Skip to main content
  • 2304 Accesses

Abstract

Multivariate harmonic analysis technique has been employed widely in determining cyclic variations of multivariate time series.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Further Reading

  • J. Aalto, P. Pirinen, J. Heikkinen et al., Spatial interpolation of monthly climate data for Finland: comparing the performance of kriging and generalized additive models. Theor. Appl. Climatol. 112, 99–111 (2013)

    Article  Google Scholar 

  • M.W. Ashiq, C. Zhao, J. Ni et al., GIS-based high-resolution spatial interpolation of precipitation in mountain-plain areas of Upper Pakistan for regional climate change impact studies. Theor. Appl. Climatol. 99, 239 (2010)

    Article  Google Scholar 

  • N.M. Atakishiyev, L.E. Vicent, K.B. Wolf, Continuous vs. discrete fractional Fourier transforms. J. Comput. Appl. Math. 107, 73–95 (1999)

    Article  Google Scholar 

  • B. G. J. Brooks, Applying Wavelet and Fourier Transform Analysis to Large Geophysical Datasets. In: Computational Science (G. Allen et al (eds)), Lecture Notes in Computer Science, vol 5545. Springer, 2009

    Google Scholar 

  • C. Candan, M.A. Kutay, H.M. Ozaktas, The discrete fractional Fourier transform. IEEE Trans. Signal Process. 48, 1329–1337 (2000)

    Article  Google Scholar 

  • X. Chen, P. Xing, Y. Luo et al., Surface temperature dataset for North America obtained by application of optimal interpolation algorithm merging tree-ring chronologies and climate model output. Theor. Appl. Climatol. 127, 533–549 (2017)

    Article  Google Scholar 

  • W. Cheney and W. Light, A course in approximation theory, Brooks/Cole Publishing, 2000

    Google Scholar 

  • R.A. DeVore, Nonlinear approximation. Acta Numerica 7, 51–150 (1998)

    Article  Google Scholar 

  • S. Eghdamirad, F. Johnson, A. Sharma, Using second-order approximation to incorporate GCM uncertainty in climate change impact assessments. Climatic Change 142, 37–52 (2017)

    Article  Google Scholar 

  • J. Fan, J. Meng, X. Chen et al., Network approaches to climate science. Sci. China Phys. Mech. Astron. 60, 010531 (2017)

    Article  Google Scholar 

  • I. Fountalis, A. Bracco, C. Dovrolis, Spatio-temporal network analysis for studying climate patterns. Clim. Dyn. 42, 879–899 (2014)

    Article  Google Scholar 

  • E.D. Giuseppe, G.J. Lasinio, S. Esposito et al., Functional clustering for Italian climate zones identification. Theor. Appl. Climatol. 114, 39–54 (2013)

    Article  Google Scholar 

  • S.V. Henriksson, P. Ralsanen, J. Silen et al., Quasiperiodic climate variability with a period of 50–70 years: Fourier analysis of measurements and Earth System Model simulations. Clim. Dyn. 39, 1999–2011 (2012)

    Article  Google Scholar 

  • A.L. Kay, S.M. Crooks, H.N. Davies et al., Probabilistic impacts of climate change on flood frequency using response surfaces I: England and Wales. Reg. Environ. Change 14, 1215–1227 (2014)

    Article  Google Scholar 

  • R. Kandel, Understanding and Measuring Earth’s Energy Budget: From Fourier, Humboldt, and Tyndall to CERES and Beyond. Surv. Geophys. 33, 337–350 (2012)

    Article  Google Scholar 

  • K. Kikuchi, An introduction to combined Fourier-wavelet transform and its application to convectively coupled equatorial waves. Clim. Dyn. 43, 1339–1356 (2014)

    Article  Google Scholar 

  • V.A. Narayanan, K.M.M. Prabhu, The fractional Fourier transform: theory, implementation and error analysis. Microprocessors and Microsystems 27, 511–521 (2003)

    Article  Google Scholar 

  • M. Ogurtsov, G. Kocharov, M. Lindholm et al., Evidence of solar variation in tree-ring-based climate reconstructions. Solar Phys. 205, 403–417 (2002)

    Article  Google Scholar 

  • S. Samanta, D.K. Pal, D. Lohar et al., Interpolation of climate variables and temperature modeling. Theor. Appl. Climatol. 107, 35–45 (2012)

    Article  Google Scholar 

  • E. Sejdic, I. Djurovic, L. Stankovic, Fractional Fourier transform as a signal processing tool: an overview of recent developments. Sig. Process. 91, 1351–1369 (2011)

    Article  Google Scholar 

  • E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, 1971

    Google Scholar 

  • Z. Wu, E.K. Schneider, B.P. Kirtman et al., The modulated annual cycle: an alternative reference frame for climate anomalies. Clim. Dyn. 31, 823–841 (2008)

    Article  Google Scholar 

  • Z. Zhang, Approximation of bivariate functions via smooth extensions. The Scientific World Journal 2014, 102062 (2014)

    Google Scholar 

  • F. Zwiers, S. Shen, Errors in estimating spherical harmonic coefficients from partially sampled GCM output. Climate Dynamics 13, 703–716 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhihua Zhang .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zhang, Z. (2018). Multivariate Harmonic Analysis. In: Multivariate Time Series Analysis in Climate and Environmental Research. Springer, Cham. https://doi.org/10.1007/978-3-319-67340-0_2

Download citation

Publish with us

Policies and ethics