Sampling errors in estimation of the small scales of monthly mean climate

Abstract

We examine the sampling errors in the estimation of the small scales of monthly average mean atmospheric climate as seen in mean kinetic energy. The relationships between the small‐scale mean and transient kinetic energy in the atmosphere and atmospheric flow simulations are discussed. We elucidate how the estimation of the mean depends on the number of realizations or the length of the time period of the data. Studies based on both a barotropic model and on the Commonwealth Scientific and Industrial Research Organisation (CSIRO) Mark 3 general circulation model (GCM) are performed focusing on 500 hPa and vertically averaged spectra. Results for perpetual January simulations are presented for 32, 62 and 1500 member ensembles within the barotropic model and for 1, 10 and 60 month integrations with the GCM. We find that, with too few realizations in the ensemble or averaging over just one month, the mean kinetic energy has a spurious spectrum with similar power law to the transient kinetic energy but with smaller values by about two orders of magnitude. For larger ensembles or longer averaging periods, the mean kinetic energy falls off more rapidly than the transient kinetic energy. Our results lead to the conclusion that mean kinetic energy spectra based on just one month of data, such as reported in the literature, most recently by Boer (2003), are dominated by sampling errors at the small scales.