How reliable is model calibration? Markov Chain Monte Carlo analysis of a catchment model calibration to stream monitoring data

Mathematical modelling is a commonly-used approach for understanding and quantifying the observed and unobserved processes within a hydrological system (e.g. a catchment). Typically, a model is constructed that is believed to represent the main components of the system (e.g. water and contaminant storages and fluxes), and the model is then calibrated (by adjusting uncertain parameters) to maximise the fit to observed system data (e.g. stream flow, groundwater level, contaminant concentrations). This approach implicitly assumes that the calibrated model is the best representation of reality (within the limits of the available information). However, calibrations of highly parameterized models are almost always non-unique, meaning that there are many possible model designs and parameter sets that are able to reproduce the observed behaviour with a similar level of fidelity. Furthermore, artefacts in the calibration data can lead to biased estimates of the model parameters and outputs. Despite this, parameter values and auxiliary calculations (e.g. flux totals) based on a single calibrated model run are frequently reported as results without any estimate of their reliability