Recently, I learned more about weather & climate, particularly at higher elevations in the atmosphere; I used to feel a little intimidated to think about those things, so essentially all of my posts on this blog explaining features of different climates only used surface-level weather phenomena to the greatest extent possible (and arguably sometimes to a greater extent than was appropriate or justifiable). Although the insights that I gained from such learning are not especially groundbreaking compared to my previous two posts about wind divergence or seasonal changes to subtropical ridges over oceans, I feel like I have rounded out my basic understanding of weather & climate, and I wish to share that here. These explanations make clear why there are larger weather from day to day at middle latitudes than closer to the equator or poles as well as why certain analogies, like between middle latitudes at west coasts & tropical latitudes at east coasts, have limits.
The sources that I used are many relevant pages from Wikipedia, the Columbia University interactive maps of mean monthly wind velocities, and these meteorology lecture notes from the University of Arizona. Again, I am not a trained climatologist or meteorologist; I can't guarantee that this information is accurate, and I can only say that my intuitions seem through my limited understanding to align with superficial aspects of more detailed explanations. Follow the jump to see more.
Basic Phenomena at 500 Millibars
Air pressure at the surface around sea level is around 1,000 millibars, though spatial variations lead to significant air movement leading to observable weather. This pressure is created from the column of air above the surface. Meteorologists, especially for areas at middle latitudes, frequently refer to dynamics where the air pressure is 500 millibars. This can be intuitively understood as the height of "half of the atmosphere", because the air column above that height has a downward pressure of 500 millibars on everything below, and the air column below that height also has a downward pressure of 500 millibars on everything below.
When looking at air pressures at the surface of the Earth, it is easy to imagine the surface as uniform/at sea level. However, the elevation of the surface has spatial variation, and these variations (such as the high plateaus of South Asia, Mexico, and South America) lead to distinct climatic features like the ITCZ in the summer half of the year and the settling of cold air in the winter half of the year. Meteorologists do sometimes consider maps of the height at which the air pressure would be exactly 1,000 millibars, and this can be useful for determining relative surface temperatures, but intuitive interpretation is made more difficult by the fact that the height at which the air pressure would be exactly 1,000 millibars is often below ground (and sometimes below sea level).
Maps of the height at which the air pressure is exactly 500 millibars almost never suffer from the latter problem, because these heights are usually at least 5 kilometers above sea level, which is taller than almost all mountains. (The only exceptions are the Himalayas, Karakoram Mountains, Andes Mountains, and maybe a few other mountains that I'm forgetting.)
Meteorologists care so much about the height where the air pressure is exactly 500 millibars because this is the height where the wind divergence has the smallest magnitude essentially everywhere. (I imagine that this could be determined as something like the root mean square or norm \( \left( \frac{1}{4\pi} \int_{0}^{2\pi} \int_{0}^{\pi} |\nabla \cdot \vec{v}(\theta, \varphi)|^{2} \sin(\theta)~\mathrm{d}\theta~\mathrm{d}\varphi \right)^{1/2} \).) That said, the divergence isn't exactly zero, because zero divergence everywhere would imply no vertical motion of air and therefore no weather.
The height at which the air pressure is 500 millibars gives information about the temperature at the surface. If the air at the surface is relatively warm, then it expands, so one must go higher into the atmosphere for the air pressure to reach 500 millibars. If the air at the surface is relatively cool, then it contracts, so one does not need to go as high into the atmosphere for the air pressure to reach 500 millibars.
Thus, higher heights at 500 millibars implies warmer surface temperatures, and the inverse holds too. The most important point may be that the height at 500 millibars is highest near the equator and lowest near each pole. By basic calculus, a function will vary most slowly near a local extreme and most quickly at some point between local extremes. This means that the temperature & pressure at the surface & at higher elevations spatially vary slowest near the equator & each pole and fastest at the middle latitudes.
Differences in Dynamics at Different Latitudes
The fact that the temperature & pressure at the surface & at higher elevations spatially vary slowest near the equator & each pole and fastest at the middle latitudes has important consequences for weather in each latitude regime.
