What innumeracy (and lack of government oversight) can lead to: Wildly outrageous numbers masquerading as fact

Much like a lack of understanding relatively small changes over relatively long periods of time (such as with evolution or with inflation) can cause some people to make massively incorrect assertions, so, too, can a lack of the ability to grasp really large numbers lead to making assertions that are orders of magnitude implausible (or even impossible).

I read a story at PhysOrg about a new piece of research out of the Stephen M. Ross School of Business at the University of Michigan:

The idea of corporate social responsibility to manage common-pool resources such as water, forests and pastures is flawed, says a University of Michigan researcher.

Aneel Karnani, associate professor of strategy at the U-M Stephen M. Ross School of Business, says that when a common-pool resource is left without any enforced property rights, it results in degradation and destruction of the resource.

Karnani uses an in-depth case study to make his point—groundwater use by Coca-Cola Co. at its Kaladera plant in the state of Rajasthan in India. The groundwater level in Kaladera has dropped significantly from 9 to 39 meters below ground in the last 20 years.
The plant operates four bore wells that are 100 meters deep. In its early years of operation, the plant withdrew about 200,000 cubic meters of groundwater per year. In recent years, the company has reduced its water usage to about 100,000 cubic meters annually, or about 0.2 percent of total water extraction.

...

Coca-Cola says the Kaladera plant's water consumption is minimal and has little impact on the local groundwater regime. It also says it has built rainwater harvesting structures around Kaladera that recharge the groundwater aquifers with 15 times the volume of the water extracted by the plant.

The story doesn't go into the numbers much further than what I present above, but - immediately - the numbers look kinda "hinky" to me. Why? Well, 200,000 cubic meters per year is a lot of water extraction. (100,000 cmy is also pretty big.) Just how big is 100,000 cmy?

Well, the number of 2L bottles of Coke that 100,000 cubic meters per year will fill is 50 million bottles of Coke, which is equivalent to 3.2 bottles of Coke every second. (That's equivalent to a little more than 9.5 cans of Coke every second!)

That means that - in order to actually "recharge groundwater aquifers with 15 times the volume of the water extracted by the plant" using "rainwater harvesting structures around Kaladera", the Kaladera plant will need to collect 1,500,000 cubic meters per year.

Is that feasible?

Well, we need to know what the annual precipitation is in that area in order to determine the amount of rainfall that would need to be captured to reach 1.5 million cubic meters.

Looking at Google Maps, we find that the Kaladera plant is located in the Jaipur district of the Indian state of Rajastan. According to India's Central Research Institute for Dryland Agriculture, the Jaipur district is in a "semi-arid" region that receives an average of 563.8 mm of rainfall each year (Wikipedia's page on Jaipur district cites 668 mm, based on BBC Weather). Converting this into meters, we get 0.5638 m (0.668 m), and if we then divide this number by 1,500,000 cubic meters, we can find the area necessary to capture "15 times the volume of the water extracted by the plant":

The plant would need a rainwater harvesting system that covers an area of 2,660,517 square meters (2,245,508 square meters), or roughly 2.7 square kilometers (2.2 square kilometers).

And this doesn't even take into account losses due to evaporation and interception!

So, does Coca-Cola's assertion that it's recharging the aquifer with "15 times the volume of water extracted by the plant" through only using "rainwater harvesting structures around Kaladera" seem feasible? Nope. Not at all. Not unless Coca-Cola has over 2 square kilometers of land set aside for the sole purpose of collecting all rainwater that falls on the landscape. And - at least from Google Maps - it doesn't look like the Coca-Cola plant's foot print is even 0.5 square kilometer.