Estimation, Part II

To an order of magnitude, how much water do Americans use each year watering their lawns? How does this amount of water compare to the amount of water Americans drink each year?

Life as we understand it requires water. That's enough of a given that we sent two of the most remarkable engineering feats in history 483 million kilometers (that'd be $4.83\times10^8$ kilometers if we're sticking with scientific notation) just to see if it had ever existed on another planet. We use a lot of water every year keeping ourselves alive, either by drinking it or using it to irrigate vital crops. But the most irrigated crop in America--one covering three times as much area as all of America's cornfields--is grass. About how much water does that take, then? This one's a bit of a sequel to my second post, in philosophy if not in subject matter.

Along with my usual collaborators Anne Madoff, Jennifer Shi, and Louise Decoppet, I started by just trying to approximate the area covered by lawns in America (there's an exact figure at the link above, but we didn't have that at the time, and that number includes nonresidential grass such as public parks--all the calculations here are based on our own estimations). There are $3*10^8$ people in the United States, about half of whom live in suburbs. We figured that people living in suburbs are more likely to be part of a family rather than living alone, so we assumed three people as the average suburban household size. That gave us $5\times10^7$ as our total number of suburban homes. It's likely that many of those homes don't have lawns, but since we were disregarding lawns in urban areas, so we assumed that the surplus and deficit would roughly cancel each other out--$5\times10^7$ suburban homes, then, meant $5\times10^7$ lawns.

So how big is the average lawn? We debated that one for a while, eventually deciding on an even 100 square meters. 10x10 meters is pretty small for a lawn, so we anticipated that this would give us an underestimate, but a reasonably close one. Our next question was how much water a square meter of lawn would need. I was pretty shocked when, after some googling, we hit on three liters per day per square meter, again as a conservative estimate (some sites recommended as much as six). Across our $5\times10^7 \: 100$-meter lawns, that worked out to a whopping $1.5\times10^{10}$ liters per day for the entire country. Since many places don't need year-round watering (in an awful lot of the country it is, for a sizable fraction of the year, too cold to water or too rainy to need it) we decided to multiply the daily number by 300, rather than 365. The arithmetic is simple enough that you may have done it in your head already, but just for the visual impact of it I'm going to toss up what it worked out to resplendent in all its zeroes and commas as well as in scientific notation.\[3\times10^2\times1.5*10^{10} = 4.5*10^{12} = 4,500,000,000,000 \: liters\] A bit of extra research showed that that figure was, as we had suspected, an underestimate--as it turns out, Americans use about $3.5\times10^{10}$ liters per day--just about double what our estimate was, and averaged over all 365 days of the year. Still, we were solidly within an order of magnitude of the actual figure.

Ridden with zeroes as it is, that number still exists in something of a vacuum, so we followed it up by trying to work out the second part of the question--how does it stack up against the amount of water that we drink every year? The human body requires about two liters per day of water, which across the entire US population works out to about $6\times10^{8}$ liters of water consumed per day. Over a full year, that's $2\times10^{11}$ liters per year. A lot? Absolutely. But still a full order of magnitude less than what we devote to our lawns.