Mudslide Meteorology and Math


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The results of a mudslide. Image credit: NOAA

The results of a mudslide can be devastating. Image credit: NOAA

The record March rainfall in Washington is the immediate cause of the mudslides which have so far claimed 21 lives. But there is math and physics, too, and changing weather patterns raise serious questions about where it’s safe for people to live.

The Weather In Seattle

Seattle is a rainy place in the winter — not so much for the total amount of precipitation as for the constant drizzle and light rain. This March has been different. In the first seven days, more rain fell than in an entire normal March; recent deluges pushed the total for the month to a record of nearly ten inches, three times normal.

What’s The Cause Of The Downpours?

When in doubt, blame the weather on the Polar Vortex. This winter has been characterized by a jet stream, part of the polar vortex, which has been unusually powerful. The origin of the problem is over the poles, where dramatic warming has taken place.

The warming has caused temperatures to rise at jet stream altitudes, and the whole polar vortex system has been displaced to the south. The end result has been frigid temperatures in the central and eastern U.S., snow and ice storms through the center of the country, and — unusual rain in the Pacific northwest.

What Is Typical March Weather In Seattle?

The average wind in Seattle is from the west, and this brings moist oceanic air to the city most of the winter. With a normal jet stream pattern, rain is produced on a regular basis, but rarely in copious amounts.

With this year’s enhanced jet stream flow, the storms were more powerful and the rains nearly biblical. The rain saturated the ground until mud began rolling down hills. That’s the weather side, but there is a math and physics side to the story also.

Angle of Repose of a Pile Of Stuff

If you dump a bag of flour on the floor, it will settle into a conical shape, The angle of repose is defined as the interior angle this cone makes with the floor.

Substances such as soil, gravel, sand, flour, and clay have characteristic angles of repose. Here are some sample angles of repose expressed in degrees:

  • Wheat flour: 45
  • Rock: 90
  • Ashes: 40
  • Dry sand: 34
  • Bark: 45
  • moist soil: 34

The Math And Physics Of A Pile Of Earth

The terrain involved in the Washington mudslides is a composite of many materials: soil, rock, organic matter, sand. No research has been done on the angle of repose of this sort of material amalgamation, but one would assume it has a correlation with the individual substances. Each hillside has a different mixture. Each hill has established a profile that is consistent with its angle of repose.

One of the simplest ways to change the angle of repose is to change moisture content. For substances such as sand or soil, the angle of repose initially increases as moisture is added — the ground becomes more stable. However, when the soil becomes completely saturated, the angle of repose decreases drastically. When enough water has fallen on susceptible places in hilly terrain, a mudslide will occur.

Angle of repose of sand and soil in degrees:

  • Dry sand: 34
  • Wet sand: 45
  • Saturated sand: 15
  • Moist soil: 34
  • Saturated soil: 26

A mudslide is simply the ground’s physical response to its having been saturated: The angle of repose readjusts to the new conditions.

Is This A Sign Of Global Warming?

No single event can be traced directly to man’s interference with the atmosphere. Rain happens, and this particular event could have occurred with or without climate change. But one thing is clear: this sort of event will become more common as the earth warms and the atmosphere is able to hold more moisture.

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