I live just a couple hundred miles south of the arctic circle, and personally I hate the time of year where we "accelerate" into the equinoxes (equinoxii?). The rate of change is just too fast and too disruptive, and you _really_ see its effects on people. And then DST comes in and makes it even worse.
The difference as you climb in latitude is really shocking. Even just another 3-400 miles south of here, the rate of change is way less severe.
Anyway nice work and cool article! I've done some of these rough calculations myself before to plot out the change just to verify that I'm not insane for hating this time of year, and you did a way better job than I ever did :)
I grew up here, so it's "home" so to speak. Well, technically my childhood home was a few hundred miles further south than where I am now (Fairbanks, Alaska). It's definitely an extreme climate to live in, but there are a ton of things to do outdoors, and although the daylight changes are very extreme, the excessive summer daylight makes that part of the year truly amazing.
I do think the extreme polar opposites in daylight and temperature for summer and winter solstices contribute to people here being a little...unbalanced. But for a lot of people, the unique landscape, low population, and abundance of outdoor activities make it worthwhile.
When living in Stockholm, I came to appreciate the various levels of twilight and darkness, rather than thinking of day and night so strictly. The sun being low on the horizon also scatters light across the sky in ways that are very beautiful and last much longer than sunrise and sunset in Australia where I grew up.
Similar experience for me but probably even more extreme.
I'm originally from São Paulo, Brazil, the Tropic of Capricorn almost cuts through the city itself. Sunrises and sunsets are very quick events, sitting somewhere to watch it would take some 30 minutes, and then darkness.
Even after 10+ years of living in Sweden I still get mesmerised by sunrises and sunsets here, they last for so long and I get to be awed by the changing of colours, shadows, shapes, for hours. It's one of my favourite things to do during summers, just to be out somewhere by a lake with some friends, having food and drinks, and watching the endless twilight.
Having grown up around the same latitude as Stockholm, one thing I never realized until last year when visiting tropics is how my subconscious associates warmth with long evenings. Being used to summers where you could basically read a book outside at 11PM, it felt really weird to be outside in tropic heat, but complete darkness by 6PM.
Catches me every time too. And it's so quick. You can go in to a shop to pick up a packet of crisps thinking it's daytime, but actually is quarter past 6, so you come back out and it's full dark!
I'm in the southern UK, and I'd take our late-May/early-August "it's light while I'm awake and dark while I (should be) asleep" all year round if I could get it.
You could become peripatetic and seek out the spot of opposite latitude during the dark season. So you could have 15 hours of daylight, 12 hours of daylight, then 15 hours of daylight again. I've thought that with idle rich amounts of money I'd get a very large yacht and sail the pacific rim in time with the seasons, perpetual spring, summer, spring, summer.
We have different definitions of rich. It's not just the cost of living. It's also the time and to deal with the governments to allow this, it's having the money to spend the time, it's the job that allows this, it's the time away from family not being catastrophic for someone's wellbeing. Frankly, this is vastly infeasible for 99% of people. I'd easily consider the remaining 1% "rich" in some way
The first time I visited the tropics, I never realised how much I associated the dark with it being cold!
We went for dinner in the afternoon, sun was up, it was blazing hot, everything normal so far. We had dinner while the sun set in a nice air-conditioned restaurant, so it was dark when it was time to leave, and I walked out into the tropical night and was so confused why it was still warm and moist outside!
> When living in Stockholm, I came to appreciate the various levels of twilight and darkness, rather than thinking of day and night so strictly.
In Chile you get somewhat long days and short days too, especially in the south, but instead of trying to be super precise about sunlight, the afternoon and night blend in and sort of crossfade. You end up with "8 de la tarde" (8 in the afternoon), and "6 de la noche" (6 at night) depending on the season.
I think I have used "8 in the afternoon" even as close to the equator as Atlanta (~34 N). Our latest sunset is 8:52 pm, surprisingly late, because we are very far west in our time zone.
7/8/9 de la noche (vs tarde) is used by 60/97/100% of American Spanish speakers vs 1/16/97% of European Spanish speakers. I wonder if the difference is due to Spain's generally late sunsets.
It would be interesting to redo this analysis with a corpus that indicates seasons though.
"One of the more interesting features I hadn’t appreciated before is that when you get close to the Arctic circle, the length of the days is essentially a zigzag, straight up from the winter solstice all the way to the summer solstice and back down again."
I had noticed this too and wondered if it was exactly true, with the "zigzag" being straight lines - I thought there might be a simple proof of this fact based on some trig identities. There's not, because it's not true - the lines aren't exactly straight, even if you ignore solar refraction - but it's a very good approximation.
The graph looks like it's straight up interpolating between a sine curve and a tangent curve, it's so cool that way. (The calculations are more involved than that).
