1. Trend assessment (A. V, 2.4.4) Identification of trends in pollutants
long-term anthropogenically induced upward trends and trend reversal
base year or period from which trend identification is to be calculated
calculation of trends for a body or group of bodies of groundwater
statistical demonstration of trend reversal and level of confidence

2. Trend assessment (A. V, 2.4.4) Procedure
Identification of current practise and identification of lacks (with regard to WFD)
Establishing of a set of candidate methods fulfilling the requirements of WFD
Evaluation of candidate methods using test data sets provided by project partners. Evaluation critera: applicability, interpretability, statistical validity/confidence and statistical power.

3. Trend assessment (A. V, 2.4.4) Is there a trend reversal?
Functions of trend assessment
Graphical presentation of trend
Formal statistical tests asking the questions:
Is there a trend reversal?
Is there a systematic trend (not only random fluctuation)?
Is there a seasonality effect?
Is there a linear or monotonic (upward/downward) trend?
Is the level in the final year significantly below the level three years ago?
Side product: Target assessment.
Is the current level below the limit value?
Is the predicted level after three years still below the limit value?

4. Trend assessment (A. V, 2.4.4) Candidate methods for trend assessment
Regularization (quarterly, half-yearly or yearly)
Spatial aggregation (over all stations in GW body) by
arithmetic mean, median, 70% percentile or
kriging mean, CL of kriging mean or
maximum likelihood
Trend analysis
Test of Mann-Kendall
Theil slopes (in case of a linear trend)
LOESS smoother
Linear and quadratic regression

5. Trend assessment in data sheet
Example: ES0409 Nitrate
0.01 < p-value < 0.05:
significant trend at 5% significance level, but not significant at 1% level,

6. Power analysis
Comparison of Mann-Kendall and the linear trend test based on the LOESS smoother

7. Trend reversal (1st option)
What is a trend reversal?
No monotonic trend ...
... but a downward trend
in the subsequent differences

8. Trend reversal (1st option)
Detection of monotonic trends with the test of Mann-Kendall
Example:
8 positive backward differences and 12 negative backward differences
Test statistic S = 12-8 = 4 < 15
Conclusion 1: There is no significant monotonic trend

9. Trend reversal (1st option)
Detection of downward trend in subsequent differences
Example:
Differences:
0 positive differences and 15 negative differences
Test statistic: S = 15-0 = 15 >11
Conclusion 2: There is a significant downward trend in subsequent differences
Conclusion 3: There is a trend reversal in the series

10. Trend reversal (1st option)
Example: UK002 Ammonium

11. Trend reversal (2nd option)
What is a trend reversal?
„There is a quadratic trend component having a maximum within the time interval of measurements“
„The confidence interval for the maximum is within the time interval of measurements.“

12. Trend reversal (2nd option)
Example FR001_Fri Nitrate

13. Trend reversal (3rd option)
What is a trend reversal?
„Some years ago there was a significant change of the slope and a change from upward to downward.“

14. Trend reversal (3rd option)
Example: DE001 Chloride

15. Trend reversal 1st opt (MK): robust, but not powerful
2nd option (quadratic trend): not robust, but fairly powerful; although in case of non-quadratic trends a misspecification is possible
3rd option (2-section model): not robust, but fairly powerful (for a period of yrs)

16. Power analysis What is the probability of detecting a monotonic trend?
This depends on
intensity of the trend
trend detection method
significance level
random variability of data from year to year
length of time series

17. Power analysis
What is the detectable trend (which can be detected with a probability of 90%)

18. Power analysis Example: FR001 Frd Nitrate 1973-1999
Method: Linear Trend based on LOESS
Trend intensity: Increase by 20% (whole period)

19. Analysis of quarterly/half-yearly data
Gain of using data with higher time resolution:
increase of power (more or less)
seasonality has to be taken into account
sampling procedure (selection of sites) may become crucial

20. Some requirements
For the detection of linear/monotonic upward trends: 6 yrs
For the detection of trend reversal: yrs

21. Further procedure proposed
Assess the gain of analysing quarterly(half-yearly data
Specify a proposal for an overall procedure (starting point, early warning signal etc.)
Assess the impact of measurements below LOQ/LOD on different assessment techniques (eg. replacement by maximum LOQ/LOD)