Differences in Weather Fluctuations in Different Latitude Regimes

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.

Differences in Strengths of Subtropical Ridges Over Oceans

Earlier this year, I wrote a post about how subtleties in the convergence and divergence of large-scale surface winds can explain many features of local climates. However, as I thought about it more, I realized that I still wasn't satisfied with my understanding of why the seasonal variation in strength of a subtropical ridge over an ocean depends on the ocean in consideration. Specifically, the subtropical ridges over the Pacific, Atlantic, and Indian Oceans in the southern hemisphere as well as over the Atlantic Ocean in the northern hemisphere are stronger (higher pressure) during those respective hemispheres' winter halves of the year, but the subtropical ridge over the Pacific Ocean in the northern hemisphere is stronger during the northern hemisphere's summer half of the year.

Having looked more at the Columbia University interactive maps of mean monthly wind velocities, I am reasonably more confident that I can explain these & related phenomena mostly through surface wind dynamics, though the explanations aren't complete. 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 these explanations.

Subtleties of Wind Patterns Affecting Precipitation

Last year, I wrote a long post on this blog giving the most general intuitive explanations possible for the existence of different climate types, based on different configurations of land & ocean at different latitudes, and used that to explain broad & subtle features of actual climates of most locations. As I alluded to in that post, I had a lingering question of why, at tropical latitudes, there are so many east & poleward coasts that have dry seasons despite those coasts getting ordinary easterly (sometimes with a poleward originating component too) tradewinds throughout the year largely perpendicular to the coast. My confusion is because at those latitudes, the water & land temperatures are warm enough even in the winter half of the year to suggest that humid air from over the ocean could unstably rise above air over land & lead to precipitation. Examples include but are not limited to the north (poleward)/east coast of Central America, the north (poleward) & east coasts of islands in the Caribbean, some parts of the coast of Brazil, the east coast of the southern part of India, and the east coast of the northeastern part of the mainland of Australia. I also had a question about why the north coast of Egypt did not get precipitation in the summer half of the year despite getting northerly onshore winds from over the Mediterranean Sea, which is warm enough that despite the air over land becoming considerably hotter then, humid air from over the Mediterranean Sea could in principle rise above dry air over land, leading to instability and therefore precipitation. Additionally, I had a question about why the subtropical ridge over each ocean (more prominently over the Atlantic & Pacific Oceans in the northern hemisphere) is more poleward along the eastern edge of the ocean even though the western edge has warmer currents (suggesting lower pressure along the western edge than along the eastern edge along the same latitudes).

I could not think of satisfactory answers until very recently. Ironically, although that linked post from last year referred to concepts beyond surface-level wind patterns & air pressures, these answers depend mostly on surface-level wind patterns along with the knowledge of what different surface-level wind patterns imply for vertical air flow. The sources that I used are many relevant pages from Wikipedia and the Columbia University interactive maps of mean monthly wind velocities; unfortunately, the latter resource will be shut down in 2026 April due to funding difficulties. 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 these answers.

FOLLOW-UP: Learning and Making Sense of Differential Geometry in General Relativity

This post is a follow-up to the previous post [LINK] in which I tried to make sense of the mathematics of differential geometry, especially in the context of general relativity, and proposed notation that may be less confusing, more consistent, and arguably more powerful than traditional notation given the existence of a metric in general relativity. With similar motivations, this post explores how some of the ideas of electromagnetic (EM) theory may change on curved manifolds. Follow the jump to see more.

Disability, History, Wilderness, Natural Parks, and Urban Spaces (Part 3)

This post is a follow-up to a post [LINK] explaining my mindset toward the notion of "wilderness" and appreciation of natural scenery versus urban scenery in the US. (That in turn was a follow-up to a post [LINK] about an essay by the environmental history professor William Cronon regarding the delusional or dishonest way that many Americans & Europeans have come to see notions of "wilderness" since the 19th century.) This post, which was not part of my original plan for this series of posts, was motivated by a recent vacation that I took with my family to eastern Washington & northern Idaho (which together form part of the inland Northwest, along with eastern Oregon & southern Idaho). In particular, my family & I, with me sitting in my manual wheelchair being pushed by them, took hikes on trails, usually built on former freight railroad tracks, that were paved with asphalt which was as smooth as advertised (smoother than many roads and much smoother than many asphalt walkpaths, including in some other state parks that we visited in that region).

There were specific instances when hiking on those trails where I felt like I was being hypocritical or unduly entitled, possibly at least superficially in contrast to my views & beliefs that I have articulated in the linked posts preceding this post in the series. This post is an exploration of those sentiments of hypocrisy & entitlement. Follow the jump to read more.

