Tons of Rain

On Thursday last week, the Schenectady weather forecast I have in my Bloglines feed called for “Tons of Rain,” which I thought was amusingly unprofessional. I mentioned this to Kate yesterday (after it had, in fact, rained quite a bit), and she said “I wonder how much rain you would need to make a ton?”

Being a physics nerd, of course I had to try to come up with an answer.

We know that one cubic centimeter of water has a mass of one gram, so a (metric) ton of water would be 1,000,000 cubic centimeters, or one cubic meter. Our yard is about 20m x 50m, so if rain covered our yard to a depth of one centimeter (which has happened before), that would amount to about one ton of rain.

Of course, it doesn’t rain just in our yard, and they certainly don’t forecast rain for just our yard. It rains over the whole region, and they do forecasts for the whole region. If you take the region in question to be Schenectady county (as good a choice as any), Wikipedia helpfully tells us that the area of the county is about 543 km2, or 5.4 x 108 m2, so one ton of water would cover that area to a depth of a bit less than 2 nanometers. You wouldn’t even notice the grass being wet.

So, how much rain is a ton of rain? Not much at all. An unimpressive rainstorm, with a tenth of an inch accumulation (the lowest category listed in NASA’s classification) amounts to a bit more than a million tons of rain in Schenectady county alone. (There’s a similar estimate at this blog by a biologist in Minnesota, and not the one you’re thinking of, either.)

The lesson here: Water is really heavy.

Comments

  1. #1 mollishka
    October 28, 2007

    Reminds me of the fact that a barn-megaparsec is about one tenth of a fluid ounce.

  2. #2 Abbie
    October 28, 2007

    Jeez, how much is a ton of cloud?

  3. #3 Johan Larson
    October 28, 2007

    A 100 m^2 yard? Surely zoned for scientists, to facilitate back-of-the-envelope calculations.

  4. #4 JohnnieCanuck, FCD
    October 29, 2007

    Abbie, after some poking around at NOAA and USGS, whose numbers don’t all agree, I have the following:

    From NOAA;
    A cubic kilometer of dry air at a typical 2 km height and 2 degrees C weighs 1.007 million tonnes.
    At a water vapour partial pressure of 7mb out of 795, the same volume of moist air weighs 1.003 million tonnes.
    They then conclude that this is the weight of a cloud of this volume, which leaves me uncertain.
    Assuming they are correct I calculate that 7/795 = 0.9% of the moist air mass is water, or approx. 9000 tonnes.
    1 tonne would then occupy a cube roughly 48 meters on a side.

    Corrections requested.

  5. #5 Clay B
    October 29, 2007

    JohnnieCanuck, that looks about right but that would be just the water vapor. Oddly enough, the liquid cloud amount is usually less than the vapor.

  6. #6 Eric Lund
    October 29, 2007

    Our yard is about 20m x 50m, so if rain covered our yard to a depth of one centimeter (which has happened before), that would amount to about one ton of rain.

    I think you slipped a decimal point here. That’s a 1000 m^2 lot (i.e., 0.1 hectares or about 1/4 of an acre), so you only need 1 mm of rain to get a ton. That’s a minuscule amount: according to the almanac at Weather Underground, ALB averages 0.11 inches (about 2.8 mm) of rain a day at this time of year. So getting “tons” of rain is in fact normal for Chateau Steelypips.