Nitrate concentrations in surface water are most often interpreted using the 90th percentile, according to the method initially recommended at a national-level by the “SEQ-Eau” (System of evaluation of the river quality), and then in the Technical assessment guide of the water state meeting the criteria of the Water Framework Directive. The principle is to select the highest measure on 90% of the measurement series in order to avoid taking into account exceptional situations value. However, the result depends on the frequency of measurements (which varies between years and stations), as well as on the low number of sampling per year and the seasonal variability of the concentrations. Which precautions are needed to interpret these results from limited samples? How can the calculation of the 90th percentile be improved? How to compare two percentiles in time if the sampling dates vary between years? Following the pioneering work of Caroline Bernard-Michel (2006), we first compare the empirical calculation of the 90th percentile (which is only based on measured concentrations) with different methods: -Weighting of data to take into account the dates of measurements; -Linearization of percentile function to mitigate the discontinuities of the empirical percentile function; -Calculation for the current year from data of two or three consecutive years, to increase the number of measurements for the estimation; -and Impact on the characterization of inter-annual(or two and three-year) variations. We then return to the modelling of the histogram and its reverse, the percentile function. In the presence of a limited sample, the variance of the data set, which represents the dispersion’s variance of a point among N (N is the annual number of measurements), is substantially lower than the dispersion’s variance of a point in the segment representing the year. To correct this, a method of histogram "dispersion" is applied. Finally, practical recommendations are given on the number and dates of measurements to calculate the percentile and its inter-annual variations.

### Calculation of annual 90th percentile on time-series of nitrate concentrations in surface water

#### Abstract

Nitrate concentrations in surface water are most often interpreted using the 90th percentile, according to the method initially recommended at a national-level by the “SEQ-Eau” (System of evaluation of the river quality), and then in the Technical assessment guide of the water state meeting the criteria of the Water Framework Directive. The principle is to select the highest measure on 90% of the measurement series in order to avoid taking into account exceptional situations value. However, the result depends on the frequency of measurements (which varies between years and stations), as well as on the low number of sampling per year and the seasonal variability of the concentrations. Which precautions are needed to interpret these results from limited samples? How can the calculation of the 90th percentile be improved? How to compare two percentiles in time if the sampling dates vary between years? Following the pioneering work of Caroline Bernard-Michel (2006), we first compare the empirical calculation of the 90th percentile (which is only based on measured concentrations) with different methods: -Weighting of data to take into account the dates of measurements; -Linearization of percentile function to mitigate the discontinuities of the empirical percentile function; -Calculation for the current year from data of two or three consecutive years, to increase the number of measurements for the estimation; -and Impact on the characterization of inter-annual(or two and three-year) variations. We then return to the modelling of the histogram and its reverse, the percentile function. In the presence of a limited sample, the variance of the data set, which represents the dispersion’s variance of a point among N (N is the annual number of measurements), is substantially lower than the dispersion’s variance of a point in the segment representing the year. To correct this, a method of histogram "dispersion" is applied. Finally, practical recommendations are given on the number and dates of measurements to calculate the percentile and its inter-annual variations.
##### Scheda breve Scheda completa Scheda completa (DC)
2014
Geostatistics for Environmental Applications
52
52
M. Donati; C. de Fouquet; G. Deronzier; K. Petit; R. Bruno
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11585/315718`
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