Why Is Culture Day Said to Be So Often Sunny?
― Weather records have bumps, even from pure chance
Culture Day, November 3, has long been called a "sunny singularity day". It is true that autumn is a season when sunny high-pressure systems pass often. But whether one single day is unusually sunny is a different question. With only a few years of records, a day with no special cause can still look like a "sunny day".
Many people plan a school sports day or a Shichi-Go-San photo shoot for the November holiday weekend.
You may have heard a parent or grandparent say, "Culture Day is usually sunny, so it'll be fine."
Can one day on the calendar really be favoured by the sky?
There are two reasons: one in the sky, one in the numbers
From October to November, dry high-pressure systems drift in from the continent one after another. It is true that this is a season with many sunny days anyway.
Sunny or not sunny is like a lottery drawn every year. After only a few dozen draws, every date shows big bumps.
The first is about the whole season. The second explains why one particular day stands out. Let's take them in order.
Autumn sunshine: high-pressure systems drift in from the west
In autumn, the westerly winds high above Japan shift south. Carried by these winds, high-pressure systems born over the continent travel from west to east. They are called travelling high-pressure systems.
Inside a high-pressure system, air sinks slowly, so clouds have trouble forming. The air is dry, so you can see far and clearly. That is what lies behind a fine autumn day.
But after a high comes a low. That is why autumn weather changes every few days. The date a high arrives shifts from year to year. So "sunny as a season" and "sunny on the same date every year" are, strictly speaking, different things.
Why does "that one day" get picked out?
This is the heart of the matter. To work out the "share of sunny years" for a date, you have no choice but to count through past records, year by year. With 100 years of data you count 100 draws; with 30 years, 30 draws.
Look at Figure 1. It is a made-up record. For every day from October 20 to November 15, we decided the "true chance of sun is 60%" and let the lottery run year by year. No day has any special reason. Even so, the dots bounce up and down, and some days poke out of the band.
With 30 years of records, the band is about 18 points wide on each side. So even if the true figure is 60%, it is not unusual for a day to look like 78%. And a year has 365 days. Some of them will step outside the band by pure chance. The calculation gives about 8 days a year (details in the fold-out at the end).
People notice only the days that stick out. If that day is a holiday, it is even easier to remember. This is how sayings like "it's always sunny on such-and-such a date" are born.
So what about November 3?
In weather terms, a singularity day is explained as "a day on which a particular kind of weather appears with a probability too high to be chance, compared with the days around it". The key phrase is "too high to be chance". So whether a day is a singularity day depends on whether it keeps sitting outside the band in Figure 1 even as the record gets longer.
November 3 became famous because old records, from Tokyo and elsewhere, are said to show a higher share of sunny days than the days around it. It falls in the period when travelling highs pass often, so there is a seasonal basis. On the other hand, some point out that it fades when the period of records is changed. The present understanding is that we cannot say the saying is all chance, or all real.
It is sometimes said that the opening ceremony date was "chosen because it is a sunny singularity day". But some take the view that, in the statistics, October 10 is not especially sunny. The fine weather on the day itself may simply have strengthened the saying.
Summary
Autumn is a sunny season because travelling high-pressure systems pass through, and that is a solid reason. But to say "only one particular day is sunny", the day has to rise above the bumps of chance. A few decades of records are surprisingly short for telling chance apart.
What makes it sunny is the "season".
Whether that one day is special depends on whether it lies outside the band of chance.
For how an autumn sky comes to look high and clear, read "Why does the autumn sky look higher than the summer sky?". For a saying that relies on weather moving in from the west, see the story that a red sunset means a fine day tomorrow.
- On the Japan Meteorological Agency website, open "Past Weather Data Search" and choose the observation station nearest your town. You can look back through the daily weather summaries year by year.
- For November 3 and a few days either side, count how many of the past 30 years were "sunny".
- Next, flip a coin 30 times and count the heads, and repeat that about five times. Compare how much the results vary from round to round with how much the weather counts vary.
The number of heads can differ by 10 or more between rounds, even though the chance is the same every time. The trick with the bumps in weather records is to compare them with this kind of "wobble" first, and only then think about what they mean.
For those who want to know more ― terms, formulas and links to textbooksEach part is labelled with its level, from junior high science to university specialist courses
- Junior highCovered in junior high school science and maths
- High schoolCovered in high school Earth science and maths B (statistical inference)
- High school+Advanced high school material, or a textbook sidebar topic
- UniversityUniversity specialist courses (statistics, climatology) not taught in high school
- ResearchNot yet taught as settled fact even at university; researchers are still studying it
Junior highTerms: this phenomenon has names
- Singularity day: a day on which a particular kind of weather appears with a probability too high to be chance, compared with the days around it. There are sunny singularity days, rainy singularity days and so on.
- Travelling high-pressure system: in spring and autumn, a high that moves from west to east across Japan. It is sunny while it passes, and the weather tends to break down after it leaves.
- Sunny-day rate: for a given date, the share of recorded years that were sunny. It is the "share of sunny years" in this article.
