Data space inversion for efficient uncertainty quantification using an integrated surface and subsurface hydrologic model

Abstract. Hydrological numerical modelling is generally designed to provide predictions of uncertain quantities in a decision-support context. In the implementation of decision-support modelling, data assimilation and uncertainty quantification are often the most difficult and time-consuming tasks. This is because the imposition of history-matching constraints on model parameters usually requires a large number of model runs. Data Space Inversion (DSI) provides an alternative (and highly model-run-efficient) method for predictive uncertainty quantification that avoids the need for parameter estimation. It does this by evaluating covariances between model outputs used for history matching (e.g. hydraulic heads) and model predictions based on model runs that sample the prior parameter probability distribution. By focusing on the direct relationship between model outputs under historical conditions and predictions of system behaviour under future conditions, DSI avoids the need to estimate or adjust model parameters. This is advantageous when using such as Integrated Surface and Subsurface Hydrologic Models (ISSHMs). These models are characterised by long run times, a penchant for numerical instability and/or complex parameterisation schemes that are designed to maintain geological realism. This paper demonstrates that DSI provides a robust and efficient means of quantifying the uncertainties of complex model predictions, at the same time as it provides a basis for complementary linear analyses that can explore issues such as data worth. DSI is applied in conjunction with an ISSHM representing a synthetic but realistic stream-aquifer system. Predictions of interest are fast travel times and surface water infiltration. Linear and nonlinear estimates of prediction uncertainty based on DSI are validated against a more traditional approach to prediction uncertainty quantification which requires adjustment of a large number of parameters. A DSI-generated surrogate model is then used to investigate the effectiveness and efficiency of existing and possible future monitoring networks. This demonstrates the benefits of using DSI in conjunction with a complex numerical model to quantify prediction uncertainty and support data worth analysis in complex hydrogeological environments.