Different Types of Wet Summer Climates in the Plains of the US

As I have cataloged climates of places around the world, starting with the contiguous US, in order to categorize them according to the climate classification system that I have in mind (which I alluded to in my previous post [LINK]), I have noticed that climates in the contiguous US which have wet summer halves of the year & dry winter halves of the year, especially those in the northern Plains states as well as in the state of Montana east of the Rocky Mountains, have dry winter halves of the year because of cold air coming from the seasonal system of high pressure from the settling of cold air over the Great Basin or directly from the settling of cold air to form a system of high pressure over those specific regions. However, these climates have wet summer halves of the year for different reasons in different regions. 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 the explanation.

Warmer Middle Latitude East Coasts than West Coasts in South America

Even though I published a post on this blog a few months ago [LINK] about my intuitions about climates of the world that do a much better job of explaining actual climates than any prior posts about climate on this blog (so I will not link to those posts within this one except for specific reasons) and therefore made me feel satisfied with my understanding of the climates of the world, there was one bit of dissatisfaction that lingered. At the end of that post, I alluded to creating a new climate classification system that would address some of the problems that I have seen in the Köppen & Trewartha climate classification systems. My specific problems with those climate classification systems are in the middle latitudes: at these latitudes, in the Köppen categorization, the climate type "Cfa" commonly found in North America almost never transitions within the same continent to the climate type "Cfb" commonly found in Europe, and in the Trewartha categorization, the Mid-Atlantic & Northwest regions of the US are assigned the climate type "Do" despite having extremely different climates (the latter particularly having noticeably drier & cooler summers, which the the Köppen categorization does a much better job of capturing). Even my modification of the Trewartha categorization didn't fully satisfy me, as there is still almost never any geographic continuity from the climate types "Dfak" to "Dfbk".

The actual new climate classification system that I have in mind will be the subject of a future post. However, thinking through my new climate classification system involved me looking at climate data from various places, and in that process, I saw that in the middle latitudes in South America, locations along the east coast have significantly higher annual average temperatures than locations along the west coast at the same latitudes due to having shorter & warmer winters. This is a significant contrast to the middle latitudes in North America & Eurasia (which are the only other continents that have significant landmass in the middle latitudes), where locations along the east coast have significantly lower annual average temperatures than locations along the west coast at the same latitudes due to having longer & colder winters. This can be seen in the following table of continents, latitudes, locations, and annual average temperatures.

Latitude (degrees)	Continent
	South America	North America	Eurasia
38	West: 11.5 degrees Celsius (Lebu, Chile) East: 14.0 degrees Celsius (Mar del Plata, Argentina)	West: 12.7 degrees Celsius (Bodega Bay, US) East: 13.3 degrees Celsius (Ocean City (Maryland), US)	West: 16.3 degrees Celsius (Sines, Portugal) East: 12.8 degrees Celsius (Sendai, Japan)
38.75	West: 12.3 degrees Celsius (Temuco, Chile) East: 15.4 degrees Celsius (Bahía Blanca, Argentina)	West: 11.9 degrees Celsius (Point Arena (California), US) East: 13.9 degrees Celsius (Rehoboth Beach, US)	West: 17.4 degrees Celsius (Lisbon, Portugal) East: 11.4 degrees Celsius (Minamisanriku, Japan)
42.5	West: 11.6 degrees Celsius (Castro, Chile) East: 13.6 degrees Celsius (Puerto Madryn, Argentina)	West: 12.2 degrees Celsius (Gold Beach (Oregon), US) East: 11.1 degrees Celsius (Boston, US)	West: 14.8 degrees Celsius (Pontevedra, Spain) East: 7.9 degrees Celsius (Tomakomai, Japan)
46	West: 7.1 degrees Celsius (Balmaceda, Chile) East: 13.2 degrees Celsius (Comodoro Rivadavia, Argentina)	West: 10.8 degrees Celsius (Astoria (Oregon), US) East: 6.2 degrees Celsius (Sydney, Canada)	West: 13.5 degrees Celsius (Rochefort, France) East: 7.0 degrees Celsius (Wakkanai, Japan)
49.25	West: 5.8 degrees Celsius (El Chaltén, Argentina) East: 9.8 degrees Celsius (Puerto San Julián, Argentina)	West: 9.5 degrees Celsius (Tofino, Canada) East: 4.4 degrees Celsius (Eastport, Canada)	West: 11.0 degrees Celsius (Cherbourg, France) East: 0.9 degrees Celsius (Poronaysk, Russia)

