How is long-range weather forecasting different than short-range forecasting?
Short range forecasts are based off of observed and extrapolated data and how systems are moving. Long range forecasting are created off of computer models.
There is in fact no chaos when it comes to weather, but an inability to measure every variable, mostly due to lack of funding (the cost for very accurate weather forecasts would be many times more than what is currently spent). That is where computer modelling comes in. We take what we are seeing and measuring and we look at the motion. Then computer takes the variables that we have measured and extrapolates numbers for the areas that are missing. Using this data it creates a model that is mostly correct. This provides a short range forecast that is fairly accurate.
Now, the computer has extrapolated some of the data on the short term forecast which fills in missing gaps, and it will be correct for many of this gaps, but not all of them. When you increase the time frame for the forecast you are building a new model based on the first model, which has extrapolated data and gaps in it. Each successive model that you build off of that one will have more and more errors because you are building off of the initial errors.
After a few hours the accuracy starts dropping off rapidly so that the 5 day forecast is usually not great and anything beyond that is almost pointless.