Polar latitudes
At polar latitudes, the height at 500 millibars will consistently be lowest in that hemisphere, as the air will be coldest there. Most weather will come from random incursions of warmer air from more equatorward locations. Otherwise, the temperature is not large enough to promote significant evaporation of water that would then lead to precipitation. Additionally, imaginary surfaces of constant temperature in the atmosphere generally align with imaginary surfaces of constant pressure in the atmosphere, with the direction of increasing temperature aligning with the direction of increasing pressure (almost always downward).
Tropical latitudes
At tropical latitudes, the height at 500 millibars will consistently be highest, as the air will be warmest there. Additionally, the Coriolis force will be smallest there. Additionally, imaginary surfaces of constant temperature in the atmosphere generally align with imaginary surfaces of constant pressure in the atmosphere, with the direction of increasing temperature aligning with the direction of increasing pressure (almost always downward).
The minimal spatial variation in height at 500 millibars means that most surface wind will be from areas of high to low pressure at the surface, not driven by dynamics at higher elevation. Moreover, the height at 500 millibars being so high allows significant convection. This means that precipitation can come from:
- Quasi-convective processes in a given place over land, bringing moisture through sea breezes at smaller scales or the ITCZ at larger scales, or
- Tropical cyclones, which form from convection over a warm ocean (far enough from the equator for the Coriolis force to be large enough to initiate cyclonic rotation but also far enough from the poleward subtropical ridge for the water to be warm enough to lead to convection).
During the summer half of the year, these processes happen regularly almost every day. Precipitation is typically suppressed in the winter half of the year when the subtropical ridges over oceans move toward the equator and cold air settles over land at subtropical or middle latitudes, such that those tropical locations get diverging (accelerating) tradewinds. The exception to this precipitation regime is that along some east coasts at tropical latitudes in Eurasia (such as some parts of southern section of the east coast of India, the east coast of Sri Lanka, and some parts of the coast of Vietnam), the ITCZ moving so far poleward in the summer half of the year means that the reversed westerly tradewinds have little moisture left when reaching those east coasts, while in the fall season, the ITCZ moving over those locations brings most precipitation for those locations for the year, but even in those cases, precipitation is fairly regular in the expected time of year.
Middle latitudes
Middle latitudes are where the "interesting" (in the sense of less regular) phenomena happen. These latitudes are where the heights at 500 millibars have the largest spatial variation. The Coriolis force has a moderate magnitude at these latitudes. Furthermore, these significant spatial variation mean that imaginary surfaces of constant temperature in the atmosphere are no longer guaranteed to align with imaginary surfaces of constant pressure in the atmosphere, so the directions of increasing pressure & temperature could be other than purely downward and could even oppose each other horizontally.
The height at 500 millibars at middle latitudes usually isn't large enough to allow significant quasi-convective precipitation in-place. (Exceptions include North America & Asia supporting the ITCZ during the summer half of the year.) Most precipitation at middle latitudes is frontal and particularly comes from the interactions between dynamics at the surface & where the air pressure is 500 millibars. Understanding this requires understanding how air moves at that height at 500 millibars at middle latitudes, which is somewhat different from how air moves at that height at 500 millibars at tropical or polar latitudes.
At 500 millibars at middle latitudes, air moves geostrophically. This means that to a good approximation, there is no net force that would let air at that height move to different pressures, so the wind is parallel to the imaginary surfaces of constant pressure. The speed at each point is determined by the balance of the Coriolis force with the pressure gradient force. In the northern hemisphere, the Coriolis force at the surface leading to wind moving to the right around centers of high pressure or left around centers of low pressure means that at the height where the air pressure is 500 millibars, the wind must have larger heights (where the pressure at the same height would be larger) to the right & smaller heights (where the pressure at the same height would be smaller) to the left. For the southern hemisphere, exchange the words "left" & "right".
