Atmospheric Dynamics For Dummies.
By: Aaryan Harshith
Tags: Climate Change, Physics, Technology, Writing, Science

Hey, What Are You Even Talking About?

Before talking about the technical details behind a term I just threw into the air, it might help if I went over what it actually meant. Well, to describe things in the simplest way possible without oversimplifying things, atmospheric dynamics is the study of how air moves around.

And no, we aren’t dealing with the air in a Febreeze can or a bag of potato chips here. I’m talking air on a planetary scale. Everything you’ll be learning today surrounds the main factors that drive this motion, how we can predict it, and the unexpected ways it affects you.

To start, we’ve got to internalize balance, and how nature absolutely loves it.

A Little Thought Experiment

Imagine you took Earth out of the constant chaos of space and gently let it levitate in a special container. Inside, no object or force would have any influence over it. No sun, moon, space rocks, atmosphere, or even its own spin from the big bang.

Ignoring the fact that this would be impossible on so many levels, and how most of us would instantly freeze into human-flavoured Ben and Jerry’s popsicles, the atmosphere wouldn’t move.

Yeah, that’s probably the last thing we should be paying attention to (since we’d all be extremely dead), but isn’t that interesting? It means that atmosphere doesn’t just move around on its own. Something has to move it.

If you’re starting to question if this article was made for third graders, just bear with me and think about this:

Without some sort of external factor forcing the atmosphere to move, it won’t. Even if something did force it to move, it would eventually come to a standstill. As expected, force is where all motion starts. A lack of force is where all motion ends.

The only question left is where these forces come from.

The short answer’s heat.

Well, it’s more like radiative heating from the sun, but I’m guessing you can see why I just stick with calling it heat.

But wait — why does heat matter at all? Well, because the atmosphere wouldn’t be all that exciting without it.

A Light Review ¯\_(ツ)_/¯

Okay, so we know how force leads to motion, and how motion tends to disappear over time without force. But, the atmosphere never stops moving, and that can only mean one thing. There’s something out there that forces things to move 24/7 here on Earth.

Introducing, the sun!

For now, let’s simplify it down to a big hot sphere that emits a lot of light.

Light’s made up of oscillating particles called photons. Photons energized at different levels oscillate at different speeds. We can measure this by seeing photons as waves moving up and down through space, and measuring their wavelength (λ) — or the distance between two peaks or troughs in their path:

The full range of a photon’s possible oscillation rates forms the electromagnetic (EM) spectrum. That’s where all the colours of the rainbow come from — along with lots of other things we can’t see at all.

On the right end of the spectrum, you’ll see the low-energy/high-λ radio waves that let you listen to your favourite FM channel in your car. To the very left, you’ll see high-energy/low-λ gamma rays. They’re the wavelengths you don’t want your lightbulbs to emit, unless you want to develop cancer in the near future.

If you’re struggling to see that, imagine holding a rope and moving it up and down. The more energy you put into moving the rope, the more “waves” end up forming on it. Photons work the same way. Higher energies means lower wavelengths, and vice versa.

Anytime an object’s energized, the electrons in its atoms go on a vacation and shift out of their normal orbits for a bit:

When they fall back down, they release their energy by releasing photons. This results in a distribution of photons emitted at different wavelengths and intensities.

If you plotted those intensities and wavelengths, you’d get what we call a Planck curve. Since every object’s made of atoms, everything radiates light in unique curve-like distributions depending on how it’s energized.

Objects usually get their energy in the form of heat, so they eventually release their heat over time by radiating light. So, the peak of an object’s Planck curve and the area underneath it (the intensity of its radiated light) depend on its temperature:

The Sun’s Planck curve matches pretty closely to the 5000K curve. Most of its radiation is visible.

Hotter objects emit more light than cooler ones, and emit most of their light at higher energy levels. Looking at the graph above, you can see how that translates into hotter objects having their peaks closer to the left, and a larger area (integral) under their curve.

We have fancy name for this: black-body radiation. As you’ll see later on, it’s a pretty idealized way of looking at how things emit energy, but it lets us predict light’s behaviour with insane accuracy.

To help us work with radiated light, we’ve got two special laws. One’s called the Stefan-Boltzmann (SB) Law, which lets us find the intensity of any object’s radiated light with its temperature alone. The other one’s called Wien’s Displacement Law, which lets us locate where an object’s radiation peak would be — also using just its temperature:

For example, we can use the SB law to calculate that the sun (with an average surface temperature of 6000 Kelvins) emits about 63 million Watts of energy per square meter. That’s a lot of energy.

