E-Book Overview
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.
E-Book Content
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. d r r o b i n c r o c k e t t 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. A Primer on Fourier Analysis for the Geosciences RO B I N C RO C K E T T University of Northampton University Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia 314–321, 3rd Floor, Plot 3, Splendor Forum, Jasola District Centre, New Delhi – 110025, India 79 Anson Road, #06–04/06, Singapore 079906 Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning, and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107142886 DOI: 10.1017/9781316543818 © Robin Crockett 2019 This publi