Imaginary surfaces of constant height at 500 millibars, which are related to imaginary surfaces of constant pressure around those heights, are spaced most closely together at middle latitudes, and closer spacing increases wind speed. The wind at that height almost exclusively moves from west to east. Thus, those bands of strong winds constitute the jet stream, which airplane pilots exploit when traveling from west to east. Mathematically, the jet stream is the inflection curve of height at 500 millibars (where that height has the largest spatial variation).
An equatorward incursion of cold air implies lower heights at 500 millibars there than further east or west, and a poleward incursion of warm air implies higher heights at 500 millibars there than further east or west. These fluctuations at the surface cause but can also be reinforced by fluctuations in that band of closely spaced pressure surfaces (the jet stream). An equatorward incursion of cold air is called a trough, while a poleward incursion of warm air is called a ridge.
Around the most equatorward extent of a trough, the Coriolis force partially cancels the pressure gradient force in the direction toward the center of curvature of the jet stream around the trough, so the wind moves slowest. Around the most poleward extent of a ridge, the Coriolis force adds in the same direction as the pressure gradient force in the direction toward the center of curvature of the jet stream around the trough, so the wind moves fastest. This means that when moving from a trough to the next ridge to the east, air at the height where the pressure is 500 millibars will accelerate. This implies divergence at that height, which in turn implies low pressure/convergence as air lifts from the surface. If that system of low pressure starts or moves from over a large body of water, it will lead to precipitation. (This is very different from how I used to think that precipitation during the winter half of the year along west coasts at middle latitudes came from the convergence of the prevailing westerlies originating from the subtropical ridge over the ocean to the west with cold air settling over the continent. That does sometimes happen, but it is not the dominant cause of precipitation during the winter half of the year along west coasts at middle latitudes.) Meanwhile, when moving from a ridge to the next trough to the east, air at the height where the pressure is 500 millibars will decelerate. This implies convergence at that height, which in turn implies high pressure/divergence as air falls to the surface and therefore a lack of precipitation at the surface.
The large spatial variations in pressure & temperature at middle latitudes are associated with large temporal variations in those things at those latitudes too. The troughs & ridges that define the jet stream may change in amplitude or shift in longitude over several hours or days. This is what it means for the middle latitudes to be affected by transient systems or high or low pressure that generally do not affect tropical or polar latitudes (with an important exception at tropical latitudes being tropical cyclones, but again, those are not affected as much by dynamics at the height where the air pressure is 500 millibars).
In most continents at middle latitudes, in the winter half of the year on average, the west coast is under a ridge (implying warmer air) while the east coast is under a trough (implying colder air). This means that transient systems of low pressure form just to the west of a west coast, bringing precipitation. These systems of low pressure can also bring precipitation to the east coast as the jet stream fluctuates, as long as there is enough moisture nearby to flow into those systems of low pressure; this is only not the case in Eurasia, which is so big that such systems of low pressure dissipate before reaching the settled pool of cold air over Asia. Additionally, transient systems of high pressure form over land just to the east of a west coast, bringing warm dry air to the west coast & cold dry air further east.
This precipitation is very different from monsoonal precipitation or tropical cyclones experienced at tropical latitudes during the summer half of the year, so the motion of the subtropical ridge over an ocean is not enough to establish an analogy between precipitation regimes experienced by east coasts at tropical latitudes & west coasts at middle latitudes. (Moreover, where a subtropical ridge exists over an ocean, east coasts to the west of that ocean do not support deserts, because the warmth of the ocean current along its western edge extends deep into the ocean, so upwelling does not cool the ocean along that edge enough. This means that the subtropical ridge over an ocean during the summer half of the year recedes from the east coast of a continent that lies west of that ocean.)
In most continents at middle latitudes, in the summer half of the year on average, the west coast is under a trough while the east coast is under a ridge. The east coast being under a ridge usually implies support of something like the ITCZ, bringing precipitation. The west coast being under a trough reflects the subtropical ridge over the ocean to the west & upwelling along that coast ensuring atmospheric stability, not that the west coast is cold; in fact, atmospheric stability prevents the formation of clouds and therefore enhances solar heating. Between those is a system of low pressure over land, implying further support for the ITCZ. (The situation is more complicated in Eurasia due to its much bigger size than other continents.)
