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?????

 

[RDK]

The so called 1 in 100 year event is really an event with a probability of an event of that magnitude or greater of 0.01 in any year.

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!

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

http://www.kitsonengineering.com

 

[IRstuff]

Interesting discussion.

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

 

[RDK]

IRstuff

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

http://www.kitsonengineering.com

 

[IRstuff]

Thanks for the info.

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

 

[RDK]

I didn’t realize, but am not surprised by these assists in predicting MTBF.

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

http://www.kitsonengineering.com

 

[bplech]

laugh, anything that can go wrong will go wrong. maybe be use 150% of 100 year.

 

[davidjh]

I'm an x-aeronautical engineer who wandered into this thread and finds it very interesting. The misunderstanding of basic terms (or misnaming of basic terms) was also widespread. The use of probability of a failure was introduced in systems analysis. Consideration of failure in Structure and powerplant was handled differently. However the FAA has been changing these and moving toward a probability based approach there as well. There is a ton of material available from the FAA. The discussion above regarding changing/updating probability values have a correlation in that there is movement to increase the stringency for ultra-large-capacity passenger airplanes such as the Airbus 380 because the consequences of a "catastrophic" failure (even being of low probability) are so severe. The "benchmark" level was "ten to minus 9th". The fundamental philosophy for higher probability failures was (1) they must be shown to not be catastrophic, (2) the airplane has to be shown to be able to "continue safe flight", and (3)could exceed its "design loads" during the safe flight phase. Good discussion!!

 

[cvg]

they are likely using a risk assessment approach. Probability of failure X consequence of failure = risk. For example:

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"?

 

[wolfhnd]

This is the strangest thread we have ever had .

 

[BRIS]

thus if the divorce rate is 30% and the average man gets married at aged 30 and lives to 84 there is a 99% probability that he will either die bankrupt or will be drowned in a 100 year flood.

 

[wolfhnd]

We just as well keep it going lol. The whole problems is that we have enough statistical data to determine what the probability of a certain flood is but we don't have much data for determining the cost associated with that flood is.

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.

 

[cvg]

How about this -

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?

 

[BRIS]

Using over conservative design is a major cause of failure of drainage schemes. If you design for a 100 year storm and then provide freeboard you will then find that your downstream structures are washed out during a flood event. The correct procedure is to check the safety of downstream structures at flows resulting from upstream channels running at bank full discharge not the design (100 year) discharge. The 100 year flood is the flood that has probability of EXCEEDANCE not a probability of occurrence. Its probability of occurrence is zero.

Brian

 

[cvg]

Interesting!

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.

 

[wolfhnd]

I recently designed a drainage structure at a slide repair. The existing structure was an 8x6 RCB. I used a 6x4 pipe arch to extend it under the new slope. Using Pondpack I determined the extent of storage required upstream and purchased enough property to allow for the detention.

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.

 

[IRstuff]

I think that is an interesting example of how much the greater good encompasses.

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

 

[wolfhnd]

The property that would be damaged in this case was developed at about the same time the road was built. It is an odd set of events. The fill has mostly been done by heavy equipment companies for storage.

Your right the current federal practice of buying and not repairing property is a wise one for the long term.

 

[cvg]

Put another way, the property owners downstream weren't really left holding a bag... They made a decision to put in the 60 inch pipes. Obviously, these have less than the 100 year capacity and less than the existing 8 x 6 box. They saved a lot of money by doing this. They took a measured risk that by doing this, they wouldn't experience a flooding loss, or cause anyone else harm. However, they could have (and should have) known that eventually, the slide would be removed, or the culvert extended, or the government would improve the entire watercourse to minimum standards, or possibly a large flood would come along and wash the slide out and the channel is back up to it's original capacity.

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.

 

[BRIS]

CVG - not all engineering is dictated by legal interpretations of the US litigation system. I have spent the last 30 years working on development projects in developing countries where engineering is dictated solely by economics and not by risk of legal actions.

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

 

[SiPaul]

Just to weigh in. The 100 year storm is taken as rainfall in 24 hours - generally. In our area it is 7.2 inches. We get storm cells that dump the EQUIVALENT of a 100 year storm in an hour or two. These cause flash floods and damage; however, I have not seen 7.2 inches in 24 hours.