Gap filling and noise reduction of unevenly sampled data by means of the Lomb-Scargle periodogram Institute of Applied Physics and Oeschger Centre for Climate Change Research, University of Bern, Switzerland
Received: 25 Jan 2008 – Published in Atmos. Chem. Phys. Discuss.: 04 Mar 2008 – Published: 24 Jun 2009Abstract. The Lomb-Scargle periodogram is widely used for the estimation of the power spectral density of
unevenly sampled data. A small extension of the algorithm of the Lomb-Scargle periodogram permits
the estimation of the phases of the spectral components. The amplitude and phase information is
sufficient for the construction of a complex Fourier spectrum. The inverse Fourier transform can
be applied to this Fourier spectrum and provides an evenly sampled series (Scargle, 1989).
We are testing the proposed reconstruction method by means of artificial time series and real
observations of mesospheric ozone, having data gaps and noise. For data gap filling and noise
reduction, it is necessary to modify the Fourier spectrum before the inverse Fourier transform is done.
The modification can be easily performed by selection of the relevant spectral components which are
above a given confidence limit or within a certain frequency range. Examples with time series of
lower mesospheric ozone show that the reconstruction method can reproduce steep ozone gradients around sunrise and sunset and
superposed planetary wave-like oscillations observed by a ground-based microwave radiometer at Payerne.
The importance of gap filling methods for climate change studies is demonstrated by means of long-term
series of temperature and water vapor pressure at the Jungfraujoch station
where data gaps from another instrument have been inserted before the linear trend is calculated.
The results are encouraging but the present reconstruction algorithm is far away
from being reliable and robust enough for a serious application.
Citation: Hocke, K. and Kämpfer, N.: Gap filling and noise reduction of unevenly sampled data by means of the Lomb-Scargle periodogram, Atmos. Chem. Phys., 9, 4197-4206, doi:10.5194/acp-9-4197-2009, 2009.