Also signal analysis people will enjoy this natural system producing "almost pure" triangle and square waves. Nudge the plot to 66.55 degrees and it's at the most triangle wave point. :)
I'd say the graph's qualitative behavior is correct. Once you get to the arctic circle, there are singularities in the rate of change of the length of daylight.
For example, if you're at the North Pole, the sun is below the horizon all winter, and then on the vernal equinox rises above the horizon and does not set again until the autumnal equinox. So, formally, the rate of change in daylight is zero all year long, except on the equinoxes when it is infinite. Any latitude above the Arctic Circle will have these kinds of singularities.
In practice there are some corrections to the amount of daylight that I discuss at the bottom of the article, the most important of which is the effect of atmospheric refraction. If you were standing on the North Pole, you'd actually observe the Sun appear to rise some time before the vernal equinox.
The opposite also happens, where the sun is below the horizon for months or weeks, and at the end of that period, it will inch towards the horizon, and you expect sunrise, but nope, it'll move furrther again... of course there'll be twilight (followed by night), but you might not see the orange ball of bright light for weeks or months.
Coming from middle of Sweden I remember the first time I spent a midsummers night in Lund in the south if Sweden and was astonished that the night was in fact dark! In my hometown, well below the arctic circle, the month of June is still constant daylight.
This phenomenon became very interesting to me after moving approximately 14 degrees further north (on the northern hemisphere) and experiencing not just shorter and longer days, but more rapid changes in day length during spring/fall.
The impact this has on daily life is larger than I had anticipated, and in general reducing the intensity of the cycle is a selling point for cities closer to the equator. It’s been nine years since my migration north, and I’ve only moved further north so this isn’t a deal breaker for me. It’s mostly something from my childhood and young adulthood that I took for granted. I’m now eagerly awaiting the day when my normal waking time is during dawn, which should be in early April.
I’m still significantly further south than Northern European countries mentioned in this thread. Maybe life has more moves north for me in store.
The seasonal extremes of daylight are so extreme up here in Finland that the cycle of night & day seems a bit less like a 24-hour cycle and a bit more like a 365-day cycle.
An artifact of this is that my 5yo might not see a dark sky for the entire summer, unless we keep him up awake for the traditional Midsummer hangin'-out.
This is surprising. I had always assumed that the length-of-day function is essentially a sine wave everywhere on the planet, and that the derivative would thus be another sine wave shifted by 90 degrees.
When the day length is maximal/minimal (solstice), the day length change rate is near zero, and vice versa. That's still true in the more accurate model, even though the shape of the functions is more distorted.
The calculated daylight even downplays the actual light at the high (or low) latitudes quite a bit. E.g. at latitude 60 there's a "nominal" midsummer night of about four hours, but it doesn't really get dark, as the light from the refraction is quite strong even with the disk not being visible.
Not exactly; even after the sun is fully below the horizon there's some light. See the interactive graph - the times aren't long enough for twilight. But you can use a larger value of "a" in the equation above it to make that change.
That's called "twilight". In the section "Atmospheric refraction and the solar limb" there's a modified sunrise equation with a variable "a" and text suggesting a correction of 50 minutes of arc there.
If you replace 50 minutes with:
- 6 degrees, you get the times of "civil twilight" (roughly speaking, when you don't need light outside). At 60 degrees north at midsummer the minimum altitude of the sun will be about -6.5 degrees so almost all of the nominal night is civil twilight.
- 12 degrees is "nautical twilight" (horizon clearly visible)
- 18 degrees is "astronomical twilight" (sky is dark enough for all astronomical observations).
(It's possible that those are defined as 6 degrees + 50 minutes, etc.)
And it's not just "sunset + X minutes" where X would be a constant. In the winter this X is much shorter than in the summer.
For me X is then a "travelling" value which in the winter is at 1/3 between sunset (0°) and civil dusk (-6°), and in the summer it goes up to 2/3. Calculated as the moment when the blinds go down.
You made me check the code and actually I have it the other way around (and with different ratios, winter=-6°, summer=-2°), because else the blinds would go down too late in the summer (after 22:00).
I just pulled up Whitehorse, Yukon (at the 60th parallel), and sure enough, the longest day of the year is essentially always day: https://www.timeanddate.com/sun/canada/whitehorse. Almost 5 hours of civil twilight, but civil twilight is still daytime in my book.
Twilight is caused by scattering rather than refraction. There's sunlight bouncing around in the atmosphere, keeping the sky non-black even after sunset.
Even during the "night," the sky stays illuminated enough that it never truly feels dark. It definitely challenges the idea of what nighttime means and makes the summer feel almost magical, but I imagine it can also mess with your sleep patterns!
> On the equator, every day of the year is exactly 12 hours long
But surely that is not true, as the Earth's rotation is tilted. Is this supposed to be a year round average? Despite calling out more advanced corrections one can make, this doesn't seem to be mentioned anywhere?
