Saturday, May 11, 2013

Weather Math

Each morning brings gifts from God in many facets. Our ability to become a non-professional atmospheric scientist while expending minimal time in formal preparation is one of those gifts. Expressed another way, everyone can be an armchair weather observer. Weather statistics are often part of our observations. One of the first questions to be answered each morning is, “What is the temperature?"  Meteorology is one of several science topics for which I discovered an early fascination. Its reality is effortlessly accessible whether we are indoors or outdoors. Weather events provide a ready-made topic of conversation, supply opportunity to hone observational skills, and supply occasion for light-hearted commentary.

A few of my former class members may have become professional
meteorologists because of their early fascination with the weather. Perhaps they were captivated by the thermographs and barographs we used to automatically record temperatures and barometer readings a week at a time on revolving drums with an ink stylus. One of my former students possessed a truly unique fascination with weather. I still have a vivid memory of Kevin passing my room and poking his head into my open classroom doorway while we were watching Weather Channel radar images approaching a few miles to our west. Kevin made no secret of his love for weather topics. Another embedded memory occurred when huge, golf-ball sized snowflakes began to fall during one science class. “Quickly, put on your coats…I’ll meet you all just outside the exit door downstairs.” The flakes were easily “catchable” in the students’ mouths. It became an impromptu recess. The next day’s newspaper carried accounts of the event. One student gratefully reminded me of that incident several times before the school year ended.

Rarely some of my students would complain that they found a certain activity “boring.” Sometimes this related to the mathematics necessary to quantify their science discoveries. I developed an appropriate comeback for this common lament. I asked them “Are you boring?” The effect of my question was somewhat curative. In the long run, young people need to learn the fascination inherent in more ordinary things and events surrounding them. With thoughtful engagement, perhaps our children could learn that even mundane events deserve a share of their attention. Mathematical skills may hold some degree of fascination even for students and adults who avow dislike for math. Teachers and parents should work in tandem to help young people discover interest-inspiring activities in everyday situations. This idealized goal is achievable, but young and old must work at their objective.

Most adults may not fully understand certain regularly used weather terms. We refer to humidity--the water vapor present in the air. The air surrounding us includes water in vapor form. “Absolute humidity” relates to the ratio of mass of water vapor/m3 of air. At maximum, air holds just a few grams of water vapor/m3 of air. One m3 of air has a mass of approximately 1.3 kg. The percentage of water vapor in air varies between 0% and 4%, generally on the lower end of this range. Usually, the 1.3 kg of air/m3 (1300 g, or 2.86 lb) contains only a few grams of water vapor, perhaps 30g at maximum. These terms and statistics, however, are never part of our friendly television weather journalist’s forecast for laypersons.

Another term and related statistic is commonly used by media forecasters--relative humidity. To understand this common weather forecaster’s term, we must dig somewhat deeper. To illustrate the meaning of relative humidity, let’s pretend we take an exam with one hundred questions. Classroom test scores are usually converted to percentage, meaning per hundred. If we answer 75 correctly, our score is 75%.  Likewise, on a 20 question test, our score for 15 correct would also be converted to a percentage score of 75%.

When the local forecaster reports the relative humidity as 75%, he means that at the present temperature, the air contains 75% of the amount of water vapor necessary to saturate the air. The percentage is calculated by dividing the numerator (actual quantity) by the denominator (possible quantity). The key is understanding the meaning of “at the present temperature,” because when the temperature becomes warmer or cooler, the carrying capacity of air in terms of how much water vapor could be present also changes. Warm air is able to “hold” more water vapor than cold air; cold air is able to hold less. (Some writers object to the term “hold” in this context. Older books use the term as a conceptual aid.) A useful analogy is possible using a porous sponge. When it contains 75% of the water necessary to saturate it, we see that it could hold a little more. In the case of this sponge, if we fill it to 100% of capacity and try to add more, some liquid water will not be able to enter the sponge. It is 100% full. Another way to expel water is to reduce the carrying capacity of the sponge by squeezing it into a smaller volume. Squeezing the sponge reduces its carrying capacity, but it may still be regarded as 100% full.

In connection with the previous paragraph, we cite one more intriguing fact about relative humidity. A graphic representation of relative humidity over 24 hours almost always shows the relative humidity in the warmest part of the day is lowest. It is highest in the coolest hours around dawn. This phenomenon relates most closely to the carrying capacity of warm air (highest) and cool air (lowest). The actual amount of water vapor remains the same, but the temperature changes. Over a few days, additional water vapor could be added or subtracted to the air by arrival of distant air masses. The relative humidity could rise or fall, but for a different reason. Relative humidity would rise if the fraction’s numerator increases; it would fall if the denominator increases.

Perhaps readers have discovered more about weather math than they wanted to know. Mathematics is a divine gift which helps God’s children make sense of the world. We recognize greater or lesser mathematical gifts in every human. The world is more comprehensible through application of mathematics. Our ability to rationally quantify our world’s phenomena helps us understand the world as an orderly place because of our inherent mathematical aptitude. God created an orderly cosmos which reflects his character. Our earliest morning thoughts should include recognition of God as Creator of an ordered cosmos.