Junior highHigh schoolChecking with a formula: how big are the bumps of chance?
Let p be the true chance of sun on a given day and n the number of years recorded. If we treat each year's weather as a "lottery that hits with probability p", we can calculate how much the counted sunny-day rate wobbles.
| In symbols | σ ＝ √( p × ( 1 − p ) ÷ n ) |
| In words | Wobble of the sunny-day rate ＝ the square root of "chance of sun × (1 − chance of sun) ÷ number of years recorded" |
| Where it comes from | The spread in the share of hits when you draw a hit-or-miss lottery n times (the standard deviation of the binomial distribution divided by n). With 4 times as many years, the wobble is halved. |
| True chance of sun p (Figure 1 setting) | 0.6 (60%) |
| Years recorded n | 30 years, or 100 years |
| Chance of landing above twice the wobble by accident | About 0.023 (about 2.3%) |
| Days in a year | 365 days |
| Symbol | Meaning and unit |
| p | True chance of sun (a share from 0 to 1, no unit) |
| n | Years recorded (years) |
| σ | Size of the wobble in the counted sunny-day rate (a share, no unit) |
| Chance of no sun | 1 − 0.6 ＝ 0.4 |
| Multiply the two | 0.6 × 0.4 ＝ 0.24 |
| Divide by 30 years | 0.24 ÷ 30 ＝ 0.008 |
| Its square root (wobble σ) | The square root of 0.008 is about 0.089 |
| Half-width of the band (twice the wobble) | 0.089 × 2 ≒ 0.18 |
| For 100 years, change the divisor | 0.24 ÷ 100 ＝ 0.0024 |
| Its square root | The square root of 0.0024 is about 0.049 |
| Half-width of the band at 100 years | 0.049 × 2 ≒ 0.098 |
| Days a year that land above the band by chance | 365 × 0.023 ≒ 8.4 |
With 30 years of records, a day whose true chance is 60% can easily look like 78% or 42%. And about 8 days a year look like "sunny days" through pure chance. Even with 100 years, a wobble of about 10 points remains. To be called a singularity day, a date has to clear this width by a wide margin.
High schoolHigh school+The seasonal basis, and the statistical trap
High schoolIn Earth science you learn that in autumn the westerlies shift south and travelling highs and lows pass in turn. In maths B you learn the binomial distribution, and that the scatter of a sample share is inversely proportional to the square root of the number of years. Singularity days are where these two meet.
High school+Weather has a tendency to last for several days (persistence). So a peak made by chance tends to show up not on one day but across several neighbouring days. "Higher than the days around it" alone makes it even harder to tell from chance.
UniversityThe multiple-comparison problem, and testing singularity days
Checking all 365 days and picking the most striking one is what statistics calls the multiple-comparison problem. A result that is rare for a single day will certainly turn up somewhere if you look at enough days. University statistics teaches methods such as the Bonferroni correction, which tightens the standard according to how many comparisons were made. In climatology, the approach has been to draw a smooth curve of seasonal change and judge a singularity day by how many standard errors a day deviates from it.
📖 Derivations and further reading: Standard error (Wikipedia, in Japanese) ／ Multiple-comparison problem (Wikipedia, in Japanese)
ResearchWhat is still not clear
- How many real singularity days are there? Under strict standards, many of the sayings are said to fall within the range of chance. Which ones survive changes with the period and place used.
- Is there a "calendar rhythm" that produces singularity days? The meanders of the westerlies are thought to have patterns that tend to occur at set times of the season. Whether that pins things down to a specific date is not clear.
- Will warming move singularity days? If the pace of the seasons changes, former singularity days may fade, it has been pointed out.
So the content of this article too is "an explanation within what is known today". Before believing a saying, or laughing at it, compare it first with the width of chance. That is the basic way to read records.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Junior high | Science, year 2 "Weather and its changes"; maths "Probability" | Highs and sunny weather, the lottery comparison |
| High school | Earth science "Motion of the atmosphere"; maths B "Statistical inference" | Travelling highs, the wobble formula |
| High school+ | Persistence of weather | Chance peaks spanning several days |
| University | Statistics, climatology | Multiple-comparison problem, judging singularity days |
| Research | Seasonal change of climate | How many real singularity days exist |
| ― | Links to daily life | Scheduling events, living with sayings |
- Japan Meteorological Agency (気象庁), "Forecast Terminology" (explanations of singularity day and travelling high-pressure system)
- Singularity day (Wikipedia, in Japanese)
- Standard error (Wikipedia, in Japanese)
- Multiple-comparison problem (Wikipedia, in Japanese)
- Meteorological Society of Japan (日本気象学会), ed., Encyclopedia of Meteorological Science (『気象科学事典』), Tokyo Shoseki (東京書籍)
※This article is a popular-science explanation for general readers. The figures given are rough guides to help you understand how things work. Figure 1 is a made-up record for illustration, not real observations. For decisions about events, check the Japan Meteorological Agency forecast on the day.