Wednesday, July 07, 2010

Probabilistic Design of Water Infrastructure

I am writing an article on statistical methods to optimize water infrastructure design. The idea is very simple: normally we use "design population", "design demand" etc. but reality is not like that but probabilistic. There is a certain probability that the demand in 2030 will be this and another probability that it will be that. Infrastructure such as pumping stations, tanks, etc. comes in discrete capacities, that is, a tank for 2000 cu me may cost 10,000 dollars, and the next one is 5000 cu m and will sell for 30,000 dollars. If my design number indicates 6000 cu m I will order the more expensive tank. But using statistics, it may well be that 5000 cu m will be sufficient in 99% of the time and the 1% may be less than the statistical error. Or let them have no water for five minutes once every ten years. Another way of looking at this is that the 6000 cu m tank will be needed only when 3000 independent consumers open their faucets at the same time - what is the probability of this happening in my lifetime or better, till the next elections?

Another issue that should be dealt with probabilitically is the number of cubicles in the toilet. What is the probability that all the cubicles are occupied and how much time has to wait the next person to access one? It is a gaussian distribution thingie, but no one ever calculates anything. We just look the Ministry of Health table and adopt the number written there. Space, in many cases, is critical, and my Clients are desperate to minimize the number of cubicles, but you cannot negotiate with a table. Which was designed with the worst case ihn mind, such as a sport stadium where everybody runs to releave himself during the half time, and they have multiplied this worst case scenario by a security factor of 100%, so no one - ever - will come to protest to the Ministry that they approved a poorly designed project.

You know, Israelis are in the lookout for these cases so they can accuse the authorities of being corrupt or for some other evil intension, like putting the interest of the rich (builders) before the interest of the defenseless public. I am aware that if I submit a design that has less than the number of cubicles ordered by the official table and try to defend my position by probabilistic calculation, the bureaucrats will hate me forever, for asking them to think and for committing the most imperdonable sin of forcing them to take a decision.

Mark Doane said...

Or let them have no water for five minutes once every ten years.

Yes, but what happens if that five minute window is the exact time when the fire department needs water to put out a raging fire?

I think probabilistic design is very much needed for building designers, but I would hesitate in using it to design city water networks. In practice though I think that most new water systems constructed on the fringe of the Phoenix Metro Area are private and as such are built as small as possible, thus conforming to your new design philosophy even if the system planners out there have never heard of it.

In fact, now that I think of it if the future water systems of AZ will all be private then I can imagine a future where fire hydrants will no longer be installed, pipes will be smaller and fire departments/businesses will be expected to bring their own extinguishing material to fires. Future building codes may require that newly built structures be extra fireproof so that fire departments don't have to spray water on neighboring houses in order to prevent a fire from spreading. Eventually, fire hydrants will be eliminated during pipe replacements and water customers using old buildings that need an onsite hydrant will be charged extra. The elimination of water-based fire fighting, and the new building codes thus required, will drive up the cost of construction but oversized water systems have always been a form of cost shifting from property owners to cities and counties.

In fact, now that I think about the matter further, public sewage systems are not financially self sustaining as private businesses unless there is a market for second class water. Most developments and individual homeowners are perfectly capable of treating wastewater onsite without the help of a government department.

Here is a link from a city just south of Mesa:

I actually live half a mile from Gilbert road here in Mesa and I drove past this while heading south on Gilbert one day.

Mark Doane said...
This comment has been removed by the author.
Mark Doane said...

My rambling comment above is not just speculation, but is partly based on how water is managed in the neighboring city of Apache Junction. Between Mesa and AJ there is an unincorporated gap that also has no sewage system and like AJ uses a private water company. The unincorporated gap also has no government fire department and is protected by the private Rural/Metro corporation.

If all of the public water departments in AZ were to be privatized eventually these investor owned companies would seek to limit their investment in hydrants and larger lines. I went to the website of the AZWC and looked for information on who owns and finances the hydrants and all I found was this and this.

Hydrant relocations and private fire connections are paid by the government and the customer respectively, but I wouldn't be surprised if the government requires the AZWC to pay for new public hydrants.

But if my vision of the future is correct then hydrants will be obsolete and fires will be extinguished using foam.

J said...

You have put your finger on the dominant tendency here in Israel too, to say, the tendency of the authorities to transfer responsability to private entrepreneurs. The Fire Dept. requirements here are increasingly heavy and expensive for the owners, for example, they demand 1,400 liter per minute flow at 4 atmosphere from tap water, actual measurement by a water engineer, but that is not enough, they want a cerrtificate from the water supply company that they guarantee that supply. Of course, the water companies are unwilling to guarantee anything and they reserve the right to stop supply any time they want (for repairs and so on).
Therefore the owner is required to build up tremendous water reservoirs, like 200 cu m steel reservoir built for a fashion shop in Netanya (a Client of mine). Extremely expensive, while the shop sells Chinese fashion at 10 dollar a piece. I mean I cannot see how they can make money at all. Regarding foam and other methods, the Fire Dept. is very old-fashioned and will not allow those newfangled "untested" technologies. Without the Fire Dept. permit, insurance companies will not insure and the City will close the shop. i play acording to the rules but am tired of working stupidly just for the money. Arent we all?

Mark Doane said...

I have never in my life seen a structure in the Valley of the Sun with a reserve water tank for fighting fires.

You have put your finger on the dominant tendency here in Israel too, to say, the tendency of the authorities to transfer responsability to private entrepreneurs.

I was arguing that the retail water supply system here in the Valley is oversized so that property owners may avoid costly fire protection schemes on their property. If such water systems are oversized then newer developments built on raw land could get away with smaller pipes and no hydrants if they had better building codes. Having thought through the matter I think no such savings will occur.

Let me give you an example of what inspired my comment. About six months ago I was engaging in my idle hobby of looking over the local online real estate listings for central AZ instead of achieving anything with myself. I went to the tab for empty lots for sale and I entered a maximum price of \$30k just to see what would pop up. I came across a lot just big enough for a trailer, driveway and small yard waaaaay out of the Valley on the outskirts of Eloy for \$3k. In order to get to this piece of the Promised Land I had to drive a good 40 miles from my houses and search along backroads to finally find the property on my second expedition down there. When I found the lot it did not look like anyone had spent \$200k per dwelling on infrastructure like you estimated for Detroit. The farm fields down there are all rectangular, so the farmer had divided one of his fields into small lots, left spaces between the lots for streets and deeded the streets to the county. Somehow the farmer was able to convince AZWC and APS to extend water lines and electric lines to the plots. Thinking about the matter, there fire hydrants there so no real savings is probably possible under current laws.

On another note, the lot was surrounded by other lots that were occupied by other trailers and homes but most of the streets were still just dirt. I think Pinal county refrained from paving any of the streets until after the new homeowners began to pay property taxes. Since most of the roads out there are dirt anyway most of the homeowners probably didn't care that they had been neglected.