100 yr Storm (How often Does it Really Occur?) 8

[Jeeman]

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?????

 

[CarlB]

This general topic (but not your specific question) has been discussed in the Storm/Flood forum. It's been a long time but I'm pretty sure that it's easier to work with the probability of it NOT happening in any one year, and you can mulitly this to get probabilty for other periods. So probability of not having a 100 year event in a 30 year period is (1-0.01)^30 = 0.74, so the probablity of it occurring is (1 - 0.74=0.26) or 26%. Same approach for 100 years gives 63%. So in any 100 year period the chance of a 100 year storm is 63%. But I believe it's still true that for a very long period of record, the 100 year storm does occur on the average once every 100 years, which is actually part of the definition of a 100 year storm.

Hope this helps, and that the old college brain cells haven't failed me.

Carl

 

[DaveVikingPE]

The 100-year storm, flood, etc. can occur ANY TIME! So look out! The 100-year storm can happen 365 days a year - though unlikely.

With that in mind, though, the proverbial 100-year event is "unusual" enough to cause substantial (note: not "significant&quot 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?

 

[ishvaaag]

I think this is a code subject...if warming has some effect, the code needs to recognize. Also if it is wanted to specify different calculations for different target useful lives of the buildings the code needs to elect the closed form giving the forces...for I have seen different fromulations being in use for windstorms and earthquakes, so the nature of the phenomenon seems be influencing what statistical prediction tools we need to use. In short, a 2 pages clarification on that wouldn't do any harm in future codes and texts.

 

[austim]

Just a point to remember - the 100 year event is one which is EXCEEDED once in 100 years on average.

 

[Bayou]

The 100-year event has nothing to do with 100 years. The definition is that the 100-year event has a 1% probability of occurrance during any given year.

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.

 

[Rich2001]

From Fema website

http://www.fema.gov/mit/tsd/fq_term.htm#frequt3

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

 

[ishvaaag]

So CarlB has it right...even in the final comment. I would be concerned on any definition of some level of flood assumed to be one a 100 years' flood that occurs somewhere 5 times in 20 years. This would indicate the need -or at least the convenience- to correct the stated level of the 100 year flood, for recent data would be indicating that such level would be locally and presently corresponding actually to one 4 years' flood.

 

[Jim6758]

Don't forget that there are also 500 year events and PMFs (Probable Maximum Floods). Rich 2001 has it right. 100 year rainfalls don't always produce 100 year floods. A lot depends on the prior rainfall, storage capacity in upstream reservoirs, the direction of the rain pattern in relation to the shape of the basin, speed of the event,etc. Conversely, a less than 100 year rainfall event can produce a 100 year flood if conditions are working against you. I remember the hurricane generated front that stalled out over Albany, Texas in 1979? after a prolonged drought. They cloud seeded into the thunderbumber for 6 hours. I seems to recall that it produced 28 inches in 24 hours and remains the record rainfall in this area.

 

[AllenS]

If a 100-year storm occurs 5 times in 20 years the definition would need to be revised? No. Climatology is based on much longer cycles that 20 years. If you flipped a coin 20 times and it came out heads 12 times you wouldn’t revise the probability of getting heads on a coin toss to 60%.

 

[cvg]

The occurrence of a "100 year storm" 5 times in 20 years may indeed indicate the need to review the local hydrology. In a perfect world we would have ample data to accurately predict the 100 year storm, however, most regions in the US have less than 100 years of data. The accuracy of rain gauge measurements taken 100 years ago could be questionable. The number and geographic location of rain gauges may also be insufficient. It is also very likely that continual climate change and global warming also is changing our hydrology. Therefore, it is entirely likely that what we call a "100 year storm", may be statistically correct, however, the statistics are weak due to the lack of data. This points out the need for continued data collection, review and frequent update of isohyetal maps and depth - duration data so that we can more accurately define the 100 year storm. We also need to be careful not to confuse the storm with the runoff. As stated previously, a 100 year flood may be caused by a storm which is less than a 100 year event.
Chuck
cgopperton@stantec.com

http://www.stantec.com/

 

[ishvaaag]

As can be deduced from my previous post, I agree with cvg in the need of revision. Very probably what happens is that the evaluation got not so finer as to discover that locally there is a pot of higher frequency. So the geographical contour lines for the flood level adscribable to the zone needs be modified, there the probability experience is proving is higher, and it is better to come to terms with reality.

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.

 

[Jeeman]

Thank-you all, this has been a most interesting discourse.

 

[wolfhnd]

The question is really one of margin of safety. 100yr storm design is arbitrary. What you need to consider is what damage to property and life you are will to endure to use a cheaper structure. Since we are dealing with public money most of the time for large structure the public should but never will tell us what is an acceptable risk. Most designs have a margin of safety so you need to take that in to consideration too. Since all drainage design is based on observed rainfall it is pointless to consider what might happen we can only know what has happened. Structural design is the same way, you test a beam and when it breaks you assume all the other similar beams will break at the same load. That's just a practical way of going about you work. If you had not noticed most of the formulas we use don't make any sense because they are full of empirical data. Why should 100yr flood tables be any different.

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 . This is a {do you want to live forever?} kind of discussion.

Does anyone here really think that a 20% change in climate is going to out strip the safety factors already in place?

 

[jugglerbri]

Jeeman,

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

 

[Bayou]

jugglerbri,
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.

 

[jugglerbri]

Bayou,

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

 

[IRstuff]

One thing that often difficult to wrap one's brain around is that these statistics are only for extremely large distributions.

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

 

[roakesh]

Ok. How about 5 yr storm. Most of the municipality design their storm sewer to handle 5 yr storm. What is the probabality of getting 5 yr storm in any given year?

 

[cvg]

Probability and return period are inversely related. The formula is:

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