Be not afraid! No knowledge of math is required for this week’s weather moment.
The geostrophic approximation is one of the most fundamental equations when it comes to weather and the artistic science of forecasting the weather. Despite looking complicated, it is very simple with regards to what it actually means.
- ∂p/∂(x/y) refers simply to how quickly the pressure changes from West to East or North to South. This is known as the pressure gradient.
- ρ is the density of the air
- f is the Coriolis parameter
- v is the speed of movement
I’ll quickly go over what each of these are.
The Pressure
The pressure is simply a measure of the force the atmosphere exerts at a specific point. The most common pressure is MSLP, or mean sea-level pressure (which is always the “ground-level” pressure). It is what most of us see when we see the evening weather report on the news. This value is in reality a measure of the mass of the atmosphere. A higher pressure means you physically have more mass pressing down on a particular location. We can get a pressure from anywhere in the atmosphere. If we take it from some height above the ground, it is lower than what the MSLP is beneath it, since there is less air above that point than beneath it.
The Density
The density of air is the amount of mass in a cubic meter of it. This value pretty much never changes, except when moving up and down through the atmosphere.
The Coriolis Parameter
The Coriolis Parameter is a measure of the Coriolis Force, or the apparent curvature that shows up in atmospheric motions due to the earth spinning beneath it. The key thing to take away here is that it is only dependent on how far away from the equator the moving air is. The further towards the poles, the bigger the Coriolis Parameter
The Velocity
This is very simple, it is a measure of how fast the air is moving. This is essentially how fast the wind is.
What It All Means
The geostrophic approximation is based on a few basic assumptions:
- The Coriolis Force balances the horizontal pressure gradients
- The flow has no acceleration (the wind speed does not change)
- Horizontal velocites are much larger than vertical velocities
- The only external force is gravity
- The effects of friction are negligible
So what does this tell us? If we look at the first two equations for movements North/South or West/East, we can simplify them with everything we now know. We’ve said that density doesn’t change, and that the Coriolis force only depends on how close to the poles you are.
So, for any given point at any given time, we can simplify all this down to saying that the wind speed, v, is equal to the pressure gradient. Very simple, and very easy to understand. It is this basic principle that lets the weatherman on T.V. explain to you that as the back lines (of constant pressure, or isobars) become squished together, the winds will be faster. And as they become wider spaced, the wind speeds will die down.
If these black lines were isobars, we would see fast winds on the left-hand side, where they are bunched together, and slower winds where they are spaced further apart.
While what happens in the areas where we live (namely, the ground), are influenced by the fact that friction plays an important role, the general idea of the geostrophic approximation still holds. With this knowledge, you should be able to look at a surface map of Canada and the Northern US and very quickly determine if it will be windy wherever you’re interested. I’ll attach a surface map pointing out where, by using this simple theory, we can tell where winds may be a concern.
Next week, separating the upper atmosphere from the boundary layer.
Low pressure systems are the “engine” that drive weather. They are what interact with warm and cold fronts, and they function to convert and dissipate the energy stored within the fronts. These systems have a “traditional” or “classical” progression that can be observed.
Frontal Wave
The first sign of the development of a low pressure system is the appearance of a frontal wave. This is a slight bend in an area of high thermal contrast. This is the beginnings of the warm and cold fronts.
Surface Low Appearance
As the wave tightens, and the cold front becomes more perpendicular to the warm front, the low pressure center appears on the inflection point of the warm and cold fronts (where the two fronts attach to each other). The low will then move with the mean flow aloft, following the troughs of upper-level waves (more on that later). As the low moves, the fronts move along with it. And naturally, the weather associated with those fronts moves along as well.
Mature Low
A satellite image depicting a mature low pressure system. The cold front is represented by the blue line, the warm front by the red line, and the trowel by the blue/red half-arrows. The center of the low circulation is marked by the large L.
One funny characteristics of cold fronts is that they are often faster moving that warm fronts. This can result in the warm front moving “along” the warm front and lifting the warm air up. This is called an occlusion process. The warm air aloft then is pulled towards the low and around it, rising in height. This warm air aloft is called an occlusion, or more frequently today, a trowel.
A mature low will have 4 distinct areas and kinds of precipitation: warm front precipitation, cold front precipitation, occlusion/trowel precipitation, and “wrap around” precipitation. Wrap-around precipitation is the weather that occurs in extremely close proximity.
Low Dissipation
Eventually, the warm and cold fronts pull themselves off the low pressure system. It can be likened that the “gas” for a low pressure system is the temperature contrast present in the fronts. When the fronts leave the low, warm air wraps around it and soon there is no more sharp temperature contrasts. When this happens, the low will “fill in” and dissipate.
Why Is It Called A Low Pressure System?
When a low pressure system begins to form, air is pulled in towards the center of it. We have discovered that, more or less, air in the atmosphere doesn’t like to compress. So instead of compressing as all this air meets in one place, it pushes air upwards. This creates a circulation where air moves in towards the low at the surface, rises some height, then flows out and away from the low. This results in low pressure near the surface, where the air is rising, and higher pressure somewhere above, where the air is moving outwards. Thus, a low pressure system is called such because the surface pressure is actually lower than the areas around it. As it “dies,” the surface pressure will return to the normal pressure around the low.
