I do not have any literature which clearly explains how numerical weather prediction models work once initial data is provided to them. Can any one provide literature which clearly explains how they work operationally besides theoretical books?
Hi. A rather exhaustive book is "Atmospheric Modeling, Data Assimilation and Predictability", by Eugenia Kalnay. Important subjects like data assimilation are treated in detail, so I would recommend it.
It is a big question, maybe you are just interested in step by step mechanical process rather than dynamics of NWP. If you want detailed description then go with Gabriel Perez Jordan answer or you can also read Numerical Techniques for Global Atmospheric Models: Tutorials.
Dear you would love this website to understand NWP and related things
https://www.meted.ucar.edu/training_detail.php?topicSorting=15&languageSorting=1&module_sorting=publishDateDesc
Cheers!