How Much Water Is 55 Billion Gallons Of Rainfall?

As the water season began (at least that is what is reported by the news) in early October of this year, news accounts will be arising discussing various rainfalls.  Certain accounts will detail the much needed rainfall while others might even scare readers of the excess rain and the damage that might follow.  Regardless, the way the news agencies reports rainfall is often misleading and uneventful.  Below, I discuss one example from the "Los Angeles Times."

How Is Rainfall Reported?

Over the course of the last year, I have started to write about the reporting of rainfall.  I am constantly amazed at the subtlety with which large volumes of rain are reported after a given storm.  This problem of mine started back near the end of 2015 -- after reading a report of a storm.



Before I get into the initial motivation to investigate news reports about volumes of rain fall, I would like to say that I am still baffled why the news reports "inches" of rainfall while total volumes in units of "cubic feet."  I would prefer the units of total rainfall reported in units of "gallons" -- personally.  The reason is that I can visualize using a few metrics (large volumes -- pools, stadiums, etc.) to compare the reported values to.  Although, one could argue that my request is just unique to me and I could just as easily perform dimensional analysis to get the units that I feel comfortable with.  Fair enough!



During the end of the month of December of 2015, large volumes were reported and I wrote an initial blog post about this rainfall in following month.  Accuracy was not the first and foremost during this storm -- which concerned me.  The reason why is in the numbers.  Let's take a look briefly at the reported numbers which in some cases were skewed or miscalculated.



In that blog post, the news reported a number based on the weather service of 65 billion gallons of water from a single storm -- which is an enormous amount of rain.  One of my family members told me this factoid and stated that 65 billion gallons of water equated to increasing the water level of Lake Tahoe by 6 inches.  Meaning, that enormous amount of rain if collected and poured into Lake Tahoe would result in an increase of 6 inches of height to the lake.



After hearing that number, I sat back and thought -- Wow -- that means that Lake Tahoe is larger than I thought.  This factoid bothered me for a few days.  As a result, I decided to carry out a few calculations which are shown in the blog post.  I will get to the point.  The result of the calculation gave a volume that was very different than the volume reported by the news.



What was I to make of this disparity in volumes?


Did I make a mistake in my calculation?


Did my approximation not make sense?


Check out the blog to understand my full thought process in calculating using a simple approximation -- that of a cylinder.  The result of the calculations revealed that the total volume of rainfall in that particular storm was 6.5 billion gallons NOT 65 billion gallons.  A factor of 10 different in the reported statistic.



Should we be concerned by the lack of accuracy in reporting?  



Yes.



Two major results came from that practice:


1) The volume I calculated was correct.


2) The weather station corrected their reported volume after checking their calculation.


3) I learned a better method by which to perform dimensional analysis of rainfall using reported volumes.



Out of this exercise came the correction of the weather station.  Again, all of this is in the blog post.  Additionally, I learned that method by which the weather stations use (one of the methods) to calculate the volume of rainfall in a given storm.



After carrying out the exercise and writing the blog, I decided that from that point on forward, I would watch news accounts of rainfall volume in the future.  Further, I would look out for reported statistics and try to put them into perspective for the reader using dimensional analysis.  The result has been the blog posts that make up this site.



The results of previous blog posts this year so far regarding the total volume of rainfall have been collected into a table shown below:

Note: Click on any of the cities to access original blog post (with calculations) on this site -- (1) Bladen County, (2) Goldsboro, (3) Lumberton, (4) Smithfield, (5) Raleigh, (6) Rocky Mount, (7) Haiti, (8) China, (9) Elliot City, (10) Huauchinango, (11) Louisiana -- and I forgot (12) Macedonia



The first seven storms listed in the notes above are a result of Hurricane Matthew which ripped through the Eastern part of the USA originating from Haiti.  The last five storms listed are storms that have occurred due to unusual rainfall this year.   Recently, the Associated Press covered this in a story about the National Oceanic and Atmospheric Administration released report on rainfall this year around the world with implications toward Climate Change.



Regardless, the enormity of the storms are worth writing about.  With that in mind, let's move onto the reported value of rainfall over the season thus far in Folsom (California) of 55 billion gallons so far.

How Much Is 55 Billion Gallons Of Rainfall?