Using Wien’s Law, we can also see that the Sun radiates most of its light out at 0.5μm — or the visible (VIS) part of the EM spectrum. This light eventually gets absorbed by Earth and heats it up.

Why?

Because photons can transfer their energy to any particle they collide with and make it move around faster. And, by definition, heat is the measure of how fast the particles in a substance are flying around.

Earth has a lot of particles, so photons radiated by the sun heats up its land and atmosphere on contact. This specific type of heating’s called radiative heating, since it originates from…well, EM radiation. See? Scientists actually can name things well sometimes. You just won’t see that trend continue for the rest of this article, though.

A Balancing Act

Anyway, what do you think happens to this absorbed light? How does it end up changing how air moves around? Wanna guess?

Well, it turns out that light doesn’t inherently have any impact on how air flows. More than anything, it’s how this light gets distributed across Earth that forces movement. Here’s what I mean.

At any given time, you can expect the regions near Earth’s equator to get a lot more radiative heating than the poles. That’s because the equator’s almost always directly facing the Sun’s rays, while light barely skims the Poles and doesn’t heat them up very much:

It’s why you can expect warm weather all year-round near the equator, while you’ll see polar bears sleeping on ice sheets if you go way up North.

If you could map how much radiation Earth absorbs from space, you’d see a strong heat-band wrapping right around its equator. That’s called a zonal band. More heating at the equator creates an inequality across different locations on Earth, called a temperature differential.

But remember — nature hates inequality, so it tries balance our temperature differential. How? With winds and ocean currents.

Warm air near the equator flows towards cooler areas to balance its heat out. Water does more or less the same thing. Think about what’d happen if you put a piping hot cup of coffee right next to a bag of fresh ice:

“The warmer object (the coffee) would lose its energy to the cooler one (the bag of ice) until they’re at about the same temperature. You’d be left with useless ice and a sad excuse for iced coffee. “

You get the same sort of phenomenon happening on Earth all the time. But you have to remember, zonal heating from sun continues to mess this equilibrium back up. We’re dealing with a never-ending game of order vs. chaos here. You’d get a similar effect if you modified the coffee-and-ice analogy a bit:

This time, picture the coffee boiling on a stove and the ice sitting in a freezer. You’d still see heat transfer between the two, but a new source of external energy prevents either object from losing its original temperature.

Now that’s a lot more realistic.

If you could tell where heat was flowing around in an environment, you could predict its atmospheric and oceanic movement. That’s because air and water are the only vehicles that carry heat around on Earth and let this transfer happen. To figure out what they’ll do next, all you’ve got to do is follow the heat.

Except, that doesn’t really work. Here’s where things get complicated.

Atmospheric “Gears”

Let’s try visualizing something else. Let’s go back to our Earth-in-a-box and try adding an atmosphere and a sun into this experiment. Since there’s still have no sense of spin here, you’d end up with a zonal spot of radiation and heating — with the other side of Earth staying completely dark and icy.

In climatology jargon, you’d call this a single-cell (Hadley) circulation model. From the hotspot, we’d get warm air near the equator rising up and moving toward the cooler poles — kinda like how air right next to your fireplace heats up and carries that heat to every room in your house.

If you’ve every heard of the term “tidal locking” when someone talks about the Moon, they’re referring to the fact that one of its sides always faces Earth. If our moon had an atmosphere, it’d follow this exact type of circulation.

But even looking at single-cell circulation, we’re dealing with a much too simple way of looking at the situation. Here’s where rotation comes in (and messes everything up).

With a rotating planet, you’d still see rising air moving poleward and sinking back down to the Equator, but something’s different now. For starters, we’d now have a zonal heating band.

Here’s what I mean.

With a rotating object, solar radiation that normally would’ve stayed set on one spot would distribute evenly across a region surrounding the equator.

In real life, you can expect air near the zonal heating band to rise and move towards the Poles, while slowly sinking and returning back to the equator over the surface. This sort of motion forms the largest convection cell on Earth: the Hadley Cell.

On the other hand, you’d expect the opposite event to take place over the Poles. Since solar radiation barely ever makes direct contact here, you know it’s cold here. Now, cool air at the surface of the poles moves toward the equator while hugging Earth’s surface. As that air moves to a warmer region, it rises and returns back to the Poles to complete another cell — the Polar Cell:

This leaves us with a final cell that’s sandwiched between the first two, known as the Ferrel Cell. From what modern science tells us, these cells aren’t really driven by any huge temperature differential. We think it’s mostly there since it has to exist. Think of it this way — you can’t have two gears working together while they spin in the same direction:

Think of those paradoxical gears as the Polar and Hadley Cells. The Ferrel Cell would serve the same function as a third gear you’d put in between the two. It would spin the opposite way and keep things running smoothly.