That table shows that consistently poleward of 40 degrees in latitude, the west coast of South America is colder than the east coast of South America at the same latitudes, whereas the opposite holds for North America & Eurasia at the same latitudes (in the other hemisphere). Especially given that the warm current along the western edge of the Atlantic Ocean in the southern hemisphere turns away from the east coast of South America at a latitude of approximately 40 degrees even around the southern hemisphere summer solstice such that the water temperatures of 10-16 degrees Celsius at those latitudes are comparable to the water temperature along the west coast of South America at the same latitudes (in contrast to North America around the northern hemisphere summer solstice, where the water temperatures of 18-22 degrees Celsius along the east coast are much warmer than the temperatures along the west coast at the same latitudes) and given that the poleward tapering of the shape of South America means that the climates in that latitude range are dominated by the prevailing westerlies blowing throughout the year, this was a surprising result for me. Moreover, although the Gulf Stream being so warm even at the latitudes of Europe along with the seasonal system of high pressure from the settling of much colder air thereby being much stronger over North Asia compared to North America certainly amplifies the temperature difference seen in Eurasia, it does not fully explain this distinction, as the water temperatures along the west coast of North America at those latitudes are similar to those along the west coast of South America at those latitudes (in the other hemisphere). 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 the explanation.

More Quantitatively Founded Intuitions About Climates

My last post on this blog [LINK] about my intuitions for climates was over 1 year ago, in 2024. Since then, I have continued to read more about climates of the world. Later in 2024, I was particularly more careful to look at maps of mean surface-level wind velocities. This led me to start to carefully catalog the climates of the world and attempt to explain them based on mean surface-level pressures & wind velocities along with qualitative ideas about the differences between air masses at different temperatures & humidity levels. I felt satisfied doing so for Oceania as well as for Africa in the southern hemisphere. I did so for South America at the middle latitudes (which is entirely within the southern hemisphere) too, and I thought of continuing through tropical latitudes in South America, near-equatorial latitudes in Africa, and thereafter all tropical, subtropical, middle, and subpolar latitudes in the northern hemisphere. However, as I looked more carefully at these maps and compared them to actual climate data from various locations, I started to think that my understanding of these climactic processes is too limited, especially by my focus on qualitative understanding of surface-level phenomena, to be able to come up with accurate explanations. (Even looking back at the post linked at the beginning of this paragraph and even older posts linked within that post, I can see how many things I have said in those posts that I know now to be inaccurate.) Because of that, I shelved the idea of continuing with these detailed explanations until much more recently, when I started looking more carefully at maps of sea/ocean surface temperatures and at calculations of air density at various pressure levels, humidity levels, and temperatures. This made it possible for me to reinforce my intuitions about temperatures & precipitation distributions at various locations in the aspects in which they were correct and fix them in the aspects in which they were wrong. Thus, this blog post is meant to be that originally-intended compendium of explanations for climates in various parts of each comment in tropical, subtropical, middle, and subpolar latitudes (excluding Antarctica).

The sources that I used were many relevant pages from Wikipedia, the Columbia University interactive maps of mean monthly wind velocities [LINK] & mean monthly sea/ocean surface temperatures [LINK], the European Centre for Medium-range Weather Forecast static global maps of mean surface-level air pressures in different astronomical seasons [LINK] (though this website has very recently started displaying a warning that the maps are now out of date), and the OmniCalc air density calculator [LINK]. 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 these explanations.

Disability, History, Wilderness, Natural Parks, and Urban Spaces (Part 2)

This post is a follow-up to a post [LINK] about an essay by the environmental history professor William Cronon, which in turn was about the ultimately delusional, dishonest, or hypocritical (the particular adjective depending on one's viewpoint) way that many Americans & Europeans since the 19th century have viewed the ideas of "wilderness" and of being close to said "wilderness". That essay, recommended to me by a friend, strongly resonated with me because of my own ambivalence, developed over the course of the 3 years that I physically lived in California with my opinions strongly shaped by my lifelong disability and events that happened to me related to that (particularly being hit by a car [LINK]), about the ways that people in the western half of the contiguous US value "wilderness" or natural parks that don't make a lot of sense to me or don't seem coherent to me based on how most natural parks in the US as designed today exclude people with disabilities in many different ways. Because I have written notes about these and other events & thoughts in my life consistently for the last several years, I think it makes the most sense to first structure this post chronologically to lay out the development of my ambivalent mindset toward the extent to which other people have a particular positive view of "wilderness" that they highly value and then summarize these points more coherently in another section. I should warn that the chronological narration is quite repetitive in writing only because similar ideas occurred to me in marginally different from different stimuli at many different points in my life. In any case, I think that presenting the chronological narration is the most honest way to present my mindset, because "showing my work" makes it much less likely to mislead anyone (including me, as my specific memories naturally become more hazy over time) into assuming that I have felt or thought a certain way for longer than I actually have. Follow the jump to see more.

