Papers on Climate and Atmospheric Physics
Factors affecting the detection of trends: Statistical considerations and applications to environmental data
Article first published online: 21 SEP 2012
Copyright 1998 by the American Geophysical Union.
Journal of Geophysical Research: Atmospheres (1984–2012)
Volume 103, Issue D14, pages 17149–17161, 27 July 1998
How to Cite
1998), Factors affecting the detection of trends: Statistical considerations and applications to environmental data, J. Geophys. Res., 103(D14), 17149–17161, doi:10.1029/98JD00995., et al. (
- Issue published online: 21 SEP 2012
- Article first published online: 21 SEP 2012
- Manuscript Accepted: 4 MAR 1998
- Manuscript Received: 10 NOV 1997
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 (σN2) and autocorrelation coefficient (ϕ) of the noise. For a typical range of values of σN2 and ϕ 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.