Remember way back when I said that forecast skill will improve not so much by improving our knowledge of the physics but by raising the computer power and grid resolution?
Yes, but just throwing more computer power at the problem will never take you as far as you can go. You also need to be clever to find practical, perhaps less physical, ways to make the models. And you need good measurements, both in terms of quality and quantity.
The recent improvements in the short term forecasts haven't only come from a smaller grid size. The brute force-like grid forecast is the starting point for a number of ad hoc adjustments. (The grid size is also adaptive, so the grids are smaller where it's likely to make a difference) For instance, measurements from nearby weather stations are fed back along with the initial prediction using a Kalmar filter to make adjustments. I.e. when the prediction of the original model doesn't quite seem to match actual measurements, the final forecast gets adjusted accordingly. Adjustments are also made for elevation differences within a grid. And for very short term forecasts, up to 90 minutes ahead, radar data is used. A forecast for the next day can be 100% accurate in that there will be afternoon showers over an area, but it can not realistically predict where those showers will be. Once the showers have formed, instead of rerunning the models with impractically small grid sizes, the movement of the showers can be tracked and predicted by simple algorithms. Much like you would do manually if you sit at work and look at the weather radar trying to find the best time slot for riding your bike home. Finally, it's always a good idea to read the text forecast written by a meteorologist experienced in interpreting the model output, who knows the limitations and local factors.