In Garissa, Kenya, which is almost exactly on the equator, the day length varies between 12 hours 6 minutes and 12 hours 9 minutes. So it is 12 hours if you are rounding to hours.
Pontianak in Indonesia is right on the equator (I'm seeing 1 minute 14 seconds south latitude at Wikipedia).
timeanddate.com gives (https://www.timeanddate.com/sun/indonesia/pontianak) variation between about 6.5 minutes and 7.5 minutes above 12 hours, long at the solstices and short at the equinox. The difference is due to the sun setting vertically at the equinoxes and at a slight angle to vertical at the sunset.
It's true. Highly recommend getting a globe in your hands to convince yourself about stuff like this. Close one eye, pretend you're the sun and observe the effect the tilt has and how it has no effect on the equator (apart from changing the angle of the sun; interestingly the sun's path alternares between being in the north sky and being in the south sky).
You'll also be able to understand time zones and great circles (flight paths) better with a globe.
It's true that the Earth does not usually take exactly 24 hours to rotate, it's only 24 hours on average over the course of the year. However, the difference is only ever off a few seconds at most. Those seconds pile up across the days around perihelion and aphelion amounting to several minutes cumulatively but that doesn't affect the length of the day, only the amount that solar noon differs from noon on the clock.
The reason that days are a few minutes longer than nights at the equator is due to atmospheric refraction which makes the sun visible a little before it actually has "risen" and similarly, keeps it visible a little after it has "set".
It's always interesting how it affects how people think about the day. If you look outside and it's dark then it's easy to think that the day is basically over, even though the time might say otherwise.
I really appreciate the long winter nights and long summer days in Norway. Being able to wake up to the sun as early as 04 and enjoy it until after 23 is great, and the UV is only high during the middle of the day. Long summer days are awesome. Long winter nights are probably not as appreciated, but I enjoy those too.
I'm trying to find the darkest corner of the earth to chill in so I can actually get some work done. I can't get anything done when the sun is out and people are out and about. Maybe I'll move to that Italian village that has the giant sun mirror thing.
I personally like extremes. My ideal scenario would be a dark room where I can get work done, and then every hour or so, I take a five-minute break outdoors in direct sunlight.
I spend most of the day in a fairly dark room, but make sure to get at least 20 minutes of sunlight on my bare skin and eyes every other day -- but it's not because I like extremes: it is because sunlight is good for me, but LED light bulbs are bad for me or at least they are if they are of typical brightness and they are on most of the day.
July - September, yes, we have oppressive sunshine.
Spring/fall tend to be cloudy & rainy, and November to February-ish is referred to as "the big dark" - the days are short and the sun is low and obscured by clouds when it's above the horizon. Sounds like you'd get a lot done then (as do many people here).
Calgary, AB enters the chat:
Calgary, Alberta, is considered the sunniest city in Canada, with an average of 333 sunny days and 2,396 hours of sunshine annually.
Fifteen years ago, I moved from Orlando to Seattle, and almost 20 degree change in latitude. On top of that, Orlando is famously hot and sunny and Seattle famously cold, cloudy, and rainy.
Despite that huge change, I adapted to the new climate just fine. I don't mind the gloom or the cold. The six months of gray skies don't get my down like they do a lot of people.
But even after a decade, I still haven't gotten used to how much the day length changes. Every summer my brain keeps expecting the sun to go down any second now while it sits up there near the horizon giving an extra two hours of daylight. Every winter it feels like the sun disappears too early.
It’s rarely super hot or super cold like a lot of places.
You get these ridiculously long summer days that last forever. It’s perfect for athletics and hiking and spending time on the water.
And likewise you get these wonderfully wet and dark winters which are perfect for life’s other joys: coding, reading, playing video games, boardgames, drinking coffee, etc.
I love places like San Diego / LA but I wouldn’t want to live in a place that is always a perfect summer day.
I was in Seattle Sept-Dec of 2008 on an internship and I remember feeling some of this. Based on what people had said, I was geared up for four months of a soggy, misty mess, but it wasn't that at all— the autumn there was splendid, with tons of breezy, cool days where the sun still shone, with the trees around my place in Madrona showing brilliant colour for weeks on end.
That's much of the west coast (west of the cascades). I moved from Seattle to the Bay Area, and it's basically the same weather except somewhat shorter summer days and winter nights, WAY more sunshine, and generally about 10f warmer. Except in the summers where these days it seems like Seattle has more 95+ degree days than the peninsula does.
I love 4 seasons. But the weather and day length make for a difficult half-year from Oct - Mar. The NE corridor has some of these traits, but it was a lot easier to deal with there. In the NE, rain & grey-skies aren't as persistent. In Seattle, a month can go by without seeing the sun.
The downside of the historically mild climate is a lot of older homes weren't built with energy efficiency in mind and now in 2025 we have to deal with that inefficiency on our energy bills :'(
It's the same in the UK vs Southern Europe and Japan where I've lived before. People complain about the wet weather, but it's not that IMO what really gets to you, it's the dark winters with so little daylight compounded with the abundance of cloudy days.
