Monday, August 13, 2007

Day, night, and the turn of seasons: Basics

So far, most of the climate postings here have been about a cartoon of real climate, an "average" world of spring and fall, early morning and early evening. Real climate is not like this; it's a chaotic system always varying, although remaining within a "band." As a rule, averaging climate, especially in space, is not legitimate; it's better to think of this "band" or range as "climate," rather than any average.

Averaging in time is justified, if the average is taken over a fixed time period fundamentally independent of the climate dynamics. Daily and yearly averages, over 24 hours and 365 days, respectively, are the most basic climate averages.* These periods are properties of Earth's orbit and revolution having nothing to do with climate. They do influence climate, of course, but climate doesn't influence them. They're autonomous properties of the Earth that can be taken as independent clocks. Their influence on climate is obvious if you analyze climate variations in time, with the possibility of an infinite spectrum of such periods. The daily and annual cycles are almost always the strongest signals resulting from such an analysis.**

A time average of a function of time f(t) over a period T is: av(f, T)tt+T dt f(t)/T .

We're all familiar with many of the changes associated with these periods, the cycle of day and night, and the cycle of seasons. The Earth's axis is titled with respect to its orbital plane (by about 23.5o) and the plane of the Sun's motion through the sky (ecliptic). The tilt is fixed with respect to the distant stars, but not with respect to the Sun. As the Earth orbits the Sun over a year, the Sun's daily orbit through the sky changes its angle relative to vertical, depending on latitude. These changes affect the insolation the Earth's atmosphere and surface receive. And the insolation changes over the course of the day, reaching its maximum at local noon and its minimum at local midnight. Because of the lag of hours, these are not the hottest and coolest times of the day. The land, water, and air take time to respond to the inflow of heat. The hottest and coolest times are typically 4 hours after noon and about 4 hours after midnight, respectively. The annual insolation variation reaches its maximum at summer solistice (June 21) and minimum at winter solistice (December 21). The lag of seasons means that the hottest and coldest times of year come about 8 weeks afterwards; mid-August and mid-February, respectively.

While the daily variation of insolation would happen regardless of Earth axis tilt (unless the tilt were 90o), the exact variation by season depends strongly on the tilt. In fact, seasons wouldn't occur at all without tilt, and the tilt creates a connection between geographic latitude and seasonal variation that doesn't exist for daily variation. Not surprisingly, the mildest annual variations are experienced by the tropical latitudes. They get the most insolation over the course of the year. The largest relative variation occurs in the polar regions, and they receive the least insolation over the year. The surface inside the polar circles (the latitudes around the poles within the tilt value of 23.5o) go through 6 months of the year with no sunlight. Within the polar circles, night=winter and day=summer.

Other differences between day and night are coupled to differences between land and sea, or land and air, or sea and air. The switching of convection, temperature inversion, and evaporation between day and night was mentioned earlier. By day, the surface layer of atmosphere over water exhibits a temperature inversion connected to a downward heat flow that supports evaporation; while over land, the air exhibits a steep temperature lapse rate that supports strong upward convection. This difference is the source of cooler daytime air temperatures over water and the formation of summer thunderstorms over land. By night, the situation is reversed. Over water, the temperature inversion switches to a strong lapse rate that supports a strong upward heat convection that cools the ocean off. (Water cools off more slowly than air.) The land experiences a temperature inversion in the surface air layer, as the ground cools off more quickly than does air. Nighttime air temperatures over water are higher than over land. These differences in heat flow and temperature explain the cycle of winds on the coast: landward (ocean breeze) by day, seaward (land breeze) by night.

The next two climate postings will take a closer look at the consequences of these cyclical variations, both in terms of "normal" climate and as focal points for understanding what happens if the atmosphere accumulates more infrared (IR)-active gases (water vapor, carbon dioxide, methane) and acquires a larger IR opacity.

POSTSCRIPT: The peculiar persistence of molecular oxygen (O2) in the atmosphere was mentioned earlier. It seems every number and every molecule gets its own book these days. Thus oxygen gets Nick Lane's fine if curious Oxygen: The Molecule That Made the World.
* We could also consider the lunar month (29.54 days) as an another fundamental astronomical cycle. But the Moon's light, reflected from the Sun, is not a significant energy source for the Earth's climate. The Moon does influence the tides of both oceans and atmosphere.

** A branch of mathematical physics called Fourier analysis does just that: break complex motions down into a sum of simple cyclical motions, each with a different period. In general, there are an infinite number of such periods; the relative strength of each period's contribution to the motion is called the Fourier or frequency spectrum of the motion. Future postings will introduce Fourier analysis as a tool for breaking down complex time evolution into simple parts, while also emphasizing the limitations of Fourier analysis if the motion is chaotic.

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