Edit: Downvotes for simply asking a question. sigh.
I also recall the ECMWF had surprisingly accurate long range forecasts based on ensembles. It could predict 500mb heights out two weeks, no sweat.
Re: your comments... My guess is that a gpu isn't suited for use in an operational model due to data access patterns (and possibly not even helpful with the solver). But again, I'm not a computational pde guy. Also, perhaps machine learning would be useful but that would be post-processing or perhaps parameterizing sub-grid phenomenon. There's already a process called model output statistics (MOS) for adjusting raw fields from a weather model.
I've been out of the field for ten years now, but it's really nice to see improvements to the core physics to this degree.
I'm still skeptical of your supposed two week 500 heights forecast from the ECMWF model. I live near the western Pacific (i.e. the data hole) and it's really easy to find crazy model solutions after 7 days. And I'm pretty sure you weren't looking at the Southern Hemisphere.
You're probably right to be skeptical, for the record I was only a forecaster for a short period of time over ten years ago... didn't even serve my full four year commitment as I volunteered to get out under the Air Force "force shaping" at the time. I was stationed near Rammstein and we created forecasts for Europe. I was referring to the ECMWF ensemble products, specifically.
Where GPUs shine for PDEs is if you have a lot of extra work for each node, for instance if you have complex chemical reactions or thermodynamics, or if you have a high-order method that requires lots of intermediate computations.
If you don't believe me, you can download the PETSc code and test the ViennaCL solvers versus the regular ones.
> A modern 5-day forecast is as accurate as a 1-day forecast was in 1980, and useful forecasts now reach 9 to 10 days into the future (1). Predictions have improved for a wide range of hazardous weather conditions, including hurricanes, blizzards, flash floods, hail, and tornadoes, with skill emerging in predictions of seasonal conditions.
> ... Data from the NOAA National Hurricane Center (NHC) (13) show that forecast errors for tropical storms and hurricanes in the Atlantic basin have fallen rapidly in recent decades.
This covers some decades, to be sure, but it's a pretty big improvement.
edit: I see that neuronexmachina found the same article. It's a good read if you want an overview of how weather prediction has changed.
In [2] there is a slightly different claim, "A modern 5-day forecast is as accurate as a 1-day forecast was in 1980, and useful forecasts now reach 9 to 10 days into the future."
Chart 3.2 of [3] shows this; by 2001 the 5th day forecast improved to be as good as the 3rd day of 1980, establishing the trend line.
Googling about yields a few other studies and articles in a similar vein.
It is important to note that forecast improvement is not linear in effort. It takes more complete and accurate sensor data and far more computation to extend the forecast on the out days due to the chaotic nature of the mechanisms modeled.
[1] https://rmets.onlinelibrary.wiley.com/doi/full/10.1002/qj.25...
On the other hand, I suspect it might not be noticeable if the forecast you always read just says "40% chance rain, high 80, low 50". It might be more noticable if you look at the hour-by-hour forecast for a specific location and see when the rain is predicted to start and end.
But by mentioning machine learning, I'm guessing you are looking at a different timescale, i. e. "within the last two years". And any progress in the short term will be slow compared to what we have seen in other domains such as image recognition etc.
I'm no expert on weather forecasting, but I believe the explanation may be that forecasts have long been (among the) best financed "big data" problems out there. That means they incorporate lots and lots of domain-specific work. As a result, naive machine learning models currently still lag all the specialised work, which in turn isn't structured in a way to easily take advantage of progress in, say, GPUs.
Note these error statistics do not represent true model error as the official track and intensity forecast -- while informed by model output -- are determined by human forecasters.