Another fascinating point from Nate Silver’s The Signal and the Noise is where he talks about how far into the future we can forecast weather. It’s one thing to forecast what tomorrow’s weather will be like, but what about next weekend’s weather? Or next month’s? Silver provided one chart, with data courtesy of Eric Floehr at ForecastWatch.com, that highlights just how hard it is to forecast weather. I’ve reproduced that chart below.

This chart compares three major weather forecasting methods:

Persistence: This method assumes that tomorrow’s weather will be a lot like today’s weather. Tomorrow’s temperature will be today’s temperature ± a few degrees. Climatology: Since we have decades of historical weather data, we can average what happened in the past on each day to forecast what the weather will be like. This method assumes that the weather on July 4, 2014 in East Lansing, Michigan will be a lot like the weather in East Lansing on July 4 in all the previous years. Commercial Forecasting: Now that the National Weather Service provides so much data about the current weather, we can simulate the weather down to the molecule and create a model of what the weather is going to be like tomorrow.

As we’d expect, persistence forecasting performs pretty terribly. If you just take a look at your local weather for the past week, it’s rare for temperatures to follow a linear pattern of rising or falling temperatures for more than a day. Even averaging historical data is consistently off the mark by as much as 7°F. The real winners here are the weather models, which can forecast the correct temperature within 4°F up to 3 days out.

But even weather models have their limitations: Any forecasts more than a week out are going to be less accurate than climatological forecasts on average, which we’ve already established makes for a pretty poor baseline. By a week out, small inaccuracies in the weather models build up exponentially, to the point that the model is predicting temperatures far divorced from reality. This observation leads me to wonder why commercial weather forecasting sites like AccuWeather even bother providing forecasts up to two weeks out, considering we’d be better off just looking at the historical averages at that point.

So don’t bother looking past the 5-day forecasts on your favorite weather site. More likely than not, their forecasts are wrong.