17 August 2023 — 1530 mdt
A quick and dirty measurement of a smoke plume
By James Conner
Located on the east side of the reservoir six miles southeast of Hungry Horse, the Ridge Fire (Facebook page) — a dangerous fire that, should winds drive it north, could threaten the Highway 2 corridor to West Glacier and Apgar Village — blew up two weeks ago, producing a towering column of smoke that was easily visible twenty miles to the west.
I saw the plume rising over the Swan Range as I crossed the Highway 93 overpass driving east on Two Mile Drive. I wish I could have gotten a photo, but there was no place to stop and cars behind me. Later, at Harbor Freight’s parking lot, I used my iPhone to photograph the plume. At that point, didn’t know which fire — there were several in the general vicinity — was producing the plume.
The Ridge Fire’s plume from Harbor Freight’s parking lot.
Two hours later, at my hilltop home two miles west-northwest of old downtown Kalispell, I photographed the plume, took magnetic bearing from my front yard using lensmatic and hand bearing compasses: 46° magnetic, plus 13° east declination, for a true bearing of 59 degrees. Using an inclinometer, I determined that the altitude of the plume’s top was eight degrees, five degrees above the summit of the Swans.
From my front porch, in order of distance, Kalispell’s hospital, the Swan Range, and the Ridge Fire’s smoke plume.
After dinner I checked the usual internet sites to identify the fire. There were several fires, but except for the Ridge fire, which was almost a thousand acres, all were a couple dozen acres or small. A visit to inciweb.com yielded the fire’s latitude and longitude, which I plugged into Google Earth Pro, which already had my home’s coordinates. The measuring tool put the smoke plume 21.4 miles to the NE on a bearing of 58 degrees The smoke was roaring up from the Ridge fire.
With those data, I could estimate the height of the smoke plume using simple trigonometry — tan(8°) * 21.4 miles * 5280 = 15,900 feet. Adding to that an estimated 4,000-foot base elevation indicates the fire’s smoke column topped out at approximately 20,000 feet.
When the distance to the object being measured is know, the math is simple.
That number comes with caveats.
The top of the smoke column might not have been directly above the fire’s reported latitude and longitude. If it wasn’t the baseline wasn’t 21.4 miles.
The inclinometer, which reads to half a degree, might have been out of calibration. If the true altitude was 7 degrees, the column’s height would be 13,900 feet. If 9 degrees, 17,900 feet. So to be safe, the column’s height ASL (ground elevation plus smoke) probably should reckoned as 20k feet plus or minus 2,000 feet — assuming the baseline isn’t appreciably shorter or longer.
Taking a simultaneous altitude several miles away would have solved the baseline problem. But as this graphic from the Appalacian Mountain Club reveals, the math is more complicated.
Mathematically, the problem is identical to triangulating a tree top or a distant mountain; probably closer to triangulating a distant mountain.
Larger, easier to read image. This is how remote mountains are triangulated.
Wondering how to do it? You’ll need the position of the fire, your position, a way of measuring the altitude of the top of the smoke plume, a reference for the mathematics involved, and a computational device such as a slide rule or scientific calculator.
Let’s start with the reference. American Forests publishes a free 86-page manual (PDF) for measuring large trees. In it, you’ll find everything you need for measuring mountains, giant conifers, and columns of smoke. Scientific calculators are widely available. Slide rules are not, but they can be purchased from various websites (or inherited from one’s great uncle, the engineer). Abney levels and inclinometers can be purchased from Amazon. And if so inclined, you can make a rudimentary inclinometer with a protractor, string, straw, and washer.
Finding the fire’s position. Use a good compass to get a bearing on the smoke plume (keep your phone at least a couple of meters away from the compass), and an inclinometer or Abney level to measure the plume’s altitude.
Next, go to Google Earth to locate your position, from which you’ll use the line tool to lay your compass bearing on the map. You also can determine your position with your smart phone’s GPS function or a handheld GPS receiver.
Finally, go to https://inciweb.nwcg.gov/ for the latitude and longitude of fires along your compass bearing. Enter the coordinates into Google Earth. The biggest fire by acreage probably is sending up the smoke.
If you are not sure you have identified the fire, drive a few miles to the right or left of your compass bearing. Take a bearing at this location. Where the bearings intersect in Google Earth is likely to be the fire’s location.
If Google Earth isn’t available, there are many online calculators for reducing lat/long to a distance and bearing. And by assuming the Earth is flat, there’s a way to reduce the lat/long differences using the Pythagorean Theorem, but I’ll save that tutorial for another time.
Now, reduce your data to an estimated height of the plume above ground level. Avoid spurious precision. Your altitude measurement probably is plus or minus a degree, and standard procedures do not account for refraction or the curvature of the earth. I usually round my estimates to the nearest thousand feet, and provide the values for plus or minus half a degree.
The agencies fighting the fire often have access to sophisticated technologies for measuring clouds. There is, for example, a satellite that can obtain highly accurate measurements. But don’t assume that technology will be used on every fire.
Finally, if you’re interested in wildfire smoke, in 2022 the U.S. Forest Service published a fine report on the subject.