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).It is demonstrated that the method yields comparable results to a corresponding conditional Monte Carlo approach. Detailed statistical analysis of the conditional Monte Carlo simulations showed the following additional central results:(1)Conditioning with piezometric head information in the Monte Carlo approach yielded a high correlation between the transmissivity values and the recharge values. Subsequent regression analysis for the Monte Carlo results revealed that the given head measurements together with the random recharge values determined the transmissivity values used to describe the aquifer. The derived explicit linear relationships allow to calculate the transmissivity values directly from the random recharge values without inverse modelling for this study.(2)A covariance analysis of estimated parameters was performed. Derived confidence ellipses showed narrow confidence bounds for estimated recharge and transmissivity values.(3)While frequency distributions for velocities in the conditional Monte Carlo approach follow a log-normal distribution, this is not the case for piezometric heads. Here, Weibull-, Rayleigh-, FRatio and Gamma-Distribution perform more satisfactorily, in particular in the reproduction of the observed skewness of the output distributions.As the proposed FOSM-method is based on a Taylor Series approximation, its application is restricted to moderate cases of model input parameters uncertainty.