Unlike the Hadley circulation model, the addition of rotation leads to a circulation system with three distinctly moving air cells per hemisphere. You’ll be able to see this effect at different degrees on any planet that rotates over its own axis. As expected, Earth’s a great example of this.

There’s just one tiny catch.

Remember how I said that you just needed to “follow the heat” if you wanted to predict atmospheric motion? Now, it would be literally be that simple if we were dealing with a tidally locked planet where deflection wasn’t a factor. Unfortunately, Earth has neither of those things going for it, so its spin adds a pesky layer of complexity to things.

That layer of complexity’s called the Coriolis force.

If Only Earth Stayed Still…

A couple hundred years ago, the French army hired a mathematician named Gustave Coriolis to figure out why their cannonballs kept veering to the right of where they wanted to shoot them.

With some experimentation, Coriolis later blamed it on an imaginary force that came up in spinning bodies.

Isn’t that weird? If you wanted to shoot a cannonball perfectly straight, that’s exactly where you’d think to aim, right? But, if you aimed perfectly straight on a planet like Earth, your ammunition could swerve thousands of kilometres. “But why?”, you might ask.

It all has to do with the magic of reference frames.

Long story short, there’s multiple ways of looking at things. Unless you were in a certain Tesla Roadster that’s been floating around in space since 2018, I’m guessing you live on Earth. And unless you live on the North Pole, you probably have a high tangential velocity relative to Earth’s rotation axis. AKA — You’re probably spinning really fast right now.

Here’s the catch. Since you’re on Earth, though, you’re experiencing things from the reference point of the average human. That means you don’t feel Earth spinning, and the only proof is that the rest of the universe looks like it’s spinning around you.

Earth’s a bit different from an outer-space reference point. Let’s look at things from here, now:

Now that you’re not part of your Earthbound reference frame, it’ll look like the Earth’s spinning while the universe is dead calm. Notice how nothing’s really “moving” unless you specify what its moving relative to.

Alright, then. We already know what happens when we try aiming “straight” at a target in an Earthbound reference frame. Thats’ what happened to the French army’s cannonballs that never seemed to hit their targets — at least from their point of view.

Why not take a look at this from a bird’s eye perspective over the North Pole? Yeah, you guessed it. We’re having another thought experiment.

Let’s say you’re Na-Pole-Eon — the fictitious leader of Arctic Army. You were chilling at Santa’s house at the North Pole when one of France’s misfired cannonballs crashed your Christmas Party.

Now you’re mad, and you want to get ’em back with some sweet revenge. And coincidentally, you’ve got a few cannons of your own.

Okay, pause. From our new point of view above the North Pole, you’d be at the very centre of Earth, which looks like its’s a plain circle now:

Let’s take the time to note something here. Any point on Earth’s surface rotates relative to an axis of rotation. Think of it like a line that passes through the poles here. The closer you are to this axis of rotation, the lower your tangential velocity — or the amount of distance you cover with one rotation.

The further you are from the rotation axis (eg. if you’re on the equator), you’ll cover more distance in the same time and your tangential velocity will be super high. It’s pretty easy to see this effect since Earth essentially looks like a flat surface from our view. You could equate this effect to a merry-go round or a record player, where any point near the edge moves faster than the centre.

So, what happens when you shoot a cannonball towards France? Well, you could say the cannonball leaves it reference frame. It’s motion doesn’t depend on the rotation of the Earth anymore, but it still carries roughly the same tangential velocity as the place it originated from, which is about zero.

Why? Since the Poles don’t spin relative to Earth’s axis of rotation.

Tangential velocities across Earth aren’t equal. Like I said, points near the equator have a higher tangential velocity relative to Earth’s rotational axis vs. poleward ones. That means the area you’re targeting (France) is spinning faster than where you’re shooting from (The North Pole)

So, even though your cannonball’s forward motion doesn’t depend on Earth’s rotation after you shoot it, its tangential velocity is still going to be lower than the point it’s headed towards, since it’s spinning faster. That’s going to make France whizz right past the cannonball — making your artillery land somewhere out in the Atlantic Ocean:

In short, France rotates faster than you and the cannonball you shoot towards them. That’s why you miss.

But remember, France can’t look like it’s rotating to people on Earth. Earth can’t look like its rotating on an Earthbound reference frame.That’s why it seems to them like the cannonball flew off to the right, when it really didn’t. Up from space, though, we don’t even see a difference. It just looks like you shot your cannonball straight into an ocean while France waved goodbye.

