A forecast method that is right in principle fails if the answer arrives after the weather does. Early attempts to predict weather from the equations of physics collapsed because people could not solve the nonlinear equations fast enough for the result to matter. Speed of calculation, not the theory, was what held things back.
When a craft depends on one practitioner's lifetime of local experience, it remains more art than science. Its knowledge stays tied to particular people and places, and it cannot easily be checked, passed on, or carried somewhere new. Weather forecasting worked this way, as a 'guessing science', for much of the early twentieth century.
A field changed only when three ingredients arrived at once: a wide network of observations, people trained in the right mathematics and physics, and a machine that could do the arithmetic. Each had existed in weaker form earlier without transforming anything. In weather forecasting, war supplied the observing network and the trained people, and the new digital computer supplied the arithmetic.