<p>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.</p> <p>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.</p>

Groundwater resource management is an increasingly complicated task that is expected to only get harder and more important with future climate change and increasing water demands resulting in an increasing need for fast and accurate decision support systems. Numerical flow simulations are accurate but slow, while response matrix methods are fast but only accurate in near-linear problems. This paper presents a method based on a probabilistic neural network that predicts hydraulic head changes from groundwater abstraction with uncertainty estimates, that is both fast and useful for non-linear problems. A generalized method of constructing and training such a network is demonstrated and applied to a groundwater model case of the San Pedro River Basin. The accuracy and speed of the neural network are compared to results using MODFLOW and a constructed response matrix of the model. The network has fast predictions with results similar to the full numerical solution. The network can adapt to non-linearities in the numerical model that the response matrix method fails at resolving. We discuss the application of the neural network in a decision support framework and describe how the uncertainty estimate accurately describes the uncertainty related to the construction of the training data set.