This probably isn't quite what you mean, but WRF (Weather Research and Forecast) model is an open source and actively developed weather forecast model you can run at home or on the cloud: https://www.mmm.ucar.edu/weather-research-and-forecasting-mo...

If you collect your own weather data at scale, you can write assimilation routines to get WRF to incorporate your data into the model runs along with NOAA/MADIS/etc-provided data.

I know that's more complicated than you are suggesting but it's worth mentioning.

There are a lot of simple ways to do home weather forecasting. You can write your own Dark Sky clone by downloading/scraping/APIing your local radar station and then write your own wind predictor a few hours into the future based on rain movement or simple statistics from recent local wind data.