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The Water Residence Time distribution is the equivalent of the impulseresponse of a linear system allowing the propagation of water through a medium,e.g. the propagation of rain water from the top of the mountain towards theaquifers. We consider the output aquifer levels as the convolution between theinput rain levels and the Water Residence Time, starting with an initialaquifer base level. The estimation of Water Residence Time is important for abetter understanding of hydro-bio-geochemical processes and mixing propertiesof wetlands used as filters in ecological applications, as well as protectingfresh water sources for wells from pollutants. Common methods of estimating theWater Residence Time focus on cross-correlation, parameter fitting andnon-parametric deconvolution methods. Here we propose a 1D full-deconvolution,regularized, non-parametric inverse problem algorithm that enforces smoothnessand uses constraints of causality and positivity to estimate the WaterResidence Time curve. Compared to Bayesian non-parametric deconvolutionapproaches, it has a fast runtime per test case; compared to the popular andfast cross-correlation method, it produces a more precise Water Residence Timecurve even in the case of noisy measurements. The algorithm needs only oneregularization parameter to balance between smoothness of the Water ResidenceTime and accuracy of the reconstruction. We propose an approach on how toautomatically find a suitable value of the regularization parameter from theinput data only. Tests on real data illustrate the potential of this method toanalyze hydrological datasets.

computers and geosciences

Water Residence Time Estimation by 1D Deconvolution in the Form of a  l2-Regularized Inverse Problem With Smoothness, Positivity and Causality  Constraints