What are the advantage of using computer for weather foresasting instead of the manaul system

By the time the job was completed manually, you would be explaining history, not predicting the weather. Manual forecasting involved a thermometer and a barometer. Maybe a hygrometer and anerometer if you were really serious about it. It wasn't until the development of computers and electronic data transfer that it became more than a local, one day, educated guess.

The advandage is being able to store large amounts of data from many locations and digest the data quickly enough to produce advance notice of the many weather events that affect our lives. Manually you would be on the phone to the next city asking, "Hey Fred, what does it look like over there?"