I should mention that this is an extremely brief overview of low pressure systems. If you would like to learn more, there are entire books written on the subject, and to this day it is still an area of active research.
Next week, land and sea breezes!
Filed under: Cold Front, Convection, Precipitation Events, Synoptic Features, Thermodynamics
The weather effects each of us, every day. A lot of people have expressed to me interest in learning about the weather, but it’s definitely not easy. I’ve decided that each week, I’ll post a short-ish post explaining the basics of various weather phenomenon; this week: The Cold Front.
For many people, cold fronts are one of the most noticable weather events out there. They are fast moving features that often produce severe weather and result in drastically different weather after they have passed through.
Formation
All over the globe, air has a tendency to form into large areas with similar characteristics. We call these air masses. One example is could be a large area where it is hot and humid. In the wintertime, often there are extremely large areas of cold, dry air. These air masses move through the atmosphere, and fronts are developed. A cold front is the boundary on the leading edge of colder air moving into warmer air. It does not matter how cold the cold air mass is or how hot the hot air mass is, as long as they have a temperature difference, the cold front will form.
Structure
Cold fronts have a very defined structure that is based on a simple physical principle: density.
From high school physics, we know that the density of a gas is defined by it’s temperature and it’s pressure. Similar to how oil and vinegar have different densities, so do warm and cold air. Cold air is more dense than warm air. Because it is heavier, as the cold air (blue) pushes into the warm air (red), it begins to undercut the warm air and push it upwards at a very sharp angle. This causes a very narrow, relatively intense band of precipitation to form along cold fronts. Cold fronts move fairly quickly as the cold air digs underneat the warm air, and the weather associated with the front will be fairly short lived at any one location, usually lasting no longer than a few hours.
Common Weather
In the summer time, the passage of a cold front can often produce thunderstorms, or other significant weather features such as squall lines, supercells, and mesoscale convective complexes. These are all different forms of organized thunderstorms that last for a very long time. Due to the sharp upward push of the warm air, cold fronts can often produce short-lived, severe weather such as heavy rain with potential flooding, thunderstorms with large hail, and even tornadoes. In the summer, cold fronts can offer a reprieve from hot, humid weather. In the winter, the passage of a cold front can result in long stretches of cold weather and clear skies.
Next week, warm fronts. If there are any questions regarding this week, just leave them in the comments!
Filed under: Precipitation Events, Synoptic Features, Thermodynamics, Warm Front
Warm fronts are, in many ways, the complete opposite of cold fronts. They often cover a large area and are slow moving, bringing extended periods of precipitation. They often produce large amounts of rain or snow (depending on season), and may contained a sizable amount of embedded thunderstorms in them.
Formation
A warm front is formed in the same mechanisms as cold fronts; the warm front is the boundary of warmer air moving into cooler air. Again, like a cold front, the actual temperature of the air does not matter, as long as it is warmer than the air it is moving into.
Structure
Warm fronts have a defined structure as well, and it is significantly different than a cold front’s structure.
As the warm air moves into the colder air, it encounters air that is more dense than it. Opposite of the actions of the cold air moving into the warm air, the warm front slopes over top of the cold air, as warm air slowly overtakes the cold air, gently being lifted over top of the cold air at the same time as it moves the cold air out. This produces a front that is very different in appearance when compared to a cold front. Instead of being narrow and extremely sharp, warm fronts are extremely wide features, sometimes in excess of 500km, that feature a very gradual slope to their fronts. The passage of a warm front, due to it’s size, can often take 6-12 hours, and in some cases, as long as a day.
Common Weather
In the wintertime, warm fronts make snow. A lot of snow. A majority of the snowfall in East Coast North America winter storms comes from the warm front. In the summer time, warm fronts often bring prolonged periods of light to moderate rain. Cloudy conditions are widespread with warm fronts.
In fact, a warm front is easily detectible and can be forecast by a few keen observations out your window. The clouds associated with a warm front have a very distinct progression: first high cirrus clouds will move in. They are the ones that are extremely high up and wispy looking. They will gradually get lower and lower until there is some thicker mid-level cloud. This cloud no longer looks wispy and is thick enough to mostly block out the sun. These clouds will continue to get lower and lower until low clouds show up, which are close to the ground, and completely block out anything above them. Often if you spot this progression over several hours, some sort of precipitation is likely on it’s way.
In the summer time, warm fronts can offer the conditions necessary to produce Mesoscale Convective Systems, which are a cluster (often you can draw a circle around them) of organized thunderstorms that are usually severe and can last 12-18 hours (although likely only 2-3 hours in any one given location). As well, warm fronts often have thunderstorms embedded in them in the summer months.
The weather behind a warm front is not as definite as the weather behind a cold front. It may be completely sunny, it may be cloudy, or it really can be anywhere in between. The one thing for sure is that it’s warmer than it was before, and often it’s more humid as well.
Sorry it’s late, but I hope you enjoyed this! Next week we’ll talk about low pressure systems and how these [warm and cold] fronts work in relation to the larger picture!
