Sunday, February 19, 2017

How Much Dirt Would It Take To Fill The Rose Bowl Stadium?

A couple of days ago, I was writing a blog post with calculations regarding the overflow of the Oroville Dam up near Sacramento (California, USA).  While watching the coverage of the ongoing disaster of draining the dam of enough water to prevent a further overflow, I came across this article from the news website "NBC" titled "What About LA County's 14 Dams?" discussing the aging infrastructure in California.  Specifically, the author was discussing the local dams here in Southern California.  One major issue is the 'run-off' of sediment which collects in the bottom of the dam and can result in 'clogging' of the control valves which let water through.  Here is an excerpt which caught my eye regarding the volume of sediment:

Spencer said some 2.4 million cubic yards of dirt needs to be removed from Devil's Gate - it's all remnants of storms following the Station Fire in 2009. That is reportedly enough sediment to fill the Rose Bowl three times over.

If you are a consistent reader of this blog, then the paragraph should jump out at your eyes.  The statistic reported definitely needs to be verified.  You are probably wondering the following question:

How does a person go about verifying such a statistic?

In the following paragraphs, I will walk you through the steps -- enjoy!

In order to start the dimensional analysis of verifying the statistic above, the values for the metric need to be known -- specifically, the volume of the Rose Bowl Stadium.  I wrote a post last year in which I used the Rose Bowl Stadium as a metric to understand the daily leak at the Aliso Canyon Gas Facility.  In that post, I noted that the volume was difficult to determine since I was unable to find a suitable value for the 'height' of the Rose Bowl Stadium wall.  Additionally, an article in the LA Times from 1994 gives similar dimensions.

Instead, I decided to ask the internet website "Answers.com" for the answer and received a value of 20,000,000-cubic feet.  In a recent search, I found an old document with the two dimensions of an ellipse -- North to South = 880 feet, East to West = 695 feet, Circumference = 2,430 feet.  Here is a picture of the Rose Bowl Stadium below:

If the value of 20,000,000 cubic feet is taken as a reference to use as a metric of the volume of the Rose Bowl Stadium in Pasadena, CA (USA), then the answer to the beginning of the post is simple.  To fill the Rose Bowl, the amount of dirt required would be 20,000,000 cubic feet of dirt.  The total volume of dirt that can be held in the Rose Bowl Stadium is written in scientific notation below:

As I mentioned above, the disaster that has occurred in Northern California at the largest water reservoir, the Oroville Dam, has caused the public works sector to start looking at other possible breaches in other dams located in California -- of which there are on the order of 1500 dams -- Wow!

In the news story above, the author highlighted in the excerpt chosen that the Devil's Gate dam (in Pasadena, California) had a large amount of sediment (dirt) built up in near the exit.  The enormous amount was reported to be 2.4 million cubic yards of dirt.  Written in scientific notation, the amount of sediment sitting in Devil's Gate dam is shown below:

This sediment build up can potentially cause a back flood by building up too much water (by not letting the water through the dam).  That could be a major problem.  According to the article above, the amount of sediment build up is equivalent to filling the Rose Bowl Stadium over 3 times.  The question I posed above was the following:

How does a person go about verifying such a statistic?

In order to start the verification of the reported statistic above, a conversion factor is needed.  Upon inspection of the two values above, you can see that the total volume of the Rose Bowl Stadium is expressed in units of 'cubic feet'.  Whereas, the total volume of build up sediment is reported in units of 'cubic yards'.  In order to do a direct comparison of the two values, the units need to be the same.

With the conversion factor now in hand, a conversion of units is possible from 'cubic yards' to 'cubic feet' as shown below:

Now with the volume of dirt expressed in units of 'cubic feet,' a direct comparison of values can be done to verify the reported claim in the article above:

The result of the comparison of the two values (reported sediment build up) and the volume of the Rose Bowl Stadium has been accomplished.  Further, the statistic reported in the article above is true.  The amount of dirt sitting on the bottom of the Devil's Gate dam is equivalent to filling up the Rose Bowl Stadium more than 3 times.

Conclusion...

After I verified the report above, I started to wonder how long it would take construction crews to remove that large amount of dirt.  That is no small feat.  Where does the dirt go? How much time will pass before the sediment is built up again?  Furthermore, if the Devil's Gate dam is just one of 1500 dams in California, how much dirt needs to be removed from the other dams?  How much infrastructure repair is required of all of these dams?

These are unanswered questions that will become a large problem if not attended to in the future.  The Oroville dam is a terrible disaster that has displaced over 200,000 people so far.  More damage is expected with the next rain storm this week.   More money will need to be diverted to infrastructure repair if future disasters like Oroville are to be avoided.

Until next time, have a great day!