If you look at it that way, the Coriolis “force” isn’t really a force. It’s more like an optical illusion that makes things look they’re moving in unexpected ways. From a different perspective though, you wouldn’t even be able to see it. Still, we can observe its effects all the time — at least here on Earth. That’s why we treat it like a force. It kind of is and isn’t at the same time.

It’s really just a byproduct of what happens when you’re viewing objects move around while you’re on a rotating reference frame. It all depends on where you look at things from. As a result, objects that would normally move in straight up and down in a non-rotating planet end up curving in weird ways on a rotating one.

Maybe if Earth wasn’t spherical, you wouldn’t have a tangential velocity differential at different latitudes and you (Na-Pole-Eon) might’ve had the last laugh. But, it turns out that the gravity of any sizeable object in space ends up squeezing it into a sphere anyway.

As long as that’s true, you won’t be able to get your revenge.

If you really wanted to hit your target, you could account for that speed difference and aim for where France would be after the time it’d take for your cannonball to reach there. In scientific terms, you’d have to match the tangential velocity of the ball with the tangential velocity of the point you’re aiming for. That’s a bit complicated, though.

If only you could ask Coriolis for some help. He even wrote an equation you could generalize to any rotating planet — letting us see how much deflection would influence objects there:

Yeah, it looks intimidating, but it’s deceptively simple. If we translated this equation into words, it’d tell us that the magnitude of an object’s deflection depends on the its latitude, mass, speed, and how fast its host planet rotates. Cranking up any one of these variables acts like a multiplier on the result, which makes sense.

Think about this, though.

The object in question can be literally anything . That includes air itself. In atmospheric science, we call a chunk of air with distinct properties an air parcel. As it turns out, air parcels are at the mercy of Coriolis, too.

That means the entire atmosphere is.

An easy way to visualize this effect would be to imagine this scenario in vector format. In short, vectors are arrows. Their length signifies their magnitude (or power), and their tips tell us their direction:

This makes it a whole lot easier to map how air parcels move around and what forces act on them. Hint: there’s more than just the Coriolis force, but I’m guessing you could figure that out with the length of this article.

Remember this, too. Although the formula for the magnitude of the effect stays constant, the direction of deflection switches between hemispheres. It’s always to the right in the Northern Hemisphere, and to the left when you’re below the equator.

Wait. Why the switch in directions?

It’d be a bit too much to explain the full answer here, but in a nutshell, the sense of tangential motion (rotation) switches when you migrate down to the Southern Hemisphere.

Of course, it’s not like the actual spin of planet changes when you move from hemisphere to hemisphere. That’s just how it looks like from a bird’s-eye view over the South Pole vs. the North Pole:

Unlike the Northern Hemisphere, where higher tangential velocities are below the North Pole, the Southern Hemisphere has higher tangential velocities above the South Pole. And so, you’d see objects curve in opposite directions in each Hemisphere.

Let’s put this into practice.

Let’s say you have a 100m³ large parcel of warm air that’s slowly headed from the equator to the North Pole to try and transfer some heat. Right now, it’s about halfway there — cruising over New York at about 40°N latitude. Assuming an air density of 1.2 kg/m³, we can multiply density by volume to figure out that our parcel weighs 120kg.

After plugging in a speed (U) of 10m/s, and a constant rotation rate (Ω) of 0.0041666° per second (360° per day for Earth), you’d end up with a Coriolis force of 0.1 Newtons — pushing our parcel ever so slightly towards the right.

Don’t forget, though. You don’t have to see this as a real force. This just says that from an Earthbound perspective, our parcel that’s supposed to move straight will seem to curve as if a 0.1 Newton force was acting on it.

But, as the parcel moves closer to the Pole and its latitude increases, the effect’ll get a bit stronger. That makes the curve more and more noticeable over time. It’s also why this effect doesn’t just lead to a straight deflection, since the rate at which it influences objects changes constantly as they move to different latitudes.

We’re also working with volume here. Any increase to that variable has a cubic effect on the amount of air in our parcel. With parcels that clock in at 100’s of km³, the force gets multiplied billions of times over, and that’s where you’ll really see deflection working its magic.

And with that, we’ve unlocked half the puzzle of atmospheric dynamics.

Pressure Systems

Yeah that’s right. We’re not done yet. Not even close.

To sprinkle in some extra difficulty into your mental workout, I want to unveil the fact that nature doesn’t just like to balance heat. It likes balancing a whole lot of other things as well. If you don’t believe me, think back to the last time you popped a balloon.