Temperature-wise, most of the UK is actually quite moderate compared to central Europe. It's winter darkness that gets to you.
I think what's fascinating about it is the daylight changes you experienced in the 20 deg latitude change you experience from Orlando to Seattle are dwarfed by the changes from a ~15 degree latitude change from Seattle to Anchorage. By the time you're getting close to the pole, you can see huge differences in solstice minimum/maximum sunlight by moving just a few hundred miles north or south.
I really struggle with this at daylight savings switches when I work in offices where I can see a window. It takes me a couple of weeks to adjust. In one direction I find I work later than I intended. In the other direction I find myself ready to leave and realize it's only 4:30
Could be so the time is better synchronised with the rest of Europe, which is relevant for business reasons. I seem to recall reading recently about some other country doing exactly that (though it wasn’t Norway).
Mexico used to have daylight savings even though they're close enough to the equator that it doesn't make sense - that's to harmonize with the US. When they did have daylight savings time, though, the state of Sonora didn't, because it borders Arizona, which doesn't.
Yeah, I hate it. I don't need more light in the morning, I'd rather have that as a bit more visibility when skiing after work. And it anyways only takes like two weeks before the gained light in the morning is gone.
25th of october day is from 08:21-17:39,
26th of october from 07:24-16:36 after dst,
and then 17th of November we're at 08:19-15:43 (so back to dark mornings). I'd rather the 17th have light until 16:43.
My buddy went to Norway and was super upset because the sun never set in the part of Norway he was staying in and he had no idea it would be daylight almost the majority if not the entire day. He also said his Norwegian family was getting upset with him because he wasn't sleeping and keeping everyone up due to his lack of day/night reference.
I live at ~64 deg latitude in the USA (Alaska) and 100% agree with everything you said. The timing of sunset has such a profound effect on when you consider the day "done". In Dec it's painful to haul myself outside at 5 or 6 PM since it's "night time" already. Meanwhile in June, at 11PM/23:00 when it's still bright out I have to remind myself to home and go to bed so I'm not a tired wreck at work the next day :)
Very interesting discussion! I did a less theoretical approach a while ago to calculate the same thing: I just go to timeanddate.com, find the city I'm interested in, go to its sun page (example for New York https://www.timeanddate.com/sun/usa/new-york), and find the table that shows the difference in daylight minutes per day. No math or programming needed, just copy-paste and some buttons in Excel.
Not as satisfying as a derivation here, but a quicker way to get the answer.
EDIT: I did a spot check for Rovaniemi, Finland. This city is far north enough that the sun is up all day (66.5 degrees). But the graph on this page seems to be a little bit off: it requires an even higher latitude for that to show up.
Moving to Northern Canada has made me really really appreciate Spring. Going to work in the dark then going home in the dark is exhausting. I'm at 56ºN. I imagine it's worse for those who are even further North.
The whole "6am sunrise and 6pm sunset every day of the year" thing at the equator is kind of mind blowing.
Another maybe counterintuitive fact is that (to a reasonable approximation) everywhere on earth gets the same number of hours of daylight over the course of a year.
Funny because growing up in the tropics I thought sunset and sunrise were synonymous with those times of the day, and learning people in other parts of the world experienced shrinking/lengthening day/night cycles was mind blowing. You mean it's 8PM in the night but the sun's still in the sky?
I was at a wedding in Sweden near midsummer with a lot of international guests. They were quite surprised to get out of the reception dinner at 10pm and see that the sun was still up. We were below the arctic circle, so no midnight sun, but it doesn't really get dark during the night, you get an hour or two of twilight, and then the sun rises at 2am again.
I travelled to Stockholm from North America a few decades ago, right around midummer. Worst jetlag of my life.
The problem was that 20 hours of daylight, especially having 2:30 AM feel like 6:30AM. It was impossible to get an adequate amount of sleep. The paper thin curtains in the cheap hotel where I stayed did nothing to block out the light.
If I am ever in that part of the world at that time of year again, I will be bringing a sleep mask and seeking out a hotel with proper blackout blinds or curtains.
I would have thought that for places that close to the arctic circle would be a national crime to not have full black out curtains. The difference being the punishment based on what nation the crime was committed.
You can just bring or buy some pop-up travel blackout blinds made for babies. We used those with great effect when visiting my parents' summer house in Northern Norway in the summers when the kids were young.
Bonus, they now work as great blackouts in my home office for video calls when I do not want sunshine and clouds to change my green-screen effects etc.
I live in the south of England and experienced this in Scotland. I was trying to get somewhere to pitch my tent but rapidly running out of light, or so I thought. It was the height of summer and it just never really got dark. Maybe England isn't as different as I think it is, but it was strange to find my assumption that night=dark was quite wrong.
