Explore the application of particle filters in data assimilation through this comprehensive lecture. Delve into advanced techniques for integrating observations and short-range forecasts to estimate atmospheric states and uncertainties. Learn how particle filters contribute to weather prediction, climate monitoring, and understanding environmental processes across land, atmosphere, and oceans. Gain insights into this powerful mathematical approach used by leading operational weather forecast centers worldwide, and discover its potential for enhancing climate variability analysis through historical data reanalysis.