Bayesian ranking of Pareto optimal solutions for an ecohydrological model

Multi-objective calibration has frequently been suggested as a way to reduce hydrological model uncertainty. This is particularly attractive with the increase of remote sensing and spatial data in hydrology. Multi-objective calibration can involve calibrating on two data sets, for example streamflow and leaf area index, to help constrain model parameters. Trade-offs between different data sets complicate multi-objective results, which can be visualised using Pareto fronts. The ‘best compromise’ solutions are included on the front but identifying the overall best solution can be difficult. Pareto fronts have also been used to visualise the trade-off between validation and calibration results to diagnose underperformance in differential split sample tests. In recent work, we combined multi-objective calibration based on two data sets with a Pareto front for both calibration and validation results. This work showed how these fronts shift depending on the data used and depending on the objective function used for the calibration. While this allowed identification of the ten “best” solutions in validation, these best solutions did not originate from a specific region in the calibration front, suggesting no simple optimal trade-off. An alternative approach to dealing with uncertainty in hydrological models has been the application of Bayesian approaches. The posterior error and parameter distributions not only signify the likelihood of the parameters but also define the relative information of different input data sources. Combining a Pareto front with a Bayesian framework allows visualising the local uncertainty of the solutions. Using an ecohydrological model that is calibrated on MODIS16 evapotranspiration or MODIS13 LAI and streamflow for a forested catchment in south-east Australia, we extend our earlier work to determine the information content of the datasets. We identify differences in parameter uncertainty for the different Pareto optimal solutions, identified in the data set trade-off, particularly for the “best” solutions in validation.