Yes, though a location at 45 degrees N/S only gets 70.7% as much sun power per area due to not being perpendicular to the sun's light, and even less on the ground due to extra atmosphere to pass through.
Appropriately enough, that "everywhere on earth gets the same number of hours of daylight" fact came from a solar system salesperson, who didn't go out of his way to emphasize the atmospheric effects here at ~49°N.
The silver lining is that our longest days are often our sunniest.
When we were in Hawaii I think the only reason we caught the sunset is because we were less than 400 yards from a beach. By the time you know the sun is going down you are about to be in the dark.
Movies about vampires in the Arctic Circle are fun but vampires at the equator would be more terrifying for the humans at dusk and for the vampires at dawn.
> The whole "6am sunrise and 6pm sunset every day of the year" thing at the equator is kind of mind blowing.
You can take this further. Look at weather and seasons. Here's Nairobi's yearly averages[0]. You can see that both temperature and precipitation are fairly consistent. On the other side of the continent Libreville[1] has a bit more precipitation variance but still low temperature variance. Let's got to South America with Macapa[2] and Quito[3] and let's keep going and land in Kuching[4].
Essentially in these regions, there are no real seasons. At least in the sense that many think of them. Things do change, but winter isn't that different than summer.
I know there are variances, but the scale masks a bit of what's going on. So let's look at London[5], Osaka[6], Auckland[7], Los Angeles[8] (often joked at for having no weather), Seattle[9], and Oslo[10]. As you can see, these are extremely different situations. It even has large effects on how people think about weather, time, and other things.
It's funny how what is so obvious and normal to some are completely different to others. Sometimes seeming as if we live in different worlds. In some sense, we do, and I think we often forget that.
I lived in East Africa for a while and you’d get kick out of the way time is referred to in Swahili, “midnight” is 6am, and the first hour of the day 7am etc. makes a ton of sense when sunrise is around the same time each day!
There is the same number of hours of daylight, but near the poles you sleep through a lot of those hours in summer. So you experience far fewer hours of daylight.
Another mind blowing thing about the equatorial sun is seeing it above you! Where I grew up, the sun is never higher that 30 degrees.
Living at the equator most of my life, it's actually funny how schedules are messed up when the sunrise is half an hour earlier or later. Traffic becomes chaotic because some people insist on getting home before sundown, or things like people becoming uneasy that the school starts before sunrise.
Weather is fun too, because it changes by +/- 3 degrees throughout the year. The heat makes my bedroom door expand. We had an argument with the housing developers because we had custom doors that didn't fit. But turns out it was passing all the tests when they ran it, and not in hotter periods of the year.
> Another maybe counterintuitive fact is that (to a reasonable approximation) everywhere on earth gets the same number of hours of daylight over the course of a year.
Not the same amount of usable daylight though as the amount you have to waste to get a decent amount of sleep all year around varies by latitiude.
DST really bothers me. I actually have a wall clock set to local solar time, so that I can quickly see what time it "really" is. For some reason I've always been very sensitive to when sunrise and sunset is, and having them offset makes my brain feel weird.
Yeah I have to say the north of Europe is bad folks. Winters are terrible. You just go to work/school in the dark and come home in the dark. There’s also less snow now than twenty years ago which means even less light.
In the summer it’s light outside for more hours than you are awake. Okay wow, so what? It’s a nice novelty. But it doesn’t make up for it. Not remotely.
Midsummer is a sad time because now I know that I will lose X minutes every day of light.
Using DST is just the extra bit of small cruelty on top of that.
DST only really makes any sense at mid-latitudes. If you go close enough to the poles it just seems silly to move around that hour - does it really matter if the sun is up from 2 AM to 10 PM or from 3 AM to 11 PM?
DST is completely silly as far north as the Nordics. The rate of change in daylight is so rapid around the equinoxes, that the effects of DST are erased in less than two weeks. It's completely useless.
Shortest day where I currently live has 5h49min of daylight. My childhood home had full month of no daylight. You definitely have shortage of daylight as you move towards poles.
I’m in the Netherlands (around 52ºN) and in my opinion DST is counter productive, especially considering the effects of global warming.
Summers are getting hot, to the point where it’s uncomfortable to be outside while the sun is out. It’s barely tolerable in the shade, assuming you don’t move too much. It only gets comfortable outdoors after sunset. During workweeks this means you barely have any usable outdoor time before you need to go to sleep. It also means your bedroom has little chance to cool down before you need to go to bed. Summer nights are nice when you’re outdoors, but DST robs us of the best hours to be outside.
If we’re going to move the clock in summer, we should move it backwards another hour. It would mean 2 more hours (compared to the current DST) of nice summer nights, instead of extra hours of scorching sunlight. I suggest we call it ‘Moonlight Saving Time’.