Progression of Winter Storms across the Contiguous US

This winter has featured many winter storms over the contiguous US that have swept from the west coast to the east coast. In previous posts, I have discussed basic intuitions for why different climates occur in different regions [LINK], my assessment of the deficiencies of the Trewartha climate classification system [LINK], what I would change about the Trewartha climate classification system [LINK], how my proposed changes to the Trewartha climate classification system can be applied to understand what climates occur where in middle latitudes [LINK], why popular understanding of the effects of the Gulf Stream over the Atlantic Ocean on the climate of Europe is incorrect in many ways [LINK], and why different climates occur in coastal locations on different coasts at different latitudes [LINK]. These posts have suggested, among other things, that many winter storms on the east coast of the US would come from warm moist air from over the Gulf of Mexico or mild moist air from over the Atlantic Ocean colliding with cold dry air over the continent, but these collisions would be somewhat more sporadic because the prevailing westerlies, which would have dumped moisture primarily over the west coast, would be weak & dry by the time they reach the east coast. Thus, it is somewhat surprising to me that these winter storms seem to be driven by the prevailing westerlies over the continent. The following is my attempt to intuitively explain, based only on sea-/surface-level temperatures, air pressures, and air flows, why this happens. 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.

Why this happens in North America

This happens in North America mainly because of the arrangement of landmasses & seas/oceans. In the winter half of the year in North America, the subtropical ridge is strongest around 30 degrees in latitude (north of the equator) to the west of the continents of North America in the Pacific Ocean & of Africa in the Atlantic Ocean. Prevailing westerlies generated by the subtropical ridge over the Pacific Ocean bring moisture to the west coast of the US and turn clockwise due to the Coriolis force, meaning that around the time the prevailing westerlies reach the Rocky Mountains, they may have turned more toward the Gulf of Mexico, though this is not guaranteed to happen every time. In doing so, the prevailing westerlies, by this point colder & drier, can pick up warm moist air from the Gulf of Mexico. This clockwise turn by the Coriolis force is reversed within the Gulf of Mexico by southerly winds coming from air coming clockwise off of the subtropical ridge over the Atlantic Ocean, so this newly warmed & moistened air turns toward the east coast of the US, bringing moisture there before moving east & turning clockwise (again due to the Coriolis force) over the Atlantic Ocean toward Europe. This is how the subtropical ridge can function like a conveyor belt of moisture. Essentially, the continent of North America & the Atlantic Ocean are both narrow enough (with respect to the ranges of longitudes), and the Gulf of Mexico with warm water is favorably placed, to ensure that this can happen. That said, the prevailing westerlies will not always turn clockwise enough to go over the Gulf of Mexico and then counterclockwise enough to go over the east coast of the US, which is why the prevailing westerlies are more likely to bring moisture to the west coast of the US but only sporadically do so for the east coast of the US.

I should clarify that the storms that sweep across the contiguous US are often localized highly mobile systems of low pressure. They internally turn counterclockwise, but the motion of the centers of these storms is affected by the aforementioned prevailing westerlies coming from the subtropical ridges over the eastern Pacific Ocean & Atlantic Ocean in the northern hemisphere.

Why this does not happen in other continents

This does not happen in other continents because of unfavorable arrangements of landmasses & seas/oceans. I will give details for each continent in turn.

Eurasia

In the northern hemisphere, Eurasia & the Pacific Ocean are much wider (with respect to the range of longitudes) than North America & the Atlantic Ocean, so the conveyor belt effect is lost there; this point is amplified by the much stronger system of high pressure forming due to the settling of cold dry air over the continent in the winter half of the year. Additionally, the Indian Ocean (which would supply warm moist air) is not far enough from the equator and there are too many mountains in between for the Indian Ocean to function analogously to the Gulf of Mexico.

South America

The east coast of South America in the middle latitudes would refer to the east coast of Argentina. There is no major body of water immediately to the north (toward the equator) of Argentina analogous to the Gulf of Mexico, so although the subtropical ridge over the Atlantic Ocean to the west of South Africa is somewhat close by, the prevailing westerlies are largely dry by the time they reach Argentina and have no way of replenishing moisture & warmth before reaching the east coast.

Africa

In the southern hemisphere, Africa does not extend much into the middle latitudes. Thus, this issue is moot there.

Oceania

Oceania does not extend much into the middle latitudes and is surrounded by much more water, keeping the temperatures more moderate anyway (so there is less opportunity for big temperature contrasts between land & water to form, which would lead to stronger winter storms). Additionally, the Pacific Ocean in the southern hemisphere is much wider (with respect to the range of longitudes) than the Atlantic Ocean in the northern hemisphere, so the conveyor belt effect is lost there.