The high pressure in the balloon quickly balances out with the pressure in your room — with a *boom* sound that’s always sure to scare somebody. Like heat, pressure likes to spontaneously move from high levels to lower levels. Unlike heat, though, nature can balance pressure almost instantly.

This tendency for high pressure gases to move towards low pressure ones is called the pressure gradient force. Why? Because this force is exactly what allows nature to balance pressure when there’s an inequality at different locations (AKA, a gradient).

We‘ve got a law to help us work out where these gradient are, and it’s called the Ideal Gas Law. I like to call it the IGL for short.

Sure, it doesn’t have nearly as many cool-looking Greek letters as the Coriolis Force equation, but it comes in super handy.

This equation helps us understand the behaviour of a set of gases (called perfect gases) that work in easily predictable ways. Fortunately, gases like Nitrogen, Oxygen, and Argon fall into this category in most conditions. That makes the air in our atmosphere a perfect gas too, since those three elements add up to over 99% of its composition.

You might’ve worked with the IGL in university, but most likely in a format that looked something like PV = nRT. This version of the formula relates the pressure and volume of a gas to its temperature and the amount of molecules that make it up. Simple enough:

In the context of atmospheric science though, we aren’t really interested in the number of molecules. Here, we’re more interested in the density of air, since the atmosphere isn’t in much of a container to begin with. That’s why we modified the formula a bit to give us an idea of pressure without volume.

Since the atmosphere’s completely open, we use something else to measure pressure, and that’s weight. A straightforward way to understand this would be to ask why the ocean’s pressure increases with depth.

That’s mainly because the deeper you go, there’s more water above you and pushing down on you. It’s that simple.

The weight of pushing down on you is proportional to the pressure you experience. What I just went over is the the core of what’s known as the Hydrostatic Law. It’s the same story for how air above us exerts pressure on us, but it’s too tiny for anyone to notice.

So, to get a better idea of what’s going on, let’s start by observing how hydrostatic pressure can impact global weather patterns.

Let’s say we have two areas of flat land that are exactly identical. The only difference between the two situations is what’s going on with the air above them. In the first surface, warm temperatures cause air above the surface to rise. This means less weight directly on the ground — resulting in a low pressure system.

In our second surface, cooler temperatures lead to air sinking from higher altitudes down to the ground. Now, more air molecules are directly pushing down on on Earth with their weight, and we get an area of high pressure.

What does knowing this help us with?

Well, it doesn’t help with anything on its own, but it changes everything when we combine it with the other piece of the puzzle we learned about from earlier. Yeah, I’m talking about the Coriolis effect.

The Final Piece.

Geostrophic balance.

It drives literally every instance of atmospheric motion — not just on Earth, but any rotating planet. And yet, when was the last time you heard anyone talk about it? Probably never.

Well, you heard it here first. If you fully understand the mechanics of this, you can be an Airbender. Okay, maybe not, but you can at least try impressing someone with your flawless understanding of pressure systems. Ready or not, your training starts now.

Put on your thinking hat. It’s time for another thought experiment.

Here, let’s look at Earth from above, where we’ve plotted the planet with an imaginary set of special lines called isobars:

If we translated the roots of that word from Greek to English, we’d see that it means “constant pressure”. If you were anywhere on that line, both the weight and air pressure on you would stay the same.

If you moved to another isobar, you’d experience a different pressure from the first one, but it would be constant as long as you stay on the line.

Let’s use these isobars to illustrate a pressure gradient. We’ve labelled an isobar at the North end with a high pressure of 1030mBar (millibars), which tends to be the most common unit to measure atmospheric pressure.

The isobar at the South end of the map maintains a pressure of 1000mBar. If you look back to earlier, we’ve got a textbook example of a pressure gradient. To be exact, there’s a gradient of 30mBar over the distance of five isobars.

Now, let’s also say you were inside this pressure field and you were holding an air parcel. When you let it go and give it the chance to move freely, where do you think it’d fly off to?

As I mentioned a while ago, air moves from areas of high pressure to lower pressure. That means air’s going to want to flow from the top isobar to the bottom one to equalize its pressure. In other words, you should expect your parcel should move Southward — following the pressure gradient force.

The larger your parcel’s volume, the larger this force, since there’s more area for the pressure to push on. But, as you’ll discover later on, the force per unit volume on the air parcel remains the same, so a larger parcel doesn’t get pushed any faster or slower than a smaller one.

Normally, this would be case-closed for a non-rotating planet, but then again, Earth rotates. That means we’ve got to revisit good ‘ol Coriolis.

Seriously, sometimes I wish Earth would stay still.

But hey — I’d much rather deal with some extra math than politely wait for a planet to lose its rotational speed over billion of years. That’s just how the cookie crumbles, my friend.

