Monday, July 18, 2016

How Much Rain Did China Really Receive?

A recent news story broke about flooding in China due to a torrential rainstorm recently.  This rain has caused considerable damage and destruction both to buildings and structures along with the loss of life.  In order to truly understand the meaning of the picture below, I thought that a short blog post using dimensional analysis to compare to recent water stories hitting the news this year would be appropriate.  Here is the picture of a stadium in China taken from a news story:

Source: Quartz

How does this picture compare with others describing disasters earlier in 2016 thus far?

The following will be a series of calculations illustrating the numbers relative to earlier numbers reported in earlier blog posts on the site.

Torrential Flooding In China

In a recent video displayed on the website of the 'New York Times,' titled "Flood Ravages Southern China" -- the extent of the flooding is clearly visible.  The video is short (less than a minute) and worth watching:

Where did all of this water come from?  Obviously the sky, but why in periodic downpours?

At first, I thought that China along with the rest of the world needs the water that is possible due to nature.  There is a limit to the need, where, need turns into excess with improper construction that ends in disaster.  This is extremely unfortunate.  From a viewer's standpoint -- thousands of miles away, the amount of water contain in one or two feet of water seems inconsequential.

Although, according to the news site 'InsuranceJournal' in an article titled 'China Floods Kill 173, Cut Transportation Links; Hit to Economy Expected,' the total amount of water was distributed over a large land mass area.  Here is an excerpt describing the rain and destruction:

The Ministry of Civil Affairs said flooding and rain associated with the typhoon affected more than 31 million people in 12 provinces, submerged more than 2.7 million hectares (6.7 million acres) of cropland and caused 67.1 billion yuan ($10 billion) in damages.

That is a large amount of water to drop from the sky.  The damages are enormous at least in number along with the huge number of people adversely affected (31 million over 12 provinces).  Descriptions of events differ greatly depending on the sources.  Coming from a journal whose audience is mainly from the insurance sector, crop damage would be of great importance.  At the same time, reporting on the effect on the GDP would be appropriate out of a journal of this sector.  Here is a description taken from the article describing the negative impact on the GDP as a function of flooding below:

China’s National Development and Reform Commission said in a statement Sunday that fruit and vegetable prices had “risen significantly” in some flooded regions. It asked local authorities to “closely monitor prices” and implement price controls if needed.

Flooding will boost consumer prices in July and August by about 0.2 percentage point to levels above 2 percent, Zhou Jingtong, director of macroeconomic research at Bank of China Ltd. in Beijing, wrote in a note. The CPI rose 1.9 percent from a year earlier in June, less than a 2 percent gain in May, the National Bureau of Statistics said Sunday.

Economists said the floods would have both short- and long-term implications for the world’s second-largest economy. Food and product shortages could materialize soon from supply interruptions as transport hubs were paralyzed and factories and offices closed in some of China’s most industrialized provinces.

Economists suggest that the effect is unknown and will show itself in later quarters the year in terms of GDP.  For the purposes of this blog site, I am concerned with understanding the dimensions of the reported statistics.  Therefore, after reading about the enormous amount of rain,  I wondered how much water was in that reported volume?

I decided to carryout a few calculations below.  I will walk you through my calculations of the water below.  In order decided to compute the amount of water in the volume described above -- 2.7 million hectares and 2 foot deep, the conversion of how many hectares are in a square mile has to be obtained.  Typically, the volumes of water that are reported in the popular news are cast in units of "cubic feet" -- therefore, to get to cubic feet, we will have to go through square miles.  First, the conversion from hectares to square miles is shown below:

With the conversion factor known, the dimensional analysis of hectares to square miles is possible as shown below:

The first line of the calculations above is the conversion of hectares into square feet.  Since the objective was to eventually calculate a volume for a meaningful comparison, the calculation includes the conversion from square miles into square feet.  In the second line of the calculation, the area of the water is expressed in square feet is multiplied by the value "2 ft" (which represents the height of the rainfall).  The calculated value is in units of cubic feet which is a volume.  What does the number above represent?

The calculated number -- 580 billion cubic feet represents the total rainfall (a volume) that fell on 2.7 million hectares of land in China -- WOW!!!!

How Large Is 580 Billion Cubic Feet?

In order to put that volume into context, we need to return to an old post (back in January) titled "How Much Water Is In A Few Inches Of Rain?" where I verified a statistic (volume of rain) that was reported by the popular news.  Through researching where the 'error' propagated from, I determined that the weather forecasting service center made a "late night" calculation error.  At least, that was the response from the service that I received.  Read that blog to find out more about that fiasco.

