A quantitative estimate of the effect of aliasing in climatological time
series
Roland A. Madden
National Center for Atmospheric Research
Richard H. Jones
University of Colorado Health Sciences Center and the Geophysical
Statics Project, NCAR
Effects of aliasing on climatological time series have been studied in the past
(e.g. Gray and Madden, 1986; Edwards, 1987). But, because of the considerable
interest in climate variations on decadal and longer time scales, there is still
a need for quantitative estimates of what these effects might be. The increasing
availability of long time series of observed and simulated data allows analysis
of slow variations, but aliasing can introduce serious problems for
interpretation. We present a diagram to be used to estimate the amount of
aliasing that can be expected for various averaging lengths and sampling
periods. Results suggest that the problem is larger than one might have
expected, and that many studies of low frequency variability may be seriously
compromised by aliasing.
We use daily pressure data from a long record to provide an example of
aliasing effects (Section 2). A moving 91-day average is passed over the data to
approximate what one would expect for seasonal data. The 91-day averages differ
from normal seasonal data in that one is available each day, not just four times
per year. These daily, 91-day averaged data are taken as the unaliased time
series. Quantitative aliasing effects are first determined in the time domain by
subsampling the daily values (Section 3a). Next, aliasing effects are considered
in the frequency domain by considering the spectrum of the 91-day averages
(Section 3b). A first order autoregressive (AR1) model for daily data gives
results similar to that of the example pressure data. Finally, the AR1 model is
used to provide a range for the fraction of aliased variance one can expect in a
spectrum as a function of differing averaging lengths and sampling intervals
(Section 4).
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Hongjun Zhang:
zhangho@ucar.edu