Variations of Coastal Monsoon Climates with Latitude

I have learned about different aspects of the Earth's climate and shared what I've learned over 5 posts in 2022, including basic intuitions for why different climates occur in different regions [LINK], my assessment of the deficiencies of the Trewartha climate classification system [LINK], what I would change about the Trewartha climate classification system [LINK], how my proposed changes to the Trewartha climate classification system can be applied to understand what climates occur where in middle latitudes [LINK], and why popular understanding of the effects of the Gulf Stream over the Atlantic Ocean on the climate of Europe is incorrect in many ways [LINK]. Ultimately, my learning about different aspects of the climates of the world was done with the personal aim of understanding why cities on opposite coasts of the US at the same latitudes have such different climates, with those on the west coast having characteristically mild to hot arid rainless summers & cool (but not cold) rainy winters and those on the east coast having typically warm or hot humid rainy summers & cool or cold slightly drier but still rainy or snowy winters. I did learn about that to a great extent, but as I learned more, I started to question whether my previous intuitions (from when I started learning about different climates) were correct. Follow the jump to see more and the resolution to this problem. 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.

Myth of the Effects of the Gulf Stream on the Climate of Europe

Recently, I happened to come across articles online [LINK] clarifying that there are some competing explanations for why the climate of Europe immediately to the east of the Atlantic Ocean is milder in the winter than the climate of North America at similar latitudes immediately to the west of the Atlantic Ocean but that the Gulf Stream in the Atlantic Ocean only plays a minimal role. It got me to think whether I have unwittingly repeated the myth of the importance of the Gulf Stream for the climate of Europe in recent blog posts like my most recent one about climate types [LINK]. Having gone through that blog post, I can say more confidently that I did not repeat that myth with respect to the big picture of Europe's climate, but there may have been certain aspects of Europe's climate (especially in eastern Europe) for which I overstated the effect of the Gulf Stream, so I want to set the record straight in an effort to not spread known misinformation or myths as if they were facts. Follow the jump to see more details. 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.

Where Different Climate Types Do or Do Not Occur in Middle Latitudes

As a follow-up to a recent post [LINK], I've been able to somewhat comprehensively catalogue & categorize climates of different population centers roughly in the middle latitudes (23-67 degrees, which are outside of both the tropics and the polar circles) in each continent to understand why certain climate types occur in certain continents and not others. This post explains that further. 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.

For the rest of this post, I will use the modification of the Trewartha categorization that I explained in the recent post. Each climate label in this categorization has four letters, with the first being uppercase and the remaining 3 being lowercase.

Climate categorization definitions

First letter

The first letter can be A, B, C, D, E, or F. Climate types have the first letter F (polar) if if the mean temperature of the hottest month is less than 10 degrees Celsius. Climate types with the first letter B (semi-arid or arid) are defined based on precipitation thresholds regardless of mean temperatures each month; this will be explained soon. If a climate type does not meet a precipitation threshold for the first letter B, then the first letter is A (tropical) if the mean temperature of the coldest month is at least 18 degrees Celsius, C (subtropical) if the mean temperature of the coldest month is less than 18 degrees Celsius but 8-12 months in the year have a mean temperature of at least 10 degrees Celsius, D (intermediate) if 4-7 months in the year have a mean temperature of at least 10 degrees Celsius (which means the mean temperature of the remaining 5-8 months, including the coldest month, must be less than 10 degrees Celsius), or E (subpolar) if 1-3 months in the year have a mean temperature of at least 10 degrees Celsius (which means the mean temperature of the remaining 9 to 11 months, including the coldest month, must be less than 10 degrees Celsius). These conditions are the same as in the Trewartha categorization.

The precipitation threshold for climates with the first letter B is \( H = 10(T - 10) + 300S \), where \( T \) is the mean annual temperature in degrees Celsius and \( S \) is the fraction (between 0 and 1) of yearly precipitation that occurs in the summer half of the year (inclusively between April through September in the northern hemisphere, or October through March in the southern hemisphere). These conditions are the same as in the Trewartha categorization.

If the mean temperature of the hottest month is less than 10 degrees Celsius, then the climate type automatically has the first letter F (polar). This holds even if the climate type would otherwise qualify for the first letter B (arid or semi-arid), because close enough to the pole, the air is too cold to hold much moisture anyway, and features of the vegetation are more influenced by the coldness than the dryness per se; more precisely, as a climate becomes colder, less moisture from the ground is lost to evapotranspiration, so the amount of precipitation needed per year to avoid a climate type with the first letter B (arid or semi-arid) is lessened anyway. If a climate type does not qualify for the first letter F (polar) but the yearly precipitation is \( P \leq 2H \), then the climate type has the first letter B (arid or semi-arid); otherwise, the first letter must be A (tropical), C (subtropical), D (intermediate), or E (subpolar) depending on the mean temperatures of the hottest and coldest months and the number of months with mean temperatures of at least 10 degrees Celsius. These conditions are the same as in the Trewartha categorization.

Second letter

The second letter depends on the first letter. If the first letter is B (arid or semi-arid), then the second letter denotes whether the climate is either semi-arid or arid. A semi-arid (steppe) climate, with the second letter being 's', has \( H < P \leq 2H \). An arid (desert) climate, with the second letter being 'w', has \( P \leq H \). These conditions are the same as in the Trewartha categorization.

