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Abstract. Detection of long-term, linear trends is affected by a number of factors, including the size of trend to be detected, the time span of available data, and the magnitude of variability and autocorrelation of the noise in the data. The number of years of data necessary to detect a trend is strongly dependent on, and increases with, the magnitude of variance (o-2•) and autocorrelation coefficient (qb) of the noise. For a typical range of values of o-2• and 4> the number of years of data needed to detect a trend of 5%/decade can vary from -10 to >20 years, implying that in choosing sites to detect trends some locations are likely to be more efficient and cost-effective than others. Additionally, some environmental variables allow for an earlier detection of trends than other variables because of their low variability and autocorrelation. The detection of trends can be confounded when sudden changes occur in the data, such as when an instrument is changed or a volcano erupts. Sudden level shifts in data sets, whether due to artificial sources, such as changes in instrumentation or site location, or natural sources, such as volcanic eruptions or local changes to the environment, can strongly impact the number of years necessary to detect a given trend, increasing the number of years by as much as 50% or more. This paper provides formulae for estimating the number of years necessary to detect trends, along with the estimates of the impact of interventions on trend detection. The uncertainty associated with these estimates is also explored. The results presented are relevant for a variety of practical decisions in managing a monitoring station, such as whether to move an instrument, change monitoring protocols in the middle of a long-term monitoring program, or try to reduce uncertainty in the measurements by improved calibration techniques. The results are also useful for establishing reasonable expectations for trend detection and can be helpful in selecting sites and environmental variables for the detection of trends. An important implication of these results is that it will take several decades of high-quality data to detect the trends likely to occur in nature. IntroductionThe impact of human intervention in a changing environment has brought about increased concern for detecting trends in various types of environmental data. A variety of studies

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[1] Global ozone trends derived from the Stratospheric Aerosol and Gas Experiment I and II (SAGE I/II) combined with the more recent Halogen Occultation Experiment (HALOE) observations provide evidence of a slowdown in stratospheric ozone losses since 1997. This evidence is quantified by the cumulative sum of residual differences from the predicted linear trend. The cumulative residuals indicate that the rate of ozone loss at 35-45 km altitudes globally has diminished. These changes in loss rates are consistent with the slowdown of total stratospheric chlorine increases characterized by HALOE HCl measurements. These changes in the ozone loss rates in the upper stratosphere are significant and constitute the first stage of a recovery of the ozone layer.

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,