How does weather forecasting actually work?
By solving physics equations on a grid, starting from the best available picture of the atmosphere right now — and the limits of forecasting come from the fact that small errors in that starting picture grow, rapidly and unavoidably.
The process:
Observation. Data from surface stations, weather balloons, ships, buoys, aircraft and — supplying the overwhelming majority — satellites. Millions of observations are gathered continuously and unevenly across the globe.
Data assimilation. Observations are combined with a short forecast from the previous run to produce the best estimate of current conditions. This step is as important as the forecast model itself and is where much of the improvement of recent decades came from.
Numerical modelling. The atmosphere is divided into a three-dimensional grid, and the equations governing fluid motion, thermodynamics, radiation and moisture are stepped forward in time. This is why forecasting consumes some of the largest supercomputers in the world.
Parameterisation. Processes smaller than the grid — individual clouds, turbulence, convection — cannot be simulated directly and are approximated statistically. This is the largest source of model error.
Post-processing, correcting known local biases.
Why forecasts have limits. The atmosphere is chaotic: tiny differences in initial conditions grow exponentially, so two nearly identical starting states diverge into completely different weather. This is not a technology problem — it is a property of the system, and it places a hard ceiling on deterministic forecasting of roughly two weeks.
How forecasters handle this: ensembles. The model is run many times from slightly different starting conditions. Where the runs agree, confidence is high; where they diverge, it is low — and the spread is the forecast's honest uncertainty. A "30% chance of rain" comes from this.
Why forecasts are far better than their reputation. A five-day forecast today is about as accurate as a one-day forecast was in 1980 — an improvement of roughly a day of skill per decade.
Why they still feel wrong: probabilities are interpreted as promises, timing errors are read as total failure, and people remember misses.