Tuesday, August 14, 2007

Day, night, and the turn of seasons: Subtleties

Usually, we think of daily and seasonal variations in terms of the lower atmosphere, since that's where "weather" happens, as we understand it. But there are important cyclical variations in the upper atmosphere associated with the daily period of the Sun and the monthly cycle of the Moon. The important physical forces driving these changes are variations of gravity and the solar ultraviolet (UV) radiation introduced earlier as the key energy source that makes the upper atmosphere thermally and chemically different from the lower atmosphere.

The strongest gravitational force affecting both oceans and air is that of the Earth. It's almost perfectly spherically symmetric in its influence, and its pulls solid earth, ocean water, and atmospheric air into almost perfect spheres (isostasis). But the Sun and the Moon also exert significant gravitational influence on the Earth - about equally, actually.* The influence manifests itself in modifying the Earth's overall motion, but also differentially, in the sense that the Moon and Sun are a little closer or a little farther away from the Earth's surface, depending on the time of day and month. It's this difference of gravitational pulls between near side and far side of the Earth (as seen respectively by the Sun and the Moon) that gives rise to ocean tides. The tides are complicated by the presence of two bodies acting with two characteristic periods: day and month.

While the ocean tides are the most obvious consequence of differential gravity (tidal forces), the solid earth and the atmosphere also experience the same differential pulls. Solid earth doesn't bend as much under the same tidal forces, but tides can influence cracks in the solid and trigger earthquakes. The atmosphere also gets pulled into a ellipsoidal (football) shape, just the like the oceans. Gravity doesn't care about the distinction of upper and lower atmosphere, and in fact, tidal variations are largest in the upper atmosphere. But there is some detectable tidal effect all the way down to the surface. We can integrate the hydrostatic equilibrium condition [slope of pressure = -density*(gravitational acceleration)] from the surface to the top (where the pressure is very small) for an atmospheric column of cross-sectional area A and mass M,
   P(surface) = P(top) + (gM/A) ,
assuming g is constant with altitude. Over the course of a day or a month, M is assumed not to change, even if the distribution of mass (given by the density as a function of altitude) does change. The resulting gravitational tidal variations in pressure are about one part in 10,000.

The Sun has another effect in this connection. Earlier, the ultraviolet part of the insolation that's captured by the upper atmosphere was treated as constant. Of course, it varies over the day and contributes an additional expansive and heating effect on the upper atmosphere. Late at night, the effect is subdued. Thus the full phenomenon of atmospheric tides is a result of tidal forces from the Sun and the Moon, with the Sun having an additional daily effect of pumping UV radiation into the upper atmosphere during daylight hours. This pressure variation is actually much larger than the gravitational effect, about 15 parts in 10,000.

The Sun's UV output is strongly modulated by another cycle so far unmentioned, the solar magnetic cycle. Unlike orbital motion, this cycle is not exactly periodic, but has a varying period ranging from 9 to 11 years. The UV effect on the Earth's upper atmosphere itself varies not only by day, but also over the heliomagnetic cycle. It's impossible to say, without a detailed understanding of heat transport in the upper atmosphere, what the parallel temperature variations will be exactly. But naively we expect a range roughly the same relative size, about 1-2 parts per 1000, or about (1-2)(300 oK)/1000 = 0.3-0.6 oC.**

The simple binary contrast of day and night might lead to the conclusion that climate is symmetric between the two. In some ways, it is. But overall, day and night are asymmetric.

The Sun is the energy source for climate. The most basic asymmetry is the difference between day and night: the presence or absence of the Sun. For half the day, light is flowing in as heat flows out; for the other half, only heat flows out.

A more subtle but important asymmetry is associated with clouds. Crudely speaking, clouds block out light by day (by upward reflection), but hold in heat at night (by absorption and downward re-emission). But they provide efficient convective upward heat transport both day and night. Overall, putting day and night together, the net effect of clouds is cooling.

Gravity is symmetric in its tidal effects between nighttime and daytimes sides of the Earth. But the UV enhancement of upper atmospheric tides happens only by day. So its impact on surface pressure and temperature is mainly a daytime effect.
* The Moon is 1/81 the mass of the Earth; the Sun is much farther away, but its much larger mass almost exactly compensates for its larger distance. The two bodies end up exerting almost equal gravitational pulls on the Earth. For that reason, the Earth-Moon system is really a double-planet system.

** The atmospheric gravitational tides are a simple prediction of Newtonian gravity and were first measured in the 19th century. But the larger solar effect was not fully understood at the time, since UV radiation was just being discovered and the nature of atomic and molecular absorption had barely been guessed at. It wasn't until the 1960s that this mystery was fully unraveled.

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