And so, we’ve got to deal with deflections again. A helpful place to start would be to assume we’re in a certain Hemisphere. This way we’d always know which direction the Coriolis effect’s acting on. I’m biased, so I’ll choose the Northern Hemisphere for now.

Right when you release your huge parcel of air into the gradient, it’s going to behave almost the same as it would in a non-rotating planet. The Coriolis Force still acts like it always would, but it’s barely noticeable here. That’s because it takes time for the pressure gradient force to make the parcel speed up. Slow parcel speeds (low U values) mean a tiny Coriolis force.

So, in the beginning, you’ll get the parcel moving in more or less the average of those two vectors’ directions.

But, as the parcel gets pushed faster and faster by the pressure gradient, it’ll boost the intensity of the Coriolis force.

Remember, the direction always stays 90° to the right of our parcel’s motion vector in the Northern Hemisphere. As our parcel moves in new directions from this tug-of-war, you’d update this formula and see that the Coriolis Force ends up pulling the air in a new direction every time the parcel changes its trajectory.

The only thing really that changes here is the magnitude of that Coriolis vector and the parcel’s overall trajectory:

So, as your parcel continues to speed up, you’d see it slowly curve to the right of the gradient force as the Coriolis vector gains strength. And it’ll keep curving to the right more and more — all the way until your Coriolis vector cancels out your pressure gradient force vector.

Over time, the Coriolis force acts in such a way on the air parcel so that its magnitude matches the pressure gradient force, but tugs the parcel in exactly the opposite direction. That’s geostrophic balance.

That leaves the parcel in an interesting situation. The pressure gradient force was originally pushing it, but the Coriolis effect didn’t let it move that way. But, since your parcel’s still experiencing lots of force, it has to move. And so, it end up moving left in this pressure field — parallel to the isobars.

The bigger the original pressure gradient, the faster the air would to move.

In its current situation, we’d say that the air’s flowing in geostrophic balance. This makes geostrophically balanced air an exception to the almost universal rule that high pressure moves toward low pressure. In any other situation — like if you deflated a bike tire — you’d see air travelling perpendicular to the isobars like there’s no tomorrow.

Notice how this is really clear-cut, too. The parcel can’t travel to the right, since the Coriolis force would then be to its left. In the Northern Hemisphere, that’s impossible.

Okay, okay. All this might sound like nonsense when I try explaining things with words. To get some experience, let’s study at a map that I pulled straight from a meteorology textbook:

For some more context, you’ll see that the image highlights low pressure and high pressure areas, along with isobars being indicated with solid lines. In reality, they tend to look more like contours than straight lines. Inside these isobar contours, though, we see these cute little feather thingies.

For some reason though, we gave them the much more dangerous-sounding name of wind barbs. Ouch.

Anyway, wind barbs are like vectors. The direction that their ends point toward is the direction the wind’s blowing. We describe the equivalent of magnitude here with a set of long notches, short notches, and black triangles.

Each of those indicators corresponds to a wind speed. By adding up all the symbols on a barb, you’ll be able to calculate the wind’s speed in knots. Short notches are worth five knots, long notches are worth ten, and black “pennants” are worth fifty.

A knot’s about 1.15 miles per hour, but I still wonder why we had to create a whole new unit for this. Couldn’t we have just used miles? Well, that’s besides the point.

What you should really look out for here is the isobar spacing. In this map, the pressure difference between any two adjacent isobars should be 12 mBar. The best practice in meteorology is usually 2mBar or 4 mBar, but I guess this map wanted to be special.

Isobars that are tightly packed together will have a higher pressure gradient vs. the same isobars spaced further apart. That’s because you’ll get that same 12 mBar pressure change over a shorter distance.

Since the pressure gradient’s much higher in tight groups of lines, that means the pressure gradient force’s going to rise along with it. A stronger pressure gradient force means faster geostrophic winds that run along our isobars. That’s exactly what we see.

First of all, I don’t see a single barb in there that isn’t running parallel to the contours. Second, the wind speed really does pick up as the isobars get more packed. Up near the US-Canada border with high pressure gradients, you can see winds with black pennants at over sixty knots, while the central US stays at thirty or fourty.

I think the verdict’s pretty clear. Geostrophic balance dominates the atmosphere. And now you actually know how it works!

But all this valuable information doesn’t have to stay in words, either. We can describe the final speed of our unconventional air parcel with the formula. In fact, I have a feeling you could guess how it works yourself:

It shouldn’t be super hard to grasp what going on here. We borrowed most of this formula from the Coriolis force, after all.