In a recent story in the 'Los Angeles Times' titled "A tale of two droughts in California: Wetter in the north, still bone dry in the south" the disparity of rainfall between Northern and Southern California was discussed with varying numbers reported which would make a person mind spin.  One excerpt that stuck in my mind was the following regarding rainfall received in Folsom:

The recent rains were enough to force federal officials to begin releasing water from Folsom Lake to protect against flooding for the first time since March, said Louis Moore, a spokesman for the Bureau of Reclamation, which manages the reservoir. Since the beginning of December, Folsom has risen more than 20 feet — an increase of about 55 billion gallons.

Now, if you are a reader of this blog, then the number 55 billion gallons should stick out of the excerpt above along with the number 20 feet.  Further, with the previous blog posts on this site, you will understand my need to understand the magnitude of large numbers like this.  Numbers that are truly incomprehensible.  I believe that the value of 55 billion gallons of rainfall qualify for the analysis typically found on the site.



To start such an analysis to put the enormous number into perspective, a metric is needed.  A metric serves as a 'ruler' of measurement.  Metric's specifically take away all ambiguity when defined.  What?  I know that is confusing.  Basically, we need a measurement to compare the volume too.



Let's choose 3 volumes and see how the statistic of 55 billion gallons compare.  The 2 volumes will be: 1) World's largest pool  2) Lake Tahoe.



1) World's largest swimming pool:



To start an analysis of the volumes is to ensure that the 'units' of measurement are the same.  That is, for the example at hand, the volume of the World's Largest Swimming Pool needs to be expressed in units of 'gallons' to be directly compared to the volume reported above of 55 billion gallons.



The World's Largest Swimming Pool is shown below:

Source: Twisted Sifter



The volume of the enormous swimming pool is a whopping 66 million gallons.  That is huge.  If we express the volume of rainfall reported in the article in scientific notation, the number would look like the following shown below:

Remember, if the volume were written out in long form, the value would appear as follows: 55,000,000,000 gallons!  Expressing the number in scientific notation allows us to express the number in a compact form.  The volume of the World's Largest Pool can be expressed similarly in a compact scientific notation.



Since the units are of the volume are expressed in 'gallons' -- the number of swimming pools that could be filled with 55 billion gallons of rainfall can be directly determined by dividing the two volumes as shown below:

Wow!  The result can be interpreted as the following:



55 billion gallons of rainfall would fill 830 - World's Largest Swimming Pools!!!!!!!!!



How does one visualize that number of swimming pools?



Note: Since my last blog post using swimming pool in San Alfonso del Mar -- another pool built by the same company has built the new "world's largest swimming pool" -- Crystal Lagoon located in Sharm-el-Sheikh, Egypt.



Can you visualize a total volume of 830 of the above pools?



I cannot.  Maybe another metric is needed to better grasp the enormous volume of rainfall.



Sometimes our choice of a metric does not necessarily cast the volume in a graspable light.  For instance, trying to visualize the total volume of 830 World's Largest Pool combined is too difficult.  Maybe another analysis is useful with a larger metric to cast the volume is needed.



 In order to get a better grasp of the volume, a larger volume is needed to serve as a 'metric' to compare enormous volumes too.  55 billion gallons is not a typical volume.  Therefore, a larger volume is needed.  On a previous blog post on this site, Lake Tahoe has been used as a metric for extremely large volumes -- which this qualifies as that category.



Below is a picture of Lake Tahoe from Space:

Source: Snow Brains

Upon inspection of the photo above, Lake Tahoe is a huge lake.  The total square area of the Lake is 191 square miles.  In order to use this value as a reference to cast 55 billion gallons of rainfall into perspective, a little math will have to be performed.  But, we will take the process slow.  If at any point, you (the reader) need clarification, please leave a comment in the blog post below.



To start with, an equation for the volume of Lake Tahoe is needed.  Above, the surface area of Lake Tahoe is given as 191 square miles.  An expression (or equation) for the volume of an irregular shape like a lake is the following:

According to the expression above, the volume can rainfall can be determined by knowing the amount of rainfall that a storm delivered across a surface.  Meaning, if a circle is the two-dimensional surface, then by understanding how much water fell on the circular surface, the determination of the volume of a cylinder is possible.  By the way, the units of volume are 'cubic feet' or 'cubic mile' - etc.  Cubic feet is most likely easier to visualize -- since most of us have an idea of the dimension of a foot is in comparison to inches of rain.



Since in the present case, a volume is known, then in order to understand the magnitude of 55 billion gallons the question becomes the following:



How many feet would Lake Tahoe rise if 55 billion gallons were dumped into the Lake?



