Factors affecting the detection of trends: Statistical considerations and applications to environmental data

Abstract

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

Dead time effect on the Brewer measurements: correction and estimated uncertainties

“…The Brewer network provides a variety of products such as the total columns of ozone (TOC) (Kerr et al, 1981), SO 2 (Cappellani and Bielli, 1995) and NO 2 (Cede et al, 2006;Diémoz et al, 2014), the aerosol optical depth (AOD) Gröbner and Meleti, 2004;Meleti and Cappellani, 2000) as well as global and direct irradiance spectra (Bais et al, 1993(Bais et al, , 1996. These measurements have supported scientific research for more than 30 years, enabling the investigation of their shortand long-term variability (Glandorf et al, 2005;Weatherhead et al, 1998;Zerefos, 2002) and interactions among them and among other atmospheric constituents (Bernhard et al, 2007). Additionally, good-quality ground-based measurements are very useful for the validation of satellite products which, under specific conditions, may be highly uncertain (Fioletov et al, 2002).…”

Snow trends in Northern Spain: analysis and simulation with statistical downscaling methods

“…Both features remain approximately constant from 1970 onwards, which includes the period in which a significant trend is detected (from 1975 onwards; Section 3.1). No trend analysis has been performed for the period 1957-1970 as the number of stations available each year varied significantly during this period and, thus, the trend results may be biased (more information about trend detection influencing factors can be found in Weatherhead et al, 1998).…”

Nature's style: Naturally trendy

“…There is typically little argument about the magnitude of observed trends whether estimated by eye or statistical methods [Craigmile et al, 2004] (although D. Koutsoyiannis (personal communication, 2005) has expressed doubts about the existence of a rigorous and consistent definition of trend). The statistical significance, or p-value, associated with an observed trend, however, is more difficult to assess because it depends on subjective assumptions about the underlying stochastic process [von Storch and Zwiers, 1999;Woodward and Gray, 1993;Weatherhead et al, 1998]. In this paper, we consider the idea introduced by Hurst [1951] and discussed by others [Mandelbrot and Wallis, 1969a;Klemeš, 1974;Lettenmaier and Burges, 1978;Potter, 1976;Potter and Walker, 1981;Hosking, 1984;Bras and Rodriguez-Iturbe, 1985;Vogel et al, 1998;Koutsoyiannis, 2000] that HC records are realizations of physical processes whose behavior exhibits long-term persistence (LTP).…”