The weather system is a complicated example of what's known as a chaotic system in mathematics. Most people have heard of the "butterfly effect", or the idea that a tiny perturbation of a system will exponentially grow into large-scale differences of behavior over time. This fundamentally limits our ability to predict the future with confidence.

An important parameter of any chaotic system is the Lyapunov time, which is the timescale over which perturbations grow large. The weather is a very complicated system, but current estimates for its Lyapunov time are around 15 days. Thus, any knowledge you have about particular weather conditions today won't inform your predictions very much for the weather in 15 days or so.

That being said, weather is driven by predictable factors like solar input, seasons, ocean currents, land topography, and so on. So at any given point on the Earth you can make some prediction of what the temperature, precipitation, and so on are likely to be on a given date, based on historical data. Those climate averages give you some degree of predictability.

So a way to think about it is:

• Weather forecasters are pretty good at telling you what will happen tomorrow.
• When they look out to 21 days from now, they can only predict based on historical climate data.
• Between "tomorrow" and "21 days from now", the accuracy of predictions gradually declines, because of chaos as well as limitations in the quality of our data and models.