In order to start the calculation, a unit conversion is required to move on.  The second line of the volume expression states volume in terms of 'units of miles'.  This is not useful when discussing rainfall -- which is usually reported in units of 'inches'. If the calculation is carried out with units of 'miles,' then the results of the calculation would be expressed in 'miles' -- which would be difficult to interpret.



Rather than get an answer that is difficult to interpret, a conversion can be performed to units of feet from miles.  There are 27,880,000,000-square feet in a square mile.  With this conversion factor available, the units conversion is easy and shown below from square miles to square feet:

Next, take the answer (in square feet) and plug the value into the original volume above:

Shown above is an expression for volume with a value for the area (191 square miles) inserted.  There are still two unknowns left -- volume of rainfall and height.  In order to plug a volume into the above expression, a 'unit' conversion is necessary from 'gallons' to 'cubic feet'.  There is 0.133681 cubic feet in 1 gallon.  With the conversion factor in hand, the conversion is simple as shown below:

Next, if the volume of rainfall is plugged into volume equation above, we are left with one equation with one unknown (height) as shown below:

If we rearrange the above expression to solve for height from the total volume, we get the following:

Wow.  The following result states that if 55 billion gallons of water was dumped into Lake Tahoe, the water level would rise 1.4 feet in total.  That is just under 18 inches (1.5 feet).



Can you visualize the change in height?



Of course - why?  Because, I am 5 feet 7 inches tall.  I could stand next to the Lake (shown below) and visualize roughly the water level rising to my knees.  I can easily imagine Lake Tahoe filling up by 1.5 feet.  What I did not realize is that Lake Tahoe is enormous.



Further, take that measurement and look out onto the Lake and the visualization of 55 billion gallons comes into focus.  The choice of Lake Tahoe as a metric fits the dimensional analysis much better.  Half the battle in performing dimensional analysis problems is choosing the correct 'units' and 'metric' by which to compare the stated (reported) value in the popular news to.



Again, here is another picture of Lake Tahoe shown below (not from space):

Source: Lara Farhadi

Conclusion . . .

In the paragraphs above, a couple of metrics (world's largest pool and Lake Tahoe) to cast the enormous volume of 55 billion gallons of rainfall into perspective.  Both volumes represent two extremes of the entire spectrum.  Using the process of dimensional analysis, we were able to compare the volumes to the reported volume of 55 billion gallons.  Prior to this analysis, any attempt toward understanding the true magnitude of the statistic.



Too often, reading the news results in a lack of understanding of the true magnitude of large numbers.  Whether these numbers represent volumes, heights, miles traveled, electricity generated, there is a need to try to understanding them.  The avenue by which to do so is through 'dimensional analysis'.  The process is rewarding when you arrive at a result.  Regardless of the result.  Often times, more thought and analysis is needed to make further sense of the statistics.



Until next time, Have a great day!

How Do We See The Invisible (sub-atomic particles) In The Visible Region?

How is the invisible to the naked eye made visible to the naked eye?  Today, with the advancement of technologies many can view the invisible into the visible region through a microscope.  An electron  microscope allows us to see molecular frameworks with the use of electrons -- amazing.  Other forms of measurement involve indirect detection like looking for a "green fluorescent protein"(GFP) tag which lights up when a given expression or event occurs.  Of course, in the last case, the sample has to be exposed to light in order for the GFP tag to fluoresce.



The radioactive decay of the element Radon can be made visible through the use of a "Cloud Chamber."  Recently, I ran across a video demonstrating the visibility of radioactive decay and could not stop thinking about how cool the demonstration was.  Therefore,  I decided to share the demonstration with you.  Additionally, I will draw parallels with the "trails" that are visible after flying aircraft leave the sky.

Visualizing Radiative Decay!

Most of us have an idea of what radioactivity is - right?  Something along the lines of 'sub-atomic' particles being given off which are highly energetic?  Sound familiar?  Maybe not.  Lets consult our good friend 'Wikipedia' to help us out with a definition of 'radioactive decay'.  Here is an excerpt:

Radioactive decay (also known as nuclear decay or radioactivity) is the process by which the nucleus of an unstable atom loses energy by emitting radiation, including alpha particles, beta particles, gamma rays, and conversion electrons. A material that spontaneously emits such radiation is considered radioactive.

