From Single Reference to Interval-Based Calibration: A Paradigm Shift in Hydrological Modelling with Diverse Remote Sensing Data

Hydrological modelling in ungauged basins faces significant challenges due to the lack of in-situ measurements for model calibration and validation. Remote sensing (RS) data has emerged as a valuable alternative, providing spatially distributed estimates of key hydrological variables such as precipitation, evapotranspiration (ET), and vegetation dynamics. These datasets not only serve as model inputs but also are increasingly used for model calibration and validation, thereby reducing uncertainty and enhancing the model applicability. Despite this potential, a major challenge lies in the discrepancies among different RS products for the same variable. Differences in satellite sensors, retrieval algorithms, and assumptions lead to significant variability in RS products, complicating their integration into hydrological models. This variability makes it difficult to select the most reliable product, particularly in data-scarce regions. Traditional practices often involve applying and comparing multiple RS products in regional studies. Different basins frequently yield different best products, resulting in low model transferability across regions. Alternatively, ensemble products created through data fusion of various RS datasets are used as a single reference to reduce uncertainty. Nevertheless, in both cases, the model parameter space is constrained and refined based on a single representative dataset. The reliance on a singular reference makes the model highly sensitive to biases or inaccuracies in the chosen dataset and overlooks the inherent uncertainty across the spectrum of available RS estimates. This limitation becomes particularly concerning for high-dimensional hydrological systems, where the issue of model equifinality arises and becomes more pronounced as model complexity increases. To address this limitation, we explore an interval-based model calibration strategy that incorporates multiple RS datasets instead of the traditional reliance on a single reference. A suite of algorithms with varying levels of complexity, including Set-Membership, Interval Penalty Minimization, Distributionally Robust Optimization, and Bayesian approaches, are applied to calibrate the Soil and Water Assessment Tool (SWAT) model using multiple RS-based ET products in the Adige River Basin, Italy. The conventional single-reference calibration approach serves as a benchmark for comparison. The interval-based calibration approaches go beyond identifying a single best parameter set by generating optimum parameter spaces, worst-case optimal sets, and probabilistic parameter distributions, providing a more holistic assessment of model performance by accounting for both optimal solutions and associated uncertainties. The results demonstrate the advantages of interval-based calibration in capturing the inherent variability in RS data, offering new insights into the integration of diverse datasets with hydrological models, particularly in data-scarce regions. By embracing the full spectrum of variability across multiple RS products, this strategy can reduce dependency on potentially biased datasets, increase model robustness and transferability.