Screw half measures like DST, as an office worker I have a dream of working in winter from 16:00 till 24:00, sleeping from 01:00 till 09:00 and enjoying my sunlight for the rest of the day. I would fit right in working remotely for a company somewhere in the Far East.
Of course, the worst part is that often in winter we don't get sunlight at all, only a gray-ish cover of clouds in the sky :(
Play with timeanddate.com's times. It gives the total amount of civil twilight for the day (which is split in half). For example at Atlanta (https://www.timeanddate.com/sun/usa/atlanta) there's 58 minutes per day at the summer solstice, 55 at the winter solstice, and 50 at the equinoxes. As you go poleward those numbers increase but it's always summer solstice > winter solstice > equinox. This is basically down to the angle between the sun's path and the horizon and I think I get why that would be different in summer than in winter but I can't get my head around the fall/spring bit.
I think the angle under which the sun rises/falls is steeper in spring/autumn. And summer/winter is less steep. And in summer it bends upwards when under the horizon, making summer sunset longer than winter. I'm not sure if these are the right words - it sounded better in my head!
You'd be able to do it based on the math in the article. Civil twilight lasts from sunset until the Sun is 6° below the horizon. So in the spherical law of cosines in the article, you'd just set a to be -6° instead of 0.
While southern Florida is hardly at the equator, living here has really highlighted how northern-hemisphere and temperate-centric the online sphere - tech in particular - tends to be.
We don't get spring/summer/autumn/winter so much as rainy and dry season; heat pumps are irrelevant; natural disasters come in the form of hurricanes, and weather is either sunny or stormy; the days don't change in length much; and so on and so on.
It's a bunch of little things, but it's been surprising to me how often they come up in discussions, and just how rare (sub)tropical-specific problems and topics are in comparison. It makes me wonder what it's like to live somewhere even further removed from the natural world of the north.
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[ 3.7 ms ] story [ 250 ms ] threadThe difference as you climb in latitude is really shocking. Even just another 3-400 miles south of here, the rate of change is way less severe.
Anyway nice work and cool article! I've done some of these rough calculations myself before to plot out the change just to verify that I'm not insane for hating this time of year, and you did a way better job than I ever did :)
nox -> noctes, so equinoctes, if you're feeling Latin
I do think the extreme polar opposites in daylight and temperature for summer and winter solstices contribute to people here being a little...unbalanced. But for a lot of people, the unique landscape, low population, and abundance of outdoor activities make it worthwhile.
I'm originally from São Paulo, Brazil, the Tropic of Capricorn almost cuts through the city itself. Sunrises and sunsets are very quick events, sitting somewhere to watch it would take some 30 minutes, and then darkness.
Even after 10+ years of living in Sweden I still get mesmerised by sunrises and sunsets here, they last for so long and I get to be awed by the changing of colours, shadows, shapes, for hours. It's one of my favourite things to do during summers, just to be out somewhere by a lake with some friends, having food and drinks, and watching the endless twilight.
I'm in the southern UK, and I'd take our late-May/early-August "it's light while I'm awake and dark while I (should be) asleep" all year round if I could get it.
We went for dinner in the afternoon, sun was up, it was blazing hot, everything normal so far. We had dinner while the sun set in a nice air-conditioned restaurant, so it was dark when it was time to leave, and I walked out into the tropical night and was so confused why it was still warm and moist outside!
On the other hand, reading a book outside in normal daylight will hurt your eyes. The paper reflects too much light.
Kindles solve this problem by being gray; I've never understood why Amazon went on to develop a "Paperwhite" model. Paper is too white!
In Chile you get somewhat long days and short days too, especially in the south, but instead of trying to be super precise about sunlight, the afternoon and night blend in and sort of crossfade. You end up with "8 de la tarde" (8 in the afternoon), and "6 de la noche" (6 at night) depending on the season.
7/8/9 de la noche (vs tarde) is used by 60/97/100% of American Spanish speakers vs 1/16/97% of European Spanish speakers. I wonder if the difference is due to Spain's generally late sunsets.
It would be interesting to redo this analysis with a corpus that indicates seasons though.
Where I’m at in Aus it’s day light till 10pm at the summer solstice.
No sun to really speak of at the winter solstice though.
I had noticed this too and wondered if it was exactly true, with the "zigzag" being straight lines - I thought there might be a simple proof of this fact based on some trig identities. There's not, because it's not true - the lines aren't exactly straight, even if you ignore solar refraction - but it's a very good approximation.
Is the graph correct at those extremes? Like North Pole?
Also signal analysis people will enjoy this natural system producing "almost pure" triangle and square waves. Nudge the plot to 66.55 degrees and it's at the most triangle wave point. :)
For example, if you're at the North Pole, the sun is below the horizon all winter, and then on the vernal equinox rises above the horizon and does not set again until the autumnal equinox. So, formally, the rate of change in daylight is zero all year long, except on the equinoxes when it is infinite. Any latitude above the Arctic Circle will have these kinds of singularities.
