Determination of stochastic well head protection zones by direct propagation of uncertainties of particle tracks

A popular method for the determination of catchment zones is the construction by particle tracking. A new approach is presented, allowing to quantify the uncertainty of particle paths and catchment zones by the direct propagation of uncertainties of aquifer parameters into the uncertainty of the location of contaminating particles. This is achieved by applying the conditional First-Order Second Moment (FOSM) method to both the discretised groundwater flow and the particle tracking equations. Beside of the mean particle tracks, the standard deviations (σx, σy) of the location (x, y) of a particle within the 2-dimensional flow field are directly calculated. This allows calculating probabilities for which particles can be found within their ‘uncertainty cloud’. By starting particles at all gridpoints of the groundwater model this method is applied to the delineation of stochastic well head protection zones. The performance of the proposed new method is shown for the determination of capture zones for an aquifer in Gambach (State of Hessia, Germany).