## Is mathematical pi used in meteorology?

The ratio of a circle’s circumference to its diameter is a constant value. The size of the circle does not matter; this ratio is always the same value and is called pi.

The existence of this constant was known by the Babylonians and the Egyptians dating back to at least 2000 B.C. The numerical value is represented by the Greek letter for p, or π.

The first three digits of pi are 3.14, so today — March 14 — is often celebrated as pi day with pie. The value of π turns out to be an irrational number: Its decimal form neither ends nor becomes repetitive. The exact value is unknowable. About a decade ago, a researcher calculated the value to 2.7 trillion digits.

You might have first encountered pi in early classes on geometry or trigonometry. You learned that pi, along with the radius, is used to calculate the circumference of a circle, the area of a circle or the volume of a sphere. Since cloud droplets are near spherical, pi is used to calculation how much water is in a cloud knowing the number and size of the drops.

Because of pi’s relationship to the circle and to spherical coordinate systems, it appears in many formulas in many areas of mathematics and physics. Meteorology is a physical science, steeped in math, so we inevitably encounter pi.

Pi appears in the field of electromagnetics, which is used to describe how light travels through the atmosphere. It is used in equations that describe why the sky is blue.

Pi appears in equations describing processes that are periodic, and therefore is intimately associated with waves. Atmospheric patterns and the movement of the winds can be described as waves. So, pi appears in mathematical equations that describe the movement of weather systems. The waviness pattern of the jet stream can be described by its “meandering ratio,” which includes the value of pi.

A world without pi, and pie, would be very different.

Steve Ackerman and Jonathan Martin, professors in the UW-Madison department of atmospheric and oceanic sciences, are guests on WHA radio (970 AM) at 11:45 a.m. the last Monday of each month. Send them your questions at stevea@ssec.wisc.edu or jemarti1@wisc.edu.

Category: History, Meteorology

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## Is Wisconsin getting windier?

Before we delve into the question of whether Wisconsin is getting windier, let’s review some basics regarding wind.

Wind is moving air. Weather reports include observations of wind speed and direction measured at the height of 10 meters (33 feet) above the surface. If the wind speed is strong — greater than 17 mph — and highly variable, the weather report will include the wind gust, which is the maximum observed wind speed.

Wind direction is the direction from which the wind is blowing. A north wind blows from the north toward the south.

One way to answer the windier question is to average the wind speed measured over a city over a year, and so determine the annual wind speed. The change in the annual wind speed over a long period of time indicates the long-term trend in wind speed.

Madison has a record of wind speed observations dating back to 1948. The accompanying graph shows the annual average wind speed for Madison for a given year. The trend is decreasing wind speed over this time period. So, Madison is getting less windy with time.

Observations at Milwaukee also go back to 1948 and show a decreasing trend as well. The wind speed at Eau Claire also has trended slower since 1960s. There is no clear trend for the city of La Crosse.

If we calculate an average wind speed over each month for the entire time period of 1948-2022, we find that the month of April is the windiest with an average wind speed of 11.4 mph. The March average wind speed is 11.3 mph, greater than the February mean of 10.4 mph.

So, with respect to the monthly mean wind speed, March is windier than February and April is windier than March in Madison. After April, the monthly mean wind speed declines. The lowest monthly mean occurs in August, with 7.0 mph.

Steve Ackerman and Jonathan Martin, professors in the UW-Madison department of atmospheric and oceanic sciences, are guests on WHA radio (970 AM) at 11:45 a.m. the last Monday of each month. Send them your questions at stevea@ssec.wisc.edu or jemarti1@wisc.edu.

Category: Climate, Meteorology

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## How are we doing for snowfall this season?

Despite the persistence of snow and ice on the ground this winter, since our first real covering appeared just after Christmas Day, it has been a remarkably snowless winter thus far.

After Thursday night’s 2.7-inch snowfall, the season total for Madison rose to a paltry 21.4 inches, which places us well behind the average for the season to this point, which is 41.3 inches.

Just how unusual is this amount?

It turns out that about 25% of the time a winter season accumulates less than 30 inches of snow in Madison. In 138 seasons, dating back to 1884-85, Madison has had only 33 winters in which the total snowfall remained below that threshold — the last one of those was 2002-03, when only 28.8 inches accumulated.

Thirteen seasons have received less than 25 inches of snow, the last one being 1967-68, when only 12.7 inches fell. That season was the most recent of only five seasons in which less than 20 inches of snow fell in a season — the other four were 1933-34, 1913-14, 1901-02 and 1894-95. Of those five, the all-time least snowy winter was 1901-02 when, unbelievably, only 4 inches accumulated for the season.

