Currently there's a big 'storm' over the predictions by the MetOffice in the UK. They predicted a mild, wet winter, while we have the coldest temperature on record in Northern Ireland and solid snow on the ground, normally rare in December.
It's something I'd love to have a play with, not that I'm claiming I can beat them, but was wondering what algorithms are out there currently that people are working with? What datasets do they base it on?
Possibilities presumably include neural networks modelling input with fitness being the accuracy of the prediction, complex mathematical models, or even the 'same as yesterday' prediction which I've heard claim (although not seen evidence) that it's more reliable for single-day prediction (although obviously drops off after that).
Ideally like to hear from some developers in weather centres or who get access to the supercomputers, it'd be interesting to hear approaches...
In short, if you intend to build and run your own forecasting model, you will face three major problems:
As far as I know, access to good meteorological observations costs a lot of money. You need to have observations from all over the globe and model the state of oceans and atmosphere for the whole planet. Alternatively, you need to obtain so-called lateral boundary conditions from someone who calculates a global model.
I'm not and I've never been affiliated with Met Office, but I used to port and optimize a version of their Unified Model to a supercomputer at our center a couple of years ago. Here's how I remember the model.
Met Office has been developing their Unified Model for the last 20+ years, we're talking about millions of lines of code that contain state of the art ocean/atmospheric models and numerical algorithms. Check out this section of (outdated) User Guide for a glimpse of scientific methods used in their model. It's a fruit of, give or take, half a century of well-funded, extensive research by a large community of smart people. If there was a simple solution that would consistently give better results than the complex models, someone would've probably implemented it by now.
To conclude, I guess it's very hard to get even remotely satisfactory results in weather forecasting by building a model from scratch, unless you're a MSc/PhD in atmospheric physics and you've got a couple of years of free time on your hands.
The first forecasting models were run in the middle of 20th century on machines that cannot match with today's cellphones, so, technically, you could calculate something on your PC. However, this type of job is often done on very, very powerful machines. In fact, 10 systems in the Top500 are dedicated solely to weather forecasting and climate research.
UPDATE It's possible to obtain the source code of the WRF model for free, together with some met data. Note that WRF, Unified Model, COAMPS, and many other models are written primarily in Fortran.