What we did
Dr. Scheffler collected and saved (nearly) all the German language tweets for an entire year. She then selected all the tweets that included the German phrase for "good morning" (Guten Morgen). We then analyzed the data to find what time each morning the phrase really starts to take off, and called that the "onset of twitter activity" (i.e. what time people woke up).
What we found
The data can be best explained visually. Here is a plot of what time the sun rises (in Frankfurt) throughout the year. Winter is near the middle, and the "fall back" and "spring ahead" of Daylight Savings Time are shown as dashed lines. We don't change the clocks on this plot, to make it easier to see how wake times relate to the sun.
Now here's what wake times look like on weekdays:
Throughout the year, the typical* wake time on a weekday is around 5:50 am (in local time). You can see that there are a few weekdays that look very different from typical. Those are holidays, and the bunch in the middle are the days between Christmas and New Years.
Now here's what it looks like on Saturdays:
And here's Sundays:
You can see that during the late fall winter, and early spring, the wake up times on weekends are closely related to the time that the sun comes up. But then Daylight Savings Time comes and the relationships break down. Here's what it looks like with all the data together:
The gap between the blue compared to the black and red lines shows you how badly people are punishing themselves by using an alarm clock. About 80% of people in Europe use alarm clocks, which means that they aren't getting a full night's sleep. But what can we do about it?
Take a look at the difference between the blue and red lines. You can see that at the end of March, they're almost reaching each other. If they were to touch, it would mean that millions of people would manage to wake up fully rested without needing an alarm clock.
The plot shows that Daylight Savings Time lasts too long. If it started later in the spring and ended earlier in the summer (or if it was eliminated altogether), millions more people would get a good nights sleep. We would be healthier, feel better, be less likely to be involved in car crashes, and our entire society would be more productive. High school and university students would benefit in particular, because they need to sleep in the latest. Schools would have fewer disciplinary problems, students would fall asleep less often in class, and because they are alert, they would learn more.
If you'd like to read our full paper, it's freely available online. If you'd like to have a laugh and hear more about how terrible Daylight Savings Time is, here's John Oliver asking how it's still a thing:
* This might seem a bit early, and it is. It's related to the method we chose to select a single time. Long story short, some people wake up earlier than this, most people wake up later, but the time shown here is the most stable measure for start of twitter activity.