What determines the accuracy of the weather forecast?

In general, weather forecasts are improving thanks to improvements in computer models, observations and our understanding of the atmosphere. The accuracy depends on the purpose of the forecast and how far it spreads. The forecast for the coming days of maximum temperature is good up to 3 or 4 days; However, the same forecast for the week is pretty bad.

The National Meteorological Service is seriously testing its weather forecasts as part of improving forecasting in general. To the public, accuracy may be less important than the usefulness of a forecast.

Hurricane forecasting has improved to the point where it can be used to predict landfall several days in advance. The National Hurricane Center did not release four-day hurricane track forecasts six years ago, but they are now issuing forecasts at a higher level. Hurricane intensity forecasts, however, have improved little since 2000.

Improving forecast accuracy
All of these measurements are fed into computers operated by the United States government or other countries. The European Union is the main source of weather data, but the British, French, Germans, Japanese, Canadians and Chinese have their own models.
Computers take these initial conditions and then use mathematical equations to make a prediction. There is no perfect algorithm because the Earth is so large that it is impossible to have observational data for every particle of air.
Because each computer model uses a different mathematical formula, each weather forecast may be slightly different.
Outputs or “solutions” to equations are usually maps that show things like pressure, temperature, and rainfall in a particular geographic area. Higher-powered computers receive higher resolution maps, which means they are more accurate.
Ultimately, there are differences that come from different computers, and then organizations have their own formulas and meteorologists who adjust those forecasts further.