It's Always Sunny in Miami, and Not So Much in Boston

My old roommate and I were involved in a vicious feud. You see, he liked to open the windows when it was warm out; however, he always neglected to go back and close them when it inevitably got cold again. This resulted in me shivering for a few hours before I realize that, while it was 75 degrees only a day ago, it's now 55 degrees and I should really put on some pants.

 The essence of the problem can be described in visual form:

This is a common problem for anyone who's lived in New England, where any Uber trip between April and June is likely to involve complaints about the weather. 

Just how common is this problem? I set out to find just how fickle the daily temperature is among the top 25 US cities. In choosing these cities, I used a combination of metrics: population, GDP, and net migration. The analysis was done using the statistical software R, with weather records from Weather Underground. (For a more detailed, technical view of how I worked with the data, click here)

I first set out to find the variance of the weather for these cities as a measure of volatility. I used daily high temperature data for all 366 days of 2016 (a leap year). I ranked the cities by their temperature variance, in descending order, below:

But what does this really mean? Variance is defined as the squared sum of deviation from the mean. In other words, a high variance in this context would mean that a city has many days in which the temperature is much different than the average temperature for the entire year. This could mean many days of ping-pong hot and cold weather, or simply a very pronounced changing of the seasons. Let's look at a temperature graph of a few selected cities. I've ordered them from high to low variance:

       

We see that cities with high variance, such as Minneapolis and Denver, have temperatures that reach a wide range throughout the year, and while there's a definite pattern (cold winter, warm summer), there are still sharp week-to-week and sometimes day-to-day changes - see Boston's dip to a high of about 60 degrees in July and then a jump to the 90s a week after. On the flip side, cities with extremely low variance such as Miami and San Francisco have much flatter, lower-amplitude graphs. Amazingly, Miami's daily high temperature hovers between 72 and 92 degrees Fahrenheit a full 90% of the year!

This doesn't fully answer my original question - in which cities are you most likely to experience the frustration of making a completely new daily evaluation of your window openings, how many layers to wear, and whether or not to finally put away your winter clothes for good? To answer this, I've calculated the temperature swings of each day over the previous day. I've chosen a difference of +/- 10 degrees as an arbitrary metric for "pain-in-the-butt-weather". Let's see the results:

So, almost every third day in Boston seems to be a jump in temperature. However, in Miami, you can paint a pretty accurate weather forecast of tomorrow if you've been outside today. I guess now we know why Pitbull is so happy.

PS -I also calculated the number of days in a year with a 20+ degree temperature swings. Denver leads with 21, but almost all cities have 10 or less of these days (Miami and San Francisco have 0). So, if you wake up one morning and it's 20 degrees colder or hotter than the day before, do note that this is pretty rare, and therefore definitely merits complaining (I'll be here to listen!)