If the first letter is A (tropical), then the second letter denotes whether the climate is a tropical rainforest climate or a tropical wet-and-dry climate. If at least 10 months each have at least 60 millimeters of precipitation, then the second letter is 'r' (tropical rainforest climate). Otherwise, the climate is a tropical wet-and-dry climate; the second letter is 'w' if the dry season is during the winter half of the year or 's' if the dry season is during the summer half of the year. These conditions are the same as in the Trewartha categorization.

If the first letter is F (polar), then the second letter denotes whether the climate is a tundra climate or an ice cap climate. If the mean temperature of the hottest month is at least 0 degrees Celsius but below 10 degrees Celsius, then the second letter is 't' (tundra climate); otherwise, as every month has a mean temperature below 0 degrees Celsius (implying permanent ice where water is present), the second letter is 'i' (ice cap climate). These conditions are the same as in the Trewartha categorization.

If the first letter is C (subtropical), D (intermediate), or E (subpolar), then the second letter denotes whether the climate has a dry summer or generally uniform precipitation through the year, as dry summers indicate vulnerability to droughts, wildfires, and related natural disasters. This is the main way that my modification differs from the original Trewartha categorization. If all of the following conditions hold, namely that the driest month is in the summer half of the year, the wettest month is in the winter half of the year, the wettest month has at least 3 times the mean precipitation as the driest month, and the summer half of the year has at least 3 months where the mean precipitation is at most 40 millimeters (including the driest month, by definition), then the second letter is 's', indicating a dry summer. Otherwise, the second letter is 'f', indicating a humid summer. Unlike the Köppen categorization, neither the Trewartha categorization nor my modification to it allow for the second letter to be 'w', which would indicate dry winters, when the first letter is C (subtropical), D (intermediate), or E (subpolar), and this is for two related reasons. First, there is no particular climactic or ecological feature unique to places with dry winters, as the dryness corresponds to the time of the year with the least amount of sunlight and the lowest temperatures; this is unlike when the second letter is 's' (dry summer), because dryness in the summer allows for temperatures to become arbitrarily high in the absence of precipitation (even if average temperatures are somewhat more moderate, as may happen when moisture comes in other forms like fog), which can easily lead to wildfires as is characteristic of places that have climate types with the second letter 's' (dry summer). Second, the threshold \( H \) for precipitation for a climate type to have the first letter B (arid or semi-arid) is defined to depend not only on the average temperature for the year but also on the percentage of precipitation in the summer half of the year, because evapotranspiration rates increase as the temperature increases. This means that for two places that have the same average temperature for the year, the one that has a greater percentage of precipitation occurring in the summer half of the year will experience more evapotranspiration because the temperatures in that half of the year are higher, so the climate type there is more likely to have the first letter B (arid or semi-arid) under the Trewartha categorization or my modification of it even if the Köppen categorization would make the first letter C (subtropical) or D (continental) with the second letter 'w' (dry winter), because that becomes the more salient feature of such a climate; if the climate type doesn't have the first letter B (arid or semi-arid), then there is less of a salient difference in the climates & ecologies of areas with climate types with the first letter C (subtropical), D (intermediate), or E (subpolar) and the second letter 'f' (humid summer) whether the winter is dry or not.

Third and fourth letters

The third and fourth letters are more needed in my modification of the Trewartha categorization for comparison of different climates to make sense, but the actual letters are the same (although at or below 0 degrees Celsius, I may have shifted things by 0.1 degree Celsius). In particular, the third letter indicates the mean temperature of the hottest month and the fourth letter indicates the mean temperature of the coldest month. Both the third and fourth letters come from the following set of letters. These letters are 'i' for temperatures of at least 35 degrees Celsius, 'h' for temperatures of at least 28 degrees Celsius but less than 35 degrees Celsius, 'a' for temperatures of at least 22.2 degrees Celsius but less than 28 degrees Celsius, 'b' for temperatures of at least 18 degrees Celsius but less than 22.2 degrees Celsius, 'l' for temperatures of at least 10 degrees Celsius but less than 18 degrees Celsius, 'k' for temperatures of at least 0 degrees Celsius but less than 10 degrees Celsius, 'o' for temperatures of at least -10 degrees Celsius but less than 0 degrees Celsius, 'c' for temperatures of at least -25 degrees Celsius but less than -10 degrees Celsius, 'd' for temperatures of at least -40 degrees Celsius but less than -25 degrees Celsius, and 'e' for temperatures less than -40 degrees Celsius. Thus, when I speak of the temperature-indicative third or fourth letters being higher or lower when comparing two climate types, such statements refer to this temperature scale.

