Heat makes people miserable. Economists have found that people would generally be willing to pay 1 percent to 3 percent of their annual income to avoid a 1 degree Fahrenheit increase in summer temperatures, for instance.

But you don't need to be an economist to understand this: Just talk to anyone who works in Washington in the summer. Or look at what people are saying on Twitter in August. Or even better, look at what 1 billion people said on Twitter in 2014 and 2015, cross-reference their locations with weather data, and then use sophisticated sentiment-analysis techniques to determine the effect of temperature and weather on people's moods.

That's what Patrick Baylis, a fifth-year PhD candidate in agricultural and resource economics at the University of California at Berkeley, recently did. He detailed his efforts in a working paper released last month, and the results are fascinating. He found that, compared with a day when the high temperature is 72.5 degrees, a day with a high temperature of 90 degrees makes the typical person experience a drop in happiness similar to the drop in happiness between Sunday and Monday.

If you know anything about happiness research, or if you are simply a human being with a job, you know that that difference is huge.

Here's what that looks like in graphical form. The shaded areas represent confidence intervals — bigger shaded areas indicate more variation in individual responses. I'll discuss the left half of the chart in a second — for now, focus on the right, showing a continual drop in happiness as high temperatures rise above 70 or so degrees.

At the heart of Baylis's research is sentiment analysis, and if you don't mind getting into the weeds for a second, it's helpful to know how this works. Certain words imply different emotional states. In the example Baylis gives in his paper, the Tweet "happy anniversary mom and dad" contains five words. "Happy" has a positive emotional connotation, and the rest of the words are essentially neutral. So that Tweet would rank overall as an emotionally positive one.

Similarly, the tweet "i can't watch matt cry" has one negative word — "cry" — and four neutral ones. So it's negative overall.

There are different techniques for weighing the relative emotional importance of various words. To cover his bases, Baylis employed four of them: One was a ranking of word emotion based on expert assessments, and another was a similar emotional dictionary that was crowd-sourced. He also used a measurement based on whether or tweets contained profanities (with the understanding that cusses generally imply negative emotion) and an algorithm that attempted to measure the tone of a tweet based on the emoticons it contained — :), :(, :D, etc.

Sentiment analysis isn't perfect. It has a hard time detecting sarcasm and irony, for instance. If I drop the f-bomb in a tweet, is it because I'm mad or because I'm excited? But, overall, it does a pretty good job of characterizing aggregate emotions, especially across a huge data set. And Baylis first checked the sentiment measures of his billion tweets by day of the week and found, as you'd expect, that people were happier on the weekends and generally less happy during the workweek.

If warmer temperatures are associated with less happiness, you might think that the negative effect of colder temperatures was just as great. But, in a mystery, Baylis's numbers don't necessarily show that. When you get colder, people's emotions start to dip, too, after a point — but by a lesser amount. And there's a lot more variation in how people respond to colder temperatures -- that's what those wide confidence intervals on the left-hand side of the chart imply.

Here's that chart again, for reference.

Baylis has some ideas for why this might be. You can always put on more clothes when you get cold — but after a certain point you can't take any more off when you're hot (this is especially true when you work in an office).

There's another possible explanation, too: "Once you get really cold, you're no longer likely to be tweeting," Baylis said in an interview. "You're just not taking your phone out."

Baylis did a lot of extra analysis to account for various confounding factors. He controlled for wealth and income (more money = more happiness). He controlled for seasonal variations, for days of week, for daily temperature spread, and for other weather effects, such as rain and humidity.

He also accounted, as best he could, for the fact that Twitter users are demographically distinct from the general population. He found that doing so didn't change his results much — if anything, he thinks his numbers may be underestimating the true effect of warm weather on mood.

Twitter users "are younger, more African-American, more urban, better-educated and wealthier" than the general public, he said. "A lot of these aspects — income, urbanity, education — would indicate that those people have more adaption to temperatures available" — for example, more access to air conditioning, better heating, better-insulated homes, etc. "This might make my results look less strong they are," he said.

Baylis ran some back-of-the-envelope calculations and found that a one-degree increase in temperature has an effect on your happiness that's similar to living in an area with a median income that is $500 lower.

This starts to have implications for what we know about the effects of global warming. Economists have done a pretty good job of calculating the costs of higher temperatures when it comes to things such as crop yields and economic productivity. But, Baylis says, "we are underestimating the social costs of carbon."

In the paper, he runs a few different scenarios to try to project the effect on happiness across the United States if temperature projections for the end of the century hold true. The numbers are very rough, almost more of a thought experiment, but they're startling: In some areas of the country, the change in temperature could be "the equivalent of replacing every Saturday and Sunday in a year with a Monday."

In other words, climate change may mean that the weekend is over, for good — at least from a net happiness perspective.

Baylis stresses that this is just a working paper and that he is working to revise it based on feedback from other economists. But his adviser at Berkeley, Maximilian Auffhammer, has good things to say about it: This study "might be the economics paper that has quantified the most broadly applicable non-monetary costs of climate change," he wrote last month.

More from Wonkblog: