Moving away from deterministic solutions: A probabilistic machine learning approach to account for geological model uncertainty in groundwater modelling

Abstract

Decision-making related to groundwater management often relies on results from a deterministic groundwater model representing one ‘optimal’ solution. However, such a single deterministic model lacks representation of subsurface uncertainties. The simplicity of such a model is appealing, as typically only one is needed, but comes with the risk of overlooking critical scenarios and possible adverse environmental effects. Instead, we argue, that groundwater management should be based on a probabilistic model that incorporates the uncertainty of the subsurface structures to the extent that it is known. If such a probabilistic model exists, it is, in principle, simple to propagate the uncertainties of the model parameter using multiple numerical simulations, to allow a quantitative and probabilistic base for decision-makers. However, in practice, such an approach can become computationally intractable. Thus, there is a need for quantifying and propagating the uncertainty numerical simulations and presenting outcomes without losing the speed of the deterministic approach.This presentation provides a probabilistic approach to the specific groundwater modelling task of determining well recharge areas that accounts for the geological uncertainty associated with the model using a deep neural network. The results of such a task are often part of an investigation for new abstraction well locations and should, therefore, present all possible outcomes to give informative decision support. We advocate for the use of a probabilistic approach over a deterministic one by comparing results and presenting examples, where probabilistic solutions are essential for proper decision support. To overcome the significant increase in computation time, we argue that this problem can be solved using a probabilistic neural network trained on examples of model outputs. We present a way of training such a network and show how it performs in terms of speed and accuracy. Ultimately, this presentation aims to contribute with a method for incorporating model uncertainty in groundwater modelling without compromising the speed of the deterministic models.