In short, we’ve stated that during a state of geostrophic flow, the magnitude of the Coriolis force has to be equal to the magnitude of the pressure gradient force. We also know that the magnitude of the pressure gradient force depends on the gradient itself and the volume of the air it acts on.

We can then express that same equation in a much longer way than before by writing out the full form of the pressure gradient and Coriolis force equations.

Then, just cancel out the volume from both sides to simplify and isolate U. We’ll be left with an equation that gives us the speed of air, given that its Coriolis Force balances the pressure gradient force on it. To explain it differently, this isolated U now represents the speed of the geostrophically balanced air.

Oh, and if you’re wondering why there’s the greek letter ϱ where there’s supposed to be an M and a U, let me show you where they went.

When we revealed our final equation, we technically could’ve just left it as:

And it would give you the same answer as our other formula if you plugged any set of variables into it.

But when we had our long equation before that, we could’ve simplified it more. By cancelling V out of the left side and dividing it out by the mass on the right side, we’d get density. That’s our ϱ variable.

That’s why I mentioned earlier that M = ϱV. And of course, the U’s gone, since we isolated it to get U-GEOS.

**P.S. Do you know what it means when we cancel out a variable from an equation? It means that the variable doesn’t serve any purpose in helping us solve it. That means the volume of an air parcel doesn’t affect its geostrophic speed. Any variables you see in the final, simplified equation do affect our answer, though.**

Well, that’s that. Yeah, it might’ve been a bit confusing at first, but you’ve gotta know this well to understand how all these ideas relate to each other. Now that you’ve graduated from the school of geostrophic derivation, let’s apply your knowledge to a more tangible situation.

Instead of air over land, let’s look at air over an ocean. With enough heating from the sun, this air begins to warm and rise. From before, we know this is going to become a low pressure area since there’s less weight on the water’s surface now.

I think I’ve also drilled the concept of pressure gradient directionality well enough into your mind now, so let’s see how things would work here.

We’d call this a low pressure system, since we see a low pressure cell of air surrounded by high pressure air. From above, this system would look like concentric circles of isobars that rise in pressure as you move outward. You’ve probably heard meteorologists talk about these things all the time, but now you know what they are.

Considering we’re still talking about the Northern Hemisphere, we’re going to be working with almost the exact same situation as before. The only difference is how our isobars are arranged differently.

A stray air parcel starting the right of the pressure field would slowly speed up from the pressure gradient force and begin to deflect more and more — all the way until the Coriolis Force matches the pressure gradient force. The only way our parcel could move here is Northward:

That’s obvious enough, but what’d happen if you let that parcel keep going?

This is where things change. In general, we know that wind in geostrophic balance travels parallel to isobars. But, now that we’re dealing with a circular pressure field, you’d see that the air would move Westward at the top, Southward at the left end, and Eastward at the bottom of the field.

It’s important to look back and think how this would function in a non-rotating planet. In that situation, you’d just have high pressure air move directly towards a low pressure centre. Except, on Earth, the Coriolis force isn’t going to let that happen.

If we look at all the calculations we tried out at different spots of the pressure field, we’re left with all our parcels geostrophically flowing counterclockwise. Yeah, the air’s still moving parallel to the isobars, but now in a circle:

We’s call this a cyclone.

Now, the naming of weather events is a huge debate on its own, but in atmospheric dynamics, any low pressure centre with air following the right direction of spin would fall under the umbrella term of “cyclone”.

To be honest, cyclones don’t even need to be anything large or deadly. At a micro-scale, a cyclone could be a little flurry of wind that makes leaves blow around in circles on your street. On the other end of the spectrum, it could be 2005’s Hurricane Katrina, which was far from a cute little gust of wind.

The one thing all cyclones share in common, though, is their pressure centre and their cyclonic flow. All cyclones have a low pressure centre. For proof, that’s usually where the eye of most storms are. Since geostrophic flow never lets air parcels reach it and there’s high suction there, that areas stays empty.

In the Northern Hemisphere — just like we worked out ourselves — all cyclones spin counter-clockwise. That’s their normal cyclonic flow. In the Southern Hemisphere, normal cyclonic flow switches because the Coriolis force switches its direction there:

Now, let’s blow your mind. What do you think happens when you have cool air sinking somewhere to create a high pressure centre?

You guessed it. You’d get a high pressure system. Here, you’d have the same concentric isobar circles, but with decreasing pressure as you move outwards. That means the pressure gradient vector reverses its direction and pushes air parcels outward, too. But, as always, the Coriolis effect cancels that motion. Here’s how that’d look in the Northern Hemisphere:

You’re left with geostrophically balanced air flowing clockwise in the Northern Hemisphere, and counter-clockwise in the land down under. That’s anticyclonic flow, which ends up forming an anticyclone. That’s right. Physics can have anti-matter, but we have entire anti-cyclones!

