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. 08.-09.03.2001

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 08.-09.03.2001

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) 08.-09.03.2001

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. 08.-09.03.2001

Statistical parameters 08.-09.03.2001

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 08.-09.03.2001

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 08.-09.03.2001

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. 08.-09.03.2001

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 08.-09.03.2001

Classical approach Example: AT154 Ammonium 1999 08.-09.03.2001

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. 08.-09.03.2001

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 = 18.7 x 70% percentile 08.-09.03.2001

Maximum likelihood Example: FR001_FRg 1984 Ammonium 38 stations <0.1, 1 station <0.2 2 stations >DL (1.2 and 4.25) 08.-09.03.2001

Maximum likelihood Example: FR001_FRg 1979 Ammonium 10 stations above DL 37 station below DL 08.-09.03.2001

Maximum likelihood Example: NL002_NL00 1999 Nitrate 8 stations <DL, 08.-09.03.2001

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 08.-09.03.2001

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 08.-09.03.2001

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 1996-1999 08.-09.03.2001

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 08.-09.03.2001

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 08.-09.03.2001

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 08.-09.03.2001

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 08.-09.03.2001

Kriging Kriging accounts for heterogenous distribution of stations downweighting of station clusters upweighting of solitary stations Kriging accounts not for areas without any stations: 08.-09.03.2001

Kriging Kriging without spatial correlation kriging mean = mean kriging 95% CL = 95% CL of arithmetic mean Example: AT250_30 1992 tetrachloroethen Arithmetic Mean: 4.114 Kriging Mean: 4.284 08.-09.03.2001

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 08.-09.03.2001

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. 08.-09.03.2001

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). 08.-09.03.2001

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 08.-09.03.2001