Radioactive decay is a stochastic (i.e. random) process at the level of single atoms, in that, according to quantum theory, it is impossible to predict when a particular atom will decay,[1][2][3][4] regardless of how long the atom has existed. For a collection of atoms however, the collection's decay rate can be calculated from their measured decay constants or half-lives. This is the basis of radiometric dating. The half-lives of radioactive atoms have no known lower or upper limit, spanning a time range of over 55 orders of magnitude, from nearly instantaneous to far longer than the age of the universe. A radioactive source emits its decay products isotropically (all directions and without bias)[5] in the absence of external influence.

Couple the description above to the picture below to get a full visualization:

Source: Inductiveload

How does a person measure radiation decay?



Hollywood offers a visual representation commonly depicted in movies surrounding the release of a 'nuclear weapon' or threat of exposure to radioactive compounds like the following shown below:

Source: Associated Press

A common instrument used to measure the amount of radiation that is being emitted off of a given sample is the 'Geiger Counter' and is shown below:

Source: TimVickers 

The instrument can sample a range of intensities.  But, what if the radiation that we are trying to measure is that of the natural background from the sky.  The background radiation is supposedly orders of magnitude than a release of a 'nuclear weapon' (which is true).



How does a scientist measure background radiation?



How about using a cloud chamber?



An instrument that is commonly used to measure radiation is called the 'Cloud Chamber' or 'Wilson Chamber' after the founder -- the Scottish physicist Charles Thomson Rees Wilson.   The structure of a cloud chamber is relatively simple.  A chamber is couple with a heater/cooler which has access to introduce a radioactive source into the interior space.  This will be demonstrated in the video below.  A picture of a cloud chamber from 'Wikipedia' is shown below:

Source: Cloudylabs

They are easily constructed and instructions for science projects involving the construction of a 'Cloud Chamber' can be found here.



As I mentioned in the introduction, I found a video which showed precisely and beautifully the radioactive decay of various elements.  The video on 'YouTube' is titled "Large Diffusion Cloud Chamber With Radon Gas Double-Decaying" and is broken down into frames below.  During frames, I commented or narrated on the content in each frame.  The overall message to take home from viewing the frames below is that the video allows us to see atoms precisely in their position from the 'alpha decay' leaving the nucleus.  The demonstration is absolutely amazing.



One more note is that the chamber is cooled at the bottom and heated slightly at the top to produce a temperature gradient.  The temperature gradient is similar to the temperature gradient in the sky as one goes to higher altitudes.  Therefore, after I show the video frames, I will draw an analogy with the "trails" from condensation commonly seen after an airplane flies across the sky.



First, lets start with a frame from the video which shows the chamber without any radioactive compound inserted.  As shown below, this is the natural background radiation that each of us are experiencing without noticing it at any given moment.



Background Radiation:

Relatively few interactions compared to the expected large amount of a concentrated decay like a 'nuclear weapon' or a 'radioactive source'.




Point Source:

Right after exposure to the cloud chamber.  Notice initially, there is a huge force of alpha decay pushing out from the source toward the other side of the chamber.  The pressure wave of alpha decay resembles the shape of the source -- a half spherical shape -- as shown below.



Point Source - 3 seconds after:

Notice the exponential diffusion of particles throughout the chamber. After a series of collisions producing further alpha decays, the motion becomes unpredictable -- as shown below.


Point Source - 9 seconds:

Still going.  Actually, the secondary decay is occurring at this moment.  The picture below shows the extent of the energetic alpha particles still colliding with more nuclei to produce (secondary) radioactive decay -- as shown still below.



Point Source - 19 seconds:

Crazy!  I wonder how long the team had to wait until the entire chamber came back to equilibrium.  The state of equilibrium would have resembled the 'background' still frame above.

Visualizing Temperature Gradients!

In the last section, the amazing demonstration of 'alpha' radioactive decay was made clear using a cloud chamber filled with ethanol gas.  I pointed out before presenting the 'still frames' of the diffusion of radiation that there exists an equivalent analogous situation that occurs on the 'macroscale'.  Not only does the event happen on the scale of everyday occurrences, the event is visible to a large audience of viewers from the ground.