In practice there are some corrections to the amount of daylight that I discuss at the bottom of the article, the most important of which is the effect of atmospheric refraction. If you were standing on the North Pole, you'd actually observe the Sun appear to rise some time before the vernal equinox.
For what it's worth, brr.fyi documents a sunset at the South Pole: (https://brr.fyi/posts/sunset) and a sunrise (https://brr.fyi/posts/redeployment-part-one)
In the extreme latitudes, you have short days where the sun just goes maybe 5 degrees into the sky and then down again: https://www.youtube.com/watch?v=Wzv_3LeA85c
And days where the sun just circles around your location on the planet: https://www.youtube.com/watch?v=in0B1OQG3-M
The opposite also happens, where the sun is below the horizon for months or weeks, and at the end of that period, it will inch towards the horizon, and you expect sunrise, but nope, it'll move furrther again... of course there'll be twilight (followed by night), but you might not see the orange ball of bright light for weeks or months.
The impact this has on daily life is larger than I had anticipated, and in general reducing the intensity of the cycle is a selling point for cities closer to the equator. It’s been nine years since my migration north, and I’ve only moved further north so this isn’t a deal breaker for me. It’s mostly something from my childhood and young adulthood that I took for granted. I’m now eagerly awaiting the day when my normal waking time is during dawn, which should be in early April.
I’m still significantly further south than Northern European countries mentioned in this thread. Maybe life has more moves north for me in store.
An artifact of this is that my 5yo might not see a dark sky for the entire summer, unless we keep him up awake for the traditional Midsummer hangin'-out.
When the day length is maximal/minimal (solstice), the day length change rate is near zero, and vice versa. That's still true in the more accurate model, even though the shape of the functions is more distorted.
If you replace 50 minutes with: - 6 degrees, you get the times of "civil twilight" (roughly speaking, when you don't need light outside). At 60 degrees north at midsummer the minimum altitude of the sun will be about -6.5 degrees so almost all of the nominal night is civil twilight. - 12 degrees is "nautical twilight" (horizon clearly visible) - 18 degrees is "astronomical twilight" (sky is dark enough for all astronomical observations).
(It's possible that those are defined as 6 degrees + 50 minutes, etc.)
For me X is then a "travelling" value which in the winter is at 1/3 between sunset (0°) and civil dusk (-6°), and in the summer it goes up to 2/3. Calculated as the moment when the blinds go down.
I'm using https://astral.readthedocs.io for this.
> On the equator, every day of the year is exactly 12 hours long
But surely that is not true, as the Earth's rotation is tilted. Is this supposed to be a year round average? Despite calling out more advanced corrections one can make, this doesn't seem to be mentioned anywhere?
timeanddate.com gives (https://www.timeanddate.com/sun/indonesia/pontianak) variation between about 6.5 minutes and 7.5 minutes above 12 hours, long at the solstices and short at the equinox. The difference is due to the sun setting vertically at the equinoxes and at a slight angle to vertical at the sunset.
You'll also be able to understand time zones and great circles (flight paths) better with a globe.
The reason that days are a few minutes longer than nights at the equator is due to atmospheric refraction which makes the sun visible a little before it actually has "risen" and similarly, keeps it visible a little after it has "set".
I really appreciate the long winter nights and long summer days in Norway. Being able to wake up to the sun as early as 04 and enjoy it until after 23 is great, and the UV is only high during the middle of the day. Long summer days are awesome. Long winter nights are probably not as appreciated, but I enjoy those too.
Spring/fall tend to be cloudy & rainy, and November to February-ish is referred to as "the big dark" - the days are short and the sun is low and obscured by clouds when it's above the horizon. Sounds like you'd get a lot done then (as do many people here).
https://www.bbc.com/future/article/20170314-the-town-that-bu...
Despite that huge change, I adapted to the new climate just fine. I don't mind the gloom or the cold. The six months of gray skies don't get my down like they do a lot of people.
But even after a decade, I still haven't gotten used to how much the day length changes. Every summer my brain keeps expecting the sun to go down any second now while it sits up there near the horizon giving an extra two hours of daylight. Every winter it feels like the sun disappears too early.
It’s rarely super hot or super cold like a lot of places.
You get these ridiculously long summer days that last forever. It’s perfect for athletics and hiking and spending time on the water.
And likewise you get these wonderfully wet and dark winters which are perfect for life’s other joys: coding, reading, playing video games, boardgames, drinking coffee, etc.
I love places like San Diego / LA but I wouldn’t want to live in a place that is always a perfect summer day.
Unless you're inland, where it's ninety billion degrees in the shade half the year.
Nice place.
I love 4 seasons. But the weather and day length make for a difficult half-year from Oct - Mar. The NE corridor has some of these traits, but it was a lot easier to deal with there. In the NE, rain & grey-skies aren't as persistent. In Seattle, a month can go by without seeing the sun.
