The classical model-based Uncertainty Quantification (UQ) analyzes a given model equation that contains a list of adjustable parameters. In this approach, the parameters are treated as random variables (with probability distributions), typically represented by randomly generated sets of parameters. In the next step, the so-called inverse UQ adjusts the parameter distributions so that all randomly generated parameter sets produce model predictions that sufficiently match the available calibration data. This way, the inverse UQ quantifies the parameter-related uncertainty that persists after calibration. However, as we use more and more (and increasingly good) calibration data, the uncertainty of the parameters diminishes, creating the impression that we know the parameters precisely and can predict the system exactly.
We aim to expand UQ for hydrological system models so that it can quantify the overall uncertainty of the modeling. This includes the uncertainty between the model concept and reality as well as between model parameters and actual system properties. To achieve this, we will enhance models with additional random components to bring uncertainty estimates back to a reasonable level. We recognize that model parameters are not invariant properties of the system but rather adjustable features in models that could take on different values under various application scenarios. Therefore, we will split parameter values into learnable and non-learnable parts to counteract the mistakenly inflated confidence in parameter estimation. Another approach is to add new random variables to parts of the model where we suspect the greatest simplifications. This makes the model less precise where we trust it the least, reducing the overconfidence in the model formulation.
