The representativity index of a simple monitoring network with regular theoretical shapes and its practical application for the existing groundwater monitoring network of the Tychy-Urbanowice landfills, Poland

The representativity index R ᵤ is a measure used in assessing the chemical status of groundwater based on monitoring studies. This index is designed to describe the spatial homogeneity of the monitoring network. The general formula for calculating the index R ᵤ includes the following parameters: average distance to the nearest monitoring point, number of monitoring points, and size of the test area. Calculations to determine the representativity index for four different shapes of the theoretical test study with the same area and the same number of monitoring points have been done. These calculations suggest that the index value depends on the shape and the position of these points, and it is less dependent on the size of the surface. An assessment of the representativeness of the monitoring network for the different numbers and configurations of the piezometers around the Tychy-Urbanowice landfills based on the mentioned index has been done as well. The best and the worst configurations of the monitoring network for these landfill sites in mathematical terms have been presented in this paper. The results are surprising: the highest index value is obtained with a single measurement point. The calculations were performed with the area of landfill and the area limited by the range of piezometers as the exclusive test area. To choose the optimal test area, representativity indicator was calculated also for the monitoring network around waste landfills, including the buffer network behind the piezometers. The difference in the values of the representativity indicator for subsequent variants is astounding. The representativity index for the same monitoring network is about 20 % higher if we consider the test area limited by external piezometers, and higher by another 20 %, taking into account the 95-m buffer zone behind piezometers. Due to increase of the representativity index value with a different width of buffer zone, the mathematical calculations of the monitoring network’s representativeness should be supported by an analysis of the geological structure and hydrogeological conditions occurring in the analyzed area.