basins every 660 feet, no matter what and also at each intersection. What is your resulting storm drainage system capable of handling?
RE: 100 yr Storm (How often Does it Really Occur?)
Brian
RE: 100 yr Storm (How often Does it Really Occur?)
a) Downstream structures would only be washed out if they were underdesigned for the design discharge.
A lawyer may make a case to a judge and jury that since Engineer A increased the flow in the river, Engineer B's downstream bridge was washed out. However, Engineer B could be held liable for not providing sufficient freeboard in his design to pass the design flood. Of course (reality check), Engineer A did not cause it to rain, so Engineer B is at fault!
b)As stated previously, the 100-year flood is the flood that has 0.01 probability of being equalled OR exceeded in any given year. If this was zero, I would be out of work.
RE: 100 yr Storm (How often Does it Really Occur?)
The reason I decided to purchase a detention area instead of extending the box was that the down stream structures for a mile had been corrupted by development. There were three boxes downstream and developers had filled in between them with 60 inch RCP's to carry the water.
The reason they were getting away with this was because over the years the box at my location had been modified by debri closing off part of the openning. The reduced capacity of the box was flooding the area up stream.
My design was for a hundred year storm which is perhaps not enough safety margin but the downstream system is sure to fail before mine. In the event that a larger storm happens the road may be washed out but the damage to property due to the other modifications to the stream that I was not responsible for will be worse.
I considered it a social responsibility to look at more than just my organizations interest when making this decission.
I could have played it safe and left the people who modified the system down stream hold the bag. In the interest of society, which is the goal of all civil engineers to serve, I think the $30,000 it cost me to buy the detention storage was the right decission.
I'm lucky to have the luxury of acting this way because as a goverment employee I have the option to look at what is best for everyone and not just a client.
RE: 100 yr Storm (How often Does it Really Occur?)
While there is the greater good of protecting people and property from the anomalous events that turn out to be not so anomalous, one could rightly ask whether it might be better that people not live in those areas that are prone to flooding.
I curious how you balance the immediate relief vs permanent relief, i.e., if the people were not there at all, there would be no need to do this in the first place and there would be no issue of whether adequate safety margin has been applied to the 100 yr event
TTFN
RE: 100 yr Storm (How often Does it Really Occur?)
Your right the current federal practice of buying and not repairing property is a wise one for the long term.
RE: 100 yr Storm (How often Does it Really Occur?)
Apparently, all of this was done without the oversight of a public agency. The very reason we have public agencies is to serve the general public, which is not always well served by individuals.
RE: 100 yr Storm (How often Does it Really Occur?)
The point is that the 100 year event is the flood that has a 26% probability of being exceeded over a 30 year life. The flood flow you calculate has practically zero probability of occurrence it has a probability of exceedance. If you design for this flood and provide freeboard then your channel will carry a higher flood flow than you have designed for. If you have designed the downstream structures for the theoretical 1 in 100 year flood and they do not have a similar excess capacity to match the design capacity of then they have a 26% probability of failure in the 30 year life. If for example the freeboard provided increases the upstream channel capacity sufficient to carry the 150 year flood then the probability of the channel flowing at bank full in its 30 year life is 18%. If you have not designed the downstream structures for this flow then you will have a very difficult task in proving that you were not negligent when the structures fail.
Some years ago I investigated a drainage project in Nigeria where downstream structures failed due to upstream drains flowing at bank full and passing up to 1.5 times the design 1 in 25 year flood. The downstream drop structures and stilling basins were designed precisely for the 1 in 25 year flood flow not for the channel capacity. The damage cost was some $20 million. The Contractor's designer was held responsible and the contractor reconstructed at his own cost.
Brian
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
I understand and do agree with the point that it is best to design everything in the watercourse to the same standard. Of course, someone has to set that standard.
This is also a problem in the US. We have recently prepared the first watercourse flood control masterplans for this region. This was in reaction to the uncontrolled development and flood control improvements that were going on in the county on the major watercourses. Developers try to maximize the use of their land, which means building as close to the river as possible. They would do this by constructiong bank lining to prevent the river from migrating towards the development. However, this just increases the risk for the owner across the river or downstream. Prudent design might be a non-structural approach, requiring a set back from the river to allow for overbank flow or for lateral migration. Or a consistent approach to types of lining, river profile, scour and sediment transport etc. Improvements should all be designed using the same hydrology model and be consistent with the masterplan.
