Effects of autocorrelation and temporal sampling schemes on estimates of trend and spatial correlation

Abstract

This paper is concerned with temporal data requirements for the assessment of trends and for estimating spatial correlations of atmospheric species.We examine statistically three basic issues:(1) the effect of autocorrelations in monthly observations and the effect of the length of data record on the precision of trend estimates, (2) the effect of autocorrelations in the daily data on the sampling frequency requirements with respect to the representativeness of monthly averages for trend estimation, and (3) the effect of temporal sampling schemes on estimating spatial reasons other than a coordinated network designed to measure global ozone change.In these studies,

Evaluation of the inter-annual variability of stratospheric chemical composition in chemistry-climate models using ground-based multi species time series

“…We have compared errors (i.e. standard deviations) in regression coefficients derived using this bootstrap method with standard MLR errors calculated using an autocorrelation model of type AR1 (Tiao et al, 1990). For our long time series, typically more than a decade, standard deviations derived with the bootstrap method are found to be in excellent agreement with MLR standard errors.…”

“…Overall, this approach was providing satisfactory results in most cases. However, it was found not to be robust for short time series when errors could be vastly underestimated (Tiao et al, 1990). As a result, we tested the bootstrapping approach; we found that it provided results (regression coefficients, associated errors) results that were close to the results obtained with the Cochrane-Orcutt approach for most cases.…”

“…A firstorder autogressive model AR1 was applied in order to take into account autocorrelation. The data were regressed against the model after a Cochrane-Orcutt transformation; the method is described in appendix A of Tiao et al (1990) (see also Bodeker and Kremser, 2015). The Cochrane-Orcutt transformation does not change significantly the values of the regression coefficients but, as expected, the associated errors increase.…”

Long‐term trend analysis of aerosol variables at the high‐alpine site Jungfraujoch

“…[21] The determination of the number of years needed to detect a long-term linear trend of a given magnitude has been extensively studied by Tiao et al [1990] and Weatherhead et al [1998Weatherhead et al [ , 2000. This number of years increases with the magnitude of the variance (s N 2 ) and the autocorrelation coefficient (f) of the data noise.…”

An objective determination of optimal site locations for detecting expected trends in upper-air temperature and total column ozone

“…2.2) to remove all known sources of variability, ω 0 is the trend magnitude in K year −1 (see Fig. 6), and φ N is the autocorrelation in the residuals (Tiao et al, 1990). This equation implies that, after the calculated number of years, there is a 90 % probability that a trend of the correct sign will have been detected, if we assume that detecting a trend means identifying a trend at the 95 % confidence level.…”