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Reading about an Arizona wildfire

Yesterday's New York Times (2002-06-24) had an front page article "Wildfires Join And Threaten Arizona Town" (by Michael Janofsky). It read in part


Two wildfires that have burned about 330,000 acres of norther Arizona in the last week merged today, becoming by far the biggest fire in the state's history. Fire officials said it could easily cover a million acres, about 1,500 square miles, before it goes out.

[...] With the fire's leading edge running for 50 miles at the north and east, plumes of bruise-colored smoke are rising 15,000 feet and are visible half way to Phoenix, 125 miles away.

[...] On Monday, its first day, the larger of the two fires, Rodeo, grew to 48,000 acres from 700 acres in just six hours.

Neat, some numbers. Let's grab some "How Big Are Things?" graph paper and explore this.

Ok, let's see...
(There are pretty pictures and maps towards the bottom... feel free to skip any stuff which bores you... please!)

An acre is ...


On the meter's Room's graph paper,
each square is 1 meter big.

Quickly eyeballing the acre,
it looks something like 65 meters on a side. You could jog across it in 10 seconds. So a million acres... is what? 106 acres, so a 103 x 103 acre square. So 65 thousand meters on a side, ie, 65 km. For maybe 65 x 65... hmm, lets just call it 4000... 4000 square kilometers.

How far is 65 km for you? (Here is the kilometer room.)
For me, well, the body of Massachusetts is only 75 km high...

Ok, let's be more precise. Google'ing for "acre meters" yields... an acre is 4047 m2. And let's see, sqrt(4047 m2) is 63.6 m. So 65 m wasn't bad for a quick eyeball. We didn't even have to count the boxes.

Moving on...

A million acres is ...

106 acres

330,000 acres
48,000 acres
700 acres
Let's move up to kilometer's Room, where things are 1000x bigger.

Here is our million acres. Shown as a square, 63.6 km on a side.

Hmm, so what is 330,000 acres?
Ok, first the quick and dirty version.   33 looks like 36, so 330,000 looks roughly like 600 x 600. And an acre is about 60 m on a side. So 6 x 10^1 times 6 x 10^2 is 36 x 10^3. So, 36 km on a side.

Ok, since I'm about to carefully draw a green square on left, let's now do a more careful run.   330,000 acres looks like a square with 575 acre sides (well, sqrt(330,000)=574.46).   575 times 63.6 m is 36570 m. So, 36.6 km on a side. Our quick and dirty version was pretty good.

And for 48,000 acres... sqrt(48000)=219. Times 63.6 m. So 13.9 km sides.
And 700 acres... sqrt(700)*63.6... 1.7 km sides.
And... I've now drawn the green squares you see on the left.
Maybe they should be red? No, toasted black? Lots of burned trees.

Hmm. Say the trees are about a meter apart. Probably a bit more than that. So a million acres, 4000 km^2, is... what? 1 km^2 is 1000 m x 1000 m. So 10^6 m2. A million square meters. So one square km is something a bit less than a million trees. And 4000 km^2... is 4 x 10^3 times 10^6 so 4 x 10^9 m2. That's 4 billion(US) square meters. Perhaps a billion trees? Yipes.

While a square is a pretty good match for a fire's shape, it does make it harder to see how much area has burned. People usually aren't great at comparing areas. So let's reshape those squares, giving them a common height, so we can just compare their width. So we can just compare a linear distance. Which is easy.

106 acres

330,000 acres 1000000 acres x 4047 m^2 / 20,000 m = 202 km.
330000 acres x 4047 m^2 / 20,000 m =  67 km.
48000 acres x 4047 m^2 / 20,000 m =  10 km.
700 acres x 4047 m^2 / 20,000 m =   0 km.
(Only about 3 centimeters. :)
48,000 acres>
700 acres
A million acres is a lot.

Ok, here is a quick look at the plume, and then, pretty pictures.
15000 feet is 4.6 km. (I Goggle'd for "feet kilometers" and found this.)
Which also give 50 miles * 1.609344 = 80.5 km,
and 125 miles * 1.609344 = 201 km.
a 50 mile edge
which is probably shaped more like this

And here is a 4.6 km high plume...

and 100 km is "half way to Phoenix" \/

I should have included an atmosphere cross-section, but I don't have a really nice one yet. There are some in kilometer's room.   5 km is about half way up through the ~10 km Troposphere. It might also have been nice to find a topo map, and add the mountains.

Pretty picture time.
There was a photo credit in the NYT article. I Google'd to it (National Interagency Fire Center), and spent some time groveling around. We are still in kilometer's room, sitting on the graph paper. Remember, things are really 1 million times bigger than they appear here :). (Otherwise, you might be able to smother the fire with your hand.(?) Though that could crush the park.)

This is a 100 km square map.
(Snipped from this large 2.5 MB map,
here under "Active Fire Maps, MODIS".)

These images are at the same scale,
but were taken at different times,
so the fire size varies.


Image (1 MB) from here.

Image (0.6 MB) from here.
The bright red is fake - it's a way to include invisible infra-red (heat) data.

Backing up by x10, ie, the kilometer's room's floor ...
106 acres, 330,000 acres, 48,000 acres
The national forest (Apache-Sitgreaves) being eaten.

atmosphere, crust, rest of lithosphere (melted crust)
Mantle beneath. Thickness varies more than shown.

The area burning is said to include high-elevation meadows and streams.

And with that, I'm out of time for the evening.
I hope you found this exploration of interest.
  - Mitchell Charity, 2002-June-25, Cambridge, Massachusetts

  Netscape 4 makes a hash of the grid backgrounds.
   But it is such a small fraction of my site traffic...
  Folks with modems... are not going to be happy.  Looks like a 2 min load time.

  Add kilopaper park map, showing the bite being taken out of the park.
  Get a better atmosphere cross-section.
  Find some ponderosa pine (?) pictures.
  Mention all the other stuff which could be done.
   Fire speed.  Plume profile and speed.  Topography!
   And BotE stuff: scales (a,v,s,T,E), energy flow.
   Trees as sunlight condensed air, both released by burning.
   Harte's Spherical Cow.
  Show transition from "you can easily do this at home, to not".
   Mention that a web tool is "in the works".

  2002-Jul-03  Corrected crust cross-section.
  2002-Jun-27  Cleanup pass.  Online.
  2002-Jun-25  Created.

(c) 2000-2003 Mitchell N Charity. All rights reserved.
Noncommercial use is fine. Otherwise, ask.