In order to quantify model risk there are two approaches used: either we work with or without a probabilistic view. In the former case, we speak about quantification of model risk, while in the latter, we call this model uncertainty.
In the probabilistic approach, one often uses a Bayesian framework which ultimately allows the model risk manager to work with a distribution of available models. In the context of model uncertainty, the approach that is most often used is one where we compute the difference between the current model and the worst case.
Both approaches share the challenge of enumerating the available models (and parameters) under consideration.
Quantified model risk and uncertainty has multiple inputs such as data quality, input data stability, output stability, robustness, model performance etc. Each of those items can individually be considered a model risk measurement as well.