Temperature inversions in theory and in Pittsburgh

I recently read Tony Sadar’s Quick Study, “Waking up to temperature inversions” (Physics Today, October 2018, page 74 ). I write to clarify a couple of points that could be misunderstood, and I have an important and interesting addition about the way that inversions form around Pittsburgh, Pennsylvania.

The Quick Study’s figure 1 could be read as indicating that sunlight intensity increases linearly from zero at 6 am to a maximum at solar noon and then decreases linearly to zero at 6 pm. In fact, sunlight intensity is not linear through the day; it follows a sine function from sunrise to sunset.

Similarly, the plot should not be understood as saying that temperature rises and falls linearly. To a first approximation, air temperature near Earth’s surface follows a sine curve from a minimum temperature near sunrise to a maximum temperature two hours after solar noon and declines along the sine curve until sunset. After sunset, air temperature falls exponentially to a minimum near sunrise.

I would also like to mention an important part of inversion formation in complex terrain. A hilltop cools much faster than the valley floor, and as a result, cooler, denser air flows downhill and into the valley. Cooler air pooling in the valley undercuts warmer air and creates an inversion, as shown in panel c in the Quick Study’s figure 2. As Sadar notes, Pittsburgh is surrounded by hilly environs.