Evaluating a data space inversion surrogate model for predictive uncertainty quantification in a coupled SWAT + gwflow model

• The performance of a fast-running surrogate statistical model based on data space inversion (DSI) was evaluated for streamflow and groundwater prediction. • The DSI surrogate model produces streamflow estimates with evaluation metrics comparable to those of the physical model (SWAT + gwflow). • DSI-based uncertainty bounds effectively captured observed groundwater heads during calibration and prediction, demonstrating strong predictive capability. • The DSI approach enables users to avoid heavy computational demands and numerical instability, while still accommodating complex parameterisations to adequately represent system behaviour. Incorporating measured data into environmental simulation models through calibration helps to improve predictive performance and reduce uncertainty. Traditionally, this process involves transferring information from observations to parameters, requiring many model runs and parameter updates. The relationships between observations (simulated equivalents) and parameters are often non-linear, which can compromise predictions. Data space inversion (DSI) explores the posterior predictive distribution by building a surrogate model based on the covariance between model outputs that correspond to 1) field measurements, and 2) predictions of interest. DSI avoids updating physical model parameters by conditioning predictions on measurements of system behaviour. DSI is applied to the Soil and Water Assessment Tool ( SWAT + ) coupled with a modified groundwater flow module ( gwflow ) for the Winnebago watershed (U.S.) to evaluate its robustness and efficiency in predicting streamflow and groundwater and to quantify associated uncertainty. The coupling with gwflow enables spatially distributed simulation of groundwater heads using cell-based aquifer properties, allowing increased parameterisation complexity compared to SWAT + alone and providing a rigorous test case for DSI. The DSI-based model predicted streamflow and groundwater head comparably to the physical model, based on acceptable model performance metrics. The DSI-based model enables computationally efficient analysis based on relationships between measurements and predictions, making it a practical tool for uncertainty assessment. Unlike the uncertainty bounds derived from the posterior ensemble of the physically-based model (quantified using iterative ensemble method), the DSI-based model’s uncertainty bounds captured observed groundwater head values during both calibration and prediction periods, highlighting its potential for decision-support modelling.