The above methods assumed that the wind stays fairly steady for twelve or twenty-four hours. They also assume that there's no transformation in the air mass over that time interval. Frequently, neither assumption is correct. Usually, when cold air masses are heading southward, they warm up. When I was forecasting in Boston, I learned the "Burlington Rule": under strong northwest flow conditions, the high temperature in Burlington, VT, will equal the low temperature the next morning in Boston, MA. The air mass warms up considerably in transit due to orography, elevation changes, and other things which space and time do not permit me to explain now. Suffice it to say that air does not generally move passively from one place to another without having its temperature change.
Most locations have similar local rules. Two weeks is not enough time to figure them out for our forecast cities, but in the real forecasting world, those rules can be quite valuable.
Other times, the whole weather pattern might be changing. The winds may be from the north today, but they might be from the east or south tomorrow. It would be a difficult and time-consuming task to work out the source region for air as it travels a tortuous path to the weather station.