Boundary-Layer Meteorology

, Volume 168, Issue 3, pp 517–523 | Cite as

A Refinement of the McMillen (1988) Recursive Digital Filter for the Analysis of Atmospheric Turbulence

  • Marco Falocchi
  • Lorenzo Giovannini
  • Massimiliano de Franceschi
  • Dino Zardi
Notes and Comments


We present a refinement of the recursive digital filter proposed by McMillen (Boundary-Layer Meteorol 43:231–245, 1988), for separating surface-layer turbulence from low-frequency fluctuations affecting the mean flow, especially over complex terrain. In fact, a straightforward application of the filter causes both an amplitude attenuation and a forward phase shift in the filtered signal. As a consequence turbulence fluctuations, evaluated as the difference between the original series and the filtered one, as well as higher-order moments calculated from them, may be affected by serious inaccuracies. The new algorithm (i) produces a rigorous zero-phase filter, (ii) restores the amplitude of the low-frequency signal, and (iii) corrects all filter-induced signal distortions.


Complex terrain Recursive filtering Signal amplification Surface-layer turbulence Zero-phase filter 


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Atmospheric Physics GroupDICAM, University of TrentoTrentoItaly
  2. 2.Dioceses of Bolzano-BressanoneBressanoneItaly

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