In brief, 10, samples i. The same technique was applied to estimate the significance of differences between median concentrations at the ten depths. Bootstrap calculations have been performed with built-in Matlab functions. Sen's slope calculations and bootstrap for series with censored data have been calculated using R The dramatic improvement in the precision of the measurements due to the change of the ICP-MS instrument in is readily visible.
This effect is noticeable for all TEs considered and is particularly strong for Cd and Sb. Before any data were treated, the autocorrelation structure of temporal series of IEL data was evaluated. Autocorrelation functions Supplementary Information, Figure SI5 show that, except for Cd, significant serial correlation exists for all elements and, consequently, the Hamed and Rao method to evaluate the significance of the temporal trends needs to be applied.
Although no shift is visible for Sr, data for this element were also treated separately. No significant trends exist for Sr. Gd concentration increases significantly — , both considering All data and IEL. Error bars in profiles correspond to the interquantile range. Lake Geneva G3. Results of All data concentration and IEL integrated element load trends before and after Gd only after Their concentrations appear to decrease in the first half of the period considered and are stationary or increase in the second half.
Since the MK method requires a monotonic trend otherwise the trend could become dependent on the initial and final dates of the time series Stevenson et al. Turning years were for Pb and for Cd and Co. All data concentrations and IEL of Cd and Co do not change significantly before the turning year and increase significantly afterwards.
However, the IEL increasing trend for Co becomes non-significant when autocorrelation is considered. Lake data at different depths were evaluated only after in order to avoid noisy data. Results of the bootstrap data treatment are shown in Table SI3 in the Supplementary Information file. Co, Gd and Mo show no statistically significant changes of their median concentrations with depth while Pb concentrations both at the surface and at the bottom are significantly higher than at other depths.
Sb also shows differences higher concentration at 0 m compared with 20 and 70 m. Sr median concentration values are higher below 20 m. Cd concentrations are lower at 2. All are positive, except for Pb at the surface, and statistically significant at all depths in the case of Cd except at one depth , Gd, Mo and Sb. For Sr, they are only significant at certain depths. Differences in Sen's slope values between depths, evaluated by bootstrap, are shown in Table SI5 in the Supplementary Information file. Co and Sr show no variation at different depths.
Mo, Pb and Sb have lower values at the surface compared to all depths in the case of Pb and to some deeper levels in the case of Mo 7. Some elements show different Sen's slopes at the bottom, smaller in the case of Mo compared to slopes at 7.
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It reflects the complexity of the data treatment, particularly the difficulty of assigning statistical significance to weak trends. The work carried out has made it possible to establish the temporal trends for TEs in Lake Geneva, but also to gain a better understanding of the methodological caveats that apply to temporal trend evaluation of TEs in freshwaters.
These are discussed below. Temporal trend resume. Results of All data concentration and IEL integrated element load trends before and after excep Pb, before and after , and Gd only after and Sen's slopes after Slopes in italics are significant only when Hamed—Rao correction is not applied. Remember that this correction could not be applied to All data.
Data in trend studies have usually been obtained from monitoring programs rather than from research-oriented projects, which implies different objectives and data quality standards. Nevertheless, our study shows that temporal trends can be followed using monitoring data, provided that it is possible to have direct access to the raw data and protocols used i. Unfortunately, this is a problem inherent to any data trend study based on monitoring data. How long does a data series need to be for a temporal trend to be detected? This depends on two factors: the strength of the change and the quality of the data.
It can be roughly evaluated by calculating the time of emergence ToE parameter, which gives the point in time when a signal finally emerges from the background noise of natural variability Keller et al. In the case of Pb and Sr, ToEs are higher in the second period because trends are stronger in the first period and compensate for the greater noise. As expected, elements with significant changes have shorter ToEs, closer to ten years. Simply substituting a fabricated value zero, detection limits, or another value for censored data can lead to wrong results in statistical data mean, standard deviation , hypothesis tests and regression models Helsel Median concentrations are not affected by left-censored data i.
Although trends are most effectively detected in uncensored data as compared to censored data, the existence of censored data will not give any spurious significant trend i. This means that statistical significance in MK is not affected by censoring. However, it has an effect on the value of Sen's slopes Table SI2. Those slopes have thus been calculated using the non-parametric method of Akritas et al. Another effect of data quality is related to the precision of the measurements that, when close to the detection limit, results in very few significant figures in the readings.
A final aspect that has, to our knowledge, never been explored in concentration trend studies, is the effect on the measured concentration values of potential drifts of the instruments over the years. We have tried to follow potential drifts by applying the same data treatment to the CRM concentrations measured Table SI6 , with no conclusive results see discussion in the Supplementary Information.
Finding statistically significant, deterministic temporal trends in time series is complicated by two features of time series: serial correlation and LTP. Hydrological time series, such as those we are dealing with, very often show positive serial correlation. Serially correlated data without any deterministic trend tend to stick above or below the average value of the series more frequently than would be the case for a purely random process.
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This increases the likelihood of identifying a significant trend where there is none. Unfortunately, deciding whether LTP is present and accounting for it requires data series longer than the ones we are studying here O'Connell et al. We therefore did not correct our results for LTP. A deeper discussion on these problems can be found in the Supplementary Information file Section SI1.
Trend studies commonly attempt to ascribe observed effects to well-defined, physical causes. This is usually done by establishing correlations, and backing them up by informally including other lines of evidence from the literature in the Discussion section Downes et al. Apart from the well-known fact that correlation is not causation, in practice, this approach is not straightforward.
Only in rare cases is the trend strong enough and due to a few, well-defined, drivers e. This type of exercise or the application of more sophisticated approaches Granger ; Kleinberg is entirely outside of the scope of this paper. It is interesting however to discuss what effects can be reasonably expected and whether the results obtained fit with existing knowledge.
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