On the smoothing of climatological time series, with application to sea‐level at Newlyn

Abstract

Summary. The common practice of collecting long‐term data in the form of calendar monthly and annual means embodies several apparently undesirable features. In an effort to improve such procedures, a sequence of high quality smoothing filters is proposed, producing from an initial data series at hourly or similar time interval a sequence of three smoothed series at: (1) 2 per day, (2) 12 per year and (3) one per year respectively. The filters are applied for demonstration to a 66 year series of sea‐levels from Newlyn, Cornwall, with associated barometric and temperature data. Series (1) is used to provide an unusually smooth profile of the sub‐tidal energy spectrum, which shows an unexpected dichotomy above and below 0.13 cycles day‐1, partially explained in terms of coherence with the pressure series. The same series is analysed at the frequencies of the lunar tidal components, with improved noise: signal ratio when barometric pressure is added to the sea‐level data with appropriate scaling. Both Mf and Mm components are found to be close to equilibrium. An analysis of the side‐band errors introduced by the irregular time‐sequence of monthly mean data in contrast with series (2), which has a uniform time interval, is presented. The error is very small at low frequencies such as 1 cycle per year (cpy) unless an exceptionally large annual term is present in the data. Series (2) and monthly mean series are compared at 1 and 2 cpy. Atmospheric pressure contributes only about 10 per cent to the total annual sea‐level at Newlyn but the residual, which is presumably due to steric changes, has less variability from one 12 yr period to another than the annual term in the raw data. The pole‐tide effect at 0.84 cpy is nearly lost in noise, but a coherence analysis of the sub‐surface pressure gives an admittance of about –36 mm aresec‐1 of the X‐component of polar motion which is again close to ‘equlibrium’. Series (3), obtained by applying a ‘banning’ filter to the duodecimal series (2), is termed the ‘hannual mean’ series. It is of course properly smoothed compared with conventional annual mean series, but not to the detriment of several‐year variations which are shown to be highly correlated with corresponding barometric series. About a third of the mean rate of rise of sea‐level in 65 yr is here attributed to a fall in mean atmospheric pressure. On subtracting the barometric effect, the residual shows no correlation with local sea temperature; probably only thermal effects of a global climatic nature are relevant. The residual mean rate of rise is about the same as the mean global rate, suggesting a stable land mass. Copyright © 1983, Wiley Blackwell. All rights reserved