Effects of mountains

Frequently, when considering transitions between climate types, I will refer to mountains lying in some direction relative to an area with a climate type and not further discuss the climate types on or across those mountains. Mountains have their own, typically polar-like, climate types and significantly break up continuity between otherwise geographically adjacent climate types in a given continent. In particular, as I discussed in a previous post [LINK], a mountain range that lies roughly along a line of longitude (meridian) creates a significant rain shadow that will depend on the direction of the prevailing winds; at more tropical latitudes, the prevailing winds are the trade winds going from east to west, so areas east of a mountain will get much more precipitation than areas west of a mountain, while at middle latitudes, the prevailing winds are the prevailing westerlies going from west to east, so areas west of a mountain will get much more precipitation than areas east of a mountain. A mountain range that lies roughly along a line of latitude usually will not create a significant rain shadow unless there is a specific warm ocean current driving wind from the equator to a pole roughly along a line of longitude (meridian), but it will block warm air going from the equator toward a pole and cold air going from a pole toward the equator; thus, it is more likely to create sharper transitions in temperature profiles (third & fourth letters in the climate type), and if this affects the position of the subtropical ridge especially around the west coast of a continent, then it can further create sharper transitions between precipitation profiles based on whether summers are dry.

Follow the jump to see further discussion of actual climate type occurrences. I will focus mostly on climates with the first letter being C (subtropical), D (intermediate), or E (subpolar), as those are the most common in the middle latitudes; there will be some discussion of climates with the first letter being B (arid or semi-arid), as there are many areas in middle latitudes that have semi-arid or arid climates, and there will be brief discussion of climates with the first letter being A (tropical) or F (polar), as those are rare outside of the tropical or polar regions respectively. I should note that this post contains two large biases in sampling. First, I have only considered population centers that are clear on Google Maps. Therefore, some of these climates may actually be more widespread in area than they look based only on where people live. Second, as I'm most familiar with North America, I may have picked more small or mid-sized cities in North America compared to other continents. Therefore, some of these climates may actually be more widespread in other continents than this post may seem to suggest.

More on Climate Categorization

This post is essentially a follow-up to a recent post [LINK] about the Köppen & Trewartha categorizations of climates; that post was in turn a follow-up to a recent post [LINK] about my intuitions of various climates. This post will discuss, more systematically & in more detail, the climates that are impossible or not typically observed in the Trewartha categorization even when consistently using the third & fourth letters to specify the hottest & coldest mean monthly temperatures respectively, the pros & cons of the Trewartha categorization, and a proposal that I thought of to address some of the cons of the Trewartha categorization. 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.

FOLLOW-UP: My Rough Intuition of Climate, Especially in the US

The previous post in this blog [LINK] went over my rough intuition of climate, primarily in middle latitudes like those of the US. Most of the broad categories that I described were largely aligned with the Köppen climate classification system (henceforth called the Köppen categorization). However, there is a more recent categorization known as the Trewartha climate classification system (henceforth called the Trewartha categorization) that is supposed to be more representative of middle latitudes like those of the US. Essentially, tropical, desert, and semi-arid climates, as well as polar and ice cap climates, are defined in the same ways between the two categorizations. The differences lie in the definitions of subtropical, continental, and subpolar oceanic/subarctic climates. One benefit of the Trewartha categorization is that it clearly separates boreal/subpolar climates from other oceanic and continental climates, whereas the Köppen categorization uses subcategories that could be a little more confusing. However, the definitions of subtropical, oceanic, and continental climates in the Trewartha categorization seem less justifiable to me. Follow the jump to see more details. 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-UP: Some Recent Troubles with pCloud and Google Chat

Almost exactly 11 months ago, I wrote a post [LINK] about problems I was experiencing with pCloud and Google Chat. I don't have any updates about Google Chat (or Google Meet), but I do have an update regarding pCloud. In the previous post, I noted that for files & folders protected by standard encryption (as opposed to stronger zero-knowledge encryption, for which this problem doesn't exist in pCloud), some files & folders require multiple attempts to transfer; I also speculated that pCloud may have been secretly deleting files & folders. After having spent more time using pCloud, I've been able to verify that my files & folders protected by standard encryption have transferred properly, and I think I've figured out why they initially seemed to require multiple attempts to transfer.

As I understand, pCloud creates a temporary folder, essentially like a cache, on the local hard drive, to transfer files before they are uploaded to pCloud. The process of transferring from the local cache to pCloud is limited by upload speeds, which are quite slow (as I mentioned in the previous post). Additionally, once the pCloud program is closed and the remote drive is unmounted, file transfer stops, so many folders & files that the user might think were transferred might not have been transferred. A good way to verify this is to leave the desktop application for pCloud open, monitor how many files as well as what total amount of data still remain to be transferred, and only close the application when all folders & files have been transferred; I like to think of it as a practice similar to leaving a torrent open for uploading after it has finished downloading.