Temperature-wise, most of the UK is actually quite moderate compared to central Europe. It's winter darkness that gets to you.
Why? What help does it make adding one extra hour to the start of the day, when the day lasts like ~4 hours.
https://www.timeanddate.no/astronomi/sol/norge/oslo
25th of october day is from 08:21-17:39, 26th of october from 07:24-16:36 after dst, and then 17th of November we're at 08:19-15:43 (so back to dark mornings). I'd rather the 17th have light until 16:43.
Not as satisfying as a derivation here, but a quicker way to get the answer.
EDIT: I did a spot check for Rovaniemi, Finland. This city is far north enough that the sun is up all day (66.5 degrees). But the graph on this page seems to be a little bit off: it requires an even higher latitude for that to show up.
Another maybe counterintuitive fact is that (to a reasonable approximation) everywhere on earth gets the same number of hours of daylight over the course of a year.
Winter is… Sunrise at 08:12AM and Sunset by 04:00PM(16:00).
You can technically use this info to guesstimate my location ;)
The problem was that 20 hours of daylight, especially having 2:30 AM feel like 6:30AM. It was impossible to get an adequate amount of sleep. The paper thin curtains in the cheap hotel where I stayed did nothing to block out the light.
If I am ever in that part of the world at that time of year again, I will be bringing a sleep mask and seeking out a hotel with proper blackout blinds or curtains.
That's not an excuse to not provide black out curtains at a hotel for international guests, but I guess people just don't think about it.
Bonus, they now work as great blackouts in my home office for video calls when I do not want sunshine and clouds to change my green-screen effects etc.
The silver lining is that our longest days are often our sunniest.
Movies about vampires in the Arctic Circle are fun but vampires at the equator would be more terrifying for the humans at dusk and for the vampires at dawn.
Essentially in these regions, there are no real seasons. At least in the sense that many think of them. Things do change, but winter isn't that different than summer.
I know there are variances, but the scale masks a bit of what's going on. So let's look at London[5], Osaka[6], Auckland[7], Los Angeles[8] (often joked at for having no weather), Seattle[9], and Oslo[10]. As you can see, these are extremely different situations. It even has large effects on how people think about weather, time, and other things.
It's funny how what is so obvious and normal to some are completely different to others. Sometimes seeming as if we live in different worlds. In some sense, we do, and I think we often forget that.
Another mind blowing thing about the equatorial sun is seeing it above you! Where I grew up, the sun is never higher that 30 degrees.
Weather is fun too, because it changes by +/- 3 degrees throughout the year. The heat makes my bedroom door expand. We had an argument with the housing developers because we had custom doors that didn't fit. But turns out it was passing all the tests when they ran it, and not in hotter periods of the year.
Not the same amount of usable daylight though as the amount you have to waste to get a decent amount of sleep all year around varies by latitiude.
In the summer it’s light outside for more hours than you are awake. Okay wow, so what? It’s a nice novelty. But it doesn’t make up for it. Not remotely.
Midsummer is a sad time because now I know that I will lose X minutes every day of light.
Using DST is just the extra bit of small cruelty on top of that.
The shortest day still has 7-8 hours of daylight. There's no shortage of daylight, we have too much work.
Summers are getting hot, to the point where it’s uncomfortable to be outside while the sun is out. It’s barely tolerable in the shade, assuming you don’t move too much. It only gets comfortable outdoors after sunset. During workweeks this means you barely have any usable outdoor time before you need to go to sleep. It also means your bedroom has little chance to cool down before you need to go to bed. Summer nights are nice when you’re outdoors, but DST robs us of the best hours to be outside.
If we’re going to move the clock in summer, we should move it backwards another hour. It would mean 2 more hours (compared to the current DST) of nice summer nights, instead of extra hours of scorching sunlight. I suggest we call it ‘Moonlight Saving Time’.
Of course, the worst part is that often in winter we don't get sunlight at all, only a gray-ish cover of clouds in the sky :(
It depends on the latitude for sure, but also I think on the time of the year?
I think the angle under which the sun rises/falls is steeper in spring/autumn. And summer/winter is less steep. And in summer it bends upwards when under the horizon, making summer sunset longer than winter. I'm not sure if these are the right words - it sounded better in my head!
While southern Florida is hardly at the equator, living here has really highlighted how northern-hemisphere and temperate-centric the online sphere - tech in particular - tends to be.
We don't get spring/summer/autumn/winter so much as rainy and dry season; heat pumps are irrelevant; natural disasters come in the form of hurricanes, and weather is either sunny or stormy; the days don't change in length much; and so on and so on.
It's a bunch of little things, but it's been surprising to me how often they come up in discussions, and just how rare (sub)tropical-specific problems and topics are in comparison. It makes me wonder what it's like to live somewhere even further removed from the natural world of the north.