The idea of 'chemtrails' is a popular conspiracy put forth to account for the seeming long white trails which follow an aircraft traversing the sky.  Here is an excerpt to describe such phenomenon taken from the 'Wikipedia' page on 'Chemtrails':

Chemtrail conspiracy theory is an unproven suspicion that long-lasting trails, so-called "chemtrails", are left in the sky by high-flying aircraft and that they consist of chemical or biological agents deliberately sprayed for sinister purposes undisclosed to the general public.[1] Believers in the theory argue that normal contrails dissipate relatively quickly and that contrails that do not dissipate must contain additional substances.[2][3] These arguments have been dismissed by the scientific community: such trails are normal water-based contrails (condensation trails) that are routinely left by high-flying aircraft under certain atmospheric conditions.[4] Although proponents have attempted to prove that the claimed chemical spraying does take place, their analyses have been flawed or based on misconceptions.[5][6]

Because of the widespread popularity of the conspiracy theory, official agencies have received many inquiries from people demanding an explanation.[2] Scientists and government officials around the world have repeatedly needed to confirm that supposed chemtrails are in fact normal contrails.[7]

With the corresponding visual description taken also from the 'Wikipedia' page for 'chemtrails' shown below:

Source: No machine

The conspiracy theorists are fascinating in their endeavor to seek an answer to this phenomenon.  Implying that the government is actively pursuing dumping chemicals into the environment in order to create such trails is non-sense.  Any particle growth with water vapor in the atmosphere will diffract light -- look at clouds.



The real culprit in the case of the so called 'trails' across the sky come from 'contrails' -- short for condensation trails -- made up of water vapor that has crystallized.  Here is the description from 'Wikipedia' for 'contrails' below:

Contrails (/ˈkɒntreɪlz/; short for "condensation trails") or vapor trails are line-shaped clouds sometimes produced by aircraft engine exhaust, typically at aircraft cruise altitudes several miles above the Earth's surface. Contrails are composed primarily of water, in the form of ice crystals. The combination of water vapor in aircraft engine exhaust and the low ambient temperatures that often exists at these high altitudes allows the formation of the trails. Impurities in the jet exhaust from the fuel, including sulfur compounds (0.05% by weight in jet fuel) provide some of the particles that can serve as sites for water droplet growth in the exhaust and, if water droplets form, they might freeze to form ice particles that compose a contrail.[1] Their formation can also be triggered by changes in air pressure in wingtip vortices or in the air over the entire wing surface.[2]

Depending on the temperature and humidity at the altitude the contrails form, they may be visible for only a few seconds or minutes, or may persist for hours and spread to be several miles wide, eventually resembling natural cirrus or altocumulus clouds.[1] Persistent contrails are of particular interest to scientists because they increase the cloudiness of the atmosphere.[1] The resulting cloud forms may resemble cirrus, cirrocumulus, or cirrostratus, and are sometimes called cirrus aviaticus. Persistent spreading contrails are thought by some, without overwhelming scientific proof, to have a significant effect on global climate.[3][4] Persistent contrails are sometimes called chemtrails in reference to the conspiracy theory regarding the undisclosed spraying of chemical or biological agents by various high-flying aircraft.

Again, as I just mentioned -- the crystals grow from water vapor attaching themselves to a 'seed molecule' and growing to the point of diffracting light.  I will give you a little known fact about 'contrails' that is not commonly known by the world.  This is in regards to the aircraft that you see at airshows.  Now that you know that the condensation has a role to play with 'contrails' -- you might be wondering the following question -- regarding air shows with fighter jets:



How do the jets make 'contrails' at a precisely given point in space in the sky?



The answer lies in the fact that the gun bay in a fighter jet where the ammunition is stored is emptied out -- for show jets.  In the space (gun bay), there is an oil container filled with oil.  There is a delivery system (via veins or tubes) that deliver the oil onto the exhaust of the jets to produce a 'contrail'.



Bet you did not know that!

Conclusion!

The ability to view the invisible is absolutely amazing.  In the paragraphs above, the size of the particle that has been shown to be visible spans from the sub-atomic of a radon nucleus to the particles (aggregates of ice crystals) in the sky.  When we look up and see a cloud, that is evidence of a particle grown from a 'seed molecule' with water vapor.  The diffraction of light gives way to the opaque (cloud) that is seen in the sky above.



Whereas, on the sub-atomic scale, the ejection of an alpha particle decaying off of a nucleus is seen as the trail from the thermal gradient.  Each is a representation of an indirect interaction.  Science offers us an explanation to a wide range of such situations.  Further, with these explanations, better decisions regarding science policy are possible in government.  Ranging from the international level to the local level, science plays a large role in the decisions.  If it does not, maybe in the future it should.  Having examples like the two above, give us an idea regarding the safety of radiation and chemicals in the sky.



Until next time, Have a great day!