# Optical Depth

^^ptical depth (usually denoted r) gives a measure of how opaque a medium is to radiation passing through it. In the sense of planetary atmospheres, optical depth measures the degree to which atmospheric particles interact with light: Values of r less than one mean very little sunlight is scattered by atmospheric particles or has its energy absorbed by them, and so light passes through the atmosphere to the planetary surface. Values of r greater than one mean that much of the sunlight that strikes the planet's outer atmosphere is either absorbed or scattered by the atmosphere, and so does not reach the planet's surface. Values of r greater than one for planets other than Earth also mean that it is hard for observers to see that planet's surface using an optical telescope.

Optical depth measurements use the variable z, meaning height above the planet's surface into its atmosphere. In the planetary sciences, r is measured downward from the top of the atmosphere, and so r increases as z decreases, so that at the planet's surface, r is at its maximum, and z is zero. Each increment of r is written as dr. This is differential notation, used in calculus, meaning an infinitesimal change in r The equation for optical depth also uses the variable K (the Greek letter kappa) to stand for the opacity of the atmosphere, meaning the degree of light that can pass by the particular elemental makeup of the atmosphere. The Greek letter rho (p) stands for the density of the atmosphere, and dz, for infinitesimal change in z, height above the planet's surface.

Mathematical equations can be read just like English sentences. This one says, "Each tiny change in optical depth (dr) can be calculated by multiplying its tiny change in height (dz) by the density of the atmosphere and its opacity, and then changing the sign warmer lower atmosphere. The troposphere is thus always mixing, and its currents are wind, creating weather.

The difference in temperature between the polar regions and the equatorial regions drive winds, and therefore weather, just as it does on Earth. There seem to be large zonal winds that roughly correlate with the banded structure. They alternate in direction between prograde and retrograde, and are so strong that they alter the rotation of the planet: They average 350 miles per hour (150

of the result" (this sign change is just another way to say that optical depth t increases as z decreases; they are opposite in sign).

To measure the optical depth of the entire atmosphere, this equation can be used on each tiny increment of height (z) and the results summed (or calculus can be used to integrate the equation, creating a new equation that does all the summation in one step). Optical depth also helps explain why the Sun looks red at sunrise and sunset but white in the middle of the day. At sunrise and sunset the light from the Sun is passing horizontally through the atmosphere, and thus has the greatest distance to travel through the atmosphere to reach an observer's eyes. At midday the light from the Sun passes more or less straight from the top to the bottom of the atmosphere, which is a much shorter path through the atmosphere (and let us remember here that no one should ever look straight at the Sun, since the intensity of the light may damage their eyes).

Sunlight in the optical range consists of red, orange, yellow, green, blue, indigo, and violet light, in order from longest wavelength to shortest (for more information and explanations, see appendix 2, "Light, Wavelength, and Radiation"). Light is scattered when it strikes something larger than itself, like a piece of dust, a huge molecule, or a drop of water, no matter how tiny, and bounces off in another direction. Violet light is the type most likely to be scattered in different directions as it passes through the atmosphere because of its short wavelength, thereby being shot away from the observer's line of sight and maybe even back into space. Red light is the least likely to be scattered, and therefore the most likely to pass through the longest distances of atmosphere on Earth and reach the observer's eye. This is why at sunset and sunrise the Sun appears red: Red light is the color most able to pass through the atmosphere and be seen. The more dust and water in the atmosphere, the more scattering occurs, so the more blue light is scattered away and the more red light comes through, the redder the Sun and sunset or sunrise appear.

m/sec) in the cloud tops! The equatorial region of Jupiter makes one rotation in nine hours, 50 minutes and 30 seconds, while the midlatitudes rotate in nine hours, 55 minutes, and 40 seconds. These strong zonal winds appear to be fairly constant in their locations and strengths, since measurements made by Voyager and Galileo agree almost perfectly.

The probe from Galileo also measured high winds as deep as the 22-bar level.The probe corroborated the measurements of 270 miles per hour (120 m/sec) at the one-bar cloud level, and found that winds increase in speed to 380 miles per hour (170 m/sec) at five bars, and remain constant below five bars to the probe's final measuring depth at 22 bars. Finding stronger, constant winds at deeper depths is support for the theory that Jupiter's winds and banded structure are driven by internal convection and heat loss from the planet, rather than from solar input at the surface.

In addition to the strong and constant zonal winds, the Coriolis effect (the effect of movement on a rotating sphere; movements in the northern hemisphere curve to the right, while movements in the southern hemisphere curve to the left) creates winds of opposite directions north and south of each zone in the Jovian atmosphere, creating many eddies.There are several kinds of oval features on Jupiter's surface that correspond to cyclonic and anticyclonic eddies in Jupiter's atmosphere (anticyclone means an area of higher atmospheric pressure than its surroundings, and cyclone means an area of lower pressure; each creates vertical winds with circular wind patterns around them). The most prominent is the Great Red Spot, discussed in the section below.

In the North Equatorial Belt there is another kind of strong con-vective cell.These are called hot spots, because their peculiar atmospheric clarity allows more direct transmission of the great heat of Jupiter's interior to its surface. Despite the heat transmission upward, scientists think that hot spots are associated with strong downwelling winds. The downwelling winds are thought to be responsible for removing clouds from the hot spots by pushing the cloud layers to areas of higher temperature, where the cloud droplets vaporize back into the atmosphere.The hot spots' lack of clouds makes them dark in visible light, since it is Jupiter's clouds that best reflect visible light and thus shine to Earth-based observers. The hot spots are far more visible in the infrared, naturally, because of their anomalously high temperatures, and scientists on Earth have observed them since the first use of infrared astronomy (they were first reported by the California Institute of Technology scientist James A. Westphal, in 1969). Scientists inadvertently learned more about these North Equatorial Belt hot spots when the probe from Galileo flew straight into a hot spot, though that particular path had not been planned. Galileo's probe's measurements, then, are not necessarily characteristic of the rest of the planet.

If downwelling winds vaporize clouds, upwelling winds should produce even denser clouds, by moving warm gas to colder temperatures, where methane, water, and other volatile compounds will condense into droplets and form clouds. (This is the same process that creates drops of condensation on the outside of a cold glass of water: The cold glass conductively cools the surrounding air, and water that had been warm enough to form a vapor loses energy and condenses into a liquid.) Large, bright clouds in Jupiter's equatorial regions are thought to be the sites of upwellings. As might be expected in symmetrical convective cells, the clear downwellings and cloudy upwellings appear to form in pairs, and often are regularly spaced along the equator. Though the number of pairs changes over time, usually there are between nine and 13 pairs around Jupiter's equator.