A Primer on Fourier Analysis for the Geosciences

Time-series analysis is used to identify and quantify periodic features in datasets and has many applications across the geosciences, from analysing weather data, to solid-Earth geophysical modelling. This intuitive introduction provides a practical ‘how-to’ guide to basic Fourier theory, with a particular focus on Earth system applications. The book starts with a discussion of statistical correlation, before introducing Fourier series and building to the Fast Fourier Transform (FFT) and related periodogram techniques. The theory is illustrated with numerous worked examples using R datasets, from Milankovitch orbital-forcing cycles to tidal harmonics and exoplanet orbital periods. These examples highlight the key concepts and encourage readers to investigate more advanced time-series techniques. It concludes with a consideration of statistical effect-size and significance. This useful book is ideal for graduate students and researchers in the Earth system sciences who are looking for an accessible introduction to time-series analysis. dr robin crockett is Reader in Data Analysis in the Faculty of Arts, Science and Technology at the University of Northampton, UK. He is a member of the IMA and the IOP and holds Chartered Scientist Status. He specialises in investigating periodic, recurrent and anomalous features in data, and has led a highly successful short course on Fourier analysis at the European Geosciences Union General Assembly for many years.