However, assuming that there is to be a design standard in place and some oversight, safety factors (freeboard is just one) are essential in engineering. For instance, there is quite a bit of uncertainty in both hydrology and hydraulics. We try to account for these uncertainties by providing a safety factor in the design.
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
"over conservative design causes downstream flooding"
Rain causes the flooding, not designs.
Property owners who do not protect themselves properly suffer flood damage.
Example:
Joe buys property in the country.
He decides that the best place to build his house is right next to the gurgling stream. He builds it, but then realizes he is very close to the creek and during the first heavy rain, the water is lapping his front porch. So, he decides to re-align the channel slightly and widen it a bit so that the next time it rains, the house won't get wet. His engineer designs the channel for 100 year flows and puts in plenty of freeboard. Joe is happy, because he knows that he only has a 26% chance of getting flooded before his mortgage is paid off!
The dominant discharge for the stream is about 25 years.
Anything over that typically flows in the overbank floodplain.
Now assume that George lives downstream and built a driveway across the creek (before Joe moved in) and only put in a 25-year culvert.
A 100-year flood comes along and George's culvert and driveway are washed out.
George claims that it's Joe's fault, because he overdesigned the channel on his property! Theoretically, the flood water would not have reached his culvert had Joe not re-aligned the channel and made it bigger. Joe should have matched the flow in George's 25 year culvert, even though the damage clearly was a result of a large flood and a small pipe.
According to the theory, Joe should have simply lived with the 25 year design standard that was set previously by George and pay for his own flood damage every 10 years or so when he get flooded. After all, George was there first.
Reality is that when the flood comes along, Joe will be high and dry in his new house. George will lose his driveway and culvert and a good part of his front yard due to the erosion caused by the overbank flow. But he expected
that, because it was only a 25 year design, and he took a risk. (He only had a 10 year mortgage, after all, and he saved a wad of cash on the 25 year culvert versus the 100 year bridge that his engineer originally recommended)
RE: 100 yr Storm (How often Does it Really Occur?)
My comments refer to main drainage and river schemes. One problem I am consistently coming across is in the design of drainage from irrigation projects. To minimise drainage cost the design allows 24 to 48 hours inundation of the drained area. Thus the design storm depth is the rainfall depth over the inundation time plus the time of concentration. The channels are designed to remove the water over 24 to 48 hours. The engineer then adds freeboard to his drain and is surprised when inundation times are reduced to only a few hours and all his bridge crossings and drop structures fail under a two year event.
Another example I have investigated recently is a major flood defence project. The project comprises several miles of earth flood embankment designed for a 1 in 50 year flood. Adjacent to urban areas a concrete flood wall is used in place of the earth embankment. The Engineer has provided freeboard is 0.5m to the earth embankment and 0.3 m to the concrete wall sections. The result is that floods, in excess of the design flood, now flood the urban areas instead of the rural areas. It may be rainfall that is causing the flood event but it is the engineer’s failure to recognise that a 50 year flood has a 0.02 probability of exceedance rather than 0.02 probability of occurrence which is causing the flooding.
The point I was making is that when you have calculated the 100 year flood to three decimal places and add freeboard you have designed the channel for a larger flood than what you have calculated. My argument is that you should then design the downstream structures for the same flood (the bank full event) that the channel is able to carry. The safety factors on structures should not be less than those on channels.
Brian
RE: 100 yr Storm (How often Does it Really Occur?)
RE: 100 yr Storm (How often Does it Really Occur?)
I agree with both of you - downstream impacts should absolutely be considered. However, this is clearly rarely done by most developers and not always checked by the agencies I have worked with. Typically, peak flows are checked for the outfall on the subject property with pre-existing conditions and then with post-development conditions. No increase in peak discharge is allowed. Good enough for government work. No investigation of what the effect is on the river, it is assumed that it always got into the river, and rarely an analysis further downstream to determine what existing infrastructure might be under designed. Therefor, the reason for undertaking watercourse masterplans. Study the watercourse, not the watershed, and establish a baseline condition and standards for future development or upgrades.