FOLLOW-UP: How to Tell Whether a Functional is Extremized

This post is a follow-up to an earlier post (link here) about how to tell whether a stationary point of a functional is a maximum, minimum, or saddle point. In particular, as I thought about it more, I realized that using the analogy to discrete vectors could help when formulating a more general expression for the second derivative of the nonrelativistic classical action for a single degree of freedom (i.e. the corresponding Hessian operator). Additionally, I thought of a few other examples of actions whose Hessian operators are positive-definite. Finally, I've thought more about how to express these equations for systems with multiple degrees of freedom (DOFs) as well as for fields and about how these ideas connect to the path integral formulation of quantum mechanics. Follow the jump to see more

FOLLOW-UP: Sexual Harassment, Power Dynamics, and Institutions

Last year, I wrote a post motivated by a case of sexual harassment and assault committed by a professor in my department against a student in his group. The incidents happened in the spring of last year, but the news about the incidents and the nominal punishment only came at the end of the year. Since then, there have been further developments, as described in this article (by Marcia Brown in The Daily Princetonian), so I am writing this post as a follow-up regarding the specific developments of this case and our department's response, even as my post last year was my attempt at exploring the broader issues at stake. Essentially, Princeton University had reason early this year to investigate further claims of past consensual relationships between that same professor and other direct professional dependents (students & postdoctoral associates), and suspended him for the spring semester and summer as they conducted their investigation. The university concluded the investigation with findings of guilt on his part of having engaged in at least one such consensual relationship, and as that is a violation of university rules, he was fired. Follow the jump to read more about my thoughts regarding this; as mentioned above, compared to my previous post on this subject, this post will have more of my raw emotional reaction to this whole process and to the specifics of this case rather than a more measured take on the broader issues at stake.

FOLLOW-UP: Personal, Corporate, and In-Between Fraud

This is a follow-up to my post from last month about the VW emissions cheating scandal and the case of the arrest of the "clock kid" Ahmed Mohamed.

Regarding the VW emissions cheating scandal, VW executives blamed (link from AP, Reuters, NBC News) "a couple of software engineers". Given how the cheat was pretty much impossible without a collaboration between many engineers of different kinds (mechanical, software, electrical, et cetera), all I can say is the following: HAHAHAHAHAHAHA!

Regarding the case of Ahmed Mohamed, it turns out that he and his family are moving (link from Jessica Contrera, Washington Post) to Qatar, and that this decision was supposedly made less than 24 hours after meeting President Obama in the White House. In my previous post, I pretty much unconditionally defended him against accusations of fraudulent behavior. I still don't believe that he personally would have brought the clock in just to incite the response from the school and police that transpired, because for one, that would require a massive conspiracy, and for another, that absolves the school and police of responsibility for their actions. That said, I am now less sure of his family's actions and motives following the arrest and its initial reporting. Clearly they took advantage of the massive publicity, and while I'm certainly not a fan of that sort of exploitation of publicity, I was hoping that would be the end of the story. Yet now, I can't believe that a Sudanese immigrant family, where the father has run for the presidency of Sudan before, would within the span of 24 hours decide to move to Qatar, unless they already had high-level connections there. My guess now is that while this story would have likely been widely shared regardless of the family's behavior, a lot of the publicity was probably due to the family's influence itself, and they were able to use that to move out to Qatar (and use the story to get the Qatar Foundation to provide Ahmed a scholarship to sweeten the deal). It probably wasn't because of Ahmed's inability to go back to school in his district, because there have been plenty of other cases of kids who have been in situations where they can't go back to school in their home districts because of similar high-profile incidents. In such cases, the family usually moves to another district within the state, another state, or maybe their home country if they immigrated here, as opposed to a totally different country. Anyway, I still do wish Ahmed the best in his studies of engineering, but I now feel at least partially duped in some way by this whole turn of events, and hope that this story finally dies once the family moves out of the country.

FOLLOW-UP: Gibbs Entropy and Two-Level Systems

As a follow-up to this post, I'm going to briefly discuss what two statistical mechanics professors (who shall remain nameless) I talked to about this had to say. For those who don't remember or are too lazy to read through, the issue is that a new paper publicized by the MIT news office claims that by adopting a view of entropy as per Gibbs as opposed to Boltzmann, negative temperature can be removed from statistical mechanics. I pointed out many issues I had with the arguments for that, and I would thereby cast doubt on the paper and premise as their wholes. Follow the jump to see what information I was able to learn after talking to those professors. (It appears that rendering LaTeX on this blog no longer works right after the takedown, so I'm enclosing any useful LaTeX formulas in dollar signs for you to copy and paste into a LaTeX renderer, if you so choose. The rendering of LaTeX in past posts is inconsistent, just as a heads-up.)