2nd derivative max for Insolation

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2nd derivative max for Insolation

Michael Ossipoff
This email originated from outside ECU.

Some months ago, due to comments about Februarius in Iowa, I looked the subject up on the Internet. I found temperature line-graphs, with respect to date, for two Iowa cities.
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Those line-graphs both were flat until Februarius 1, and then had an abrupt, sharp and brief upturn at Februarius 1.  
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Why? It suggested that maybe the daily insolation (amount of ground-warming sunshine received by the ground) there also had a sharp and abrupt upturn-point.  Of course it would be a bit earlier, with thermal timelag postponing its effect to Februarius 1.
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And yes, insolation at the latitude of Iowa's middle-latitude city, Cedar Rapids, indeed has an abrupt sharp upturn shortly before Februarius 1.
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It occurs at a Solar ecliptic-longitude of 05Aquarius, the 5th degree of Aquarius.  This year, that, was on January 25th.
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At that Solar ecliptic-longitude the insolation's graph's steepening-rate has a maximum.
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Another word for steepening-rate is acceleration.  It's also the 2nd derivative of daily insolation with respect to ecliptic-longitude.
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The point of maximum steepening-rate could be called the takeoff-point.  It could also be called a knee-point.
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Incidentally, the day-length, too, has a midqurter (not at one end of the astronomical-quarter) 2nd-derivative maximum.   ...at the Solar ecliptic -longitude 10Capricorn.  That was almost exactly at New Year's Day this year.
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In the North, even at Cedar Rapids' latitude, the day-length increases drastically as Solar-declination increases.  And day-length starts its increase early too, with its 2nd-derivative maximum, its takeoff-point, at 10Capricorn, New Year's Day.
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Already, in Cedar Rapids, the day-length has 70% of its maximum value (its value at Litha, the Summer-Solstice).
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What about Solar declination itself? It doesn't have a "knee-point" (a midquarter 2nd-derivative max), because its maximum 2nd-derivative (with respect to ecliptic-longitude) is at Yul, the Winter-Solstice.
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The takeoff-points of day-length and daily-insolation are the first astronomically-seasonally-significant days after Yul.     ...coming before Imbolc (a day of observance of the very soon-to-arrive Februarius transitional-time).
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This morning at 1155 UTC, the Solar-declination passed the halfway-point from its Yul value to its Ostara value.  The ecliptic-month of Pisces will begin early tomorrow (Februarius 19th)morning UTC.
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9 Tu
(Calendrical) Aquarius 30th
Februarius 18th, 2020