Global Warming VS. the Greenhouse Effect

Global warming posits the questions “will an increase in concentration of greenhouse gases lead to an increased global average temperature?” Whereas, the greenhouse effect is a fact that states that the average global temperature is warmer than it would be in the absence of an atmosphere due to greenhouse gases that are being absorbed and re-radiated.

Incoming shortwave (visible light and infrared) radiation gets absorbed by the Earth thus causing the ground to heat and emit longwave (infrared) radiation. The longwave radiation, then, gets absorbed by greenhouse gases (CO2, H2O, CH4) which, in turn, heats up and re-emits radiation out in every direction (some towards the Earth). Notably the cycle continues when some of that radiation, again, gets absorbed by the ground, heats the ground even more, emits even more radiation, and so on.

Geostrophic Wind (and Equations)

Geostrophic Wind is a nonaccelerating flow occurring only in the upper atmosphere (due to the lack of friction) and when the winds are considered at “steady-state” (when the PGF counterbalances the CF). In fact the geostrophic flow is simply a special case of gradient flow that arises when the wind flows parallel to the isobars.

Energy Cascade

Atmospheric waves may develop in layers of strong vertical wind shear. Like ocean waves, these too amplify and break generating smaller scale waves and eddies that become unstable (wave breaking). Through this progression of instabilities, kinetic energy may be extracted from the large-scale wind field, giving rise to a variety of small-scale motions that extend down the molecular scale—a process that inspired Richardson’s rhyme and resembles that of an energy cascade.

Energy cascades transfer energy from large (or small) scales of motion to the small (or large) scales. As indicated by the “drop in the bucket,” kinetic energy in the reservoir is transferred to smaller and smaller scales until it becomes indistinguishable from random molecular motions, becoming incorporated into the atmosphere’s reservoir of internal energy.

Conservation of Angular Momentum (Derivation of the Coriolis Force)

Angular Momentum takes into account the rotation of the object. Whereas, the conservation of angular momentum is a law of physics that states the angular momentum of a rotating object (with no outside force) remains constant regardless of changes within the system (i.e. Earth’s rotation Ω). This conservation of angular momentum will always be maintained as long as there is no net external torque acting on the object or on the system itself.

Example: Derive the Coriolis Force.

Chinook, Santa Ana and Katabatic Winds

Chinook, Santa Ana and Katabatic winds are those that flow downslope in response to the distribution of high- and low-pressure systems over and near large mountain areas, where compressing of descending air leads to adiabatic warming.

Chinook winds, off the eastern slopes of the Rocky Mountains in North America, form due to air flowing across the range. Low-pressure systems east of the mountains cause strong winds to descend the eastern slopes. Although, sometimes the presence of a large mass of cold, dense air near the base of the mountain range may prevent a chinook from flowing all the way down the slope.

Santa Ana winds, contrary to what people believe, occur in response to a large area of high-pressure which descends toward lower elevations and warms by compression causing air to flow out of the Rockies, they are not warm because they pass over hot desert surfaces. When Santa Ana’s develop, the combination of hot, dry winds, low humidity, and an abundant source of fuel can set the stage for an extensive fire that destroys a great deal of land or property.

            Katabatic winds, on the other hand, originate when air is locally chilled over a high-elevation plateau, where the air becomes dense due to its low temperature and flow downslope. These very strong gusts and lulls of winds cover much of coastal Antarctica and Greenland. They also flow out of the Balkan Mountains towards the Adriatic coast, where they are called boras; whereas, in France, they flow out of the Alps into the Rhone River Valley and are called mistrals.

Buys-Ballot Law

In the Northern Hemisphere, with the wind at your back, low pressure is to your left (and high pressure is to your right) because winds travel counterclockwise (cyclonic) around low pressure zones, again, in the Northern Hemisphere.

The Bergeron Process

The Bergeron process relies primarily on the fact that the saturation vapor pressure with respect to ice is less than the saturation vapor pressure with respect to water. Pure water droplets do not freeze at 0°C due to surface tension and the structure of water, thus in order to get a pure water droplet to freeze, it will require a temperature of -40°C.

Liquid water that is cooler than 0°C is considered supercooled. In the atmosphere, similar to cloud condensation nuclei (CCN), there exist freezing nuclei. Most of these freezing nuclei "activate" at about -10°C, which allows the cloud droplets to freeze around them. Due to the relative sparseness of the freezing nuclei, ice crystals and supercooled water droplets can coexist at the same time when the temperature is between -10°C and -40°C. This is where Bergeron's primary fact becomes important, when air reaches saturation, some of the resulting droplets will come in contact with the freezing nuclei.

From the perspective of the supercooled water droplets, the air is considered at equilibrium (saturation). Whereas, for the ice crystals, the air is considered supersaturated; when water vapor deposits onto ice crystals (deposition), thus decreasing the amount of water vapor in the air. But, for the supercooled water droplets, the air is now considered subsaturated, resulting in evaporation of droplets until the air is, once again, at saturation. This cycle, the Bergeron process (in cool clouds), continues to result in the growth of the ice crystals by deposition (or sublimation) at the expense of water droplets.

To summarize, when a cloud extends or is entirely above the 0°C isotherm, it is considered a cold cloud. In such clouds, ice crystals grow at the expense of supercooled water droplets. If vapor pressure is such that water droplets have an equilibrium that is between evaporation and condensation, then there will be excess of deposition over sublimation for ice crystals. Thus, ice crystals grow by deposition of water vapor, but that removes the water vapor from the air, which causes the water droplets to become smaller. Eventually, allowing the ice crystals to become large enough to fall from the cloud. This process causes ice crystals to take on platelike or prismlike shapes. Changes in these shapes correlate to air temperature and supersaturations. So, the shapes of ice crystals may be altered while they experience environmental changes falling through the cloud.

Coriolis Force Motion on a Latitudinal Circle

Coriolis Force—the force per unit mass that results from the rotation of the earth and acts on a moving particle with respect to the earth to deviate it.

•      Perpendicular to the axis of rotation and the velocity vector.
•      Directed to the right (in the Northern Hemisphere) and radially outward from the axis of rotation. 
•      Can only change direction, not magnitude.

Components of the Coriolis force (CF) due to relative motion along a latitude circle. Ra is the apparent radius, Re is the radius of the earth., and omega is Earth's rotational frequency.

Back Basics: Managing Spine and Disk Problems with Self-Care

Calculus I -- Chapter 1

Calculus I -- Chapter 2