Well, we can’t just keep this stuff in our heads, can we? Let’s try this out by playing a game of “Can You Spot The Cyclone?”. It’s like “Jeopardy”, but without the money, or the contestants, or the fun. Yay.

Let’s kick things off with our easiest question. Here’s some imagery from a geostationary (Earth-following) satellite. Can you spot a cyclone in the Northern Hemisphere? Bonus points for every extra one you find:

Hopefully you found one. Now, I won’t be able to go over every single hurricane and storm on that map, but I can show you the basic thought process here:

Going back to our last discussion on the normal cyclonic flow in the northern Hemisphere, we know should keep an eye out for comma-shaped clouds that seem like they’re spinning counter-clockwise. Right off the bat, I saw the big hurricane-like mass hovering over the Southeast American coast — right where Texas should be:

And yeah, it’s pretty hard to tell the direction of spin in a stationary image, but with some practice, you’ll know where you should look to get a better sense of wind’s rotation. Congrats if you got that one on the first try!

Okay. Now, let’s try working with a harder case that you’ve never seen before. In that same image from above, why don’t you try picking out a cyclone in the Southern Hemisphere? Again, there’s more than one, so you’ll get extra self-gratification points if you go above and beyond:

Don’t worry. I’ll wait.

**Play some Jeopardy music in you head while you think.**

Done?

As I warned you earlier, this one was a bit more tricky. Right now, most of the visible Southern Hemisphere’s covered in puffy clouds from a rare phenomenon called El Nino. That makes it a whole lot harder to make out cyclones from the rest of the background. Let’s see if you saw through my sneaky trap, though.

Remember — El Nino or no El Nino, geostrophic balance still dominates, and it doesn’t change normal cyclonic flow one bit. If anything, it just makes things a bit harder to see. But, that shouldn’t be a huge problem if we know what we’re looking for.

Here, cyclones look like comma-shaped clouds that seem to turn clockwise. if you accidentally picked a counter-clockwise spinning cloud, you forgot that the Coriolis force runs differently from the Northern Hemisphere, and so does cyclonic flow.

The good thing is, you had a few more options in choosing cyclones here. One of them was the low pressure system on West Coast of the tip of South America (Cape Horn). It’s pretty tiny compared to that American cyclone, but it looks like it’s the best we have in this Hemisphere right now:

You might’ve also thought of choosing that bigger swirl of air off the East Coast of South America, but that’s a bit more iffy. I’ll still give that one to you, though. People could argue that it’s just a cluster of suspiciously shaped clouds, but you could argue just as well that it’s the start of a cyclone. Kudos to you if you saw that one!

With that, you’ve just won “Can You Spot The Cyclone?”. Your award’s a nice, long pat on the back. That’s really all I’ve got for you.

Now that we’re done with all the brain-wrenching math and physics, we should be at the right point to see how all this material comes together. Let’s start off from where we just ended.

Making Connections

Over the past few sections, I covered how you needed a strong Coriolis force for large cyclones to form, since weak Coriolis forces can only cancel out weak pressure gradients. Scrolling back up to our Coriolis formula, you might make the guess that there should be lots of cyclones at the Poles.

And you’d be partly right there. At the same time though, you’d need a cell with a low enough pressure so that the pressure gradient force stays high enough from the outside.

After all — the stronger the gradient, the stronger the wind. That’s the difference between mini leaf tornadoes and hurricanes you can see all the way from space. What I didn’t stress enough was exactly what conditions we need to help create that low pressure zone.

Of course, the short answer’s heat.

The longer (and much more surprising) answer is that hurricanes actually have a critical temperature they need to form. It’s impossible to form a cyclone that’s large and fast enough to call a hurricane as long as the surface of the ocean stays below 27°C. That’s why the Poles don’t get any — even though their Coriolis deflection is off the charts.

Now, we’re in sort of a paradoxical situation. We know for a fact that the equator receives the most heating from the sun, but the Coriolis force’s almost non-existent there. The situation doesn’t really work the other way around, either. Where there’s enough heat, there isn’t enough Coriolis force. Where there’s enough Coriolis force, there isn’t enough heat.

Because of this weird Catch-22 that large cyclones get stuck in, we usually end up seeing a belt of hurricanes around Earth. That belt’s far enough from the equator to have a strong Coriolis force, while still being close enough to get past that critical temperature every once in a while. Check it out for yourself: