Weather scales

Summary: Weather scales and tools are used to help measure and classify atmospheric conditions.

Weather affects virtually every aspect of human life, including afternoon showers that might inconvenience commuters; tremendously destructive episodes, like hurricanes; and long-term occurrences, like drought, which impact agriculture and increase the likelihood of other events like wildfires. Meteorology is an interdisciplinary science that focuses on weather and short-term forecasts, typically up to a few weeks. Climatology is a science that looks at long-term average weather. In fact, many define the word “climate” in terms of the average of weather over time, both locally and globally. Mathematics plays a critical role in weather science, enabling people to quantify, compare, model, and predict weather. Valid and reliable comparisons are facilitated by the development of scales and standard systems of quantification, along with mathematical and statistical models that use those measures.

It is thought that some ancient peoples had methods for predicting the weather, though historical evidence is mixed. In the early twentieth century, mathematician Vilhelm Bjerknes and colleagues examined several measurable variables of weather and derived equations to connect them to one another. Mathematician Lewis Richardson, who contributed significantly to mathematical weather prediction and pioneered the use of finite differences in the field, reformulated the Bjerknes equations. However, they remained impractical for rapid forecasting until the introduction of computers. Another product of his work, the Richardson number, is a function of density and velocity gradients that helps predict fluid turbulence in weather and other applications. Mathematicians continue to contribute and modern forecasting involves a wide variety of mathematical techniques and models, drawing in depth from such areas as chaos theory, data assimilation, statistical analyses, scale cascades of error (related to the so-called butterfly effect), numerical analysis, vectors, fluid dynamics, and entropy. Climatologists, scientists, and mathematicians also research related phenomena like geomagnetic and solar storms.

Temperature, Pressure, and Humidity

One of the most pervasive and intuitively obvious variables used to characterize the weather is air temperature—along with air pressure and humidity in most modern reports and forecasts. Strictly speaking, air temperature is a measure of the average kinetic energy of the air molecules, measured by a variety of types of thermometers. The most common scales used to quantify temperature are the Celsius (or centigrade) scale used throughout most of the world and the Fahrenheit scale used primarily in the United States. Atmospheric pressure is measured by a barometer, whose invention is attributed to various sources including Galileo Galilei and mathematicians Gasparo Berti and Evangelista Torricelli.

There are many common units for pressure, including inches of mercury, pounds per square inch, pascals, named for mathematician Blaise Pacsal, and atmospheres. One atmosphere is defined as the mean atmospheric pressure at mean sea level, originally measured with respect to the latitude of Paris, France. Millibars are often used in weather reports and forecasts. A hygrometer measures the amount of water vapor in the air. How much water vapor the air can hold is a function of temperature and relative humidity expresses the quantity of water vapor as a unitless fraction or percentage of the possible amount of water for a given temperature. Humidity can be used in probability models to predict precipitation, dew, and fog. Further, high humidity changes the subjective feeling of the air temperature for people because high humidity reduces the evaporation of sweat. This effect is quantified as a heat index, with assumptions about many variables such as wind speed, body mass, clothing, physical activity, and exposure to sunlight. A similar concept is wind chill, which relates the subjective perception of cold. Scientist Robert Steadman has researched and mathematically modeled both of these effects and they have become a common part of weather forecasts.

Wind

Another weather variable is wind speed. In 1805, Sir Francis Beaufort, an Irish hydrographer, developed what is now called the Beaufort scale to describe and categorize the strength of the wind. The scale has 13 points ranging from zero (calm air) to 12 (hurricane-force winds). On the scale, the Beaufort number two is identified as a “light breeze,” with wind speed 6–11 kilometers per hour (km/hr) producing wind that is felt on the face, leaves that rustle, movement of a wind vane, and on the water, small, short wavelets that do not break. Further along the scale is Beaufort number five, a “fresh breeze,” with wind speeds between 29 and 38 km/hr. At this point, small, leafy trees will sway, moderate waves become longer, and there are many whitecaps and some spray. Wind speeds between 62 and 74 km/hr are classified as a “gale,” Beaufort number eight. Twigs and small branches break off trees. At sea, there are moderately high waves of greater length. Beaufort number 10 is used when wind speeds are between 89 and 102 km/hr and are “storm-force” winds. Trees are broken and uprooted and structural damage occurs. At sea, there are very high waves with overhanging crests and visibility is reduced.

Table 1: Fujita scale of tornado strength.

The terms and descriptions make it clear that as wind speed rises so does its destructive power. In fact, the force exerted by wind increases as the square of the velocity such that a doubling of the wind’s velocity leads to a quadrupling of the force: f ~ V2. Some of the most powerful winds experienced on Earth are found in hurricanes and tornadoes. Their destructive power can be astounding and has been the subject of much study and research. The Fujita scale, presented in Table 1, is used to categorize tornado strength in terms of rotational wind speed (given in km/hr) and damage inflicted by the wind. While tornadoes are generally associated with severe thunderstorms and are seldom more than 1.5 km in diameter, hurricanes can involve whole systems of thunderstorms and may be several hundred kilometers in diameter. The Saffir–Simpson scale, used to categorize hurricanes, is presented in Table 2.

Table 2. Saffir-Simpson scale of hurricane strength.

<table><thead><tr><td>Scale Number</td><td>Wind Speed (km/hr)</td><td>Storm Surge (meters)</td><td>Central Pressure (millibars)</td><td>Damage</td></tr></thead><tbody><tr><td>1</td><td>121–154</td><td>1–2</td><td>≥980</td><td>Minimal</td></tr><tr><td>2</td><td>155–178</td><td>2–3</td><td>965–979</td><td>Moderate</td></tr><tr><td>3</td><td>179–210</td><td>3–4</td><td>945–964</td><td>Extensive</td></tr><tr><td>4</td><td>211–250</td><td>4–6</td><td>920–944</td><td>Extreme</td></tr><tr><td>5</td><td>>250</td><td>>6</td><td><920</td><td>Catastrophic</td></tr></tbody></table>

Bibliography

Ahrens, Donald C. Meteorology Today. Belmont, CA: Thompson Brooks/Cole, 2007.

Lynch, Peter. The Emergence of Numerical Weather Prediction: Richardson’s Dream. Cambridge, England: Cambridge University Press, 2006.

Moran, Joseph P., and Lewis W. Morgan. Meteorology: The Atmosphere and the Science of Weather. Edina, MN: Burgess Publishing, 1986.