1. Chemical status (1) (A. V, 2.4.5)
Interpretation and presentation of groundwater chemical status (WFD - common position)
aggregation of results of individual monitoring points for the GW-body as a whole
the mean value of the results of monitoring at each point in the groundwater body or group of bodies shall be calculated; and
the mean value of these calculations for all monitoring points in the groundwater body or group of bodies shall demonstrate compliance with those standards in the manner prescribed in the relevant Directive.

2. Chemical status (1) (A. V, 2.4.5)
Interpretation and presentation of groundwater chemical status (WFD final)
the mean values of the results of monitoring at each point in the groundwater body or group of bodies shall be calculated; and
in accordance with Art. 17 these mean values shall be used to demonstrate compliance with good groundwater chemical status

3. Algorithms for data aggregation
Procedure of aggregation
1 Temporal aggregation (within year and station)
2 Spatial aggregation (over all stations in GW body) by one of the following candidate methods
arithmetic mean
median
(empirical) 70 %ile
kriging mean
upper confidence limit of the kriging mean
maximum likelihood mean
maximum likelihood 70 %ile
kriging 70 %ile (added)

4. Data sheet Results of spatial aggregation over all stations in GW body
for all methods under consideration
for all stations where data where available,
No examination of the monitoring network (locations and type of stations) was performed, and therefore the results presented cannot be considered validated.
Purpose of the results is to illustrate the method, and no conclusions on trends and compliance with limit values can be made.

5. Statistical parameters

6. Interpretation of percentiles
Represent the concentration in the GW body which is not exceeded at more than 70% (50%, 90%) of the stations (of the area of the gw body)
Do not reflect hot spots
Do not reflect outliers

7. Interpretation of mean values
Represent the average concentration of the stations in the gw body / in the area of the gw body
Reflect hot spots
Reflect outliers

8. Interpretation of confidence limits
Null hypothesis H0: gw body is not in good status
To be proven H1: gw body is in good status
Test decision at significance level alpha=5% (1%, 0.2% resp.)
not in good status if CL95% > limit value (CL99%, CL99.8%)
in good status if CL95% < limit value (CL99%, CL99.8%)
alpha denotes the probability of making a wrong decision for a good status (although the true, unknown mean exceeds the limit value); alpha could vary for different parameters.

9. Classical approach Arithmetic mean _________________
= Mean at station s
xts =measurement value, DL = determination limit (if not quantified), ns = number of measurement above DL, ps = number of measurements below DL, w = 0.5

10. Classical approach
Example: AT154 Ammonium 1999

11. Problems of classical approach
No theoretically sound concept for the treatment of measurements below DL.
Spatial correlation and inhomogenous distribution of stations are not accounted for.

12. Maximum likelihood Method for the treatment of measurements below DL
Iterative calculation of log normal distribution parameters µ and  by maximisation of
Median = exp{µ}
Mean = exp{µ+0.5²} = Median x exp{0.5²}
70-percentile = exp{µ+0.524} = Median x exp{0.524}
If  =3, then: Mean = x 70% percentile

13. Maximum likelihood Example: FR001_FRg 1984 Ammonium
38 stations <0.1, 1 station <0.2
2 stations >DL (1.2 and 4.25)

14. Maximum likelihood Example: FR001_FRg 1979 Ammonium
10 stations above DL
37 station below DL

15. Maximum likelihood Example: NL002_NL00 1999 Nitrate 8 stations <DL,

16. Maximum likelihood
Corrects for bias caused by „less than“ measurements under the assumption of log normal distribution
Pathological behavior in case of extremely large variability
Statistical assumption of log normal distribution is crucial
As the variability of data increases to infinity, ML 70 %ile is tending to 0 ML mean is tending to infinity

17. Kriging The procedure of kriging
Calculate the exponential variogram (h)=a x exp(-|h|/b)
Calculate the kriging matrix
Calculate the predicted value at each point of the GW body
The average of all predicted values is the kriging mean

18. Kriging Example: PTM5_PT00 Nitrate 1995-1999 PT087_021
PT087_024 (1998 cancelled)
1-4.5 mg/l
PT590_109
80 mg/l in 1995
40-55 mg/l in

19. Kriging Example: PTM5_PT00 Nitrate 1995-1999
Mean 1995: 20.9 mg/l
Kriging mean 1995: 28.3 mg/l
Mean 1999: 22.3 mg/l
Kriging mean 1999: 23.6 mg/l
Reduction of arithmetic mean due to cancellation of low level site PT087_024

20. Kriging
Kriging mean
Represents the average concentration in the area of the GW body
Close to the arithmetic mean, if the distribution of stations is homogenous

21. Kriging Upper confidence limit of the kriging mean 95%CL
Represents the upper confidence limit of the average concentration in the area of the GW body
Close to the kriging mean for a very large number of stations

22. Kriging
Kriging 70 %ile
Represents the 70 %ile of kriging surface + prediction error
Close to the empirical 70 %ile in case of homogenous station distribution, high density of stations and symmetric distribution of measurements

23. Kriging Kriging accounts for heterogenous distribution of stations
downweighting of station clusters
upweighting of solitary stations
Kriging accounts not for areas without any stations:

24. Kriging Kriging without spatial correlation kriging mean = mean
kriging 95% CL = 95% CL of arithmetic mean
Example:
AT250_ tetrachloroethen
Arithmetic Mean: 4.114
Kriging Mean:

25. Kriging Data requirements for the software module
EXCEL tables representing the area of the gw body and the coordinates of the stations
EXCEL table with the station mean values
Output: Word file with tables

26. Some minimum requirements
Measurements below DL:
Effect of <DL measurements should be neglectable, i.e. the maximum effect should be below of eg. 10% of the mean level.
1. Calculate „mean_min“ with DL=0
2. Calculate „mean_max“ with DL=DL
3. If the difference is lower than 10%, the effect of the DL may be considered neglectable. Otherwise the good status of the gw body cannot be proven.

27. Some minimum requirements
Distribution of stations:
At least 10 stations (or more)
Homogenous monitoring network (to be specified)
In cases of changes of stations it is up to the monitoring network manager to proof that the changes do not bias the results (to be specified).

28. Further procedure Check spatial correlation with variogram
Apply 95% CL of arithmetic mean or kriging 95% CL if necessary
Compare results with 70, 80, 90, 95 %iles