Classical model-based uncertainty quantification (UQ) analyses a given model equation that includes a list of adjustable parameters. Then the parameters are treated as random variables (equipped with probability distributions), typically represented by randomly generated parameter sets. In a next step, the so-called inverse UQ adjusts the parameter distributions such that all randomly generated parameter sets lead to model predictions that agree sufficiently well with available calibration data. This way, inverse UQ quantifies the parameter-related uncertainty that remains after calibration. However, if we use more and more (and increasingly good) calibration data, the uncertainty of parameters vanishes, and the impression occurs that we knew the parameters exactly and that we could exactly predict the system.
We wish to extend UQ for hydrosystems models such that it can quantify the total uncertainty of modeling. This includes the uncertainty between model concept and reality, and between model parameters and actual system properties. To achieve this, we will extend models by additional random components that inflate the uncertainty estimates back to reasonable levels: we will acknowledge that model parameter are not invariant properties of the system. Instead, they are only adjustment factors in models that could take different values under different application scenarios. Thus, we will split up parameter values in learnable parts and parts that resist learning, and so counteract the erroneous overconfidence in parameter estimation. Another option is to add new random variables to those parts of the model where we suspect the largest simplifications. This makes the model fuzzier where we trust it the least, and will decrease overconfidence in the model formulation.
As practical application, we will look at soil moisture models that contain water retention parameters and parameters for effective soil permeability. Ample soil moisture data (from lysimeter experiments, soil moisture networks and from remote sensing) are available at Queens University. They can be used for calibrating and testing soil moisture models, for demonstrating overconfidence, and for demonstrating the proposed concepts for overcoming overconfidence.
Uncertainty of model choice and overconfidence of parameter estimates are highly relevant problems in hydrosystems modeling, especially for non-linear compartments such as the soil/plant/atmosphere continuum. The stochastic modeling concept pursued within the SFB “CAMPOS” includes soil/plant/atmosphere models, requires uncertainty quantification and parameter inference, and suffer from the risk of overconfidence.
