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In meteorology the seasons always start at the beginning of the month the astronomical seasons start.
The astronomical seasons start around the 21st in a month so I guess it would make more sense to start the meteorological season at the first day of the month following the start of the astronomical season.
Another more logical reason to do this: for example the meteorological winter start at December 1 and ends at February 28 (or 29) in the next year so meteorology actually measures in broken years. Should the meteorological winter start at January 1 and end at March 31 then all seasons do exactly fit in the same year.
So is there a reason why meteorologists do it this way or is it just arbitrarily chosen?

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Meteorological seasons are based on temperature, whereas astronomical seasons are based on the position of the earth in relation to the sun. So meteorological winter is the three coldest months of the year (December, January, and February) and meteorological summer is the three warmest months of the year (June, July, and August). More information can be found on this NOAA web site.

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    $\begingroup$ Thanks I didn't notice that page before. $\endgroup$ – wie5Ooma Mar 2 '18 at 1:21
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    $\begingroup$ A useful related question to look at: Why is March colder than September in Northern Hemisphere? $\endgroup$ – JeopardyTempest Mar 2 '18 at 3:10
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    $\begingroup$ And it's worth noting that in many ways, astronomical seasons are actually most arbitrary. They're based on the key dates of solstices/equinoxes... but they're also not symmetric around them. You'd think winter would actually be the 90ish shortish days of the year (so Nov 6-Feb 6???). But the thing is the seasons are really about accumulated energy, and it takes time for gradually rising in Jan/Feb to erode the built-up losses of the previous months. $\endgroup$ – JeopardyTempest Mar 2 '18 at 3:12
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    $\begingroup$ This answer does a bad job at explaining why the meteorological seasons start earlier. One would actually expect them to start later according to this description of the definitions (because temperatures lag behind orbit). $\endgroup$ – leftaroundabout Mar 2 '18 at 10:58
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As JeopardyTempest commented: Actually, the astronomical seasons are defined in such a way that you should expect them to be a full 1 ½ months behind, not just 21 days! Namely, astronomical winter only starts at the winter solstice, astronomical spring only starts at the equinox etc.. A more intuitive definition would arguably be if the seasons were centered around these events. I.e., the astronomical seasons have ⅛ year lag built in.

This intrinsic misalignment is partially cancelled by another delay, the seasonal lag, which is in most places about a month. I.e. the temperature-defined meteorological seasons also lag behind the Earth's orbit, but by less than the astronomical seasons; the observation that the astronomical seasons lag behind the meteorological seasons by 21 days is just an alternative view point.

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