This introduction to atmospheric modelling covered a wide range of topics in a sadly short space. In spite of the brevity, I hope to have conveyed some of the most important ideas and approaches employed in mathematical analysis of atmospheric dynamics. In my opinion, the salient ideas are scale based analysis built on an underlying set of equations whose intractability and breadth conspire to prevent simple analysis. That progress can be made using relatively simple mathematics is remarkable. That progress is made is a tribute to the rigour and persistence of a cohort of extraordinary scientists, only some of whom have been named in this book. Ultimately, the subject has an enormously practical expression, that is the societal need for meteorological forecasts. The numerical methods that lie behind modern weather forecasts have as essential foundations the equations I have presented, and the methods I have sketched.

The compact nature of this book, and the specific focus on mathematical modelling have had a less than desirable consequence. The focus on dynamics means that I have not been able to deal with many fascinating and awe inspiring phenomena encountered in the atmosphere. I have not touched on any atmospheric optical phenomena, so I have deprived readers of the wonders and beauty of rainbows, arcs and haloes. I have dealt with neither clouds in all their variety, nor precipitation in its many forms. This means readers will have to look elsewhere to discover the mystery and beauty of a cumulonimbus or a funnel cloud, and will have to broaden their reading to understand the distinction between graupel and hail. I could not ignore atmospheric thermodynamics, but had to give it only enough attention to help in the understanding of atmospheric dynamics. Similarly, radiation in the atmosphere was treated only to the extent that it served an understanding of dynamics. I hope readers will be inspired by what I have presented to undertake their own reading of these omitted topics, and many others.