Stat analysis of seasons duration Firstly, how we can define seasons - Winter, Spring, Summer and Autumn?
There are many possibilities, let's choose average twenty-four hours temperature $\bar t$.
Next we set $t_1$ and $t_2$   (usually  $0^\circ C$  and $6^\circ C$).
Some  meteorologists define the  winter as period when $\bar{t} <  t_1$ steadily (stably).
So the summer is period, when $\bar{t} >  t_2$ stably.
Between $t_1$ and $t_2$ are placed transitional time 
 (for my purposes no matter spring or fall).
There is hypothesis that in Central Europe (and in most of Russia) 
transitional seasons will be shorter and shorter in the future.
Well meteorology is a weird science for me so let's use analytical statistics!
With Wolfram Mathematica it's possible to get a lot of weather data. 
Here is example of the analysis: for Moscow 1994-95 (and zoomed period Feb-Jun'94)  


And here is the question: how to find duration of  transitional seasons correctly enough? 
Days with $t_1 < \bar{t} < t_2$ painted green. But duration of all green days is not correct solution, 
because many of them are thaws and frosts, not transition!
So I am trying to find an algorithmic definition of transitional seasons duration.
 A: I’m going to answer on my own question.
In fact, main factor for climate is daily average insolation.
On 100 km above Earth it's value depends only from latitude and position of day in the year (orange curve). From this point, we have no any "stable" seasons, just smooth variations of warm and cold. For convenience, the period with curve above the middle may be "summer", and below -"winter".
Daily average temperature (blue points) is depends on  insolation (but on many others factors too).
In Tashkent  (pic.1)  it is close to insolation curve behavior, but in Lisbon 2001 (pic 2) looks chaotic enough  (all data are rescaled for comparison).
 
These pictures suggest me an idea. Let's call “transition“ day when
daily average temperature crosses year average temperature line.
In ideal continental climate there should be only two such days in the year.
In oceanic climate every third may be transition day. So I'd like to suggest measure for "seasonality" of the weather. It's just number of transition days on the year, divided by 365.
Here are examples of this measure for Khabarovsk and London during last decades:
 
For me it's clear that such measure makes sense, but I can't prove it, using strict stats methods.  
And now we can define what are spring and fall days, regardless of the phenologist’ assumptions and using only year average temperature.
Let's partition 365 days on samplings by 5-10 days (length of sampling is the only free parameter!) and calculate seasonality measure for every sampling.
Here are another two examples.
  
I see spring and fall seasons absolutely clear, regardless of the "vegetations temperature", "hormone level" etc.
Exact duration of transition seasons is dependent from length of sampling (but general qualia stay the same) and this is really statistic question.
That’s all, so I’ll be very glad to see some corrections and opinions.