The result from the calculations in that blog post resulted in our understanding that over the range of the Lake, 1.92 inches of rain equated to around 6.3 billion gallons of water.  Therefore, we should not be too surprised with the result above.  Still, the amount of damage is terrible and should not be minimized in any manner.  Remember, on this site, we are dealing strictly with the numbers (or facts) that are reported in the popular news.

How many hectares encompass the Lake Tahoe area?

Great question.  According to 'Wikipedia' -- the Lake Tahoe Watershed -- which consists of the mountain area surrounding Lake Tahoe and which drains into the lake is around 505 square miles.

How many 'hectares' are in 505 square miles?

To start the calculation, we need to know the conversion factor between the two areas.  The conversion is shown as an image below:

Next, how many are in 505 square miles?  Easy, just multiply 505 square miles by 258.999 hectares/square-miles as shown below:

How does 130,000 hectares compare with the reported 2.7 million above?  Here is the image of the conversion online shown below:

The Lake Tahoe watershed basin is 1/20th of the size of the 12 provinces in China that were submerged in water.  Plus, the amount of rain fall differed in the two storms by nearly 22 inches of rain -- which is a considerable (enormous) amount water.

In order to compare the amount of rain that poured down in the two regions -- Lake Tahoe and China, the volume needs to be expressed in units of "gallons."  The conversion of the volume in units is shown below:

With the volume expressed in units of gallons, a direct comparison to the volume of rain discussed in my previous blog about the rainfall in Lake Tahoe is now possible.  Dividing the two numbers yields 676 as shown below:

Below is a picture of the Lake Tahoe basin:

What does the ratio -- 676 mean?  The question can be restated to the following:

What is the equivalent volume per area for Lake Tahoe?

Equivalent Volume Per Area For Lake Tahoe?

At the end of the last section the question of equivalent volume per area was in question.  Which is to say, the amount of the rain that fell over 12 provinces in China over 2.7 million hectares is 2 feet.  Now the question is:

How many feet of rain in the Lake Tahoe region would compare to the volume in China?

To start with, a statement of equivalent ratio of feet to volume needs to be stated as shown below:

On the left hand side, there is a variable "y" in the numerator which represents the volume (yet to be determined) of the equivalent rain covering Lake Tahoe to that of China.  In the denominator, the area of the Lake Tahoe region (Lake and surrounding mountains) is expressed in hectares.

On the right hand side, in the denominator, the volume of rain (580 billion cubic feet) that fell on China is shown divided by the area -- which is 2.7 million hectares.  After rearranging the equation to solve for "y", the result is shown:

In order to compare the volume of water that fell as rainfall to the volume reported for Lake Tahoe last winter, the units of volume need to be the same -- gallons.  Shown below is the conversion from cubic feet to gallons:

Next, dividing the two volumes (China and Lake Tahoe) of rain fall will yield the multiplication factor.  The ratio can be determined below as shown:

The ratio of the two volumes of rainfall is 33.  Which means that the volume of the initial rainfall from last winter in Lake Tahoe can be used to determine the equivalent rainfall that occurred in China.  First, take the multiplication factor and determine the amount of inches as shown below:

One final conversion from inches to feet will yield the equivalent amount of rainfall in the Lake Tahoe basin as shown below:

That is an enormous amount of rain.  Clearly, one can look at the picture of Lake Tahoe above and imagine 25 feet high of rainfall as incomprehensible.  Further, to imagine that the calculated volume was spread over 12 provinces in China.  No wonder there was such a large loss in crops and infrastructure.  What a terrible disaster?  Volumes of water like this make me wonder just how much water is in the sky?  Must be a truly incomprehensible amount.

Conclusion and Homework

The point has been driven home regarding the natural disaster experienced by China over the last couple of weeks.  An enormous amount of torrential rainfall has poured down and disrupted not one city but multiple provinces.  The damage for which has yet to be truly determined and might take a while seeing the scale on which the disaster occurred.

The calculations revealed an astounding volume of 25 feet pouring into the Lake Tahoe region to be compared to the entire storm in China.  Unimaginable to say the least.  For the reader (you), I have a couple of problems for a "homework assignment" listed below based on former blogs on this site:

1) How does the volume of rainfall compare to the volume of water stored in the Mosul Dam in Iraq?

2) How does the volume of rainfall compare to the flood in Brazil late last year from a mine?

3) How many Deep Water Horizon Oil Spills is the volume of rainfall equivalent to?

4) How many of the "World's largest pool" could be filled up with the volume of rainfall?

I think that the assignment will span the full range of volumes and give you an idea of the enormity of this natural disaster.  I hope that you will view disasters like this in a completely different light after working through the problems on the blog and the site.  Have a great day!

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