Since 7 inches of snow falls in Madison in an average March, we will have to have a snowier than normal March to move past 30 inches of snow for this season.

Though it is subject to substantial revision, the forecast for the coming first two weeks of March does suggest the possibility of a couple of sizable snowfalls that just might rescue us from landing on this list of exceptionally boring winters.

Steve Ackerman and Jonathan Martin, professors in the UW-Madison department of atmospheric and oceanic sciences, are guests on WHA radio (970 AM) at 11:45 a.m. the last Monday of each month. Send them your questions at stevea@ssec.wisc.edu or jemarti1@wisc.edu.

Category: Climate, Meteorology, Seasons

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## How did the Tonga eruption affect the atmosphere?

Hunga Tonga erupted on Jan. 15 and lasted 11 hours.

It devastated the region, covering the land in a layer of ash. The eruption blasted a plume of ash and water vapor 34 miles into the atmosphere — into the mesosphere.

The Hunga Tonga plume contained only a very small amount of sulfur dioxide (SO2). Sulfur dioxide from volcanic mega-eruptions that reach high in the atmosphere can have an impact on global temperature. The mega-eruption of Pinatubo in 1991 released enough sulfur dioxide to cool the Earth’s surface for three years. The Tonga eruption will not have that kind of impact.

Lightning is common with volcanic eruptions. The turbulence in the eruption plume makes particles of ash and water collide to rub together, generating electrical charges that lead to lightning. Hunga Tonga was no exception, producing nearly 400,000 lightning strikes.

The shockwave from the eruption caused an atmospheric pressure wave that traveled around the globe. It was measured at weather stations around the world. The pressure wave circumnavigated the globe at nearly 700 mph. Associated with the pressure wave were short-lived upward motions that generated thin clouds observed at Hawaii. Satellite observations measured temperature fluctuations in the upper troposphere and lower stratosphere that accompanied the pressure wave.

The atmospheric pressure wave also pushed water all the way to Puerto Rico. This resulting wave, measuring about 4 inches in height, resulted from the atmospheric pressure wave and is referred to as a meteotsunami. Tsunamis are triggered by seismic activity; water waves driven by air pressure disturbances are called meteotsunamis.

Steve Ackerman and Jonathan Martin, professors in the UW-Madison department of atmospheric and oceanic sciences, are guests on WHA radio (970 AM) at 11:45 a.m. the last Monday of each month. Send them your questions at stevea@ssec.wisc.edu or jemarti1@wisc.edu.

Category: Climate, Phenomena

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## When was the National Weather Service created?

While successfully prosecuting the Civil War against the Confederacy, Gen. Ulysses S. Grant had learned that weather information — even if not in the form of a forecast — was extremely valuable for operations.

Then, in the years after the war, Dr. Increase Lapham, a Milwaukee scientist, lobbied Milwaukee’s congressman, Gen. Halbert Paine, to push for the establishment of a storm warning service for the Great Lakes. On Feb. 2, 1870, Paine introduced a Joint Congressional Resolution requiring the Secretary of War “to provide for taking meteorological observations at the military stations in the interior of the continent, and at other points in the States and Territories … and for giving notice on the northern lakes and on the seacoast, by magnetic telegraph and marine signals, of the approach and force of storms.”

On Feb. 9, 1870 — 152 years ago last week — a sympathetic President Ulysses S. Grant signed the resolution into law and what is now known as the National Weather Service was born. Thus, the service began its life within the U.S. Army Signal Service’s Division of Telegrams and Reports for the Benefit of Commerce.

Observations officially began on Nov. 1, 1870. Exactly a week later, on Nov. 8, Lapham issued the service’s first storm warning on the approach of a storm over Lake Michigan.

On Oct. 1, 1890, at the request of President Benjamin Harrison, Congress passed a law transferring the meteorological responsibilities of the Signal Service to the newly created U.S. Weather Bureau, which was housed in the Department of Agriculture. The Weather Bureau became the National Weather Service in 1970 with the creation of the National Oceanic and Atmospheric Administration, or NOAA.

Steve Ackerman and Jonathan Martin, professors in the UW-Madison department of atmospheric and oceanic sciences, are guests on WHA radio (970 AM) at 11:45 a.m. the last Monday of each month. Send them your questions at stevea@ssec.wisc.edu or jemarti1@wisc.edu.

Category: History, Meteorology

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